Estimating the fate of oxygen ion outflow from the high altitude cusp

We have investigated the oxygen escape-to-capture ratio from the high altitude cusp regions for various geomagnetic activity levels by combining EDI and CODIF measurements from the Cluster spacecraft. Using Tsyganenko model, we traced the observed oxygen ions to one of three regions: plasma sheet, solar wind beyond distant X-line or dayside magnetosheath. Our results indicate that 69 % of high altitude oxygen escapes the magnetosphere, from which most escape beyond the distant X-line (50% of total oxygen flux). Convection of oxygen to the plasma sheet shows a strong dependence on geomagnetic 5 activity. We used the Dst index as a proxy for geomagnetic storms and separated data into quiet conditions (Dst > 0 nT), moderate conditions (0 > Dst >−20 nT), and active conditions (Dst <−20 nT). For quiet magnetospheric conditions we found increased escape due to low convection. For active magnetospheric conditions we found an increase in both parallel velocities and convection velocities, but the increase in convection velocities is higher, and thus most of oxygen flux gets convected into plasma sheet (73 %). The convected oxygen ions reach the plasma sheet in the distant tail, mostly beyond 50 10 RE.

The magnetospheric cusps are narrow regions of open field lines, magnetically connected to the magnetosheath and the solar wind. As a result, the heating in the cusps is higher than in the polar caps. The interaction between the magnetosheath and the magnetosphere, leads to a perpendicular energization of ions. Due to strong magnetic gradients in the cusp regions, mirror 5 forces can effectively transform perpendicular energy into parallel energy. The field aligned acceleration from the mirror force becomes sufficient to overcome the gravitational potential for hydrogen and oxygen ions (Nilsson et al., 1996;Ogawa et al., 2003;Kistler et al., 2010). As the main driver of cusp outflow, ion transverse heating is analyzed in detail (e.g., Andre et al., 1990;Norqvist et al., 1996;Bouhram et al., 2003;Waara et al., 2011;Slapak et al., 2011). 10 The fate of escaping oxygen ions is determined by the ratio between their parallel velocity (along the magnetic field) and the convection velocity (perpendicular to the magnetic field). For a given solar wind condition, both convection velocity and parallel velocity increase with radial distance. The convection velocity scales with magnetic field, whereas the parallel velocity increases due to the combined effect of the mirror force and the centrifugal force. 15 Engwall et al. (2009) measured cold ions (< 100 eV, mostly H + ) in the lobe regions and calculated the typical values for lobe plasma properties (velocity, density, acceleration, etc.). As estimated by Haaland et al. (2012), most of the H + ions return to the magnetosphere. The fate of oxygen ions is not fully understood. Seki et al. (2001) concluded that over 90 % of O + return back to magnetosphere. However, this statement was challenged by Nilsson (2011), claiming that the Seki et al. (2001) study underestimated the outflowing energies of the O + ions. Seki et al. (2001) used O + energies lower than 1 keV, while Nilsson 20 (2011) measured the energies in the range 1 − 8 keV at high altitudes. Ebihara et al. (2006) traced of O + ions and stated that most of them end up feeding ring current. Their research included oxygen ions with low initial energies (<200 eV). A significant part of the acceleration along the magnetic field lines in the cusps comes from centrifugal acceleration (Cladis, 1986;Nilsson et al., 2008Nilsson et al., , 2010, and thus convection plays a considerable role. Other acceleration processes also take place 25 in the cups and will be further discussed in section 3. Slapak et al. (2017) used the Composition and Distribution Function (CODIF) ion spectrometer onboard Cluster to get insitu measurements of O + and H + in the cusp and plasma mantle regions. The plasma mantle is a boundary region of the magnetic lobes, neighboring the tailward cusp. They concluded that most of the high altitude oxygen ion outflow is transported 30 to the solar wind beyond distant X-line or to the dayside magnetosheath. Slapak et al. (2017) did not investigate the role of convection in detail, so in this paper, we further investigate the role of convection in oxygen outflow by combining Electron Drift Instrument (EDI) and CODIF data. In this paper we are trying to answer the question: What fraction of the high altitude cusp oxygen outflow returns to the magnetosphere? This paper is organized as follows: In section 2 we discuss the key Cluster instruments used and give a short overview of the data sets. The method we use is discussed in detail in section 3, along with all its assumptions and shortcomings. In section 4 we present the results for different geomagnetic conditions. Section 5 discusses the results, and a summary and conclusions are given in section 6.

5
The Cluster mission consists of four identical spacecraft flying in a tetrahedron-like formation (Escoubet et al., 2001). Cluster has a polar orbit with a period of around 57 hours. Although some modifications in the orbit have been made during the mission, the data used in this paper are mostly from orbits with perigee around 4 R E and apogee around 19 R E . Initially Cluster had its apogee in a near ecliptic plane, but it slowly moved southward due to precession. 10 Since there are not much simultaneous EDI and CODIF measurements, we combine the two datasets in parameter space, using EDI and CODIF data taken under similar geomagnetic conditions and in same region in space, but not necessarily simultaneously.

Cluster EDI data
Convection measurements used in this study are obtained from the EDI onboard Cluster. This instrument operates by injecting 15 an electron beam into the ambient magnetic field, and detecting the same beam after one or multiple gyrations. Due to the electron cycloidal motion, the electron beam can only be detected if fired in a unique direction determined by the drift vector.
The full velocity vector is calculated from either the direction of the beams (via triangulation, usually for small drift velocities) or from the difference in the time-of-flight of the electrons (usually for bigger drift velocities). The emitted electron beams have energies of 1 keV (rarely 0.5 keV) and are modulated with a pseudo-signal in order to be distinguished from ambient electrons. 20 EDI gives precise full 3D coverage, unlike the double probe instrument EFW (Gustafsson et al., 1997;Pedersen et al., 1998), which gives the E-field in the spin plane. EDI measurements are also not affected by wake effects nor spacecraft charging, which may affect double probe EFW instrument of plasma instruments. The accuracy of the EDI is not affected by low plasma densities, and actually works better if the plasma density is low. EDI, however, does not provide continuous data, and the data return is reduced in low magnetic field environments (<20 nT), or if the ambient magnetic field is too variable. EDI will also 25 have reduced data return in case of high 1 keV background electron flux. Since EDI is an active experiment it can interfere with wave measurements on Cluster, and therefore operates on a negotiated duty-cycle. More information about EDI can be found in Paschmann et al. (1997Paschmann et al. ( , 2001; Quinn et al. (2001).
The data set used in this study is from January 2002 until April 2004 for Cluster 2 (C2), from January 2002 until December

EDI data coverage
In this study we are primarily interested in convection in the cusps. In order to distinguish the cusps from the polar caps the Tsyganenko and Stern T96 magnetic field model (Tsyganenko and Stern, 1996) was used. The reason we chose to use the older model is because we use a statistical approach with over 10 years of data. On these time scales, the newer and older magnetic models do not differ much in the regions relevant for this study. 5 We identify the cusp regions using the T96 model: The cusps have open field lines which stretch beyond magnetopause.
(Since the T96 model is only valid inside the magnetosphere, field lines outside of the magnetosphere are represented as parallel with the IMF.) An example is given in the left panel of Figure 1; cusp field lines are represented in red. We also include plasma mantle data in order to compare our results with Slapak et al. (2017). The plasma mantle, in our study, is chosen as the neighboring regions of the cusp based on the T96 model. The average cusp latitudinal extent in ionosphere is around 4 • 10 (Newell and Meng, 1987;Burch, 1973).
We traced field lines from regions adjacent to the above determined cusps to the ionosphere. If the tracing landed within 2 • poleward of the cusp, we characterized them as plasma mantle data. The schematic representation is shown in figure 1.

15
The left panel shows the boundary cusp field lines (red) and boundary plasma mantle field line (blue) in the XZ GSM plane.
The right panel depicts cusp (red) and plasma mantle (blue) areas in the ionosphere. For this representation we have assumed longitudinal symmetry of the ionospheric cusps. The total number of EDI measurements is 1130 hours (448 hours are from the cusps), whereof 478 (163 from cusps) hours of data are from northern hemisphere, and 652 (285 from cusps) hours are from southern hemisphere. The larger number of measurements from the southern hemisphere is a consequence of the Cluster orbit precession. We have more EDI observations from the plasma mantle than from the cusp, since the variable cusp magnetic field reduces the number of good quality EDI measurements. The right panel of figure 2 shows the total distribution of all EDI measurements used. The data are shown in 5 cylindrical GSM coordinate system (R cyl = √ Y 2 GSM + Z 2 GSM ), and projected into northern hemisphere. Here we ignored any north-south asymmetries. The color bar indicates the number of one-minute data in each 1 × 1 R E bin. At least 3 minutes of data in each bin was required. The black line represents the average theoretical magnetopause position as in Shue et al. (1998).

Cluster CODIF Data
In order to measure parallel velocities and ion fluxes, the CODIF spectrometer onboard the Cluster spacecraft was used 10 (Rème et al., 1997). We use the data set used in Slapak et al. (2017) in which plasma mantle data ware obtained. A more detailed description of the dataset is given in Slapak et al. (2017), but for convenience we repeat some of the information.
The dataset was made using CODIF data from 2001 till 2005, and using only the months Jan-June when Cluster apogee is in the dayside solar wind. Separating O + CODIF data in the plasma mantle from the magnetosheath and the polar cap was done 15 using a few criteria. First, the inner magnetosphere was removed by using only data where R GSM = √ Y 2 GSM + Z 2 GSM > 6 R E . In order to exclude polar cap data, the plasma β number was used. Typical values of plasma β number in polar caps are below 0.01, and in plasma mantle and magnetosheath is above 0.1. Only data with β > 0.1, are used. For separation of plasma sheet and plasma mantle data, Slapak et al. (2017) used the H + CODIF data. They noticed two clearly distinct peaks in H + temperature for data with β > 0.1. They decided on the H + ion cut temperature of 1750 eV to separate two populations. Two populations had different values of densities as well. One population had higher temperatures and lower densities as expected in plasma sheet, while other population had lower temperatures and higher density as expected in plasma mantle. O + also shows these two populations with similar features. Densities in both populations are 1 order of magnitude lower than H + densities, 5 which is expected, and the plasma mantle population has wider temperature range. Still the two populations are easily distinguishable, and only data with T ⊥ < 1750 eV is used. To separate magnetosheath data from plasma mantle data, Slapak et al. (2017) visually inspected O + spectrograms. Magnetosheath is a region usually characterised with more fluctuant magnetic field than inside of magnetosphere. It is also characterised with strong H + fluxes, which contaminate O + mass channel. 10 In total we have 1422 hours of CODIF measurements. The distribution of CODIF measurements is shown in the left panel of figure 2. Here we can see the difference in data coverage between the two instruments (EDI and CODIF). The main reason for this asymmetry are the technical restrictions of the instruments. EDI has fewer measurements closer to the magnetopause because of higher variability of magnetic field, while CODIF has more measurements closer to the magnetopause because of higher fluxes in this region. In addition to EDI and CODIF Cluster data we also used solar wind dynamic pressure, Dst and 15 IMF data from the OMNI dataset (King and Papitashvili, 2005).

Method
The method used is a combination of the ones described in Haaland et al. (2012) and Li et al. (2012). If the outflowing ions can be traced to closed magnetic field lines before they reach the distant X-line at ca −100 R E (e.g., Grigorenko et al., 2009;Daly, 1986), we say they are captured and returned to the magnetosphere. If they reach the X-line before being convected to 20 the plasma sheet, the ions will be lost into the solar wind. For the highest energies, some of the ions will escape into the dayside magnetosheath directly before being convected into the plasma mantle. The method described in Haaland et al. (2012), infers that the capture will depend on the location of the ions in the Y Z GSM plane at X GSM = −10 R E . In their study the velocities and accelerations were calculated as averages. In Li et al. (2012) ions were traced for each measurement of the parallel and convection velocity. They calculated the acceleration for each tracing step. The direction and magnitude of the convection 25 velocity are given by the following equation: where the subscript 0 indicates the initial velocity and magnetic field, and i denotes the i-th step. In present paper we use a method similar to that of Haaland et al. (2007) to sample measurements and the method of Li et al. (2012) to trace particles. Compared to the polar cap, ions escaping from the cusps have a broader energy range 15 eV-5 keV (e.g., Bouhram et al., 2004;Lennartsson et al., 2004;Nilsson et al., 2012), so the mirror force and hence the acceleration and parallel velocity will vary correspondingly.
The location of the observations is very important, since there is a region of enhanced perpendicular heating in the cusps in the range 8-12 R E (Arvelius et al., 2005;Nilsson et al., 2006;Waara et al., 2010), which results in higher perpendicular 5 energies and thus higher parallel velocities due to the mirror force. If the outflowing ions are convected across the cusp to the plasma mantle before reaching this perpendicular heating region (8-12 R E ), they will not be significantly energized and retain small energies and velocities. On the other hand, if they reach this heating region, they will be accelerated and can either be convected into the plasma mantle with large energies and velocities, or escape into the dayside magnetosheath before being convected into closed magnetic field lines. In Nilsson et al. (2008), the centrifugal acceleration analysis in the cusp is 10 discussed in some detail. There is significant acceleration between 8 and 10 R E . The acceleration in that region cannot be described by centrifugal acceleration alone, and is most likely acceleration caused by wave particle interaction. Figure 3 shows typical transport paths for oxygen ions of low, intermediate and high energies.
Our main assumption is that only centrifugal force accelerates oxygen ions on their path (mirror force acceleration is included in centrifugal acceleration from Nilsson et al. (2008)). A further assumption is that no other energization takes place along the 15 particle path outside the cusps (e.g. no parallel E-fields or wave-particle acceleration). The gravitational force has no effects on the accelerations for the altitudes consider in our research, and without further energization the mirror force has little effect outside the cusps. We assume steady solar wind conditions during the tracing. For particle acceleration along the field line we use two values of the centrifugal accelerations; one value for the cusp and a different value for the lobe as in (Nilsson et al., 2008. For cusp acceleration we used values: For lobe acceleration, a l , we used a l /r = 60 ms −2 R −1 E , where the acceleration is scaled with radial distance given in Earth radii. The resulting velocity versus radial distance is shown in figure 4. The red line represents cusp velocities, and the blue 5 line represents lobe velocities. From the EDI measurements in the cusp regions we have calculated the average convection velocity scaled to the ionosphere (height where B = 50000 nT, as in Slapak et al. (2017)). The average cusp convection velocity in the ionosphere is 620 ms −1 in our data set (at ≈ 400 km altitude). As an average cusp size in the ionosphere we used 4 • in latitude (Burch, 1973). The average time to convect the most equatorward cusp field line across the cusp, is 11 minutes. Newell and Meng (1987) calculated cusp 10 widths as function of the IMF B z component. They investigated two case studies of changing IMF direction from northward to southward direction. In first case they had stronger IMF for both southward and northward direction which resulted in 3.5 • latitudinal extent for northward IMF and 2 • for southward IMF. In second case they reported 1.7 • latitudinal extent of cusps for northward IMF and 0.7 • for southward IMF. For the latter case, Newell and Meng (1987) concluded that for northward IMF the cusp size decreased due to ongoing nightside reconnection and for southward IMF the cusp size decreased because strong 15 convection rapidly closed the open cusp field lines. In this study we used values from first case in Newell and Meng (1987), where, v represents measured velocities and ⟨...⟩ denotes mean value. The bias vector is a good estimate of angular spread (see Haaland et al. (2007)). Bias vector close to zero value indicate a highly variable vector distribution, while values close to unity indicate vectors pointing in coherent direction. Figure 6 shows that the direction of convection in the cusps is very variable.

15
Bias vector values around 0.8 indicate an angular spread of around ±45 • . We see that in the cusps the bias vector values are often lower than 0.8, indicating very variable convection direction. This variability comes from the dynamic nature of the cusps.
The cusp position and size are constantly changing due to solar wind conditions (IM F , P Dyn ) as well as temporal variations in tilt angle (daily and seasonal). Therefore, when averaging convection velocities without separation of the magnitude and direction, the average velocity will have a much smaller value, than when averaging only the magnitude.
Since we use a magnetic field model, the initial convection velocity is given by the median of the magnitudes within a bin, and the direction of the convection velocity is calculated using eq. (1). The same equation is used to evaluate convection for 5 further steps. For the parallel velocity we used median values from the CODIF dataset (Slapak et al., 2017) as magnitude, and a direction is given by the magnetic field model. For the subsequent time step we add acceleration. The first 11 minutes we use the cusp acceleration, given in Nilsson et al. (2008), and for the rest of the steps we use lobe acceleration values from Nilsson et al.
(2010) -see Equation 2. The distance travelled by a particle within one time step is then the product of the velocity times the time step. We have arbitrarily chosen a time step of one minute. If the particle exits the magnetosphere within the first 11 10 minutes, we say that it has escaped into the dayside magnetosheath. If the particle ends up on closed field line before reaching the X-line we say it has returned to magnetosphere. If the particle reaches the plasma sheet beyond the distant X-line, we say it escapes into the solar wind. 12:00:00). We have chosen the equinox because it represents (more or less) a yearly average state of magnetosphere in our 5 dataset. We decided to use the spring equinox since in March the Cluster apogee is in the solar wind, and Cluster passes trough the dayside magnetosheath. Therefore, during spring the equinox we have more measurements than during the autumn equinox.
We chose 2011 because it is in the middle between minimum and maximum of the solar cycle.  Newell and Meng (1987) (∆ϕ in the table). Note that Newell and Meng (1987) correlated cusp width with the IMF Zcomponent, while we are using Dst to group the measurements. As seen from table 1, the average IMF conditions for a given Dst range are in good agreement with Newell and Meng (1987). The other parameters in table 1 are the average cusp convection scaled to ionospheric level (v i,c ), and the maximum cusp convection time (t c ). From our estimation, on average 31 % of the total oxygen flux from the high altitude cusp gets convected to the plasma sheet. The further fate of these ions and transport inside the plasma sheet is beyond the scope of this paper, but it is reasonable to assume that a fraction of the recirculated ions are eventually lost through plasmoid ejections, through the magnetopause and other loss processes.   We also present the resulting oxygen outflow for different storm conditions, using the Dst index as a proxy for storm conditions. For quiet conditions we used positive Dst values, for moderate storm conditions we used Dst values between 0 and −20 nT, and for active storm conditions we used Dst values below −20 nT. For quiet and active storm conditions for nightside measurement bins (X GSM ≤ −1 R E ) the coverage is rather poor, but this is not a major problem, since the oxygen fluxes are rather low under these conditions, thus not affecting the overall results significantly. The results of tracing for different storm 5 conditions are given in Figure 10. As seen from this figure the results are highly dependent on storm conditions. Most interesting is the tracing during active storm conditions, because most of outflow oxygen flux gets convected into plasma sheet. During strong storms, both parallel and convection velocities increase, but the increase in convection is stronger, causing a larger flux of oxygen ions into plasma sheet. In figure 11 we show the results of the tracing in starting bins in the same way as in figure 9, The outflowing O + ions are deposited closer to Earth, for storm geomagnetic conditions.

Discussion
In terms of oxygen outflow escape from high the altitude cusps and plasma mantle regions we find that most of the oxygen 5 escape the magnetosphere as shown by Slapak et al. (2017). As pointed out by Seki et al. (2002) and Ebihara et al. (2006),  oxygen ions with low energies (< 1 keV) will end up in near tail plasma sheet or in ring current. Our results show that oxygen ions reaching the high altitude cusps will mostly escape the magnetosphere. On average, 50% of the oxygen outflow flux will end up in the solar wind beyond distant X-line. 19% will escape directly into dayside magnetosheath. This sums up to a total escape rate of 69 % of high altitude cusp oxygen flux. The rest, 31 % of high altitude cusp flux is being convected in plasma sheet, mostly in the distant tail (> 50 R E ).

5
Another important issue is the escape-versus-capture ratio for different storm conditions. During quiet magnetospheric conditions, oxygen outflow and energization is relatively low, resulting in lower fluxes of oxygen in the high altitude cusp. However, in such cases, the magnetospheric convection is also low and consequently almost all of the outflowing oxygen escape. It is https://doi.org/10.5194/angeo-2019-125 Preprint. conditions. For active storm conditions, the oxygen ion flux is high, and both the parallel velocity of the oxygen ions and the convection is higher. This leads to increase in both dayside magnetosheath escape and enhanced convection into the plasma sheet. Oxygen ions are more likely to escape into the dayside magnetosheat due to their high parallel velocities. Oxygen ions 5 that get convected from the cusps into the plasma mantle will eventually be convected into the plasma sheet. There are also other processes which can further energize ions on their path during strong magnetospheric storms, and thus cause them to escape beyond X-line. For example Lindstedt et al. (2010) reported additional energization of few keV at cusp-lobe boundary during strong geomagnetic storms, caused by increased reconnection leading to strong localised Hall electric field and non adiabatic motion of the ions. 10 R E during geomagnetic storms. In our tracing, ions with such high energies in the tail around 10 R E are traveling close to magnetopause, and the results of Lennartsson et al. (2004) cannot be verified by our study . During geomagnetic storms, 73 % of the oxygen flux end up in the plasmasheet, but far down in the tail (beyond 50 R E ). The high energy oxygen ions in the 15 lobes reported by Lennartsson et al. (2004), are more likely the result of magnetospheric energization of existing low energy oxygen ions in the lobes, rather than convection of high energy oxygen ions. The overall dependence of oxygen capture during storm conditions agrees with results from , in the sense that we observe increased capture during active storm conditions, and more escape during quiet conditions. The main difference is that Haaland et al. (2012) analyzed capture rate of low energy hydrogen ions in the lobes emanating from the polar cap regions, while in this paper we have analyzed the 20 fate energy oxygen ions emanating from the cusp regions.

Conclusions
In this paper we have used Cluster EDI data in the lobes in combination with the CODIF cusp dataset from Slapak et al. (2017), to obtain parallel and convection velocities for oxygen ions. Furthermore, we used results from Nilsson et al. (2006Nilsson et al. ( , 2008 for accelerations in cusps and lobes, as well as results from (Newell and Meng, 1987) for cusp width, to estimate the loss of oxygen 25 ions originating in the high altitude cusp regions. The findings are summarized as follows: 1. Assuming that the magnetosphere terminates at a distant X-line fixed at X = −100 R E , 69 % of total oxygen outflow from the high altitude cusps escape the magnetosphere on average. 50 % escape tailward beyond distant the X-line and 19% escape to the dayside magnetosheath.
2. The oxygen capture-versus-escape ratio is highly dependent on geomagnetic conditions. Oxygen ions originating in the 30 cusp are more likely to be captured during active conditions since the majority of oxygen outflow is convected to plasma sheet, although rather far downtail.