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  <front>
    <journal-meta><journal-id journal-id-type="publisher">ANGEO</journal-id><journal-title-group>
    <journal-title>Annales Geophysicae</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ANGEO</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Ann. Geophys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1432-0576</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/angeo-44-1143-2026</article-id><title-group><article-title>Ion composition of the Earth plasmasphere observed by the PEP JEI and RPWI instruments on the JUICE spacecraft</article-title><alt-title>Earth plasmasphere observed by JUICE, V3</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Fränz</surname><given-names>Markus</given-names></name>
          <email>fraenz@mps.mpg.de</email>
        <ext-link>https://orcid.org/0000-0003-4521-2931</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Fischer</surname><given-names>Henning</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Krupp</surname><given-names>Norbert</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-4683-9533</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Roussos</surname><given-names>Elias</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5699-0678</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Wittmann</surname><given-names>Philipp</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-1843-4136</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Bambach</surname><given-names>Patrick</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Wahlund</surname><given-names>Jan-Erik</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Stenberg Wieser</surname><given-names>Gabriella</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4260-2937</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Barabash</surname><given-names>Stas</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Holmberg</surname><given-names>Mika</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2553-8395</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Zeroual</surname><given-names>Maryam</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Brandt</surname><given-names>Pontus C.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4644-0306</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Wurz</surname><given-names>Peter</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2603-1169</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Wieser</surname><given-names>Martin</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Futaana</surname><given-names>Yoshifumi</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7056-3517</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Shimoyama</surname><given-names>Manabu</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-6220-1719</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Pontoni</surname><given-names>Angèle</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Vorburger</surname><given-names>Audrey</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Galli</surname><given-names>André</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2425-3793</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Riedo</surname><given-names>Andreas</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9007-5791</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Ho</surname><given-names>George</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1093-2066</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Mitchell</surname><given-names>Donald G.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Clark</surname><given-names>George</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Kollmann</surname><given-names>Peter</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4274-9760</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Gkioulidou</surname><given-names>Malamati</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Regoli</surname><given-names>Leonardo</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7628-1510</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8">
          <name><surname>Wimmer-Schweingruber</surname><given-names>Robert</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7388-173X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff9">
          <name><surname>Asamura</surname><given-names>Kazushi</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff10">
          <name><surname>Kallio</surname><given-names>Esa</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9791-804X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff11">
          <name><surname>Opitz</surname><given-names>Andrea</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0845-0201</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff12">
          <name><surname>Grande</surname><given-names>Manuel</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2233-2618</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff13">
          <name><surname>Coates</surname><given-names>Andrew</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff13">
          <name><surname>Jones</surname><given-names>Geraint</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5859-1136</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff14">
          <name><surname>Sarris</surname><given-names>Theodoros</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff15">
          <name><surname>Fedorov</surname><given-names>Andrey</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff15 aff17">
          <name><surname>André</surname><given-names>Nicolas</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff16">
          <name><surname>Baláž</surname><given-names>Ján</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-8918-2610</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Deutsches Zentrum für Luft- und Raumfahrt, Cologne, Germany</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Swedish Institute of Space Physics (IRF), Uppsala, Sweden</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Swedish Institute of Space Physics (IRF), Kiruna, Sweden</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Astronomy Astrophysics Section, School of Cosmic Physics, Dublin Institute for Advanced Studies, DIAS Dunsink Observatory, Dublin, Ireland</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Johns Hopkins University, Baltimore, MD, USA</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>Space Research &amp; Planetary Sciences, University of Bern, Switzerland</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>Christian-Albrechts-Universität zu Kiel, Kiel, Germany</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>Institute of Space and Astronautical Science, Sagamihara, Japan</institution>
        </aff>
        <aff id="aff10"><label>10</label><institution>Department of Electronics and Nanoengineering, School of Electrical Engineering, Aalto University, Espoo, Finland</institution>
        </aff>
        <aff id="aff11"><label>11</label><institution>Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary</institution>
        </aff>
        <aff id="aff12"><label>12</label><institution>Institute of Mathematical and Physical Sciences, University of Wales Aberystwyth, Wales, UK</institution>
        </aff>
        <aff id="aff13"><label>13</label><institution>Mullard Space Science Laboratory, University College, London, UK</institution>
        </aff>
        <aff id="aff14"><label>14</label><institution>Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Greece</institution>
        </aff>
        <aff id="aff15"><label>15</label><institution>Institut de Recherche en Astrophysique et Planétologie (IRAP), CNES-CNRS-Université Toulouse III Paul Sabatier, Toulouse, France</institution>
        </aff>
        <aff id="aff16"><label>16</label><institution>Institute of Experimental Physics SAS, Košice, Slovak Republic</institution>
        </aff>
        <aff id="aff17"><label>17</label><institution>Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Université de Toulouse, Toulouse, France</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Markus Fränz (fraenz@mps.mpg.de)</corresp></author-notes><pub-date><day>21</day><month>October</month><year>2026</year></pub-date>
      
      <volume>44</volume>
      <issue>2</issue>
      <fpage>1143</fpage><lpage>1165</lpage>
      <history>
        <date date-type="received"><day>10</day><month>April</month><year>2026</year></date>
           <date date-type="rev-request"><day>22</day><month>April</month><year>2026</year></date>
           <date date-type="rev-recd"><day>7</day><month>October</month><year>2026</year></date>
           <date date-type="accepted"><day>8</day><month>October</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Markus Fränz et al.</copyright-statement>
        <copyright-year>2026</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026.html">This article is available from https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026.html</self-uri><self-uri xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026.pdf">The full text article is available as a PDF file from https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e522">During the first Earth gravity assist maneuver of JUICE on 20 August 2024 the spacecraft passed through the Earth plasmasphere for about 2 <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula>. Before closest approach at a distance of 2.1 <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the Jovian Electron and Ion spectrometer JEI of the PEP instrument suite was switched on for 40 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> in an ion mode test configuration. The high plasma density of about 3000/<inline-formula><mml:math id="M4" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (observed by the RPWI plasma wave instrument) led to a negative charging of the spacecraft which allowed a rare observation of the cold and dense plasmaspheric ion populations. Since the ions are only corotating with the Earth at a velocity of about 1 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at this distance the observed ion speed is dominated by the spacecraft velocity of about 8 <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. For this reason ions with different mass appear at different energies in the energy spectrum observed by the JEI sensor. In addition the spacecraft potential leads to specific filtering of ion masses in the observed angular distribution. By calculating the sensor response function for these specific observing conditions it is possible to quantify densities of the different ion species. This response calculation depends critically on the response of the JEI channel electron multipliers to the ion velocity and mass. Since the sensor was operated with a low post-acceleration further laboratory calibrations may be needed for this specific setup. Nevertheless we can already conclude from the observations that ions with mass <inline-formula><mml:math id="M7" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 4 <inline-formula><mml:math id="M8" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> contribute at least 25 % to the observed total ion density. A flux peak observed in the energy spectrum at 15 <inline-formula><mml:math id="M9" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> can only be explained by the presence of heavy molecular ions with mass <inline-formula><mml:math id="M10" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 30 <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Molecular ions have only been rarely detected in the outer Earth plasmasphere. The observations indicate that the JEI sensor can also be used to achieve ion composition measurements in the exospheres of the Jovian moons.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Deutsches Zentrum für Luft- und Raumfahrt</funding-source>
<award-id>50QJ2303</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e663">On the 20 August 2024 the JUICE spacecraft <xref ref-type="bibr" rid="bib1.bibx20" id="paren.1"/> made its first gravity assist maneuver at Earth with a closest approach altitude of 6850 <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> corresponding to a L-shell of 2.31 <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. At this distance from Earth the spacecraft encountered the Earth plasmasphere and several sensors – originally designed for measurements at Jupiter – were able to make new observations of the Earth plasmasphere. Here we report on the measurements of the Jovian Electron and Ion spectrometer (JEI) which is one of the thermal plasma sensors of the Particle Environment Package (PEP, <xref ref-type="bibr" rid="bib1.bibx2" id="altparen.2"/>) onboard JUICE. The observations are supported by measurements made by the Radio &amp; Plasma Wave Investigation (RPWI, <xref ref-type="bibr" rid="bib1.bibx42" id="altparen.3"/>).</p>
      <p id="d2e694"><italic>The Earth plasmasphere</italic> is a region of dense cold plasma extending between +1.5 and about 6 Earth radii (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) around the center of Earth <xref ref-type="bibr" rid="bib1.bibx9" id="paren.4"/>. The plasmaspheric ion density is usually <inline-formula><mml:math id="M15" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 10<sup>3</sup>/<inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> within 3 <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> with a plasma temperature <inline-formula><mml:math id="M19" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx16" id="paren.5"/>. Because the plasmaspheric ion population is rotating close to corotation with Earth, it has very low energy (<inline-formula><mml:math id="M21" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 10 <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) in the frame of typical spacecraft observations. This means the ion properties can only be measured in-situ with retarding potential analyzer (RPA) techniques or when the spacecraft charges negatively. The first detailed analysis of the effect of the spacecraft potential on the plasmaspheric spectrum was provided by <xref ref-type="bibr" rid="bib1.bibx43" id="text.6"/> using data obtained by the RPA instrument on the OGO-3 satellite. The most relevant cold ion composition measurements available until today were made by the RPA instrument RIMS onboard Dynamics Explorer 1 (DE 1) between 1981 and 1984 <xref ref-type="bibr" rid="bib1.bibx36" id="paren.7"/>. The RIMS instrument could in principle measure ions up to mass 32 <inline-formula><mml:math id="M23" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx5" id="paren.8"/>; the continuously downlinked dataset contains only observations of <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx36" id="paren.9"/>. This dataset was reviewed by <xref ref-type="bibr" rid="bib1.bibx18" id="text.10"/> where it is stressed that specifically the oxygen density of the outer plasmasphere (<inline-formula><mml:math id="M29" display="inline"><mml:mo lspace="0mm">&gt;</mml:mo></mml:math></inline-formula> 2 <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is highly variable and can reach beyond 1000/<inline-formula><mml:math id="M31" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> such that a specific oxygen torus might form. But on a single specific orbit during a magnetic storm the RIMS instrument was operated in a mode which allowed observation of heavier ions up to mass 46 <xref ref-type="bibr" rid="bib1.bibx8" id="paren.11"/>. On this orbit a strong flux of ions with 28, 20 and 32 <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> with similar relative abundance was observed stretching from <inline-formula><mml:math id="M33" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M34" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.1 to 3 <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. These were interpreted as <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">NO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> ions. Interestingly the flux at larger distances was observed to be accelerated along the magnetic field. These observations agreed with earlier observations by the ion mass spectrometer on the ISIS-2 spacecraft during a magnetic storm at 1400 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> altitude <xref ref-type="bibr" rid="bib1.bibx22" id="paren.12"/>. The accelerated thermal plasma was even sometimes observed at the Earth magnetopause <xref ref-type="bibr" rid="bib1.bibx37" id="paren.13"/>. Recently <xref ref-type="bibr" rid="bib1.bibx45" id="text.14"/> also reported on observations of plasmaspheric cold ions by the the Van-Allen-Probe HOPE instrument. All observations of molecular ion outflow from the ionosphere up to 2022 were reviewed by <xref ref-type="bibr" rid="bib1.bibx31" id="text.15"/> and <xref ref-type="bibr" rid="bib1.bibx44" id="text.16"/>. From these reviews it becomes clear that all more recent observations are for energized outflow (with energies <inline-formula><mml:math id="M40" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) while the cold plasmaspheric composition has not been observed again after the DE-1 measurements in 1984. A problem with the DE-1 measurements was that the spacecraft potential was not observed by an independent instrument during the observations <xref ref-type="bibr" rid="bib1.bibx7" id="paren.17"/>. Ion temperature and potential were obtained by an iterative fit to the data resulting in a plasmaspheric ion temperature of about 3000–5000 <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi></mml:mrow></mml:math></inline-formula> (0.27–0.45 <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) at <inline-formula><mml:math id="M44" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M45" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2 <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx6" id="paren.18"/>. But the authors emphasize that without knowledge of the potential the ion temperature may be overestimated. The importance of the cold ion population for magnetospheric dynamics was discussed by <xref ref-type="bibr" rid="bib1.bibx10" id="text.19"/>: the cold plasma dominates the solar wind contribution in several magnetospheric regions, it affects the reconnection and instability rates, controls the generation of waves and pulsations. Nevertheless the cold plasma is difficult to observe and observations are rare.  A comprehensive review of the instrumental limitations of cold ion observations can be found in <xref ref-type="bibr" rid="bib1.bibx33" id="text.20"/>.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e1089">Trajectory of JUICE (black line) during the flyby of the Moon (lower left corner, red crosses) and the Earth on 21 August 2024 in the GSE <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula> plane. The different lines show nominal position of the plasmapause (red, dotted) <xref ref-type="bibr" rid="bib1.bibx28" id="paren.21"/>, the magnetopause (green, dash dot) <xref ref-type="bibr" rid="bib1.bibx38" id="paren.22"/> and bow shock (cyan, dashed) <xref ref-type="bibr" rid="bib1.bibx32" id="paren.23"/>. The colored sections along the JUICE trajectory show the operation times of PEP JEI where the color indicates the count rate observed in channel 15.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f01.png"/>

      </fig>

      <p id="d2e1118">The rather high plasmaspheric temperatures (<inline-formula><mml:math id="M48" display="inline"><mml:mo lspace="0mm">&gt;</mml:mo></mml:math></inline-formula> 0.5 <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) compared to ionospheric temperatures (<inline-formula><mml:math id="M50" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 0.1 <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) observed by these early RPA instruments did pose a problem for plasma theory because no sufficient heating mechanism could be identified <xref ref-type="bibr" rid="bib1.bibx21" id="paren.24"/>. Proton temperatures were again determined from 1996–2001 by the RPA instrument on the MAGION-5 sub-satellite of the INTERBALL 2 mission. Analysis of this data set by <xref ref-type="bibr" rid="bib1.bibx26" id="text.25"/> showed that the temperature of the inner plasmasphere is closely correlated to the temperature of the upper ionosphere. Local temperature is anti-correlated to local density and drops to values below 2000 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">K</mml:mi></mml:mrow></mml:math></inline-formula> (0.18 <inline-formula><mml:math id="M53" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) for densities <inline-formula><mml:math id="M54" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 2000/<inline-formula><mml:math id="M55" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> confirming that the earlier RPA analyses may have overestimated the temperatures. The plasmaspheric temperature observations were discussed again in context of the Van-Allen-Probe mission <xref ref-type="bibr" rid="bib1.bibx16" id="paren.26"/> where proton temperatures were determined by indirect methods for two orbits confirming the results of <xref ref-type="bibr" rid="bib1.bibx26" id="text.27"/>. We note that the Van-Allen-Probe spacecraft charged positive in the plasmasphere which inhibited the direct observation of cold ions <xref ref-type="bibr" rid="bib1.bibx24" id="paren.28"/>.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1204">Trajectory of JUICE (blue symbols) during the flyby of the Earth on 21 August 2024 in the GSE <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula> plane. The red dotted line shows the nominal position of the plasmapause <xref ref-type="bibr" rid="bib1.bibx28" id="paren.29"/>. The colored section along the JUICE trajectory shows the operation time of PEP JEI where the color indicates the count rate observed in channel 15. Blue arrows indicate the JUICE velocity vector direction.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f02.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>The observation by the JUICE spacecraft</title>
      <p id="d2e1234">The ESA spacecraft JUICE was launched on 14 April 2023 on its long mission to planet Jupiter. Between the 19 and 21 August 2024 the spacecraft conducted the first ever Lunar–Earth  gravity assists (LEGA) maneuver. The trajectory of the spacecraft during the Lunar–Earth flyby is shown in Fig. <xref ref-type="fig" rid="F1"/> projected onto the geocentric solar ecliptic (GSE) <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula>-plane. Overplotted are the orbit of the Moon (red crosses), the expected position of the Earth plasmapause (red dots), magnetopause (green) and bowshock (cyan). The JEI sensor of the PEP instrument suite <xref ref-type="bibr" rid="bib1.bibx2" id="paren.30"/> was switched on only during 4 time intervals of length 40 <inline-formula><mml:math id="M58" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula>. These 4 intervals are indicated by the coloring along the JUICE trajectory which shows the count rate observed by channel 15 of the JEI sensor, which shows the highest count rates. The intervals were chosen to obtain electron measurements around the Moon and magnetopause and ion measurements in the plasmasphere and around the bow shock. In this paper we only discuss the observations made during the plasmasphere crossing. An enlarged plot of this crossing is shown in Fig. <xref ref-type="fig" rid="F2"/> in the same coordinate plane as Fig. <xref ref-type="fig" rid="F1"/>. The JEI sensor obtained science data on 20 August 2024 from 21:19 to 21:56 UTC just before closest approach to the Earth at 21:56:14 UTC. At this point the JUICE spacecraft had a distance of 13 211 <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> or altitude of about 6850 <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> at geographic latitude 24.0° and L-shell 2.31 <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e1294"><inline-formula><mml:math id="M62" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> densities predicted for the trajectory on the 20 August 2024 of JUICE by the Earth global core plasmasphere model (GCPM v2.4, <xref ref-type="bibr" rid="bib1.bibx15" id="altparen.31"/>).</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f03.png"/>

      </fig>

      <p id="d2e1338">Figure <xref ref-type="fig" rid="F3"/> shows the densities of <inline-formula><mml:math id="M65" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M67" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> predicted for the position of JUICE by the Earth global core plasmasphere model <xref ref-type="bibr" rid="bib1.bibx15" id="paren.32"/> for a Kp value of 1.7 which was prevalent during the JUICE closest approach (<uri>https://kp.gfz.de/en/</uri>, last access: 16 October 2026). The model predicts a sharp inbound plasmapause. The authors of the model note that specifically the <inline-formula><mml:math id="M68" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> density is highly variable and the model assumes constant initial ratios of 0.1 for <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and 0.01 for <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> relative to <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>. Molecular ions are not contained in the model. We may just consider the total peak ion density value of about 4000/<inline-formula><mml:math id="M72" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> predicted by the model and note that the SPICED model for the equatorial plasmasphere predicts for <inline-formula><mml:math id="M73" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M74" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2 <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and MLT <inline-formula><mml:math id="M76" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 6 <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula> an average density of 2200/<inline-formula><mml:math id="M78" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (<xref ref-type="bibr" rid="bib1.bibx25" id="text.33"/>, their Fig. 12).</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e1497">Cross-sectional view of the JEI sensor showing the principal components. The sensor is a spherical electrostatic analyzer with an “open-head” deflection system. Before ions or electrons (red trace) enter the spherical electrostatic analyzer the possible polar entrance angle is set by the deflectors. After the electrostatic analyzer ions are post-accelerated towards the ceramic channel electron multiplier (CEM) entrance, where they create an electric signal (adapted from <xref ref-type="bibr" rid="bib1.bibx1" id="altparen.34"/>).</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f04.png"/>

      </fig>

<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Instrumentation</title>
      <p id="d2e1516">The Jovian Electron and Ion Analyzer (JEI) <xref ref-type="bibr" rid="bib1.bibx14" id="paren.35"/> is one out of six sensors of the Particle Environment Package PEP onboard the Juice spacecraft <xref ref-type="bibr" rid="bib1.bibx2" id="paren.36"/>. It is specifically designed to operate in the harsh Jovian environment. The goals of JEI are to measure the electron and ion distribution functions in the energy range from 1 <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> to 60 <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi></mml:mrow></mml:math></inline-formula> with high sensitivity and time resolution and with a hemispherical field of view. For a full list of sensor properties refer to Table <xref ref-type="table" rid="TA1"/>. The other sensors of the PEP instrument are the Jovian Neutral Analyzer (JNA), the Neutral and Ion Mass Analyzer (NIM), the Jovian Energetic Neutral and Ion Analyzer (JENI), the Jovian Ion Dynamics and Composition Analyzer (JDC) and the Jovian Energetic Electron Analyzer (JoEE). Only JEI, JDC, JENI and JoEE were operating during the LEGA. Only the JEI and JDC sensors could observe plasmaspheric ions. The observations by JDC are described in an accompanying paper <xref ref-type="bibr" rid="bib1.bibx39" id="paren.37"/>. The derivation of the spacecraft potential from the Langmuir probe observations of the RPWI instrument on JUICE are described in <xref ref-type="bibr" rid="bib1.bibx42" id="text.38"/>.</p>
      <p id="d2e1550">Figure <xref ref-type="fig" rid="F4"/> shows a cross-sectional view of the JEI sensor with a typical ion path (red). The incoming polar angle with respect to the sensor <inline-formula><mml:math id="M81" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis is selected by the deflection system. The ion energy is selected by the spherical analyzer (<italic>Inner and Outer Sphere</italic>). The polarity of the deflectors and analyzer can be switched to allow measurement of both positive and negative particles including electrons. After post-acceleration charged particles are detected by one of 16 ceramic channel electron multipliers (<italic>CEMs</italic>), determining the azimuth angle.</p>
      <p id="d2e1568">The post-acceleration voltage applied between spherical analyzer and CEM entrance we call <italic>CEM_head</italic> voltage. The detection efficiency is influenced by the CEM_head voltage and the bias-voltage setting across the CEM (<italic>CEM_draw</italic> voltage). The sensor can operate either continuously in electron or ion mode, or it can alternate between both modes about every 8 <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula>. During the plasmasphere observation JEI was operated in ion mode only with a CEM_head voltage of <inline-formula><mml:math id="M83" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>250 <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> and a CEM_draw voltage of +2100 <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula>. At this setting the detection efficiency for protons is about 80 %, the detection efficiency for heavier ions is lower as discussed by <xref ref-type="bibr" rid="bib1.bibx27" id="text.39"/>. Later during the JUICE mission these voltages will be increased to achieve optimum efficiency.</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e1615">View of Earth from JUICE at 20 August 2024 21:30 UTC with the GSM frame axes. The Earth terminator (yellow) is almost parallel to the GSM <inline-formula><mml:math id="M86" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis. The spacecraft velocity vector relative to Earth (cyan) is in the GSM <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula>-plane. Figure produced by the JUICE Cosmographia software (<uri>https://www.cosmos.esa.int/web/spice/cosmographia</uri>, last access: 16 October 2026).</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f05.jpg"/>

        </fig>

      <p id="d2e1644">JEI has a minimum time resolution of 4 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> per energy step, an intrinsic polar resolution of <inline-formula><mml:math id="M89" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5°, and energy resolution of <inline-formula><mml:math id="M90" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 8 % (see Table <xref ref-type="table" rid="TA1"/>). For a mono-directional beam the energy resolution is around <inline-formula><mml:math id="M91" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 %. Elevation and energy stepping as well as integration time are set by a look-up-table and change with sensor mode. During the plasmasphere observation integration time was set to 4 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> with a data acquisition time of 3 <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> per energy step, polar stepping was set to 8 polar steps covering a polar range from 14 to 75°, and energy stepping was linear in the low energies (0 to 20 <inline-formula><mml:math id="M94" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) with a step width of 0.49 <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and logarithmic for higher energies up to 10 <inline-formula><mml:math id="M96" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi></mml:mrow></mml:math></inline-formula> with a total of 128 energy steps and a duration of 512 <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> for one scan. A complete polar scan using 8 deflector steps takes 4.6 <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula>. The average geometric factor of the angular channel 15 of the sensor has been determined in laboratory calibration as <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M100" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 3.0 <inline-formula><mml:math id="M101" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<sup>−5</sup> <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">sr</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">eV</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for an isotropic plasma distribution at pre-acceleration voltage of <inline-formula><mml:math id="M104" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1000 <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> with a nitrogen ion beam of 10 <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi></mml:mrow></mml:math></inline-formula> energy <xref ref-type="bibr" rid="bib1.bibx1" id="paren.40"/>.</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e1830">View of PEP sensors on the nadir deck of the JUICE spacecraft. The JUICE JEI coordinate frame orientation (<inline-formula><mml:math id="M107" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M108" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> blue, <inline-formula><mml:math id="M109" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M110" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> red, <inline-formula><mml:math id="M111" display="inline"><mml:mi>Y</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M112" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> green, same as spacecraft frame SC) and spacecraft velocity vector relative to Earth (cyan) at 20 August 2024 21:30 UTC are centered at the JEI ion optics entrance. Top: View of the spacecraft frame <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math></inline-formula> plane. Bottom: View of the spacecraft frame <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math></inline-formula> plane, including the field of views of the JEI CEMs. SC +X (red) is opposite to the solar direction (<inline-formula><mml:math id="M115" display="inline"><mml:mo lspace="0mm">=</mml:mo></mml:math></inline-formula> GSM/GSE +X). SC +Y is approximately parallel to GSM -Y. The model magnetic field vector for 21:30 UTC is shown in brown. Figure produced by the JUICE Cosmographia software.</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f06.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Observation geometry</title>
      <p id="d2e1917">Figure <xref ref-type="fig" rid="F5"/> shows the orientation of the JUICE spacecraft relative to Sun (yellow) and Earth together with the orientation of the geocentric solar magnetic (GSM) axes and the spacecraft velocity vector (cyan) at 20 August 2024 21:30 UTC. The yellow line indicates the Earth terminator. This principal orientation of the spacecraft was maintained throughout the observation interval. The PEP JEI sensor is mounted on the spacecraft panel which looks towards Earth during this time. This panel is illustrated in Fig. <xref ref-type="fig" rid="F6"/> which shows the location of the NIM, JNA and JEI sensors together with the orientation of the body fixed spacecraft coordinate system axes, the direction of Earth and Sun and the spacecraft velocity vector relative to Earth. The body fixed spacecraft <inline-formula><mml:math id="M116" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis coincides with the JEI sensor symmetry axis. The JEI polar field of view extends from 8 to 78° from this axis. In Fig. <xref ref-type="fig" rid="F6"/> (right) we also show the field of view of JEI azimuth sectors 1, 0, 15 and 14.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e1935">JUICE orbital parameters in Earth centered coordinates for 20:00–23:00 UTC on 20 August 2024 from top to bottom: Position vector components in GSM coordinates, GSM (black) and GSE (red) latitude, Tsyganenko96 geomagnetic field <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at JUICE position in spacecraft coordinates, JUICE velocity vector relative to Earth in spacecraft coordinates, plasma corotation vector at full corotation in spacecraft coordinates, difference vector <inline-formula><mml:math id="M118" display="inline"><mml:mi mathvariant="bold-italic">D</mml:mi></mml:math></inline-formula> between JUICE velocity and corotation, <inline-formula><mml:math id="M119" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> angle of <inline-formula><mml:math id="M120" display="inline"><mml:mi mathvariant="bold-italic">D</mml:mi></mml:math></inline-formula> (black) and <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (cyan) and <inline-formula><mml:math id="M122" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula> angle of <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">B</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (green). The Tsyganenko field and <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-shell values are calculated using the IRBEM model of the disturbed geomagnetic field for the solar wind conditions prevalent during the JUICE passage (<uri>https://prbem.github.io/IRBEM/index.html</uri>, last access: 16 October 2026).</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f07.png"/>

        </fig>

      <p id="d2e2020">Figure <xref ref-type="fig" rid="F7"/> shows position and velocity parameters of the JUICE spacecraft relative to Earth for the period of the plasmasphere crossing, from top to bottom: spacecraft position in GSM coordinates in Earth radii (<inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), spacecraft GSM and GSE latitude, magnetic field <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">B</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M127" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">nT</mml:mi></mml:mrow></mml:math></inline-formula>) in spacecraft coordinates predicted by the Tsyganenko96 model <xref ref-type="bibr" rid="bib1.bibx41" id="paren.41"/>, spacecraft velocity vector (<inline-formula><mml:math id="M128" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), and the plasma corotation velocity vector (<inline-formula><mml:math id="M129" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), the difference vector <inline-formula><mml:math id="M130" display="inline"><mml:mi mathvariant="bold-italic">D</mml:mi></mml:math></inline-formula> between both in JUICE spacecraft coordinates, and the angles of <inline-formula><mml:math id="M131" display="inline"><mml:mi mathvariant="bold-italic">D</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="bold-italic">B</mml:mi><mml:mi mathvariant="normal">geo</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in spacecraft coordinates. We here assume that the corotation is symmetric around the GSM <inline-formula><mml:math id="M133" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis. Models of the corotation predict <inline-formula><mml:math id="M134" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 92 % corotation at <inline-formula><mml:math id="M135" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M136" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2.0 <xref ref-type="bibr" rid="bib1.bibx30" id="paren.42"/>. Vector components are indicated by X(blue), Y(green), Z(red) and total T(black). The red vertical line indicates the closest approach (CA) and the blue frame the period of the JEI observation discussed in the following. Calibrated onboard magnetic field data are not available at the time of writing. We observe that the predicted magnetic field vector and the spacecraft velocity vector are both at a polar angle of 50° as seen from the JEI sensor.</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e2153">Ion energy spectra observed by PEP JEI in 4 azimuthal viewing directions during the passage of the Earth plasmasphere. The median electronic background noise has been subtracted from the spectra. Black crosses show the negative spacecraft potential observed by JUICE RPWI where the left axis gives the negative voltage. Data are averaged over 8 elevation scans (4.6 <inline-formula><mml:math id="M137" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula>).</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f08.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Ion energy spectra and potential</title>
      <p id="d2e2178">Figure <xref ref-type="fig" rid="F8"/> shows the energy spectra obtained by the 4 azimuthal sectors (CEM channels) viewing around the direction azimuth of the spacecraft velocity during the time interval 21:30–21:56 UTC on 20 August 2024. We here show only the spectral energy range 0–20 <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="unit"><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>. The higher energy range is dominated by background noise. The white line plotted over the spectra shows the negative value of the spacecraft potential measured by the JUICE RPWI instrument. We observe that all 4 channels observe an intense low energy ion spectrum with a mean energy proportional to the negative spacecraft potential observed by RPWI. The most negative potential measured by RPWI is <inline-formula><mml:math id="M139" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M140" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula>. The same effect was observed on the opposite side of the spacecraft by the Jovian Plasma Dynamics and Composition analyzer (JDC) of the PEP suite. These observations are discussed in an accompanying paper <xref ref-type="bibr" rid="bib1.bibx39" id="paren.43"/>. It is interesting to note that the RPA instrument on the OGO-3 spacecraft in 1966 measured at the same L-shell location 1.5–2.5 <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> a very similar potential between <inline-formula><mml:math id="M142" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 and <inline-formula><mml:math id="M143" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.0 <inline-formula><mml:math id="M144" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> at an estimated ion density of about 6000/<inline-formula><mml:math id="M145" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx43" id="paren.44"/>. This shows that the values observed for JUICE are not uncommon – though the potential value depends on the material properties of spacecraft surfaces. <xref ref-type="bibr" rid="bib1.bibx46" id="text.45"/> modelled the charging of the JUICE for plasmaspheric conditions at the specific time 21:56 UTC using the SPIS software (<uri>https://www.spis.org/software/spis/</uri>, last access: 16 October 2026). They derive an average surface potential of <inline-formula><mml:math id="M146" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.0 <inline-formula><mml:math id="M147" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula>, but <inline-formula><mml:math id="M148" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>4.0 <inline-formula><mml:math id="M149" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> for the shadowed vault in front of the JEI sensor. Thus the calculated potential is less negative than the observed potential. The difference may be caused by assumptions on the ion and electron temperatures used in the model.</p>
      <p id="d2e2296">Channel 15 observes the highest flux, though the spacecraft velocity vector is at the edge of the field-of-view of channel 0 (see Fig. <xref ref-type="fig" rid="F6"/>). As discussed later the reason lies mainly in the differences of the detection efficiency of the CEMs at the low CEM_draw voltage setting. Another effect is that for a small Debye length the shape of the spacecraft potential follows the spacecraft structure <xref ref-type="bibr" rid="bib1.bibx46" id="paren.46"/>. As discussed further in the next section this leads to a significant ion deflection. The rather strong signal in the neighboring channels 1 and 14 indicates that the spacecraft potential has a focusing effect, although we can not exclude some electronic and geometric cross talk between the channels as discussed in <xref ref-type="bibr" rid="bib1.bibx1" id="text.47"/>. In the following we only discuss the spectra obtained by channel 15 as this has the best counting statistics. While an acceleration by the spacecraft potential should lead to the cold thermal spectrum observed for most energy scans the sporadic extension of the spectra up to 20 <inline-formula><mml:math id="M150" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> caught our attention because they may suggest a non-thermal effect or multi-component plasma.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e2317">Top: Ion energy spectra observed over 1 <inline-formula><mml:math id="M151" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> (21:51:30–21:52:30 UTC on 20 August 2024) at 512 <inline-formula><mml:math id="M152" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> resolution by PEP JEI CEM15 during the passage of the Earth plasmasphere. The negative of the  spacecraft potential value is overplotted in black. Bottom: The median polar angle of each spectra (black stars) with respect to the Spacecraft <inline-formula><mml:math id="M153" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis and the polar angle of the JUICE spacecraft velocity (red line) relative to the Earth.</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f09.png"/>

        </fig>

      <p id="d2e2350">The top panel of Fig. <xref ref-type="fig" rid="F9"/> is a zoom into the energy spectra of channel 15 for the one minute time interval between 21:51:30–21:52:20 UTC on 20 August 2024. Overplotted in black is the negative of the spacecraft potential of about <inline-formula><mml:math id="M154" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M155" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> measured by RPWI. We observe that the energy spectra show a pattern repeated for each sequence of 8 elevation scans of the sensor. Figure <xref ref-type="fig" rid="F9"/> (bottom) shows the mean polar angle of the JEI field-of-view for each spectrum. Overplotted in red is the polar angle of the spacecraft velocity vector relative to Earth. We can see that ions are only observed at polar angles from 14° to about 60°. The mean energy of the spectrum is increasing with polar angle. High energy spikes are only observed twice during this interval at 21:51:49 and 21:51:08 UTC at polar angles of about 35°.</p>

      <fig id="F10" specific-use="star"><label>Figure 10</label><caption><p id="d2e2374">Four individual ion spectra observed in sequence around 21:51:49 UTC on 20 August 2024 by PEP JEI CEM15 without correction for the spacecraft potential. Top: Counts in linear scaling. Bottom: Conversion to phase space density assuming proton mass in logarithmic scaling. Some of the spectra allow a Maxwellian fit to the core distribution shown in blue with the derived parameters temperature (<inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M157" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>), density (<inline-formula><mml:math id="M158" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M159" display="inline"><mml:mrow class="unit"><mml:mo>/</mml:mo><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) and mean energy (<inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M161" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>) in the spacecraft frame of reference.</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f10.png"/>

        </fig>

      <fig id="F11" specific-use="star"><label>Figure 11</label><caption><p id="d2e2444">Count spectrum observed at 21:51:49 UTC by PEP JEI CEM15 at a polar deflection angle of 33.1° and attribution of flux peaks to species. The association of the spectral peaks with different ion species is explained in context of Fig. <xref ref-type="fig" rid="F14"/> below.</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f11.png"/>

        </fig>

      <fig id="F12" specific-use="star"><label>Figure 12</label><caption><p id="d2e2457">Simion<sup>®</sup> simulation of the deflection of <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (left) and <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (right) ions in a linear spacecraft potential. Ions are launched with spacecraft velocity at 1 <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> distance in a linear potential with scale height 50 <inline-formula><mml:math id="M165" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> arriving at the instrument with different polar angles <inline-formula><mml:math id="M166" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>.</p></caption>
          <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f12.png"/>

        </fig>

      <p id="d2e2516">To further illustrate the effect we show in Fig. <xref ref-type="fig" rid="F10"/> four individual spectra obtained in sequence around 21:51:49 UTC at different mean polar angles. The top row of the figure shows the counts obtained in each 3 <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> energy bin and the value of the mean polar angle (<inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>). The energy axes show the energy in the JEI reference frame without correction for the spacecraft potential. We note that the statistical error of these spectra can be obtained by the square root of the counts. The bottom row shows the same spectra converted to phase space density assuming an ion mass of 1 <inline-formula><mml:math id="M169" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi></mml:mrow></mml:math></inline-formula> and a base geometric factor as provided in Table <xref ref-type="table" rid="TA1"/> without considering CEM efficiencies. Spectra which show an approximate Maxwellian shape have been fitted with a Maxwellian with the three free parameters mean energy, temperature and density (see Appendix B). The resulting values and their fit standard deviation are printed in addition to the fitted curve (cyan). The plots are in log scale and the fit parameters are derived from 6 data points with the highest phase space density. We can see that the spectra obtained at polar angles <inline-formula><mml:math id="M170" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M171" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 14.4° and <inline-formula><mml:math id="M172" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M173" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 23.8° can be best approximated by a Maxwellian resulting in ion densities of around 180/<inline-formula><mml:math id="M174" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, temperatures of around 0.2 <inline-formula><mml:math id="M175" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and mean observed energies around 5.3 <inline-formula><mml:math id="M176" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> (including spacecraft potential). As we discuss later the rather low density value as compared to the RPWI value is caused by not considering the potential geometry and CEM efficiency in this simple approach. Further below we try to include these effects and derive much higher density values. When looking closer at the count spectrum obtained at <inline-formula><mml:math id="M177" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M178" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 14.4° one can discern 2 peaks in the spectrum which may indicate a bimodal distribution. The most interesting spectrum is the one obtained at <inline-formula><mml:math id="M179" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M180" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 33.1°. It shows different spectral peaks at higher energies with a statistical significance <inline-formula><mml:math id="M181" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 2<inline-formula><mml:math id="M182" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula>. For this reason we show an enlarged view of this spectrum in Fig. <xref ref-type="fig" rid="F11"/> where we associate the different peaks with different ion species as explained in the next section.</p>
      <p id="d2e2648">To estimate the statistical occurrence of these spectral peaks we counted the number of 4.6 <inline-formula><mml:math id="M183" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula> polar scans with peak energies above 10 <inline-formula><mml:math id="M184" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for the time period 21:47:00–21:56 UTC when the potential measured by RPWI was more negative than <inline-formula><mml:math id="M185" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 <inline-formula><mml:math id="M186" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula>: this was the case for 28 out of 108 polar scans. In all cases the peaking spectrum was observed for polar angles smaller than 30°. In all 108 polar scans the mean energy of the spectrum increased with decreasing polar angle.</p>
      <p id="d2e2691">Before discussing this observation we need to consider the total plasma density and shape of the spacecraft potential. The JUICE RPWI instrument reports an ion density of 3000/<inline-formula><mml:math id="M187" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> determined by the Langmuir probe measurement for the time 21:55:17 UTC (Jan-Erik Wahlund, personal communication, 2026). This agrees approximately with the value of 4000/<inline-formula><mml:math id="M188" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> predicted by the global plasmasphere model (Fig. <xref ref-type="fig" rid="F3"/>) when taking into account the large temporal variation of the plasmasphere. The electron temperature determined by the RPWI analysis is 0.35–0.5 <inline-formula><mml:math id="M189" display="inline"><mml:mrow class="unit"><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>. In this case the plasma Debye length around the spacecraft, which determines the extension of the spacecraft potential, is only about 8.0 <inline-formula><mml:math id="M190" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>. This means that the equipotential surfaces follow the shape of the spacecraft structures and must be considered locally as planar and not spherical (see Appendix <xref ref-type="sec" rid="App1.Ch1.S4"/>). In an accompanying paper <xref ref-type="bibr" rid="bib1.bibx46" id="text.48"/> discuss the surface charging of the JUICE spacecraft during the Earth gravity assist.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Interpretation and model</title>
      <p id="d2e2751">To illustrate the general effect of a potential with small Debye length on a plasma flow with different ion masses we show in Fig. <xref ref-type="fig" rid="F12"/> a Simion<sup>®</sup> (<uri>https://simion.com/</uri>, last access: 16 October 2026) simulation of ion trajectories in a linear and planar potential of <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M192" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M193" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5 <inline-formula><mml:math id="M194" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> at spacecraft surface and instrument and 0 <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> at 50 <inline-formula><mml:math id="M196" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> distance. Ions are launched parallel to the spacecraft surface at 50 <inline-formula><mml:math id="M197" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> distance with mass per charge of 1 <inline-formula><mml:math id="M198" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (left) and 16 <inline-formula><mml:math id="M199" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (right) and a velocity of <inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M201" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 8 <inline-formula><mml:math id="M202" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. One can see that the lighter ions reach the JEI sensor at a higher polar angle than the heavy ions. We note that Fig. <xref ref-type="fig" rid="F12"/> is for illustration of the principle only. The Simion software can not simulate a potential with exponential fall off caused by Debye shielding. The important assumptions are that the electric field is mainly vertical and ions are launched from a field-free point. In this case the ion acceleration is mainly in vertical direction such that the distance from which ions are launched has no influence on the arrival angle. A more realistic simulation could be done using the SPIS model, cited above.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e2895">Expected mean polar angle <inline-formula><mml:math id="M203" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> relative to SC <inline-formula><mml:math id="M204" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula>-axis for different initial velocities and SC potentials <inline-formula><mml:math id="M205" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="13">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:colspec colnum="9" colname="col9" align="left"/>
     <oasis:colspec colnum="10" colname="col10" align="left"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:colspec colnum="12" colname="col12" align="left"/>
     <oasis:colspec colnum="13" colname="col13" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M207" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M209" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M210" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M211" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M212" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M213" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M214" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7"><inline-formula><mml:math id="M215" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M216" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M217" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M218" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>+</oasis:entry>
         <oasis:entry colname="col9"><inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M220" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10"><inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col11"><inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M224" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col12"><inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M226" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col13"><inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>Q</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>+</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">6.0</oasis:entry>
         <oasis:entry colname="col2">5.0</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M229" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5</oasis:entry>
         <oasis:entry colname="col4">9.5°</oasis:entry>
         <oasis:entry colname="col5">18.1°</oasis:entry>
         <oasis:entry colname="col6">13.2°</oasis:entry>
         <oasis:entry colname="col7">30.5°</oasis:entry>
         <oasis:entry colname="col8">36.8°</oasis:entry>
         <oasis:entry colname="col9">6.8 <inline-formula><mml:math id="M230" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">7.7 <inline-formula><mml:math id="M231" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col11">7.1 <inline-formula><mml:math id="M232" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col12">11.6 <inline-formula><mml:math id="M233" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col13">16.6 <inline-formula><mml:math id="M234" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">5.0</oasis:entry>
         <oasis:entry colname="col2">5.0</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M235" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5</oasis:entry>
         <oasis:entry colname="col4">8.0°</oasis:entry>
         <oasis:entry colname="col5">15.2°</oasis:entry>
         <oasis:entry colname="col6">11.1°</oasis:entry>
         <oasis:entry colname="col7">26.2°</oasis:entry>
         <oasis:entry colname="col8">32.0°</oasis:entry>
         <oasis:entry colname="col9">6.8 <inline-formula><mml:math id="M236" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">7.5 <inline-formula><mml:math id="M237" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col11">7.0 <inline-formula><mml:math id="M238" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col12">10.6 <inline-formula><mml:math id="M239" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col13">14.8 <inline-formula><mml:math id="M240" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5.0</oasis:entry>
         <oasis:entry colname="col2">5.0</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M241" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0</oasis:entry>
         <oasis:entry colname="col4">9.0°</oasis:entry>
         <oasis:entry colname="col5">17.0°</oasis:entry>
         <oasis:entry colname="col6">12.5°</oasis:entry>
         <oasis:entry colname="col7">28.4°</oasis:entry>
         <oasis:entry colname="col8">34.0°</oasis:entry>
         <oasis:entry colname="col9">5.3 <inline-formula><mml:math id="M242" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col10">6.0 <inline-formula><mml:math id="M243" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col11">5.5 <inline-formula><mml:math id="M244" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col12">9.1 <inline-formula><mml:math id="M245" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col13">13.3 <inline-formula><mml:math id="M246" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <fig id="F13" specific-use="star"><label>Figure 13</label><caption><p id="d2e3494">Instrument response calculation <italic>including CEM efficiency</italic> <xref ref-type="bibr" rid="bib1.bibx27" id="paren.49"/> for different ion species arriving under the polar angles listed in the first line of Table <xref ref-type="table" rid="T1"/>  with acceleration of a <inline-formula><mml:math id="M247" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M248" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> spacecraft potential. Ions shown from left to right are <inline-formula><mml:math id="M249" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M250" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M251" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M252" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. We assume for this simulation an initial density of 1000.0/<inline-formula><mml:math id="M253" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (in spacecraft frame) per species and an initial velocity of 7.5 <inline-formula><mml:math id="M254" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Shown are the expected counts in each measurement interval of 3 <inline-formula><mml:math id="M255" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> per energy bin.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f13.png"/>

      </fig>

      <p id="d2e3611">To treat the effect analytically we assume that the potential is planar with respect to the spacecraft nadir deck. In this case the acceleration of ions by the potential is only in -<inline-formula><mml:math id="M256" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula> direction. The energy gain is given by <inline-formula><mml:math id="M257" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the spacecraft potential and q the ion charge. Since the acceleration is only in -Z direction, we can calculate the observed vertical velocity by <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mtext>sign</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the initial undisturbed vertical velocity. The sign of the vertical velocity is introduced to cover both ions moving initially towards the spacecraft deck and away from the spacecraft deck. Under the assumption of a planar potential we can then calculate the polar angle <inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> relative to the vertical axis by

          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M262" display="block"><mml:mrow><mml:mi>tan⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:mtext>sign</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo><mml:msubsup><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are the initial velocity components parallel and perpendicular to the spacecraft surface, and <inline-formula><mml:math id="M264" display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:math></inline-formula> is the ion mass per charge. The expected total observed energy per charge is <inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi>m</mml:mi><mml:mo>|</mml:mo><mml:mi>v</mml:mi><mml:msup><mml:mo>|</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>q</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. In Table <xref ref-type="table" rid="T1"/> we calculate the expected mean inclination angles for different ion species for the conditions valid at around 21:50 UTC where the spectra shown in Figs. <xref ref-type="fig" rid="F10"/> and <xref ref-type="fig" rid="F11"/> were observed. From Fig. <xref ref-type="fig" rid="F7"/> we can read the approximate initial velocities either assuming that the plasma is at rest relative to Earth in the GSE frame or rotating with corotation speed. We here compare expected angles for a spacecraft potential of <inline-formula><mml:math id="M266" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 and of <inline-formula><mml:math id="M267" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M268" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> as reported by RPWI (Fig. <xref ref-type="fig" rid="F8"/>). The polar angle of the inflow, when undisturbed by the potential, is about 45°. By Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) and illustrated in Fig. <xref ref-type="fig" rid="F12"/> the expected polar angle becomes smaller with increasing potential. The maximum ion mass we consider is 32 <inline-formula><mml:math id="M269" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M270" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>). Earlier observations of heavy molecules in the plasmasphere <xref ref-type="bibr" rid="bib1.bibx8" id="paren.50"/> suggest that molecules with mass 28 and 30 <inline-formula><mml:math id="M271" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M272" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M273" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">NO</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) may be more abundant than <inline-formula><mml:math id="M274" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. The energy resolution of the JEI sensor does not allow to separate these masses such that <inline-formula><mml:math id="M275" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is considered only as representative for the heavy molecular component. Similar spatial effects of the spacecraft potential on the ion distribution were discussed in context of the Rosetta mission <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx3" id="paren.51"/>.</p>
      <p id="d2e4029">We can see from Fig. <xref ref-type="fig" rid="F9"/> that ions are observed only for polar angles smaller than 45° in agreement with the expectation that the spacecraft potential decreases the inclination angle. We can also see that spectra observed at inclination angles <inline-formula><mml:math id="M276" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 25° show only a single or double Maxwellian distributions as the example shown in Fig. <xref ref-type="fig" rid="F10"/> (right panels). Table <xref ref-type="table" rid="T1"/> shows that spectra observed at lower angles should be dominated by light ions – mainly <inline-formula><mml:math id="M277" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M278" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M279" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mrow><mml:mo>+</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The high energy tail seen at <inline-formula><mml:math id="M280" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M281" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 14.4° may be contributed by the helium ions. Only at inclination angles <inline-formula><mml:math id="M282" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 25° we can see spectra with higher mean energy per charge and separate peaks in the spectrum as shown in Fig. <xref ref-type="fig" rid="F11"/>. We interprete these as being dominated by heavier ions. Since the peak with maximum energy per charge is observed at 15.0 <inline-formula><mml:math id="M283" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> we may conclude from the values shown in the table that: <list list-type="custom"><list-item><label>1.</label>
      <p id="d2e4116">the energy of the peak count rate observed by the JEI sensor suggests a spacecraft potential of around <inline-formula><mml:math id="M284" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 about 1.5 <inline-formula><mml:math id="M285" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> less negative than the value reported by RPWI, though this can be an effect of difference in the ground reference voltage,</p></list-item><list-item><label>2.</label>
      <p id="d2e4135">the heavy molecular component is predicted to have a mean energy per charge of 15.6 <inline-formula><mml:math id="M286" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and a predicted mean polar angle of 29.8°,</p></list-item><list-item><label>3.</label>
      <p id="d2e4147">the smaller flux peaks observed at 5–7 <inline-formula><mml:math id="M287" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are caused by the thermal spread of the light ion distribution,</p></list-item><list-item><label>4.</label>
      <p id="d2e4168">the distribution observed between 8 and 13 <inline-formula><mml:math id="M288" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> can be associated with heavier ions. We can for example not exclude contributions by nitrogen ions.</p></list-item></list></p>

      <fig id="F14" specific-use="star"><label>Figure 14</label><caption><p id="d2e4190">Same simulation setup as for Fig. <xref ref-type="fig" rid="F13"/> showing the simulated contribution of different ion species (<inline-formula><mml:math id="M289" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (black line), <inline-formula><mml:math id="M290" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (blue line), <inline-formula><mml:math id="M291" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (green line) and O2+ (orange line)) of same density to the observed count spectra for the upper 8 virtual polar angles (listed on top).</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f14.png"/>

      </fig>

      <p id="d2e4234">To better quantify the contribution to the spectra shown in Figs. <xref ref-type="fig" rid="F10"/> and <xref ref-type="fig" rid="F11"/> we made a sensor response calculation for the specific ion species and geometries listed in Table <xref ref-type="table" rid="T1"/>. We assume for all ions a common initial velocity of 7.5 <inline-formula><mml:math id="M292" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, an acceleration by a <inline-formula><mml:math id="M293" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M294" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> potential, a temperature of 0.1 <inline-formula><mml:math id="M295" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and a density of <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M297" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1000/<inline-formula><mml:math id="M298" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> for each species. We take the same density for each species to later allow a scaling to the observed count rate. We derive the expected phase space distribution for each species as a function of angular distance from the beam center as explained in Appendix <xref ref-type="sec" rid="App1.Ch1.S3"/>. From the phase space distribution we derive the particle flux using the base geometric factor given in Table <xref ref-type="table" rid="TA1"/>. But here we also take the polar angle (<inline-formula><mml:math id="M299" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>) dependence of the efficiency into account which reduces the geometric factor at smaller polar angles. We also include the dependence of the CEM efficiency on ion mass and pre-acceleration voltage (CEM_head) using the general formula for MCPs from <xref ref-type="bibr" rid="bib1.bibx27" id="text.52"/>.</p>
      <p id="d2e4328">Figure <xref ref-type="fig" rid="F13"/> shows the expected counts in each energy bin for the inclination angles listed in the first line of Table <xref ref-type="table" rid="T1"/>. The integration time per energy bin is 3 <inline-formula><mml:math id="M300" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula>. The plots divide the polar field-of-view of JEI (10–75°) into 16 sectors of 4.4° width. The JEI sensor was operated during this observation pass with a division of the polar field-of-view into only 8 sectors, but the polar full width half maximum (FWHM) of the sensor for a cold beam is only about 5° such that only every second sector shown in Fig. <xref ref-type="fig" rid="F13"/> was observed by JEI. The mean angles of the JEI polar sectors are given in Figs. <xref ref-type="fig" rid="F10"/> and <xref ref-type="fig" rid="F11"/>.</p>
      <p id="d2e4351">In Fig. <xref ref-type="fig" rid="F14"/> we overlayed the predicted contributions of the different ion species to the spectrum observed under the top 8 polar simulation sectors – only 4 of these sectors have been observed by the JEI sensor. These distributions can now be compared with the 4 observed spectra shown in Figs. <xref ref-type="fig" rid="F10"/> and <xref ref-type="fig" rid="F11"/>. Note, that the simulation uses the same density of 1000.0/<inline-formula><mml:math id="M301" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> for each species. We can see that the spectrum observed at 14.4° can have contributions of <inline-formula><mml:math id="M302" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M303" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> where the density of 177 <inline-formula><mml:math id="M304" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 45/<inline-formula><mml:math id="M305" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> obtained by fitting shown in Fig. <xref ref-type="fig" rid="F10"/> can not be directly compared because is does not contain the dependence of the efficiency on elevation angle and pre-acceleration voltage of the sensor. To obtain a more realistic density value for <inline-formula><mml:math id="M306" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (assuming that <inline-formula><mml:math id="M307" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> is minor) we may multiply the assumed density <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> by the ratio of the peak counts in Figs. <xref ref-type="fig" rid="F10"/> and <xref ref-type="fig" rid="F14"/> for the respective <inline-formula><mml:math id="M309" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> angles. We then get:

          <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M310" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">14</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">100.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">50.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2000</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">200</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">19</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">24</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">80.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">60.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1330</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">150</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">28</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">33</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">65.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">30.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2170</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">270</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">28</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">33</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">60.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">20.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3000</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">400</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>

      <fig id="F15" specific-use="star"><label>Figure 15</label><caption><p id="d2e4756">Same simulation setup as in Fig. <xref ref-type="fig" rid="F14"/> <italic>but with H</italic><sup>+</sup><italic> CEM efficiency for all ions</italic> showing the simulated contribution of different ion species of same density to the observed count spectra for the upper 8 virtual polar angles (listed on top).</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f15.png"/>

      </fig>

      <p id="d2e4780">The errors shown contain just the error of the counting statistics, but there are several other possible sources of error in these estimations such as: value of spacecraft potential, corotation speed of plasmasphere, polar angle response of the geometric factor, CEM efficiency dependence on mass and energy. Especially the latter may lead to an overestimate of the heavy ion densities. For this reason we repeated the calculation by assuming the efficiency of <inline-formula><mml:math id="M312" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> for all ions as shown in Fig. <xref ref-type="fig" rid="F15"/>. One can see that this makes a significant difference. If we now calculate densities based on this response assumption we get:

          <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M313" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">14</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">100.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">90.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1110</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">110</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">19</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">24</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">80.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">110.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">730</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">80</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">28</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">33</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">65.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">200.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">325</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">40</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">28</mml:mn><mml:mtext>–</mml:mtext><mml:mn mathvariant="normal">33</mml:mn><mml:mi mathvariant="italic">°</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">60.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">350.0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">170</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">23</mml:mn><mml:mo>/</mml:mo><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e5092">This comparison shows the significant influence of the CEM efficiency on the calibration for heavy ions. Unfortunately the JEI sensor operated during the observation with a rather low post-acceleration voltage <italic>CEM_head</italic> of <inline-formula><mml:math id="M314" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>250 <inline-formula><mml:math id="M315" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> which does not provide enough acceleration for heavy ions. The nominal post-acceleration for observations at Jupiter in ion mode is <inline-formula><mml:math id="M316" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1000 <inline-formula><mml:math id="M317" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> but for safety reasons this was not applied during the JEI operations during the LEGA. To solidify the quantitative density estimates for these observations laboratory tests of the CEM efficiency at <inline-formula><mml:math id="M318" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>250 <inline-formula><mml:math id="M319" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> post-acceleration are needed. In 2017 ion beam tests of the JEI CEMs were done at <inline-formula><mml:math id="M320" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>370 <inline-formula><mml:math id="M321" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> total ion energy with <inline-formula><mml:math id="M322" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M323" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> ions. These showed that the efficiency of the heavier ions was smaller than for the light ions by a factor of only <inline-formula><mml:math id="M324" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.8 (Istvan Szemerey, personal communication, 2026). The respective ratio for this energy returned by the MCP formula of <xref ref-type="bibr" rid="bib1.bibx27" id="text.53"/> is <inline-formula><mml:math id="M325" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.1. This indicates that the assumption of a mass independent efficiency can be more realistic for the JEI CEMs. In addition to these considerations a specific correction of the observed densities taking into account the shape of the spacecraft potential may be applied as explained in Appendix <xref ref-type="sec" rid="App1.Ch1.S4"/>. But this correction is expected to be small compared to the influence of the CEM efficiency.</p>
      <p id="d2e5205">Nevertheless the simulation results (Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/>) show that the heavy ion contribution (<inline-formula><mml:math id="M326" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">O</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M327" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) to the total density during the JUICE plasmasphere passage is at least 25 %. Additionally, the spectral peak at 15 <inline-formula><mml:math id="M328" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is difficult to explain without considering molecular heavy ions.</p>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <p id="d2e5259">The negative charging of the JUICE spacecraft allowed a rare direct measurement of the plasmaspheric cold ion distribution by the PEP JEI electrostatic analyzer. This is a novel measurement as compared to the multiple observations by RPA instruments flown in the earlier phases of magnetospheric science. The advantage of the electrostatic analyzer is a rather high energy and spatial resolution as compared to RPA instruments. More recent missions (Cluster, MMS, Van-Allen-Probe) used electrostatic analyzers but were inhibited by tuning of the instruments to higher energies or by positive charging of the spacecraft. The PEP JEI sensor is a pure energy analyzer and has no built-in mass discrimination. As we have demonstrated above the high spatial resolution of the sensor allows to use the negative spacecraft potential as a mass filter for cold ions when they have a common bulk speed determined by the spacecraft velocity. The location of the flux peak for <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M330" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">He</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> are with 5.2 and 5.6 <inline-formula><mml:math id="M331" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> lower than expected for a spacecraft potential of <inline-formula><mml:math id="M332" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>6.5 <inline-formula><mml:math id="M333" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> as measured by RPWI. The reason may either lie in a difference between spacecraft ground and JEI electronics ground or a potential deviation at the specific location of the JEI sensor <xref ref-type="bibr" rid="bib1.bibx46" id="paren.54"/>. In our calculations we assume a value of <inline-formula><mml:math id="M334" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 <inline-formula><mml:math id="M335" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> for the potential.</p>
      <p id="d2e5326">Coming back to the statistical occurrence rate of the spectral peaks with energies above 10 <inline-formula><mml:math id="M336" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> we mentioned above that this type of spectrum was only observed on 28 out of 108 polar scans obtained during the plasmasphere passage. If we assume that the plasmaspheric composition did not change significantly during this 9 <inline-formula><mml:math id="M337" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> interval the reason for not observing the peaks on every scan must be the narrow polar field of view of only about 5° for a mono-directional beam. Since the 80° polar field-of-view is stepped through in only 8 steps the instrument frequently misses the heavy ion part of the plasma distribution. This effect can be estimated from Fig. <xref ref-type="fig" rid="F13"/> when considering that only every second polar sector shown in the Figure is actually observed.</p>
      <p id="d2e5356">One topic we have not yet discussed is the influence of the magnetic field on the observations. Observations in the outer plasmasphere (<inline-formula><mml:math id="M338" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M339" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 3 <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) indicate in addition to the cold ion distribution a significant warm ion distribution with temperature <inline-formula><mml:math id="M341" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M342" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and mean energy <inline-formula><mml:math id="M343" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 10 <inline-formula><mml:math id="M344" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx19" id="paren.55"/>. Unfortunately at the time of writing no offset-corrected magnetic field data are available from the JUICE magnetometers. For this reason we have included in Figs. <xref ref-type="fig" rid="F6"/> and <xref ref-type="fig" rid="F7"/> only the predicted magnetic field vector from the Tsyganenko96 model. As shown in Fig. <xref ref-type="fig" rid="F6"/> the predicted vector is perpendicular to the spacecraft velocity vector. A field parallel acceleration could in principle be explained by a strong electron density gradient (polar wind effect). But the observed distribution is not field parallel and any such acceleration mechanism would create a power law spectral shape <xref ref-type="bibr" rid="bib1.bibx23" id="paren.56"/> and not the observed cut-off at 15 <inline-formula><mml:math id="M345" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula>. It can also not explain the peaks in the spectrum which coincide with the modeled location for the different ion masses. Also the azimuthal angle <inline-formula><mml:math id="M346" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula> of the predicted magnetic field is at 90° (Fig. <xref ref-type="fig" rid="F7"/>), while the observed azimuth is in the range <inline-formula><mml:math id="M347" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>20 to +20°.</p>
      <p id="d2e5452">The flux peak observed in the energy spectrum around 15 <inline-formula><mml:math id="M348" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F11"/>) indicates the presence of heavy molecular ions in the mass range 30–32 <inline-formula><mml:math id="M349" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The steep fall off above 15 <inline-formula><mml:math id="M350" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> indicates that no heavier molecules than mass 32 <inline-formula><mml:math id="M351" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are present. Since the efficiency of the JEI CEMs at the very low post-acceleration voltage of <inline-formula><mml:math id="M352" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>250 <inline-formula><mml:math id="M353" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> is not well known further calibrations are needed to quantify the relative contributions of the different ion species to the observed spectra.</p>
      <p id="d2e5524">The observed ion temperatures (Fig. <xref ref-type="fig" rid="F10"/>) should in principle not depend on the spacecraft potential when the negative potential is lower than the undisturbed minimum energy for a specific ion species. But this is not the case for the spectra observed at <inline-formula><mml:math id="M354" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M355" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 14.4° and <inline-formula><mml:math id="M356" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M357" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 23.8° where the observed mean energy is very close to the spacecraft potential reported by the RPWI instrument. In this case the part of the spectrum which is lower than the spacecraft potential will be accumulated in a single energy bin and the Maxwellian fit in energy space results in too low temperatures. We discuss this effect in Appendix <xref ref-type="sec" rid="App1.Ch1.S2"/> with the conclusion that the temperature should only be derived from the upper part of the energy distribution. But this can not explain why the temperature values reported in Fig. <xref ref-type="fig" rid="F10"/> are lower than those obtained by earlier measurements using RPA instruments <xref ref-type="bibr" rid="bib1.bibx26" id="paren.57"/>.</p>
      <p id="d2e5565">If we now consider the implications of our analysis for observations by the JUICE spacecraft in the plasma environment of the Jovian moons we first note that a negative spacecraft charging was also observed by the PLS instrument on the Galileo spacecraft <xref ref-type="bibr" rid="bib1.bibx12" id="paren.58"/>. <xref ref-type="bibr" rid="bib1.bibx4" id="text.59"/> calculated spacecraft potentials for the Ganymede and Jupiter magnetospheric phases of the JUICE mission using the SPIS potential simulation software. For the Ganymede phase they predict a negative potential of <inline-formula><mml:math id="M358" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15.5 <inline-formula><mml:math id="M359" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> at a Debye length of 1.2 <inline-formula><mml:math id="M360" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> such for this phase the methods described in our analysis may be applied with some modification. For the Jupiter magnetospheric phase <xref ref-type="bibr" rid="bib1.bibx4" id="text.60"/> predict a positive potential of +4 <inline-formula><mml:math id="M361" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> at a Debye length of 120 <inline-formula><mml:math id="M362" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. In this case the common assumption of a spherical potential geometry can be applied.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d2e5626">During the first gravity assist of JUICE at Earth on 20 August 2024 the spacecraft passed through the Earth plasmasphere for about 2 <inline-formula><mml:math id="M363" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula>. Before closest approach at a distance of 2.1 <inline-formula><mml:math id="M364" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the Jovian Electron and Ion spectrometer (JEI) of the PEP instrument suite was switched on for 40 <inline-formula><mml:math id="M365" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> in an ion mode test configuration. The high plasma density of about 3000/<inline-formula><mml:math id="M366" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, as observed by the RPWI plasma wave instrument, led to a negative charging of the spacecraft which allowed a rare observation of the cold and dense plasmaspheric ion population. Since the ions are only corotating with the Earth with a velocity of about 1 <inline-formula><mml:math id="M367" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at this distance the observed ion speed is dominated by the spacecraft velocity of about 8 <inline-formula><mml:math id="M368" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. For this reason ions with different masses are separating in the energy spectrum observed by JEI. In addition the spacecraft potential leads to specific filtering of ion masses in the observed angular distribution. By calculating the sensor response function for this specific geometry it is possible to quantify densities of the different ion species. This response calculation depends critically on the response of the JEI CEMs to the ion velocity and mass. Since the sensor was operated with a low post-acceleration, further laboratory calibrations may be needed for this specific setup. Still we can already conclude from the observations that ions with mass <inline-formula><mml:math id="M369" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 4 <inline-formula><mml:math id="M370" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> contribute at least 25 % to the observed total density. A flux peak observed in the energy spectrum at 15 <inline-formula><mml:math id="M371" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> can only be explained by the presence of heavy molecular ions with mass <inline-formula><mml:math id="M372" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 30 <inline-formula><mml:math id="M373" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">amu</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Molecular ions have only been rarely detected in the outer Earth plasmasphere. With respect to the performance and operations of PEP JEI, these observations show that PEP JEI can achieve sensitive ion composition measurements in the exospheres of the moons of Jupiter.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>JEI sensor properties</title>

<table-wrap id="TA1"><label>Table A1</label><caption><p id="d2e5781">General properties of the PEP JEI sensor. Performance parameters will be updated during the JUICE inflight calibration campaign.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Parameter</oasis:entry>
         <oasis:entry colname="col2">Value</oasis:entry>
         <oasis:entry colname="col3">Comment</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Particles</oasis:entry>
         <oasis:entry colname="col2">Electrons and ions</oasis:entry>
         <oasis:entry colname="col3">alternating every 4.5 <inline-formula><mml:math id="M374" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Energy Range</oasis:entry>
         <oasis:entry colname="col2">1 <inline-formula><mml:math id="M375" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>–60 <inline-formula><mml:math id="M376" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">nominal,by design</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">1 <inline-formula><mml:math id="M377" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>–10 <inline-formula><mml:math id="M378" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">during LEGA</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">100 <inline-formula><mml:math id="M379" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>–17 <inline-formula><mml:math id="M380" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">calibration range</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Polar Range</oasis:entry>
         <oasis:entry colname="col2">8–78°</oasis:entry>
         <oasis:entry colname="col3">up to 17 <inline-formula><mml:math id="M381" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">30–60°</oasis:entry>
         <oasis:entry colname="col3">up to 60 <inline-formula><mml:math id="M382" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">keV</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">q</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Polar resolution</oasis:entry>
         <oasis:entry colname="col2">4.7–6.0°</oasis:entry>
         <oasis:entry colname="col3">depending on elevation</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Azimuth range</oasis:entry>
         <oasis:entry colname="col2">360°</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Azimuth resolution</oasis:entry>
         <oasis:entry colname="col2">22.5–45.0°</oasis:entry>
         <oasis:entry colname="col3">depending on elevation</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Geometric factor</oasis:entry>
         <oasis:entry colname="col2">3.0 <inline-formula><mml:math id="M383" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<sup>−5</sup> <inline-formula><mml:math id="M385" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">sr</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">eV</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">eV</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">isotropic per anode</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">depending on elevation and mass/q</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Analyzer constant <inline-formula><mml:math id="M386" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">19.75</oasis:entry>
         <oasis:entry colname="col3">Energy <inline-formula><mml:math id="M387" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:mi>k</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M389" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> analyzer voltage</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Maximum voltage</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M390" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3000 <inline-formula><mml:math id="M391" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Time resolution</oasis:entry>
         <oasis:entry colname="col2">4–100 <inline-formula><mml:math id="M392" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">per energy step, adjustable</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">4096 <inline-formula><mml:math id="M393" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">3d scan at 8 <inline-formula><mml:math id="M394" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 128 energy steps</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Maximum count rate</oasis:entry>
         <oasis:entry colname="col2">1 <inline-formula><mml:math id="M395" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">MHz</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">per anode</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Sensor mass</oasis:entry>
         <oasis:entry colname="col2">1.35 <inline-formula><mml:math id="M396" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi></mml:mrow></mml:math></inline-formula>/3.13 <inline-formula><mml:math id="M397" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">without/with shielding</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Electronic mass</oasis:entry>
         <oasis:entry colname="col2">0.672 <inline-formula><mml:math id="M398" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">without shielding</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Power consumption</oasis:entry>
         <oasis:entry colname="col2">3.35–5.46 <inline-formula><mml:math id="M399" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">4–16 channels</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>


</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>The PEP JEI particle distribution function</title>
      <p id="d2e6330">The PEP JEI sensor is an electro-static particle analyzer using electro-static deflectors <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx1" id="paren.61"/>. This means at a given time step <inline-formula><mml:math id="M400" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M401" display="inline"><mml:mo lspace="0mm">=</mml:mo></mml:math></inline-formula> 4 <inline-formula><mml:math id="M402" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> in the case discussed here) the sensor counts ions or electrons with a specific mean energy <inline-formula><mml:math id="M403" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and energy distribution with a FWHM <inline-formula><mml:math id="M404" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:math></inline-formula> coming from a specific polar direction <inline-formula><mml:math id="M405" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> with a polar FWHM <inline-formula><mml:math id="M406" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">θ</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M407" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 5°. The actual energy and polar width are dependent on <inline-formula><mml:math id="M408" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> (see <xref ref-type="bibr" rid="bib1.bibx1" id="altparen.62"/>).</p>
      <p id="d2e6418">JEI sweeps the energy analyzer and deflector voltages in parallel in 128 steps such that one energy spectrum is obtained within 512 <inline-formula><mml:math id="M409" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> from a specific polar direction <inline-formula><mml:math id="M410" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>. The polar hemisphere is stepped through by 8 polar steps in the range 10 to 75° measured from the sensor symmetry axis. This means specifically for cold plasma distributions polar directions between each polar step may not be covered in this operation mode. The azimuth field of view is sampled simultaneously by the 16 anodes of the sensor. But since efficiency and noise background of each anode are different we here consider only one specific azimuth sector <inline-formula><mml:math id="M411" display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula> with its width <inline-formula><mml:math id="M412" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:math></inline-formula>. In summary the sensor samples counts <inline-formula><mml:math id="M413" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> from a specific viewing direction at a given time within the sampling period <inline-formula><mml:math id="M414" display="inline"><mml:mrow><mml:mi mathvariant="italic">τ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M415" display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M416" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M417" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">ms</mml:mi></mml:mrow></mml:math></inline-formula> is the dead time between each energy step. The differential energy flux can be obtained from the count rate by <xref ref-type="bibr" rid="bib1.bibx13" id="paren.63"/>:

          <disp-formula id="App1.Ch1.S2.E4" content-type="numbered"><label>B1</label><mml:math id="M418" display="block"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>c</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M419" display="inline"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the energy geometric factor which is assumed to be constant over the low energy interval under discussion. The partial phase space density for a given plasma component with mass <inline-formula><mml:math id="M420" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> and velocity <inline-formula><mml:math id="M421" display="inline"><mml:mi mathvariant="bold-italic">v</mml:mi></mml:math></inline-formula> is then given by

          <disp-formula id="App1.Ch1.S2.E5" content-type="numbered"><label>B2</label><mml:math id="M422" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi>m</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>⋅</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi>E</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M423" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>E</mml:mi><mml:mo>/</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msqrt><mml:mo>⋅</mml:mo><mml:mi mathvariant="bold-italic">n</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M424" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">n</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the vector opposite to the viewing direction.</p>
      <p id="d2e6716">The energy geometric factor of JEI for an isotropic distribution is given in Table <xref ref-type="table" rid="TA1"/>. The factor is larger for a mono-directional flow when looking into flow direction and needs to be modeled for each case.</p>
</app>

<app id="App1.Ch1.S3">
  <label>Appendix C</label><title>A drifting Maxwellian distribution in a planar potential</title>
      <p id="d2e6729">To derive the expected energy flux for a given drifting Maxwellian plasma flow with density <inline-formula><mml:math id="M425" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>, mean velocity <inline-formula><mml:math id="M426" display="inline"><mml:mover accent="true"><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> and thermal velocity <inline-formula><mml:math id="M427" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> we can use its phase space density distribution in the observation frame:

          <disp-formula id="App1.Ch1.S3.E6" content-type="numbered"><label>C1</label><mml:math id="M428" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msqrt><mml:mi mathvariant="italic">π</mml:mi></mml:msqrt><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced open="[" close="]"><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mi mathvariant="bold-italic">v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:mi mathvariant="bold-italic">v</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:math></disp-formula></p>

      <fig id="FC1" specific-use="star"><label>Figure C1</label><caption><p id="d2e6832">Phase space distribution in velocity space (left) and energy space (right) of a Maxwellian proton distribution of thermal temperature 0.2 <inline-formula><mml:math id="M429" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">eV</mml:mi></mml:mrow></mml:math></inline-formula> and density 1000/<inline-formula><mml:math id="M430" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>  drifting with velocity 8.0 <inline-formula><mml:math id="M431" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at an angle of <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M433" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 40° with respect to the <inline-formula><mml:math id="M434" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>-axis and zero spacecraft potential. Shown is the cut through the <inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M436" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0 plane with inverted velocity signs. The dot at coordinate (0,0) is an artifact of the energy table used.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f16.png"/>

      </fig>

      <fig id="FC2" specific-use="star"><label>Figure C2</label><caption><p id="d2e6923">Same as Fig. <xref ref-type="fig" rid="FC1"/> but with a planar vertical spacecraft potential of <inline-formula><mml:math id="M437" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 <inline-formula><mml:math id="M438" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> added. The upper half of the distribution as seen from the +Z deck of the spacecraft, the lower half as seen from the -Z deck of the spacecraft.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f17.png"/>

      </fig>

      <p id="d2e6950">The respective phase space distribution is illustrated in Fig. <xref ref-type="fig" rid="FC1"/> for observation conditions similar to those described in the text. The observation plane (spacecraft nadir deck) can be thought off as the plane given by <inline-formula><mml:math id="M439" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M440" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0, that is the part of the distribution with <inline-formula><mml:math id="M441" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M442" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0 is not observed by a sensor on the deck.</p>
      <p id="d2e6991">While the flow is mono-directional the observation geometry of the sensor is spherical.  To use spherical coordinates we can express the vector coordinates by

          <disp-formula id="App1.Ch1.S3.E7" content-type="numbered"><label>C2</label><mml:math id="M443" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>n</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msqrt><mml:mi mathvariant="italic">π</mml:mi></mml:msqrt><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>×</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced close="]" open="["><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mover accent="true"><mml:mi>v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mover accent="true"><mml:mi>v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>|</mml:mo><mml:mi>v</mml:mi><mml:mo>|</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

        where <inline-formula><mml:math id="M444" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> is the distance between viewing direction (<inline-formula><mml:math id="M445" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi></mml:mrow></mml:math></inline-formula>) and mean flow direction (<inline-formula><mml:math id="M446" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) along the great circle (all angles in radian):

          <disp-formula id="App1.Ch1.S3.E8" content-type="numbered"><label>C3</label><mml:math id="M447" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mi>arccos⁡</mml:mi><mml:mo>(</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>cos⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>sin⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mi>cos⁡</mml:mi><mml:mo>|</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e7201">The sensor measures energy spectra in different spatial directions. To compare with the observations we replace the thermal velocity <inline-formula><mml:math id="M448" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by thermal energy <inline-formula><mml:math id="M449" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the mean velocity by mean energy <inline-formula><mml:math id="M450" display="inline"><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> and the total of the velocity by the respective energy and get

          <disp-formula id="App1.Ch1.S3.E9" content-type="numbered"><label>C4</label><mml:math id="M451" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi>n</mml:mi><mml:mo>⋅</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>m</mml:mi><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>×</mml:mo><mml:mi>exp⁡</mml:mi><mml:mfenced close="]" open="["><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msqrt><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi>E</mml:mi></mml:mrow></mml:msqrt><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>+</mml:mo><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e7343">This generalizes Eq. (18) of <xref ref-type="bibr" rid="bib1.bibx13" id="text.64"/> which is only valid for <inline-formula><mml:math id="M452" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M453" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0 and is illustrated in Fig. <xref ref-type="fig" rid="FC1"/>.</p>
      <p id="d2e7368">If we just consider an anode looking in flow direction (that is receiving the peak signal) we can assume <inline-formula><mml:math id="M454" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mi>f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.  In this case we get

          <disp-formula id="App1.Ch1.S3.E10" content-type="numbered"><label>C5</label><mml:math id="M455" display="block"><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>sin⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>cos⁡</mml:mi><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>cos⁡</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e7441">Using Eqs. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E6"/>) and (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E9"/>) we can thus determine for an assumed Maxwellian plasma flow the expected energy flux in each angular direction and energy bin of the sensor.</p>
      <p id="d2e7449">The effect of a potential distribution on a drifting Maxwellian distribution was first described in the seminal paper by <xref ref-type="bibr" rid="bib1.bibx34" id="text.65"/> in the context of laboratory plasma probes. But in this study it was not explicitly formulated for the planar geometry case. More recent discussions can be found in <xref ref-type="bibr" rid="bib1.bibx17" id="text.66"/> and <xref ref-type="bibr" rid="bib1.bibx40" id="text.67"/> for spherical geometries.</p>
      <p id="d2e7461">If we now introduce a planar spacecraft potential located in the <inline-formula><mml:math id="M456" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> plane the observed velocity distribution is only affected in the <inline-formula><mml:math id="M457" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>v</mml:mi><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi></mml:mrow></mml:math></inline-formula> coordinate. We use the thin-sheath approximation <xref ref-type="bibr" rid="bib1.bibx43" id="paren.68"/> which neglects effects on ions which initially are inside the volume affected by the potential. The temperature of the distribution <inline-formula><mml:math id="M458" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> given in the exponent of the equations above is not directly affected by this, but the phase space distribution in the observed velocity space is shifted such that the observed velocity and energy are

          <disp-formula id="App1.Ch1.S3.E11" content-type="numbered"><label>C6</label><mml:math id="M459" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mtext>zp</mml:mtext></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>m</mml:mi><mml:mo>-</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>|</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>|</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>cos⁡</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>-</mml:mo><mml:mo>|</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>|</mml:mo><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mtext> or:</mml:mtext></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mtext> for </mml:mtext><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>&gt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo>⋅</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi>cos⁡</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mtext> for </mml:mtext><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

        where <inline-formula><mml:math id="M460" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula> is the undisturbed angle from the <inline-formula><mml:math id="M461" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> axis and <inline-formula><mml:math id="M462" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>. That means ions which initially have negative <inline-formula><mml:math id="M463" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (that is flying towards the <inline-formula><mml:math id="M464" display="inline"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> deck) gain the full energy <inline-formula><mml:math id="M465" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, ions with initially positive <inline-formula><mml:math id="M466" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are decelerated, but are still observed as long as <inline-formula><mml:math id="M467" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>. The observed angle <inline-formula><mml:math id="M468" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given by Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>). This separation of the distribution into accelerated and decelerated ions was missed in the treatment of the problem by <xref ref-type="bibr" rid="bib1.bibx40" id="text.69"/>. When integrating the phase space distribution one also needs to consider the transformation of the volume element <inline-formula><mml:math id="M469" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dV</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>d</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>d</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:msqrt><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mi>m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:msqrt><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mi>sin⁡</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>d</mml:mi><mml:mi mathvariant="italic">θ</mml:mi><mml:mi>d</mml:mi><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:math></inline-formula>. The respective distribution in energy space is illustrated in Fig. <xref ref-type="fig" rid="FC2"/>.</p>
      <p id="d2e7894">For completeness we also show in Fig. <xref ref-type="fig" rid="FC2"/> the phase space distribution which would be observed on the opposite side of the spacecraft for the same drifting Maxwellian and <inline-formula><mml:math id="M470" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.0 <inline-formula><mml:math id="M471" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">V</mml:mi></mml:mrow></mml:math></inline-formula> spacecraft potential attracting ions towards the +Z direction. This situation is relevant for the PEP JDC sensor which is mounted on the opposite deck of the spacecraft. The respective synchronous observations of this sensor are described in an accompanying paper.</p>
      <p id="d2e7914">Interesting for the analysis of an energy spectrum <inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> observed at a specific angle <inline-formula><mml:math id="M473" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">θ</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is how to derive temperature, potential and mean energy from the spectrum. Since the spectrum is distorted for <inline-formula><mml:math id="M474" display="inline"><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> one may derive temperature from a fit to the upper leg of the distribution. The question is at which value of <inline-formula><mml:math id="M475" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> the maximum phase space density is observed.  This is the case when <inline-formula><mml:math id="M476" display="inline"><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>.  From Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E9"/>) we get

          <disp-formula id="App1.Ch1.S3.E12" content-type="numbered"><label>C7</label><mml:math id="M477" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>d</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mfenced open="(" close=")"><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:msqrt><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi>E</mml:mi></mml:mrow></mml:msqrt><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>+</mml:mo><mml:mi>E</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>⟹</mml:mo><mml:msqrt><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>/</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:msqrt><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>⟹</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:msup><mml:mi>cos⁡</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e8146">For <inline-formula><mml:math id="M478" display="inline"><mml:mrow><mml:mi mathvariant="italic">θ</mml:mi><mml:mo>&gt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> this means the maximum observed phase space density is at <inline-formula><mml:math id="M479" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mtext>pm</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mi>q</mml:mi><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:msup><mml:mi>cos⁡</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> which will allow to derive <inline-formula><mml:math id="M480" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for known drift velocity <inline-formula><mml:math id="M481" display="inline"><mml:mover accent="true"><mml:mi>v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> and angle <inline-formula><mml:math id="M482" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula>.  For a Maxwellian distribution at rest the observed width of the distribution in each spatial direction is given by <inline-formula><mml:math id="M483" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. If we define the energy <inline-formula><mml:math id="M484" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> at which the distribution falls off by <inline-formula><mml:math id="M485" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:math></inline-formula> through <inline-formula><mml:math id="M486" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:math></inline-formula>, we get for the drifting Maxwellian:

          <disp-formula id="App1.Ch1.S3.E13" content-type="numbered"><label>C8</label><mml:math id="M487" display="block"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:msup><mml:mi>cos⁡</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:msqrt><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e8357">The width of the distribution is then <inline-formula><mml:math id="M488" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:msqrt><mml:mrow><mml:mover accent="true"><mml:mi>E</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>.  That means only perpendicular to the flow direction (<inline-formula><mml:math id="M489" display="inline"><mml:mrow><mml:mi>cos⁡</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) the observed temperature agrees with the real temperature <inline-formula><mml:math id="M490" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</app>

<app id="App1.Ch1.S4">
  <label>Appendix D</label><title>Density correction in a planar potential</title>
      <p id="d2e8450">The effect of electric potentials on the plasma flow was alrea<inline-formula><mml:math id="M491" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dy</mml:mi></mml:mrow></mml:math></inline-formula> analyzed in much detail in the seminal paper by <xref ref-type="bibr" rid="bib1.bibx34" id="text.70"/> in the context of plasma probes. For convenience in the following we describe the derivation in planar geometry since the more recent papers usually assume spherical geometry <xref ref-type="bibr" rid="bib1.bibx29" id="paren.71"/>.  We generally assume that the spacecraft is located in a mono-directional plasma flow with density <inline-formula><mml:math id="M492" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and velocity <inline-formula><mml:math id="M493" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.  If the ion sensor is located behind a planar entrance grid and the flow is perpendicular to this grid we are dealing with a one-dimensional problem as shown in Fig. <xref ref-type="fig" rid="FD1"/>. Liouville's theorem in general form states that the phase space density of particles <inline-formula><mml:math id="M494" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dV</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> in a volume element <inline-formula><mml:math id="M495" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dV</mml:mi></mml:mrow></mml:math></inline-formula> of phase space is conserved along the flow, in cartesian geometry:

          <disp-formula id="App1.Ch1.S4.E14" content-type="numbered"><label>D1</label><mml:math id="M496" display="block"><mml:mrow><mml:mi>S</mml:mi><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>z</mml:mi></mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dx</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dy</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dz</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula>

        where <inline-formula><mml:math id="M497" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow></mml:math></inline-formula> denotes the number of particles and <inline-formula><mml:math id="M498" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dV</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>z</mml:mi></mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dx</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dy</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dz</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> the size of the volume element.  In 1D geometry this reduces to <inline-formula><mml:math id="M499" display="inline"><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dx</mml:mi></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mtext>constant</mml:mtext></mml:mrow></mml:math></inline-formula> since <inline-formula><mml:math id="M500" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mi>z</mml:mi></mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dy</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dz</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> is constant. Now, the quantity measured by ion sensors is the flux of ions <inline-formula><mml:math id="M501" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> with mean energy <inline-formula><mml:math id="M502" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> crossing an area <inline-formula><mml:math id="M503" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dA</mml:mi></mml:mrow></mml:math></inline-formula> perpendicular to the flow direction in a given time <inline-formula><mml:math id="M504" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow></mml:math></inline-formula> for a given energy interval <inline-formula><mml:math id="M505" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:math></inline-formula>.  In 1D the spatial extent of the volume element along the flow is given by <inline-formula><mml:math id="M506" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dx</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>v</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> and since <inline-formula><mml:math id="M507" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>v</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> we have

          <disp-formula id="App1.Ch1.S4.E15" content-type="numbered"><label>D2</label><mml:math id="M508" display="block"><mml:mrow><mml:mi>S</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dv</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dx</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mi>v</mml:mi></mml:mfrac></mml:mstyle><mml:mi>v</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>S</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow><mml:mo>∝</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula></p>

      <fig id="FD1" specific-use="star"><label>Figure D1</label><caption><p id="d2e8769">Planar geometry of acceleration by potential in velocity and coordinate space. The size of the phase space volume element does not change. Flux through surface <inline-formula><mml:math id="M509" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dA</mml:mi></mml:mrow></mml:math></inline-formula> is conserved.</p></caption>
        <graphic xlink:href="https://angeo.copernicus.org/articles/44/1143/2026/angeo-44-1143-2026-f18.png"/>

      </fig>

      <p id="d2e8786">The particle number flux of particles crossing a given area <inline-formula><mml:math id="M510" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dA</mml:mi></mml:mrow></mml:math></inline-formula> in a given time <inline-formula><mml:math id="M511" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow></mml:math></inline-formula> is given by <inline-formula><mml:math id="M512" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dA</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">dt</mml:mi></mml:mrow><mml:mo>∼</mml:mo><mml:mi>S</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>.  Liouville's theorem in 1D then states <inline-formula><mml:math id="M513" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> is constant. Thus if an instrument measures with the same energy width <inline-formula><mml:math id="M514" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow></mml:math></inline-formula> outside of the potential or inside of the potential it will measure the same particle number flux – only at a different energy.  From <inline-formula><mml:math id="M515" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> it follows also that <inline-formula><mml:math id="M516" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dE</mml:mi></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.  Here we also make the same assumption as <xref ref-type="bibr" rid="bib1.bibx34" id="text.72"/> namely that all ions are accelerated by the same energy per charge after they enter the volume affected by the potential.  This is also called thin-shield approximation <xref ref-type="bibr" rid="bib1.bibx43" id="paren.73"/>.</p>
      <p id="d2e8907">We again stress that if a sensor measures with a geometric factor which depends on energy it is irrelevant for this discussion because this happens behind the entrance grid of the sensor.  Outside of the potential the number flux is given by <inline-formula><mml:math id="M517" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, since the mean velocity <inline-formula><mml:math id="M518" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> measured inside of a potential <inline-formula><mml:math id="M519" display="inline"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given by <inline-formula><mml:math id="M520" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:msubsup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:msubsup><mml:mi>v</mml:mi><mml:mi mathvariant="normal">p</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M521" display="inline"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>|</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:mo>/</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M522" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mtext>sign</mml:mtext><mml:mo>(</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the observed ion density <inline-formula><mml:math id="M523" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is given by

          <disp-formula id="App1.Ch1.S4.E16" content-type="numbered"><label>D3</label><mml:math id="M524" display="block"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:msqrt><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

        where we define the <italic>velocity ratio</italic> <inline-formula><mml:math id="M525" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mi mathvariant="normal">p</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>v</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:msup><mml:mo>)</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt></mml:mrow></mml:math></inline-formula>.  That means the observed density is lower than the undisturbed density <inline-formula><mml:math id="M526" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> for a negative potential. We note that this is different from the usual correction for potentials with a spherical geometry where the potential focuses the flux <xref ref-type="bibr" rid="bib1.bibx29" id="paren.74"/>.</p>
      <p id="d2e9204">But there is one assumption in this derivation which may not be applicable for actual measurement situations, namely that always all particles flying through the volume element backward and forward are measured. In reality only the part of a distribution flying towards a sensor are measured. As shown in the previous section this means for example for an undisturbed Maxwellian distribution and a given one dimensional look direction only half of the distribution is observed. When an attracting potential is added a larger part of the distribution becomes visible in this look direction and lost from the opposite direction. In the Liouville picture also particles flying in opposite direction are included in <inline-formula><mml:math id="M527" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">dN</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d2e9219">Data of the PEP JEI sensor used in this study is available at ESA Planetary Science Archive (PSA) Guest Storage Facility (GSF) (<ext-link xlink:href="https://doi.org/10.57780/esa-2bb387d" ext-link-type="DOI">10.57780/esa-2bb387d</ext-link>; <xref ref-type="bibr" rid="bib1.bibx11" id="altparen.75"/>).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e9231">The data analysis was performed by Markus Fränz, Elias Roussos, and  Jan-Erik Wahlund. Henning Fischer is the lead engineer of the JEI sensor. Other co-authors supervise build and operation of JUICE PEP and provided corrections to the analysis.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e9237">At least one of the (co-)authors is a member of the editorial board of <italic>Annales Geophysicae</italic>. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e9246">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><notes notes-type="sistatement"><title>Special issue statement</title>

      <p id="d2e9252">This article is part of the special issue “The first-ever lunar–Earth flyby: a unique test environment for Juice”. It is not associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e9258">JUICE is a mission under ESA leadership with contributions from its Member States, NASA, JAXA, and the Israel Space Agency. It is the first Large-class mission in ESA’s Cosmic Vision programme. The JUICE/RPWI instrument is supported by the Swedish National Space Agency (SNSA). The German contribution to the PEP instrument suite and its operation was and is being funded by the German Federal Ministry for Economic Affairs and Climate Action/German Federal Ministry of Research, Technology and Space (BMFTR) through the German Space Agency at DLR on the basis of a resolution of the German Bundestag (Funding codes: 50QJ1301, 50QJ1503 and 50QJ2303) and by the Max Planck Society. This publication has emanated from research conducted with the financial support of Taighde Éireann – Research Ireland under Grant number [22/PATH-S/10757], awarded to MKGH. French co-authors acknowledge the support of CNES for the Juice mission. We also thank Susan McKenna-Lawlor of the Maynooth University, Ireland, for supporting the PEP instrument development.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e9263">The article processing charges for this open-access publication were covered by the Max Planck Society.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e9269">This paper was edited by Joana S. Oliveira and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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