<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<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-29-909-2011</article-id>
<title-group>
<article-title>Apparent temperature anisotropies due to wave activity in the solar wind</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Verscharen</surname>
<given-names>D.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Marsch</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Institute for Theoretical Physics, TU Braunschweig, Mendelssohnstr. 3, 38106 Braunschweig, Germany</addr-line>
</aff>
<pub-date pub-type="epub">
<day>25</day>
<month>05</month>
<year>2011</year>
</pub-date>
<volume>29</volume>
<issue>5</issue>
<fpage>909</fpage>
<lpage>917</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2011 D. Verscharen</copyright-statement>
<copyright-year>2011</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://angeo.copernicus.org/articles/29/909/2011/angeo-29-909-2011.html">This article is available from https://angeo.copernicus.org/articles/29/909/2011/angeo-29-909-2011.html</self-uri>
<self-uri xlink:href="https://angeo.copernicus.org/articles/29/909/2011/angeo-29-909-2011.pdf">The full text article is available as a PDF file from https://angeo.copernicus.org/articles/29/909/2011/angeo-29-909-2011.pdf</self-uri>
<abstract>
<p>The fast solar wind is a collisionless plasma permeated by
plasma waves on many different scales. A plasma wave represents the natural
interplay between the periodic changes of the electromagnetic field and the
associated coherent motions of the plasma particles. In this paper, a model
velocity distribution function is derived for a plasma in a single, coherent, large-amplitude wave. This model allows one to study the kinetic
effects of wave motions on particle distributions. They are by in-situ
spacecraft measured by counting, over a certain sampling time, the particles
coming from various directions and having different energies. We compare our
results with the measurements by the Helios spacecraft, and thus find that by
assuming high wave activity we are able to explain key observed features of
the measured distributions within the framework of our model. We also address
the recent discussions on nonresonant wave–particle interactions and apparent
heating. The applied time-averaging procedure leads to an apparent ion
temperature anisotropy which is connected but not identical to the intrinsic
temperature of the underlying distribution function.</p>
</abstract>
<counts><page-count count="9"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Abramowitz, M. and Stegun, I.&amp;nbsp;A.: Handbook of Mathematical Functions, Dover Publ., 1972.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Akhiezer, A.&amp;nbsp;I., Akhiezer, I.&amp;nbsp;A., Polovin, R.&amp;nbsp;V., Sitenko, A.&amp;nbsp;G., and Stepanov, K.&amp;nbsp;N.: Plasma electrodynamics – Vol.1: Linear theory, 1975a.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Akhiezer, A.&amp;nbsp;I., Akhiezer, I.&amp;nbsp;A., Polovin, R.&amp;nbsp;V., Sitenko, A.&amp;nbsp;G., and Stepanov, K.&amp;nbsp;N.: Plasma electrodynamics – Vol.2: Non-linear theory and fluctuations, 1975b.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Alexandrova, O., Lacombe, C., and Mangeney, A.: Spectra and anisotropy of magnetic fluctuations in the Earth&apos;s magnetosheath: Cluster observations, Ann. Geophys., 26, 3585–3596, &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-26-3585-2008&quot;&gt;https://doi.org/10.5194/angeo-26-3585-2008&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Araneda, J.&amp;nbsp;A., Marsch, E., and F.-Vi{ñ}as, A.: Proton Core Heating and Beam Formation via Parametrically Unstable Alfv{é}n-Cyclotron Waves, Phys.&amp;nbsp;Rev.&amp;nbsp;Lett., 100, 125003, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.100.125003&quot;&gt;https://doi.org/10.1103/PhysRevLett.100.125003&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Araneda, J.&amp;nbsp;A., Maneva, Y., and Marsch, E.: Preferential Heating and Acceleration of α Particles by Alfv{é}n-Cyclotron Waves, Phys.&amp;nbsp;Rev.&amp;nbsp;Lett., 102, 175001, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.102.175001&quot;&gt;https://doi.org/10.1103/PhysRevLett.102.175001&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Bale, S.&amp;nbsp;D., Kasper, J.&amp;nbsp;C., Howes, G.&amp;nbsp;G., Quataert, E., Salem, C., and Sundkvist, D.: Magnetic Fluctuation Power Near Proton Temperature Anisotropy Instability Thresholds in the Solar Wind, Phys.&amp;nbsp;Rev.&amp;nbsp;Lett., 103, 211101, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.103.211101&quot;&gt;https://doi.org/10.1103/PhysRevLett.103.211101&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Belcher, J.&amp;nbsp;W. and Davis Jr., L.: Large-amplitude Alfv{é}n waves in the interplanetary medium, 2., J. Geophys. Res., 76, 3534–3563, &lt;a href=&quot;http://dx.doi.org/10.1029/JA076i016p03534&quot;&gt;https://doi.org/10.1029/JA076i016p03534&lt;/a&gt;, 1971.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Bourouaine, S., Marsch, E., and Vocks, C.: On the Efficiency of Nonresonant Ion Heating by Coronal Alfv{é}n Waves, Astrophys.&amp;nbsp;J.&amp;nbsp;Lett., 684, L119–L122, &lt;a href=&quot;http://dx.doi.org/10.1086/592243&quot;&gt;https://doi.org/10.1086/592243&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Bourouaine, S., Marsch, E., and Neubauer, F.&amp;nbsp;M.: Correlations between the proton temperature anisotropy and transverse high-frequency waves in the solar wind, Geophys.&amp;nbsp;Res.&amp;nbsp;Lett., 37, 14104, &lt;a href=&quot;http://dx.doi.org/10.1029/2010GL043697&quot;&gt;https://doi.org/10.1029/2010GL043697&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Chandran, B.&amp;nbsp;D.&amp;nbsp;G., Pongkitiwanichakul, P., Isenberg, P.&amp;nbsp;A., Lee, M.&amp;nbsp;A., Markovskii, S.&amp;nbsp;A., Hollweg, J.&amp;nbsp;V., and Vasquez, B.&amp;nbsp;J.: Resonant Interactions Between Protons and Oblique Alfv{é}n/Ion-cyclotron Waves in the Solar Corona and Solar Flares, Astrophys.&amp;nbsp;J., 722, 710–720, &lt;a href=&quot;http://dx.doi.org/10.1088/0004-637X/722/1/710&quot;&gt;https://doi.org/10.1088/0004-637X/722/1/710&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Davidson, R.&amp;nbsp;C.: Kinetic waves and instabilities in a uniform plasma, in: Basic Plasma Physics: Selected Chapters, Handbook of Plasma Physics, Volume 1, edited by: A.&amp;nbsp;A.&amp;nbsp;Galeev &amp; R.&amp;nbsp;N.&amp;nbsp;Sudan, p. 229, 1983.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Elskens, Y. and Escande, D.: Microscopic Dynamics of Plasmas and Chaos, 2003.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Gary, S.&amp;nbsp;P.: Theory of Space Plasma Microinstabilities, 1993.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Gary, S.&amp;nbsp;P., Yin, L., and Winske, D.: Electromagnetic proton cyclotron anisotropy instability: Wave-particle scattering rate, Geophys.&amp;nbsp;Res.&amp;nbsp;Lett., 27, 2457–2460, &lt;a href=&quot;http://dx.doi.org/10.1029/2000GL000055&quot;&gt;https://doi.org/10.1029/2000GL000055&lt;/a&gt;, 2000.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Gary, S.&amp;nbsp;P., Skoug, R.&amp;nbsp;M., Steinberg, J.&amp;nbsp;T., and Smith, C.&amp;nbsp;W.: Proton temperature anisotropy constraint in the solar wind: ACE observations, Geophys.&amp;nbsp;Res.&amp;nbsp;Lett., 28, 2759–2762, &lt;a href=&quot;http://dx.doi.org/10.1029/2001GL013165&quot;&gt;https://doi.org/10.1029/2001GL013165&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Hamza, A.&amp;nbsp;M., Meziane, K., and Mazelle, C.: Oblique propagation and nonlinear wave particle processes, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 111, 4104, &lt;a href=&quot;http://dx.doi.org/10.1029/2005JA011410&quot;&gt;https://doi.org/10.1029/2005JA011410&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Heuer, M. and Marsch, E.: Diffusion plateaus in the velocity distributions of fast solar wind protons, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 112, 3102, &lt;a href=&quot;http://dx.doi.org/10.1029/2006JA011979&quot;&gt;https://doi.org/10.1029/2006JA011979&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Hizanidis, K., Kominis, Y., and Ram, A.&amp;nbsp;K.: Quasilinear theory revisited: general kinetic formulation of wave-particle interactions in plasmas, Plasma Physics and Controlled Fusion, 52, 124022, &lt;a href=&quot;http://dx.doi.org/10.1088/0741-3335/52/12/124022&quot;&gt;https://doi.org/10.1088/0741-3335/52/12/124022&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Horbury, T.&amp;nbsp;S., Forman, M.&amp;nbsp;A., and Oughton, S.: Spacecraft observations of solar wind turbulence: an overview, Plasma Physics and Controlled Fusion, 47, B703–B717, &lt;a href=&quot;http://dx.doi.org/10.1088/0741-3335/47/12B/S52&quot;&gt;https://doi.org/10.1088/0741-3335/47/12B/S52&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Howes, G.&amp;nbsp;G.: Inertial range turbulence in kinetic plasmas, Phys.&amp;nbsp;Plasmas, 15, 055904, &lt;a href=&quot;http://dx.doi.org/10.1063/1.2889005&quot;&gt;https://doi.org/10.1063/1.2889005&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Kohl, J.&amp;nbsp;L., Noci, G., Cranmer, S.&amp;nbsp;R., and Raymond, J.&amp;nbsp;C.: Ultraviolet spectroscopy of the extended solar corona, Astron.&amp;nbsp;Astrophys.&amp;nbsp;Rev., 13, 31–157, &lt;a href=&quot;http://dx.doi.org/10.1007/s00159-005-0026-7&quot;&gt;https://doi.org/10.1007/s00159-005-0026-7&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Li, X. and Habbal, S.&amp;nbsp;R.: Hybrid simulation of ion cyclotron resonance in the solar wind: Evolution of velocity distribution functions, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 110, A10109, &lt;a href=&quot;http://dx.doi.org/10.1029/2005JA011030&quot;&gt;https://doi.org/10.1029/2005JA011030&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Li, X., Lu, Q., and Li, B.: Ion Pickup by Finite Amplitude Parallel Propagating Alfv{é}n Waves, Astrophys.&amp;nbsp;J., 661, L105–L108, &lt;a href=&quot;http://dx.doi.org/10.1086/518420&quot;&gt;https://doi.org/10.1086/518420&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Lu, Q. and Chen, L.: Ion Heating by a Spectrum of Obliquely Propagating Low-frequency Alfv{é}n Waves, Astrophys.&amp;nbsp;J., 704, 743–749, &lt;a href=&quot;http://dx.doi.org/10.1088/0004-637X/704/1/743&quot;&gt;https://doi.org/10.1088/0004-637X/704/1/743&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Lu, Q. and Li, X.: Heating of ions by low-frequency Alfven waves, Physics of Plasmas, 14, 042303, &lt;a href=&quot;http://dx.doi.org/10.1063/1.2715569&quot;&gt;https://doi.org/10.1063/1.2715569&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Maneva, Y.&amp;nbsp;G., Araneda, J.&amp;nbsp;A., and Marsch, E.: Ion distributions in coronal holes and fast solar wind, Twelfth International Solar Wind Conference, 1216, 227–230, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3395842&quot;&gt;https://doi.org/10.1063/1.3395842&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Markovskii, S.&amp;nbsp;A., Vasquez, B.&amp;nbsp;J., and Hollweg, J.&amp;nbsp;V.: Proton Heating by Nonlinear Field-Aligned Alfv{é}n Waves in Solar Coronal Holes, Astrophys.&amp;nbsp;J., 695, 1413–1420, &lt;a href=&quot;http://dx.doi.org/10.1088/0004-637X/695/2/1413&quot;&gt;https://doi.org/10.1088/0004-637X/695/2/1413&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Marsch, E.: Kinetic Physics of the Solar Corona and Solar Wind, Living Rev.&amp;nbsp;Sol.&amp;nbsp;Phys., 3, 1, 2006.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Marsch, E., Rosenbauer, H., Schwenn, R., Muehlhaeuser, K., and Denskat, K.&amp;nbsp;U.: Pronounced proton core temperature anisotropy, ion differential speed, and simultaneous Alfven wave activity in slow solar wind at 0.3 AU, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 86, 9199–9203, &lt;a href=&quot;http://dx.doi.org/10.1029/JA086iA11p09199&quot;&gt;https://doi.org/10.1029/JA086iA11p09199&lt;/a&gt;, 1981.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Marsch, E., Ao, X.-Z., and Tu, C.-Y.: On the temperature anisotropy of the core part of the proton velocity distribution function in the solar wind, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 109, 4102, &lt;a href=&quot;http://dx.doi.org/10.1029/2003JA010330&quot;&gt;https://doi.org/10.1029/2003JA010330&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Marsch, E., Zhao, L., and Tu, C.-Y.: Limits on the core temperature anisotropy of solar wind protons, Ann. Geophys., 24, 2057–2063, &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-24-2057-2006&quot;&gt;https://doi.org/10.5194/angeo-24-2057-2006&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Marsch, E., Yao, S., and Tu, C.-Y.: Proton beam velocity distributions in an interplanetary coronal mass ejection, Ann. Geophys., 27, 869–875, &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-27-869-2009&quot;&gt;https://doi.org/10.5194/angeo-27-869-2009&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Matsumoto, H.: Nonlinear whistler-mode interaction and triggered emission in the magnetosphere – A review, in: Wave instabilities in space plasmas; Proceedings of the Symposium, Helsinki, Finland, 31 July–8 August 1978. (A80-21196 07-46) Dordrecht, D. Reidel Publishing Co., 1979, p. 163–190, edited by:&amp;nbsp;Palmadesso, P.&amp;nbsp;J. and&amp;nbsp;Papadopoulos, K., pp. 163–190, 1979.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Ofman, L., Davila, J.&amp;nbsp;M., Nakariakov, V.&amp;nbsp;M., and Vi{ñ}as, A.: High-frequency Alfv{é}n waves in multi-ion coronal plasma: Observational implications, J.&amp;nbsp;Geophys.&amp;nbsp;Res., 110, 9102, &lt;a href=&quot;http://dx.doi.org/10.1029/2004JA010969&quot;&gt;https://doi.org/10.1029/2004JA010969&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Schekochihin, A.&amp;nbsp;A., Cowley, S.&amp;nbsp;C., Dorland, W., Hammett, G.&amp;nbsp;W., Howes, G.&amp;nbsp;G., Plunk, G.&amp;nbsp;G., Quataert, E., and Tatsuno, T.: Gyrokinetic turbulence: a nonlinear route to dissipation through phase space, Plasma Phys.&amp;nbsp;Contr.&amp;nbsp;F., 50, 124024, &lt;a href=&quot;http://dx.doi.org/10.1088/0741-3335/50/12/124024&quot;&gt;https://doi.org/10.1088/0741-3335/50/12/124024&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Sonnerup, B.&amp;nbsp;U.&amp;nbsp;{Ö}. and Su, S.-Y.: Large Amplitude Whistler Waves in a Hot Collision-Free Plasma, Phys.&amp;nbsp;Fluids, 10, 462–464, &lt;a href=&quot;http://dx.doi.org/10.1063/1.1762132&quot;&gt;https://doi.org/10.1063/1.1762132&lt;/a&gt;, 1967.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Stix, T.-H.: Waves in Plasmas, American Institute of Physics, New York, 1992.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Tu, C. and Marsch, E.: MHD structures, waves and turbulence in the solar wind: Observations and theories, Space Sci.&amp;nbsp;Rev., 73, 1–210, &lt;a href=&quot;http://dx.doi.org/10.1007/BF00748891&quot;&gt;https://doi.org/10.1007/BF00748891&lt;/a&gt;, 1995.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">von Steiger, R.: The solar wind throughout the solar cycle, in: The Heliosphere through the Solar Activity Cycle, Praxis Publishing Ltd, Chichester, UK, edited by: Balogh, A., Lanzerotti, L., and Suess, S., pp. 41–78, 2008.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Wang, C.&amp;nbsp;B. and Wu, C.&amp;nbsp;S.: Pseudoheating of protons in the presence of Alfv{é}nic turbulence, Phys.&amp;nbsp;Plasmas, 16, 020703, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3068472&quot;&gt;https://doi.org/10.1063/1.3068472&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Wang, C.&amp;nbsp;B., Wu, C.&amp;nbsp;S., and Yoon, P.&amp;nbsp;H.: Heating of Ions by Alfv{é}n Waves via Nonresonant Interactions, Phys.&amp;nbsp;Rev.&amp;nbsp;Lett., 96, 125001, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.96.125001&quot;&gt;https://doi.org/10.1103/PhysRevLett.96.125001&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Wu, C.&amp;nbsp;S. and Yoon, P.&amp;nbsp;H.: Proton Heating via Nonresonant Scattering Off Intrinsic Alfv{é}nic Turbulence, Phys.&amp;nbsp;Rev.&amp;nbsp;Lett., 99, 075001, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevLett.99.075001&quot;&gt;https://doi.org/10.1103/PhysRevLett.99.075001&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Wu, C.&amp;nbsp;S., Yoon, P.&amp;nbsp;H., and Wang, C.&amp;nbsp;B.: On nonresonant proton heating via intrinsic Alfv{é}nic turbulence, Phys.&amp;nbsp;Plasmas, 16, 054503, &lt;a href=&quot;http://dx.doi.org/10.1063/1.3147924&quot;&gt;https://doi.org/10.1063/1.3147924&lt;/a&gt;, 2009.</mixed-citation>
</ref>
</ref-list>
</back>
</article>