Journal of Geophysical Research: Space Physics RESEARCH ARTICLE
Ring Current He Ion Control by Bounce Resonant ULF Waves
10.1002/2017JA023958 Key Points: • Van Allen Probes measured considerable 90 degree He ion flux (85–142 keV) variability during quiet times • The flux is anticorrelated with the compressional component of ULF wave power • The bounce resonant pitch angle scattering mechanism is suggested as a major component in the scattering of He ions during quiet times
Correspondence to: H. Kim,
[email protected] Citation: Kim, H., Gerrard, A. J., Lanzerotti, L. J., Soto-Chavez, R., Cohen, R. J., & Manweiler, J. W. (2017). Ring current He ion control by bounce resonant ULF waves. Journal of Geophysical Research: Space Physics, 122, 12,031–12,039. https://doi.org/10.1002/2017JA023958
Received 27 JAN 2017 Accepted 15 SEP 2017 Accepted article online 19 SEP 2017 Published online 8 DEC 2017
Hyomin Kim1 Ross J. Cohen1
, Andrew J. Gerrard1
, Louis J. Lanzerotti1
, Rualdo Soto-Chavez1
,
, and Jerry W. Manweiler2
1 Center for Solar-Terrestrial Research, New Jersey Institute of Technology, Newark, NJ, USA, 2 Fundamental Technologies,
LLC, Lawrence, KS, USA
Abstract
Ring current energy He ion (∼65 keV to ∼520 keV) differential flux data from the Radiation Belt Storm Probe Ion Composition Experiment (RBSPICE) instrument aboard the Van Allan Probes spacecraft show considerable variability during quiet solar wind and geomagnetic time periods. Such variability is apparent from orbit to orbit (∼9 h) of the spacecraft and is observed to be ∼50–100% of the nominal flux. Using data from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument, also aboard the Van Allen Probes spacecraft, we identify that a dominant source of this variability is from ULF waveforms with periods of tens of seconds. These periods correspond to the bounce resonant timescales of the ring current He ions being measured by RBSPICE. A statistical survey using the particle and field data for one full spacecraft precession period (approximately 2 years) shows that the wave and He ion flux variations are generally anticorrelated, suggesting the bounce resonant pitch angle scattering process as a major component in the scattering of He ions.
1. Introduction The identification and quantification of ring current particle sources and losses is an essential aspect of understanding plasma processes in Earth’s magnetosphere. To this end the Radiation Belt Storm Probe Ion Composition Experiments (RBSPICE) (Mitchell et al., 2013) on the twin Van Allen Probes spacecraft have been measuring H ion (∼45 keV to ∼600 keV), He ion (∼65 keV to ∼520 keV), and O ion (∼140 keV to ∼1130 keV) particles at a higher level of temporal and energy resolution than ever before achieved. These ring current data have been used to study fundamental particle characteristics (e.g., Gerrard et al., 2014a), particle injections and decay (e.g., Gerrard et al., 2014b; Gkioulidou et al., 2014; Keika et al., 2016), and “quiet” and “active” time ring current morphology (e.g., Lanzerotti & Gerrard, 2017). Analyses of the ring current data show that the He ion differential flux measurements can vary significantly from orbit to orbit (∼9 h orbit at a 10∘ inclination). Although such variability is expected during active times (i.e., intervals of solar disturbances, varying solar wind conditions, and/or geomagnetic activity), the fact that such variability, at a level of ∼50–100% of the nominal flux, is observed during quiet conditions is surprising. This paper reports that the variability of the He ion fluxes during nondisturbed conditions appears to be caused by bounce-resonance scattering and loss of the ions (e.g., Roberts & Schulz, 1968) due to ultralow frequency (ULF) waves with periods of tens of seconds.
©2017. The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
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This study on wave-He ion interactions is of particular importance because although heavy ions (He and O ions) constitute only a relatively small fraction of magnetospheric particles under most conditions, their role in wave generation and propagation, as well as particle dynamics, is significant (e.g., Keika et al., 2013; Kronberg et al., 2014; Liu et al., 2013). Therefore, understanding heavy ion dynamics in space plasmas becomes crucial in advancing knowledge of energy transfer in the magnetosphere. The observation of orbital He ion flux variability along with possible causes of such variability has, to our knowledge, not been reported previously. This paper is organized as follows. The next section describes the data sets used in our study. Section 3 constitutes two parts, the first of which presents an example event showing the variability in magnetic field and He ion flux data from the Van Allen Probes spacecraft. Shown in the second part of section 3 is a statistical survey to investigate the relationship between ULF magnetic pulsations and He ion flux variations. Section 4 discusses the mechanism for the wave-particle interaction and concludes the paper. RING CURRENT HE-ION CONTROL BY ULF WAVES
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2. Data Set The He ion fluxes presented in this study are from level 3 pitch angle and pressure (PAP) RBSPICE high-energy resolution, low time resolution, time-of-flight data. Vector magnetic fields are from level 3 fluxgate magnetometer data (1 s resolution) acquired by the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument (Kletzing et al., 2013). For the statistical analysis, we used data from the Van Allen Probes B spacecraft because the sampling window of the RBSPICE B instrument is larger than that for RBSPICE A. The survey covers approximately one full spacecraft precession period (23 February 2013 to 31 December 2014).
3. Observations 3.1. Example Event Figure 1 shows 90∘ pitch angle (from telescope 0 covering 85∘ –95∘ ) differential flux measurements for H ions, He ions, and O ions (first to third panels) from 2 days spanning 18–19 March 2014 (day of year (DOY) 77–78), as measured by RBSPICE aboard Spacecraft A. The geomagnetic conditions were quiet during the 2 day period (Kp < 2 and Dst > −10 nT). The spacecraft orbital configuration is such that apogee is dayside approximately near noon. Data from RBSPICE B show similar features. Overall, the flux variability from one orbit pass to another for H ions and O ions appears to be less dynamic than that for He ions as shown in Figure 1. Larger spatiotemporal-scale flux variations are, of course, observed in all flux data, which is due to orbital variability in L shell, local time and latitudinal coverage. For example, the H ions and O ions have similar structures for equivalently sampled L shells (Figure 1, fourth panel): that is, the overall flux features for orbits 1 and 4 look similar, and orbits 2, 3, 5, and 6 appear similar. However, there is considerable variability in the He ions across all orbits in a smaller temporal scale, especially at the lower energies measured across apogee, which is not seen in H and O flux data. At these energies at apogee, the “patches” of enhanced He ion fluxes vary considerably in intensity and spatial structure. We note that the higher-energy/lower L shell He ion populations are relatively consistent during quiet times, as discussed in Gerrard et al. (2014a), and references therein. For completeness, the O ions show the typical low fluxes associated with quiet times. As part of this study, we utilize data from the EMFISIS instrument on the Van Allen Probes spacecraft A. Figure 2 shows the spectrogram analysis of these data (bottom), together with the He ion data (top). The EMFISIS data presented here were calculated using the parallel (compressional) component of the magnetic field with a standard periodogram method using a data mask to remove the instrument spin harmonics. Inspection of the EMFISIS waveform and RBSPICE He ion data shows that decreases (increases) in He ions in the 60 to 100 keV energy range are associated with increases (decreases) in waveform energy with periods of ∼10–50 s (f = 20 –100 mHz), especially in the intervals across apogee. The relationship between the He ion flux and wave energy is more clearly shown in Figure 3 which is a blowup of the time period enclosed by the red dashed line rectangle in Figure 2. During the time frame of 78.25 (or 06:00 UT on the 78th day) just after the beginning of ULF emissions the He ion particle intensity becomes significant and at the same time the ULF emissions halt at the same frequencies. Once the He ion particle intensity drops, then the ULF emissions reappear. We note that this wave periodicity falls approximately into the ULF Pc3 pulsation category. In this paper, however, we refrain from calling our ULF waves “Pc3” because our study does not necessarily focus on a conventional physical process, such as solar wind-magnetosphere interactions, typically on the dayside that is known to generate Pc3 pulsations but instead the wave-particle interaction via the He ion bounce resonance mechanism as indicated in this example (Figure 2). Therefore, the ULF waves shown in this paper are pulsations with periods of 10–50 s (f = 20 –100 mHz). In an effort to quantitatively compare the variation in the He ion flux and the ULF wave power, the He ion differential flux and the ULF wave power from Figure 2, once resampled into equal and equivalent 10-min time bins, were integrated between 85 and 142 keV, and 10 and 60 s, respectively. These integrated quantities were then linearly rescaled, forming “relative quantities” of integrated differential flux and wave power. These two quantities are then linearly correlated, as shown in Figure 4. A linear correlation coefficient of −0.4 is found for all L > 3 (black data points) and a coefficient of −0.5 is found for L > 5 (red data points). These correlations are statistically significant, because the probability of calculating the same linear correlation coefficients (of −0.4 and −0.5) from a set of random data points (with the number of draw samples of N = 85 and 36, respectively) is very small (i.e., 5 reduced the range of L shells sampled), the orbital effects are diminished (i.e., the spread of the data at the lower wave powers is reduced). The cross-correlation coefficient for the example event shown in Figure 2 was obtained for the entire data range (orbits 1 to 6). The data for each orbit reveal different levels of anticorrelation, which explains KIM ET AL.
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Figure 2. (top) The 90∘ pitch angle He ion differential flux measurements as per Figure 1. (bottom) Parallel magnetic field component power spectrograms from the EMFISIS instrument aboard Spacecraft A. The He ion differential flux scale is the same as Figure 1, while the relative magnetic field power spectrogram ranges on a log scale from 0.1 (black) to 5.0 (orange) in value.
the moderate cross-correlation coefficient (−0.5) for the entire time period. As described in the following section, field and particle data in limited L ranges (near the apogee) were chosen for the statistical survey to minimize spatial effects of ring current particles. Therefore, if only the data in the higher L ranges were compared, higher cross-correlation coefficient values would have been obtained. The correlation value of −0.5, with this many samples, demonstrates that an anticorrelation is clearly present and statistically significant (although other factors may be present at times in the plasma environment). In this paper, we show an event with a rather moderate anticorrelation because there can be other factors to control the variability between the two parameters as described in section 4. 3.2. Statistical Survey Motivated by the observations shown in Figures 2 to 4, we investigated statistically the relationship between magnetic pulsations in the aforementioned ULF range and He ion flux variations over a data period covering approximately one full spacecraft precession (23 February 2013 to 31 December 2014). Wave events in the ULF range (tp = 10–50 s, f = 20–100 mHz) are first identified from EMFISIS data using an automatic detection algorithm in the frequency domain. Since the spin rate of the spacecraft is ∼90 mHz, the upper frequency for wave detection is set to 85 mHz. In spectrograms, spectral structures that exceed a power threshold of ∼1.5 dB above the mean power for the frequency bandwidth and exist for 10 min or longer KIM ET AL.
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Figure 3. Same as Figure 2 but for a shorter time period as enclosed by the red dashed line rectangle in that figure.
are considered as an event. The power threshold is determined empirically by visual inspection, so wave events are cleanly extracted from spectrograms. For this survey, the magnetic field data are transformed to mean field-aligned (MFA) coordinates (compressional, radial, and azimuthal). Since we focus primarily on temporal variations of wave power and He ion fluxes, and their correlations, only the events near the apogee of the spacecraft (apogee − 0.5 RE < L < apogee) are included in the statistical survey, to exclude any variations due to radial effect in ring current particles and to study any local time dependencies. During each period of identified wave events, trapped (90∘ ± 15∘ ) differential He ion flux data averaged in the energy range of 85–142 keV are used to calculate cross-correlation coefficients between the relative variations of ULF wave power and He ion flux. For correlation analysis, both wave and particle data are band-pass filtered (0.5–2 mHz or 8–30 min) to remove both orbital and short temporal variations. The statistical survey found approximately 1,000 ULF pulsations—He ion interaction events during the one full precession of spacecraft B.
Figure 4. Correlation between the values of Figure 2 with a linear correlation coefficient (LCC) of −0.4 for all L > 3 (black data points) and −0.5 for L > 5 (red data points). Note that the red symbols are overplotted on the black symbols.
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Figure 5 shows the global morphology of the ULF wave occurrences (Figure 5a) and 90∘ He ion flux averaged in the energy range of 85–142 keV (Figure 5b) during the survey period (23 February 2013 to 31 December 2014). The spectral powers of the compressional component (Bpar ) of the detected wave events are averaged over the occurrence rate and placed in corresponding bins in the Geocentric Solar Magnetospheric (GSM) X -Y plane. In a similar fashion, the flux data are also averaged and binned in the same coordinate plane. The bin size is 0.1 × 0.1 RE . Only quiet time (Dst > −20 nT) occurrences are shown in these panels.
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Figure 5. (a) Global occurrences of the compressional component (Bpar ) of the detected ULF waves in the GSM X -Y plane during the survey period (23 February 2013 to 31 December 2014). Each bin represents averaged wave spectral power. (b) Averaged He ion flux at 90∘ pitch angle in the energy range of 85–142 keV. These plots are binned in a 0.1 RE resolution. Note that only quiet time (Dst > −20 nT) occurrences are shown in this figure.
The statistics of the correlation analysis for the data of Figure 5 are presented in Figure 6, showing the correlation between 90∘ He ion flux variations over 85–142 keV and ULF spectral power variations for the (Figure 6, top) compressional (Bpar ), (Figure 6, middle) radial (Br ), and (Figure 6, bottom) azimuthal (Ba ) components as a function of Dst. The variations between the compressional spectral power (Figure 6, top) and He ion flux are generally anticorrelated, supporting the idea of the bounce resonance/scattering mechanism as described earlier. Further, primarily anti-correlated, weaker correlations are seen in the radial and azimuthal components. The means (standard deviations) for data falling in the range of −1 nT < Dst < 1 nT, for example, are −0.63 (0.26), −0.38 (0.18), and −0.10 (0.16), for the parallel, radial, and azimuthal components, respectively. These sample values demonstrate the strongest anticorrelation for the parallel component. For all magnetic field components, the statistics are clustered around Dst > −20 nT, indicating that the majority of the ULF wave-He ion resonance events occur during quiet times as illustrated in Figure 1.
4. Discussion and Conclusions This study is motivated by an event showing the interaction between the compressional component of ULF waves and He ion particles during quiet times. In general, ULF waves in the Pc3 range are known to be related to compressional energy derived from wave-particle interaction in the shock and foreshock or field line resonance (toroidal or multiharmonics) (e.g., Anderson, 1994; Eastwood et al., 2011; Kim & Takahashi, 1999; Yeoman et al., 2012). Our hypothesis is that He ion particles are scattered due to a bounce resonance in the presence of ULF waves whose periods are comparable to that of the bounce motion of ∼100 keV He ions near the apogee of the spacecraft (L =∼ 5–6). The bounce period (tb ) as function of L and energy is given as tb ≈
LRE (3.7 − 1.6sin (𝛼eq )) (W∕m)1∕2
(1)
where L is the L value, RE is the Earth radius, 𝛼eq is the pitch angle at the equator, W is the energy, and m is the particle mass (Baumjohann & Treumann, 1996). Bounce scattering can occur when waves have frequencies close to the bounce period of trapped particles and hence scatter them through a resonant interaction, violating the second adiabatic invariant (J). A force that perturbs the bounce motion could typically originate from a compressional (magnetosonic) pulsation (Schulz & Lanzerotti, 1974). We note that the He ions are scattered by ULF waves via bounce resonance interaction, but increased He ion flux when waves are absent or weak may not be explained. We emphasize here that even though our study focuses on the region where the spacecraft passes minimum L shells near the apogee to minimize any KIM ET AL.
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Figure 6. Cross correlations between 90∘ He ion flux variations over 85–142 keV and ULF spectral power variations for the (top) compressional (Bpar ), (middle) radial (Br ), and (bottom) azimuthal (Ba ) components as a function of Dst. The means and standard deviations for data falling in the range of −1 nT < Dst < 1 nT, for example, are marked with cyan closed circles and vertical bars, respectively.
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spatial effect of ring current particles, the observations presented in this paper are not solely temporal; that is, if spacecraft pass through the region where particles are spatially distributed while waves are not present or weak, no change of particle flux is observed. Therefore, such anticorrelated wave-particle relationship is observed as presented in Figures 2 and 3. In addition, there may be a case where the ULF wave-He ion interactions are not clearly observed (e.g., orbit 3 in Figure 2). Our study does not necessarily conclude that such a wave-particle interaction (bounce resonance) is the only mechanism that controls He ion flux. We argue that there might be other complex processes that govern the particle scattering although the statistical study shows quite a remarkable relationship (anticorrelation). One may argue that it is also possible that the other particle species (H ions and O ions) can interact with ULF waves via the bounce resonance. To discuss whether this is the case, presented here is Figure 7 showing the Figure 7. Bounce periods for 90∘ (trapped) pitch angle H (blue), He (red), relationship between L values and the bounce period for 90∘ (trapped) and O (green) ions for the lowest (85 keV, solid lines) and highest (142 keV, pitch angle H, He, and O ions over the energy range examined in this study dashed lines) energies examined in this study. (85 to 142 keV) using equation (1). The figure identifies the key periods associated with each species and can then be related to the observed ULF waves of similar periods observed by the EMFISIS instrument shown in Figure 2. For He-ions over the energy range, which show the maximum flux at L =∼ 6, it is most likely that bounce resonance occurs at the periods of interest (∼10–50 s). For H ions to interact with ULF waves of these periods, the energy should be in the lower range (142 keV) to see such interaction. However, O ion fluxes appear to be low in the energy range at higher L values. The global distribution of the ULF waves shown in Figure 5a suggests that ULF wave occurrences appear to favor particular local times: ULF wave power is rather higher near dayside (∼09:00 to 15:00 in local times) and nightside (premidnight to midnight). The dayside occurrences in the frequency range are widely reported as described earlier (e.g., ULF waves in the Pc3 range are due to interaction between ions and the solar wind). The nightside waves, on the other hand, may be due to a different generation mechanism and could be interpreted as Pc4 (f = 7–22 mHz) pulsations and their higher harmonics, which are known to be caused by injected ions from the tailside (e.g., Anderson, 1994), or broadband waves such as Pi1 (e.g., Arnoldy et al., 1998) or Pi2 (e.g., Takahashi et al., 1995) pulsations because of their similar periodicity. Unlike the wave occurrences, the He ion flux morphology shows no strong local time dependence (Figure 5b) and rather demonstrates orbit-to-orbit ring current distributions (note that the statistical survey covers approximately one precession of the spacecraft). RBSPICE observations by Gerrard et al. (2014a) show persistent He-ion populations around ∼80 keV at L =∼ 6 throughout quiet times which agree well with the steady state modeling results previously studied. The origin of the waves is beyond the scope of this paper, and thus our statistical survey focuses primarily on the bounce resonance-associated interaction between He ions and ULF waves whose frequencies are comparable to the bounce resonance frequencies of the particles. The global morphology shown in Figure 5 does not reveal the wave-particle interaction presented in this study because such interaction is on a smaller spatiotemporal scale. The bounce period of He ions between 85 and 142 keV, at higher L shells in the Van Allen Probes orbit, is between 40 and 60 s (Schulz & Lanzerotti, 1974). Thus, the statistical analysis showing anticorrelations (Figure 6) clearly supports bounce resonant pitch angle scattering of He ions with ULF waves. The strongest effect is in the compressional component, as would be expected for bounce loss. The other components of the magnetic field showed a similar, albeit weaker, anticorrelation. To the best of the authors’ knowledge, this is the first time that such wave-particle interaction of He ions has been so clearly observed. We note that other pitch angles were also examined, but the anticorrelation was strongest with the 90∘ pitch angles. This is not unexpected as the 90∘ pitch angle can also have the greater influence of bounce-resonant pitch angle scattering. The statistics show that the majority of ULF-He ion resonance events occurred during quiet times (Dst > −20 nT). Several possibilities exist for this result. First, spectral structures are identified as wave events only when they are well defined, which typically occurs during quiet times. During most active times, KIM ET AL.
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magnetic field data in the ULF range display broadband signatures, making it challenging to categorize wave events. Second, the bounce resonance is, perhaps, a dominant mechanism during quiet times because it is when particles are stably trapped so the resonance can occur more efficiently. No local time dependence on the correlation is found in the statistics (figure not shown), indicating that the bounce resonance is a prevalent mechanism to control He ion population, in particular, during quiet times for all local times. The study presented in this paper is summarized as follows: 1. An anticorrelated relationship between He ion flux and ULF waves (TP = 10–50 s or f = 20–100 mHz) is observed from particle (RBSPICE) and wave (EMFISIS) data aboard the Van Allen Probes spacecraft. 2. The He ion control by ULF waves is statistically investigated using approximately 1,000 wave-particle interaction events. The results show that the compressional component of ULF waves and 90∘ He flux (85–142 keV) variations are generally anticorrelated, suggesting bounce resonance between them. 3. The majority of the wave-particle resonance events occurred during quiet times, suggesting that the bounce resonance might play an important role in He ion scattering during quiet times. This is important information about baseline mechanisms governing ring current particle dynamics in the Earth’s magnetosphere. Acknowledgments The work presented herein was supported by the NASA Van Allen Probes RBSPICE instrument project by JHU/APL subcontract 131803 to the New Jersey Institute of Technology under NASA prime contract NNN06AA01C. The authors would like to thank the following persons/ teams: the larger RBSPICE and Van Allen Probes teams for discussions, the EMFISIS team for providing data, and Jacob Bortnik for his useful comments. All data used in this study can be obtained from the following data repositories: RBSPICE from http://rbspice.ftecs.com, EMFISIS from http://emfisis.physics.uiowa.edu, and the Dst and Kp indices from the NASA Coordinated Data Analysis Web (CDAWeb) at http://cdaweb.sci.gsfc.nasa.gov.
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