on an energy-latitude dispersion pattern of ion precipitation potentially associated with...

On an energy-latitude dispersion pattern of ionprecipitation potentially associatedwith magnetospheric EMIC wavesJun Liang1, E. Donovan1, B. Ni2,3, C. Yue3, F. Jiang4, and V. Angelopoulos4,5

1Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada, 2Department of Space Physics,School of Electronic Information, Wuhan University, Wuhan, China, 3Department of Atmospheric and Oceanic Sciences,University of California, Los Angeles, California, USA, 4Institute of Geophysics and Planetary Physics, University of California,Los Angeles, California, USA, 5Earth and Space Sciences Department, University of California, Los Angeles, California, USA

Abstract Ion precipitationmechanisms are usually energy dependent and contingent uponmagnetospheric/ionospheric locations. Therefore, the pattern of energy-latitude dependence of ion precipitation boundariesseen by low Earth orbit satellites can be implicative of the mechanism(s) underlying the precipitation. The pitchangle scattering of ions led by the field line curvature, a well-recognized mechanism of ion precipitation inthe central plasma sheet (CPS), leads to one common pattern of energy-latitude dispersion, in that the ionprecipitation flux diminishes at higher (lower) latitudes for protons with lower (higher) energies. In this study,we introduce one other systematically existing pattern of energy-latitude dispersion of ion precipitation, in thatthe lower energy ion precipitation extends to lower latitude than the higher-energy ion precipitation. Viainvestigating such a “reversed” energy-latitude dispersion pattern, we explore possible mechanisms of ionprecipitation other than the field line curvature scattering. We demonstrate via theories and simulations thatthe H-band electromagnetic ion cyclotron (EMIC) wave is capable of preferentially scattering keV protons in theCPS and potentially leads to the reversed energy-latitude dispersion of proton precipitation. We then presentdetailed event analyses and provide support to a linkage between the EMIC waves in the equatorial CPS andion precipitation events with reversed energy-latitude dispersion. We also discuss the role of ion accelerationin the topside ionosphere which, together with the CPS ion population,may result in a variety of energy-latitudedistributions of the overall ion precipitation.

1. Introduction

The ion precipitation observed by a low Earth orbit (LEO) satellite usually manifests a steep transition from anear-isotropic distribution (except for an upgoing loss cone) at higher latitudes to an empty downgoingloss cone at lower latitudes, when the satellite traverses the earthward portion of the auroral oval. Thistransition constitutes the basis of the definition of the so-called “isotropic boundary” (IB). The latitudinalprofile of ion precipitation fluxes and in turn the IB latitudes are dependent upon the ion energies, magneticlocal times (MLTs), and magnetospheric conditions. Such an energy-latitude dependence can offer usefulclues on the magnetospheric/ionospheric processes that contribute to the ion precipitation.

The curved field line geometry in themagnetotail has been well recognized as one key mechanism causing theprotons in the central plasma sheet (CPS) to be pitch angle scattered into the loss cone and subsequentlyprecipitate in the ionosphere [e.g., Sergeev et al., 1983; Buchner and Zelenyi, 1986; Ashour-Abdalla et al., 1990].The efficiency of such a pitch angle scattering process depends upon the particle energy and the field linecurvature (FLC) in the equatorial magnetosphere. More specifically, the scattering efficiency is controlled by aratio between the radius of curvature of themagnetic field line and the proton gyroradius. The smaller the ratio,the stronger the scattering rate. When such a ratio exceeds certain threshold level (~8 is often used in literature[e.g., Sergeev et al., 1983; Liang et al., 2013]), the scattering rate is so weak that the loss cone becomes nearlyempty, constituting the IB in the ionosphere. Hereafter, we shall abbreviate this scattering mechanism as FLCscattering in the paper. Since under normal magnetospheric topology, both the curvature radius of themagnetic field line and the equatorial magnetic field strength increase toward the Earth, the FLC-scatteringscenario would imply the following: (a) the IB would extend to lower latitudes for higher-energy ions and (b) at afixed point in the magnetosphere, the scattering rate would be stronger for ions at higher energies.

LIANG ET AL. ©2014. American Geophysical Union. All Rights Reserved. 1

PUBLICATIONSJournal of Geophysical Research: Space Physics

RESEARCH ARTICLE10.1002/2014JA020226

Key Points:• We investigate the reversedenergy-latitude dependence ofion precipitations

• The EMIC wave is found as oneprincipal mechanism of thereversed-type events

• Ion acceleration in topside ionospherealso contributes to reversed-type events

Supporting Information:• Text S1• Figure S1• Figure S2• Figure S3

Correspondence to:J. Liang,[email protected]

Citation:Liang, J., E. Donovan, B. Ni, C. Yue,F. Jiang, and V. Angelopoulos (2014), Onan energy-latitude dispersion pattern ofion precipitation potentially associatedwith magnetospheric EMIC waves,J. Geophys. Res. Space Physics, 119,doi:10.1002/2014JA020226.

Received 27 MAY 2014Accepted 17 SEP 2014Accepted article online 22 SEP 2014

http://publications.agu.org/journals/

http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2169&hyphen;9402

http://dx.doi.org/10.1002/2014JA020226

http://dx.doi.org/10.1002/2014JA020226

The above expectations are indeed verified in many actual observations from LEO satellites. Figure 1adisplays an event example observed by FAST on 7 February 2008. The first to third panels show the ion energyflux spectrograms in the downgoing (pitch angle 150–180°), trapped (pitch angle 60–120°), and upgoing(pitch angle 0–30°) directions. Note that for the FAST data during the last few years of its mission life, due tothe instrumental degradation, the two ion sensor heads deteriorated at different rates and thus mismatchedin the upper energy ranges they can sweep, producing spin period modulation at those high-energy bins(J. McFadden, private communication, 2013). Such contaminations are deliberately preserved in Figure 1a to

Figure 1. Examples of (a) normal-type event and (b) reversed-type event. In each subfigure, the first to third panels show the ion energy flux spectrogram indowngoing, perpendicular, and upgoing directions observed by FAST satellite. The fourth panel shows the electron energy flux spectrogram in downgoingdirection. The fifth panel of each subfigure shows the variation of isotropy ratio versus ILAT for different ion energies; a sharp drop of the isotropy ratio indicatesa crossing of the IB of ions at the corresponding energy level.

Journal of Geophysical Research: Space Physics 10.1002/2014JA020226


alert readers but are removed by default in all other FAST event plots in this paper. Nevertheless, anenergy-latitude dispersion of the equatorward boundary of ion precipitation fluxes in ~2–20 keV energyrange can be clearly seen: the IBs tend to be at lower latitudes for higher-energy protons andincrease in latitudes toward lower energies. Since the trapped flux may also have an energy-latitudedependence (e.g., due to an Alfven layer effect), a more meaningful parameter to evaluate theisotropicity of the loss cone from LEO satellite observations is the ratio between the precipitationflux and the trapped flux: a ratio of one implies a fully isotropic loss cone, while a ratio of zero impliesan empty loss cone. An abrupt drop of the ratio from ~1 to ~0 indicates the crossing of IB. We shallterm this ratio as “isotropy ratio” and use it as a practical indicator of the isotropicity of the losscone throughout this paper. To reduce the spin effect as well as other noises, the spin-averaged fluxes(~5 s resolution) are used in the calculation. The isotropy ratios of ions at different energy levelscalculated from the above procedures for the 7 February 2008 event are plotted in the fifth panel ofFigure 1a. As one can see, significant drops of the isotropy ratio occur at higher latitudes for lowerenergy protons and extend to lower latitudes for higher-energy ions. Meanwhile, at a fixed latitude theisotropy ratio tends to be larger for higher-energy ions. The above observations fully conform to theexpectations of the FLC-scattering scenario.

The FLC scattering is definitely not the only viable ion precipitation mechanism; other mechanisms mayalso exist and contribute to the ion precipitation. For example, the electromagnetic ion cyclotron (EMIC)wave has been realized as capable of scattering energetic ions in the radiation belt/ring current region[e.g., Jordanova et al., 1996; Yahnin and Yahnina, 2007; Usanova et al., 2010; Zhang et al., 2011]. Thepotential role of EMIC waves in pitch angle scattering thermal protons in the CPS region will betheoretically analyzed in section 2 of this paper. However, a specific exploration on the non-FLCprecipitation mechanisms is often subject to practical limitations under the overwhelming coexistenceof the FLC-scattering mechanism in the CPS region. The overall precipitation flux would be saturatedwhen one or more scattering mechanisms at play have reached a strong diffusion limit. Thus, if the FLC-scattering mechanism and certain non-FLC mechanism overlap in spatial location and operate in similarion energy range, it would be difficult to discriminate their respective roles or even to argue for theexistence of the latter mechanism, within the limit of currently available theories and data. This is one ofthe main reasons the wave-particle interaction mechanism, whose pivotal roles in radiation beltacceleration and diffuse electron precipitation were thoroughly studied, received much less attention inthe existing literature regarding its role in scattering thermal ions in the CPS region, where the FLCscattering is often deemed as prevailing.

In principle, for the individual role of a non-FLC precipitation mechanism to be discerned from practicalobservations, the mechanism would desirably operate in different energy range and/or in different spatialregion from the FLC scattering. Interestingly, the existence of non-FLC mechanisms can be relatively easilyinferred from one specific type of ion precipitation events, whose energy-latitude dispersion evidentlycontradicts to the FLC-scattering scenario. Figure 1b shows a FAST event on 11 December 1997 in thesame format as in Figure 1a. In the fifth panel of Figure 1b we again present the above-defined isotropyratio at different energy levels. It is straightforward to see that the energy-latitude dependence of ionprecipitation boundaries is completely different from that in Figure 1a: the IBs tend to be at higher latitudefor protons at higher energies and generally decrease in latitudes toward lower energies; at a fixed latitude,the isotropy ratio tends to be higher for ions at lower energies. Such a “reversed” energy-latitude dispersionas shown in Figure 1b is incompatible with the FLC-scattering scenario and hints at the functioning ofnon-FLC precipitation mechanisms, particularly in the keV and sub-keV energy ranges. Donovan et al. [2003]noticed a nontrivial and systematic existence of ion precipitation events with such a reversed energy-latitudedispersion from a FAST survey.

Discriminated by their opposite energy-latitude dispersion patterns, the two types of events exemplified inFigure 1 are termed as “normal-type” event and “reversed-type” event, respectively, in this paper. Thenormal-type events conform to the scenario of an overall dominance of the FLC-scattering mechanism.Even if certain non-FLC mechanism might possibly coexist, it might be overridden by the FLC scatteringand cannot be readily distinguished out from the data. The reversed-type events, on the other hand, betterunveil the existence of non-FLC precipitation mechanisms in certain energy-latitude regime and thus lay asolid foundation to the exploration of those non-FLC mechanisms, the core research interest of this study.



Therefore, we shall strategically choosethe reversed-type event as a platform forour research objective in this study. Thereare of course many other precipitationevents whichmay not be unambiguouslyclassified into either a normal type or areversed type; those events typicallycontain different trends of energy-latitude dependence of ion precipitationboundaries in different energy ranges,implying a mixture of precipitationmechanisms. An example of such“mixed-type” events is given in thesupporting information.

Upon a statistical survey over a fewmonths’ FAST data, Donovan et al. [2003]investigated the MLT distribution of

normal-type events and reversed-type events. Their results are copied and presented as Figure 2 in thispaper. A distinct MLT asymmetry of the occurrence probability of reversed-type events was revealed: theoccurrence of reversed-type events is heavily biased toward the midnight-morning sector andminimal in theevening sector. We footnote that such a MLT preference was also noticed in our searching of reversed-typeevents during Time History of Events and Macroscale Interactions during Substorms (THEMIS) tail seasonsfor this study. It is conceivable that the principal non-FLC precipitation mechanism(s) underlying thereversed-type events would also feature a similar MLT asymmetry.

In this study, we shall put forth two viable non-FLC precipitation mechanisms: the pitch angle scattering byEMIC waves in the equatorial magnetosphere and the ion acceleration on top of the ionosphere. The formermechanismwill be more focused on. The paper is arranged as follows. In section 2 we shall first introduce somebasic theories and simulation results of EMIC waves and their efficiency in pitch angle scattering CPS thermalions. We shall then present in section 3 a few reversed-type events with the conjunctive THEMIS measurementsand confirm the corresponding coexistence of magnetospheric EMIC waves in those events. In section 4 weshall summarize our main results and explain the statistical MLT asymmetry of reversed-type events via theglobal distribution and characteristic of EMIC waves studied byMin et al. [2012]. Section 5 concludes this paper.

2. EMIC Wave: Theory and Data Analysis Procedure2.1. EMIC Wave and Its Role in Scattering CPS Protons

In this section we shall introduce some theoretical backgrounds of EMIC waves and explain why this wave modecan behave as the driving mechanism of the reversed energy-latitude dependence of ion precipitationboundaries. The EMIC wave is an electromagnetic mode with frequencies below the proton gyrofrequency(denoted as ωcp hereafter). It is usually excited by the anisotropic distributions of energetic ions and tends to bequasi-parallel propagating and left-hand polarized at generation. EMICwaves have been investigated for decadeson the basis of in situ observations from various satellites [e.g., Fraser and McPherron, 1982; Roux et al., 1982;Anderson et al., 1992; Min et al., 2012; R. C. Allen et al., A statistical study of EMIC waves observed by Cluster: 1.Wave properties, submitted to Journal of Geophysical Research Space Physics, 2014] and/or from groundmagnetometers [Perraut et al., 1984; Usanova et al., 2010]. Since this study is based upon THEMIS measurements,we shall particularly refer readers to Min et al. [2012], which contains an extensive survey on the globaldistribution and characteristics of EMIC waves in the near-Earth magnetosphere using THEMIS observations.

In theory, the dispersion relation of a parallel-propagating EMIC waves in a cold plasma is given by

c2k==2

ω2¼ 1� ω2

Ne

ω ωþ ωceð Þ �X ω2

Ni

ω ω� ωcið Þ; (1)

in which ω and k// denote the wave frequency and parallel wave number, respectively, and ωΝ denotes theplasma frequency of electron (e) or ions (i). The sum is over multiple ion species. The dispersion relation of

Figure 2. Statistical MLT distribution of normal-type events and reversed-type events. Copied from Donovan et al. [2003].



EMIC waves is separated into different branches according to the ion species involved. The hydrogen(H) band with frequencies between ωcp and helium gyrofrequency (denoted as ωcHe hereafter), andHelium (He) band with frequencies lying below ωcHe, are two typical EMIC branches mostly observed andtheoretically investigated in the near-Earth magnetosphere [e.g., Anderson et al., 1992; Horne and Thorne,1994; Hu and Denton, 2009; Min et al., 2012]. Hot plasma effects may produce a significant modification tothe cold plasma description of EMIC waves near and below ωcHe but tends to be insignificant for wavefrequencies above ωcHe [Chen et al., 2011], i.e., the H-band EMIC of our core interest.

It has long been recognized that the EMIC waves can resonate with electrons, protons, and other heavier ions inthe magnetosphere [e.g., Roux et al., 1982; Thorne and Horne, 1992; Jordanova et al., 1996; Summers and Thorne,2003; Summers, 2005; Yahnin and Yahnina, 2007; Zhang et al., 2011]. However, those previous studies mainlyfocused on the roles of EMIC waves on the high-energy ions or relativistic electrons in the inner magnetosphere(radiation belt, ring current, and plasmasphere). To the authors’ knowledge, there is so far a scarcity of studiesdedicated to the role of EMIC waves in pitch angle scattering the CPS thermal ions. Recent THEMIS survey onEMIC waves [Min et al., 2012] indicated the presence of nontrivial EMIC wave activities in the nightside CPSregion (L~7–12); their potential role in interacting with CPS ions will be briefly analyzed in this study.

The gyroresonant condition of a wave-proton interaction is given by ω� k//vi// =Nωcp/γ, where γ is theLorentz factor. For quasi-parallel propagating waves, the first-order resonance (N= 1) usually dominates thecontribution to the pitch angle diffusion process [e.g., Summers et al., 2007]. To evaluate the first-orderminimum resonance energy in the nightside magnetosphere, we adopt the empirical models of Wang et al.[2013] and Yue et al. [2013]. In their models, their authors collect extensive data sets of THEMIS/Geotaildata in the Earth’s magnetospheric equator and group them according to the solar wind dynamic pressurePdyn and the Kp index. They then use the observed equatorial plasma pressure as an input to the 3-D force-balanced magnetic field solver to obtain the 3-D magnetic field configuration [Zaharia, 2008; Yue et al., 2013].The FLC in the equatorial CPS can also be deduced from the force-balanced magnetic field, and the model-inferred IBs are found as basically compatible with FAST observations for normal-type events [Yue et al., 2014].Using the equatorial distribution of ion number density [Wang et al., 2013] and magnetic fields [Yue et al.,2013] in their data set and model output, we calculate the distribution of the minimum resonant energy (Emr)of EMIC-proton interactions. For demonstration purpose, in the following presentation we shall use theirmodel results with Pdyn =0–2 nPa and Kp=2, which reflect the average solar wind condition and geomagneticactivity. Model results with other Pdyn and Kp values are also checked, and the following inferences on thedistribution of Emr with respect to the IB are not qualitatively discredited anyway. In the calculation we adoptω=0.5ωcp and ω=0.15ωcp for the H-band and He-band EMIC waves, respectively. Since Wang et al.’s [2013]data set provides only the total ion number density, we assume three ion species: the proton (H+), helium (He+),and oxygen (O+) with density ratios ηΗ+ = 90%, ηHe+= 5%, and ηΟ+= 5%, in our calculation. The results ofthe calculated Emr are shown in Figures 3a (H band) and 3b (He band). As one can see, in the inner CPS regionL~7–11, the minimum resonant energy of the H-band EMIC waves generally ranges from several hundredsof eV up to ~10 keV. The H-band EMIC wave is thus supposed to be effectively resonant with the CPS protons.Theminimum resonant energy of He-band EMIC is, however, much higher in the same region, generally rangingfrom a few tens of keV to above 100 keV. Therefore, under normal conditions, the He-band EMIC wave maynot effectively interact with the main thermal population of CPS protons in L< 10.

Relevant to our research interest, it is key to check in a statistical sense whether the resonance between theEMIC wave and the keV ions can occur at places where the local FLC no longer supports their scattering. UsingYue et al.’s [2013, 2014] 3-D force-balanced magnetic field model and their derived FLC at equator, wecalculate the FLC-scattering IB of 12 keV ions according to Rc/ρi= 8 [e.g., Sergeev et al., 1983], in which Rc and ρiare the curvature radius of the field line and the proton gyroradius, respectively. We remind readers thatthe IB bears the implication that proton with energies <12 keV can no longer be scattered by the FLCearthward of that IB. The 12 keV energy is chosen since it basically represents the upper energy limit ofpractical FAST/REIMEI ionmeasurements—the nominal upper limit of FAST electrostatic analyzer (ESA) can behigher but its uppermost energy bins are often found to be contaminated by spin period modulationsdue to the instrumental degradation in our events. As one can see from Figure 3a, up to a few RE earthwardof the 12 keV IB Emr is generally in the keV range. In other words, protons with keV energies can still bescattered by EMIC waves at radial distances where the local FLC no longer supports their scattering. Therefore,



lower energy proton precipitation led by an EMIC-proton interaction, provided that the EMICwave indeed existsthere (this condition will be discussed in section 4), can extend to latitudes lower than the FLC-scattering IB ofhigher-energy protons. This would be a favorable geometry for revered-type events to occur.

We then proceed to calculate the pitch angle scattering rates of H-band and He-band EMIC waves on thebasis of the quasi-linear diffusion theory. In the calculation, we adopt the EMIC wave model in Summers andThorne [2003] and essentially follow the procedures in Summers et al. [2007] in computing the pitch anglediffusion coefficient. Mathematical details of the computation procedure and model parameters are given inthe Appendix A. A demonstrative result is to be shown in this paper, while more dedicated and comprehensivesimulations of the EMIC-ion scattering process in the CPS, including both H-band and He-band EMIC waves,are performed in a companion study (B. Ni et al., Quantifying resonant scattering rates of central plasma sheetprotons by electromagnetic ion cyclotron waves, to be submitted to Journal of Geophysical Research, 2014).Currently, a dipolar magnetic field is assumed in the model, and we are to extend the model to nondipolargeomagnetic field in a near future. Compared to a realistic CPS configuration, the equatorial magnetic field in a

Figure 3. (a) Minimum resonant energy for protons interacting with H-band EMICwave. A dashed linemarks the 12 keV ion IBfrom Yue et al. model; dotted circles indicate radial distances R= 8, 10, and 12 RE, respectively. See text for model details andparameters involved in the calculation. (b) Similar to Figure 3a but for He-band EMIC wave. Note that the energy color scale isdifferent from that in Figure 3a. (c) The scattering efficiency of EMIC waves as a function of proton energy at different L shells.The color legends for L shells are labeled in the plot. See Appendix A for calculation details and model parameters.



dipolar model tends to be exaggerated in magnitude. To partly relieve this uncertainty, we perform thecalculations over a range of L distances from 8 to 11. This range is chosen upon the consideration of abalance between the radial location and the magnetic field strength of the IB inferred from Yue et al. [2013,2014] model: the IB is located at L~8 in the midnight and shifts to L~12 toward flank side; the average B fieldvalue along the IB (~25 nT) is close to the dipole field value at L=11 (~23 nT). Nevertheless, as we shalldemonstrate subsequently with Figure 3c, the scattering efficiency in the energy range of our key interestappears to be insensitive to the L distance or equivalently the B field magnitude, which strengthens our beliefthat the simulation results suffice for our purpose of a semiquantitative evaluation of the EMIC-protonscattering efficiency, even though the magnetic field model itself is not very accurate. The plasma numberdensity is set to gradually increase toward the Earth. The ion species involved and their density ratios arethe same as above mentioned: ηΗ+ = 90%, ηHe+ = 5%, and ηΟ+ = 5%.

In a quasi-linear diffusion theory, the efficiency of the pitch angle scattering process is usually depicted by aparameter Z ¼ DαTb=α2c [e.g., Kennel and Petschek, 1966], in which Dα is the bounce-averaged diffusioncoefficient at the edge of loss cone, Tb is the escaping time for a particle in the equatorial loss cone toprecipitate into the Earth’s atmosphere, and αc is the equatorial loss cone angle. Z>> 1 indicates a strongdiffusion limit, while Z< 1 indicates a weak diffusion. Figure 3c presents the calculated Z values versusenergies at different L distances. We note that the scattering efficiency for energies >2 keV appears to berelatively insensitive to the L distances. With a peak wave power 0.5 nT2/Hz chosen in our calculation, which isfully achievable in midnight-morning sectors according to Min et al.’s [2012] statistics (see their Figure 10), astrong diffusion condition is generally met for protons with energies up to ~10 keV. More importantly, thescattering efficiency decreases toward higher energies for CPS protons with energies >1 keV, which isoutright opposite to the scenario of FLC-scattering mechanism. Two expectations can be deduced from theabove results: (1) the wave-induced scattering rate would be higher (lower) for lower energy (higher-energy)protons. (2) Since the scattering rate is proportional to the wave power, to reach a strong diffusion condition,a relatively larger (smaller) wave power is required for higher-energy (lower energy) protons. Consideringthe scenario that the EMIC wave region has a limited radial extension with wave intensity decaying towardthe Earth, a weak diffusion limit would be encountered farther away from (closer to) the Earth for higher-energy (lower energy) protons. Consequently, the precipitation boundary of lower energy protons in theionosphere would extend to lower latitudes than that of higher-energy protons. The above expectationsconform to the features of reversed-type events of our research interest. We also calculate the scatteringefficiency of He-band EMIC wave. The minimum resonant energy of He-band EMIC wave is>20 keV at L= 11,and is even larger at closer radial distances (thus not plotted in Figure 3c). Combining with the results inFigure 3b, we infer that in the region of interest the He-band EMIC wave is unlikely to be an efficientmechanism leading to the precipitation of CPS thermal protons with energies<10 keV and causing reversed-type events. Therefore, in this study we shall exclusively focus on H-band EMIC waves.

To summarize, notwithstanding the uncertainties contained in our models, the above results neverthelessinvoke the H-band EMIC wave scattering as a plausible mechanism leading to the reversed energy-latitudedispersion of CPS ion precipitation at >1 keV energy range. We shall check this proposal via conjunctiveobservations of reversed-type events from LEO satellites and EMIC waves from magnetospheric probes inthis study.

2.2. Data Selection Criteria and Wave Analysis Procedures

THEMIS data will be used for in situ observations in the magnetosphere. The main THEMIS instruments usedin this study include the fluxgate magnetometer (FGM) [Auster et al., 2008], the electric field instrument(EFI) [Bonnell et al., 2008], the electrostatic analyzer (ESA) [McFadden et al., 2008], and the solid-state telescope(SST). The FGM/EFI instruments measure the in situ magnetic and electric field, respectively; the ESAinstrument measures the flux of thermal particles over an energy range from 5 eV to 25 keV for ions and6 eV to 28 keV for electrons; the SST measures the energy flux of suprathermal (>30 keV) particles fromspecific telescope directions.

We shall then introduce the criteria and procedures we use to select events and identify EMIC waves fromTHEMIS in situ measurements. For a reliable analysis of the H-band EMIC with wave frequencies betweenfcp and fcHe, we require that the fluxgate magnetometer low-resolution (FGL, 0.25 s resolution) data set must be



available during the interval of interest, since fcp in the inner CPS may well exceed the Nyquist frequency (1/6Hz)of the normal spin-resolution data. The EMIC wave tends to have its excitation source in the equatorialmagnetosphere, where the growth rate of EMIC instability is usually the largest. At generation, the EMIC wavetypically features a quasi-parallel wavefront and strong left-hand polarization. These two characteristics constitutethe conventional way to identify the EMIC wave from observations. However, the EMIC wave tends to becomeobliquely propagating and linearly polarized (or even weakly right-hand polarized) in the course of itspropagation away from the equatorial source [Horne and Thorne, 1994; Hu and Denton, 2009; Hu et al., 2010;Minet al., 2012; R. C. Allen et al., submitted manuscript, 2014]. More uncertainties might be involved in discerning theEMIC wave from off-equator measurements, particularly in the presence of other coexisting wave modes withoblique or quasi-perpendicular wave vectors, e.g., compressional waves/turbulences. For the H-band EMIC wavesof interest, theymay be reflected in the course of their propagation when thewave frequencymatches the localbi-ion frequency and thus cannot reach the high-latitude magnetosphere/ionosphere [Roux et al., 1982;Perraut et al., 1984]. Thus, for a more unequivocal identification of H-band EMIC waves, the probe is preferablyclose to equator, in practice judged by the conditions Bz> Bx and plasma β> 1.

Needless to say, it is unlikely that a magnetospheric probe and a LEO satellite are ideally conjugate to eachother in any realistic event. To establish a causal link between the EMIC wave measured in the equatorialmagnetosphere and the ion precipitation in the ionosphere, it is desirable that the separation between themagnetospheric probe and the equatorial footprint of the LEO satellite be smaller than the characteristicspatial size of the EMIC wave region. Unfortunately, to the authors’ knowledge there is so far a scarcity ofstatistical studies or even case studies on the spatial dimension of EMIC wave region in the nightside CPS. Leeet al. [2013] statistically estimated the size of coherent activity of dayside (6–18 MLT) EMIC waves. They foundthat the characteristic dimension of EMIC waves can be normalized by the proton gyroradius: for H-bandEMIC waves in the dayside magnetosphere, the coherent dimension is found to be 10–16 times thegyroradius of 100 keV protons. If we assume that this empirical relationship also applies to the nightside innerCPS, the coherent size of H-band EMIC waves would be ~2.5–4 RE with B~ 25 nT. No distinction betweenthe azimuthal and radial directions is made in Lee et al. [2013], but it is reasonable to speculate by commonsense that the EMIC wave region in the nightside CPS might have a larger azimuthal extension thanits radial dimension. We hypothesize that the radial dimension of the EMIC wave region is related tothe scale length of the change of magnetic field ((d ln B/dr)� 1) and/or the plasma number density(d lnN/dr)� 1 which, upon evaluations using Yue et al. [2013] model, are typically ~1–2.5 RE in the innerCPS. On the other hand, it is generally recognized that the EMIC wave is excited by the temperatureanisotropy of energetic ions. Those energetic ions can propagate via their intrinsic gradient-curvaturedrift and/or with the large-scale plasma motion. Such a propagation effect of the wave source wouldallow the waves to exist over a broader spatial range than the dimension of the wave source regionitself. Guided by the above considerations, as well as via extensive discussions with research colleagueswith expertises in EMIC waves (W. Li et al., private communications, 2013), we reach a tentativeestimation that the coherent dimension of EMIC waves likely extends to the order of ~1 h MLT (~2.5 REat L ~ 10) in azimuthal direction and 1–2 RE in radial direction in the nightside CPS. The other issuestems from the well-known inaccuracy of M-I mapping using any empirical magnetic field model. In thisstudy we shall use T89 models for the mapping effort and follow an event-adaptive approach: we selectthe Kp parameter of the T89 model according to the best overall fit between the model B fields at theTHEMIS probe location and the actual in situ observations. Considering all the above arguments anduncertainties, we postulate a geometric criterion in our event selections that, the ionospheric footprintof the THEMIS probe, based upon T89 model with tuned Kp parameter, must be within 1 h MLT and 1°magnetic latitude (MLAT) of the LEO satellite surrounding the epoch of reversed-type precipitationboundary crossing.

Our procedures to analyze the waves from THEMIS FGL data are described as follows:

1. We first decompose themagnetic field perturbations inmean-field-aligned (MFA) coordinates, including thecompressional (parallel to the mean B field, labeled as “s”), toroidal (perpendicular to both the mean fieldand the radial vector of the probe, labeled as “ϕ”), and poloidal (completing the orthogonal system, labeledas “r”) components. The mean B fields are obtained from a 256-point (64 s) Savitzky-Golay low-pass filter[Savitzky and Golay, 1964] of the FGL data. Such mean B fields are also used to calculate the ambient



fcp and fcHe. The cutoff frequency of our applied low-pass filter is ~29.6 mHz [Schafer, 2011], whichensures that a subtraction of mean B fields would not affect our core research objective, i.e., the H-bandEMIC wave in the inner CPS region (for B> 20 nT, f> fcHe> 76 mHz).

2. Based upon the above decomposition, we perform a sliding 256-point (64 s in terms of window timelength) FFT analysis on the three components of B field perturbations. The sliding step length is 128 point(32 s). The “parallel” wave power is computed from the FFT power spectral density (PSD) of the com-pressional component, while the “perpendicular” wave power is computed from the sum of the FFT PSDof the toroidal and poloidal components.

3. To help discerning the EMIC wave, we also calculate the ellipticity of the wave. The ellipticity is defined asthe ratio between the minor axis and major axis of the ellipse transcribed by the field variations of theperpendicular wave components and is in practice computed from complex magnetic wave fields in thefrequency domain according to the procedures in Kodera et al. [1977]. A negative ellipticity value implies aleft-hand polarization; a positive value implies a right-hand polarization; and an ellipticity ~0 implies alinear polarization. The ellipticity is calculated in the same time-frequency windows as the FFT PSD tofacilitate a cross check. We also calculate the degree of polarization, a measure of how pure the state ofwave polarization is, following the definition and procedure in Samson and Olson [1980]. We only acceptthe ellipticity in time-frequency windows where the degree of polarization is above 0.6.

3. Observations

To identify the reversed-type events, we resort to the FAST and REIMEI satellite data. The FAST satellite[Pfaff et al., 2001] carries a fluxgate magnetometer and four electrostatic analyzers (ESA) that measure particlefluxes of energies from a few eV to ~25 keV in various angular directions. As above mentioned with Figure 1a,FAST ion data may contain spin period beating in their high-energy bins due to the instrumental degradation.In this study, the energy bins that are seriously affected by spin modulations are flagged and discarded usingthe newly developed FAST data processing routines (in courtesy of Dr. J. McFadden). The REIMEI satellitecarries an electron/ion spectrum analyzer (EISA) [Asamura et al., 2003] which measure the particle fluxes from~10 eV to ~12 keV in various angular directions.

In this section we shall present two FAST events with the reversed energy-latitude dependence of ionprecipitation. One example of reversed-type events from REIMEI observations is to be shown in thesupporting information. THEMIS data will be analyzed to support a conjunction between the EMICwaves and the reversed-type events. We shall also discuss some other possible mechanisms of reversed-type events in section 3.3.

3.1. The 15 December 2008 Event

The event interval of interest occurred during the recovery phase of a small substorm. The observationalgeometry of the event is shown in Figure 4. We have used the T89 model with Kp= 1, whose B field outcome(see Figure 4c) is found to be on the whole closest to the realistic TH-E in situ observation among all Kp values,to evaluate the ionospheric footprints of TH-E. According to the mapping, the TH-E footprint is ~0.7 h MLTeast to the FAST meridian and within ~0.4° MLAT of the FAST latitudes at ~1030 UT, around which time areversed-type ion precipitation boundary crossing is seen on FAST.

Figure 5a shows the FAST data for the ~1030 UT pass across the southern auroral oval. The first to third panelsdisplay the ion energy flux spectrograms in downgoing, trapped, and upgoing directions. One can discern thatthe ion precipitation boundaries feature a reversed-type energy-latitude dependence according to our definitionin section 1. Figure 5b shows the isotropy ratio at different proton energy levels within ~1–11keV—we shallexplain later why we focus on such an energy range at the moment, even though the reversed-type energy-latitude dependence appears to endure toward much lower energies in this event. The spin-averaged flux dataare used in calculating the isotropy ratio, and the computation ceases when the trapped flux drops to a noise level~ 5×104 eV/cm2/s/sr/eV. As explained in section 1, such an isotropy ratio offers clue on the pitch angle scatteringrate in the equatorial CPS. Around ~70° invariant latitude (ILAT), the abrupt drop of isotropy ratio, which definesthe IB, shows a consistent trend that such a drop occurs at higher latitude for protons at higher energies andextends to lower latitudes for protons at lower energies. This trend fully conforms to the definition of the reversed-type event. No clues of upgoing ions or ion conics are found within the energy range of interest.



Figure 6 shows the observations on TH-E, which is closest to the FAST meridian among three inner THEMISprobes. Since TH-E is near the dawnside flank, the data are presented in VDH coordinate, where the H axisis antiparallel to the Earth’s dipole axis; the V axis is radially outward and is parallel to the magnetic equator;and the D axis completes the right-hand orthogonal system. The first panel displays the magnetic fieldsin VDH coordinate. The Bh component is much larger than |Bv|, and the plasma β (second panel) is above one,implying that the probe is close to the magnetic equator. There are large-amplitude magnetic oscillations inPc5/Pc6 frequency range, which is a common phenomenon in the dawnside magnetosphere [e.g., Zhu andKivelson, 1991]. Our research interest is, however, on the much higher-frequency and smaller-amplitudeoscillations of magnetic fields and electric fields (fourth panel), which are barely seen in this figure but willbe viewed more clearly in Figure 7 later. The fifth panel shows the omnidirectional ion energy fluxspectrogram, and the sixth panel shows the anisotropy index A for three different energy ranges calculatedfrom ESA full-angular-resolution mode (peif ) data. For the definition and computational details of theanisotropy index A, see Li et al. [2010]. In short, A= 0 corresponds to pitch angle isotropy. A> 0 denotes pitchangle distribution peaking at 90°, while A< 0 indicates a pitch angle distribution minimum at 90°. Thedefinition naturally reduces to A= Ti⊥/Ti//� 1, the classical definition of temperature anisotropy, for abi-Maxwellian distribution with Ti⊥ and Ti// being the perpendicular and parallel temperature, respectively.

Figure 4. (a) The satellite trajectory of TH-E on GSM X-Y plane during 10–11 UT on 15 December 2008. (b) The observationalgeometry in the ionosphere (all mapped to 110 km height). A red line with dots indicates the trajectory of FAST. A black curvewith time label at 1030 UT marks the ionospheric footprint of TH-E calculated from T89 model (Kp= 1). The contours of �65°,�70°, and �75° MLAT, and 4–6 h MLT at 1030 UT, are labeled according to IGRF10 model. (c) Comparison between the mag-netic fields (in VDH coordinates) from TH-E observations and those from T89 model (Kp= 1) at TH-E locations.



As one can see, A is close to zero for 1–5 keV ions but is distinctly positive for >5 keV ions and shows anincreasing trend toward higher energies. This observation points to the existence of positive temperatureanisotropy for energetic ions, which is a well-recognized source of the EMIC wave excitation.

Figure 7 shows a “zoomed” view of the magnetic/electric field data over a shorter time range centeringaround the FAST passage. Higher-frequency oscillations with periods of the order of ~10 s are evident on theFGL data (0.25 s resolution). Though the electric field data presented here are in spin-resolution (~3 s) only,those higher-frequency oscillations are perceptible on the electric field data as well. We have carefully

Figure 5. (a) The first to third panels show the ion energy flux spectrogram in downgoing, perpendicular, and upgoingdirections observed by FAST. The fourth panel shows the electron energy flux spectrogram in downgoing direction. (b)The variation of isotropy ratio versus ILAT for different ion energies within 1–11 keV.



checked the raw waveform data of both electric and magnetic field measurements in satellite spinningcoordinate and exclude the possibility that those waves be instrumental artifacts. Using the proceduresdescribed in section 2.2, we decompose the magnetic field oscillations into MFA coordinates as shown in thethird panel. The parallel and perpendicular wave power spectrograms are plotted in the fourth and fifthpanels of Figure 7. As one can see, there are strong wave activities at ~0.1 Hz, mainly between fcp and fcHe.These waves are mainly polarized on the plane perpendicular to the ambient B field, implying a quasi-parallelwavefront. EMIC waves in the same frequency band and during the similar interval are also present on TH-D(not shown), which is ~0.4 h MLT east to TH-E.

The sixth and seventh panels of Figure 7 present the wave normal angle and ellipticity of the waves. As one cansee, the wave normal angle is, in general, small, and the ellipticity is dominantly negative, indicating a left-handpolarization. Thus, all distinct features of EMIC waves are confirmed from the data. We conclude that theabove observations provide strong evidence of the existence of EMIC waves in the equatorial CPS. In termsof timing, notwithstanding the uncertainties involving the propagation time of the EMIC wave and its excitationsource within the magnetosphere, as well as the transit time for keV protons from CPS to reach the ionosphere,the interval of in situ EMIC wave occurrence (~1021–1031 UT) would almost certainly cover the FAST epochof reversed-type precipitation boundary crossing. We thus state that the above results provide support to apossible linkage between the EMIC wave and the reversed-type ion precipitation.

Figure 6. TH-E observations on 2008-12-15. From top to bottom are the magnetic fields in VDH coordinates, plasma β, ionflows in VDH coordinates, electric fields in DSL coordinates, omnidirectional ion energy flux spectrogram, and ion anisotropy atdifferent energy levels.



We, however, note that in this event the EMIC wave frequency band becomes close to local fcHe when thelocal B field increases with large-amplitude Pc5 oscillations. In a cold uniform plasma, there would in principleexist stopbands for parallel-propagating L-mode EMIC waves in the frequency range between each heavyion gyrofrequency and the cutoff frequency. The formula of cutoff frequencies in a three ion plasma can befound in, e.g., LaBelle and Treumann [1992] (see their equation (2)). To exemplify, for the density ratios(ηΗ+ = 90%, ηHe+ = 5%, and ηΟ+ = 5%) assumed in our model in section 2, the two cutoff frequencies are at~0.1 fcp and ~0.3 fcp, respectively. We speculate that the He+ density might be very low in the region ofobservation, such that the stopband above fcHe might not actually exist when the hot plasma modificationand/or the nonhomogenous propagation effect are included. For example, when the hot plasma effectis considered, the EMIC wave frequency can become closer to fcHe (or even cross fcHe) than that prescribedby the cold plasma theory [Horne and Thorne, 1994; Chen et al., 2011]. Since there are no direct measurementsof ion compositions from THEMIS instruments, and the source region of waves is uncertain, the aboveambiguities cannot be resolved from available data and are beyond the scope of this paper.

In the above observations and discussions we have focused on the CPS ion population at above 1 keV. As onemay have already noticed in Figure 5a, there is a distinct existence of separate ion precipitation structureswith energies below 1 keV. Those lower energy ion precipitation structures contain stronger fluxes than the

Figure 7. From top to bottom are the in situ magnetic and electric fields, the high-pass filteredmagnetic field oscillations inMFA coordinates, the FFT PSD of the parallel wave component and perpendicular wave component, the wave normalangle, and the ellipticity of the perpendicular waves. The gray curves in the fourth to seventh panels denote the ambientlocal fcp and fcHe from low-pass filtered mean B field.



higher-energy CPS population and extend to farther lower latitude, reinforcing the trend of reversedenergy-latitude dependence of ion precipitation. There are, however, no imprints of such lower energy ionpopulation in magnetospheric THEMIS measurements. We shall discuss the possible origin and mechanismof such lower energy ion precipitation population in section 3.3 later.

3.2. The 22 December 2008 Event

We shall then introduce another reversed-type event observed by FAST. Since all data processing proceduresand core features of interest are the same as in the previous event, this event will be presented briefly only,with emphasis on a few notable differences from the previous event. One major discrepancy between thisevent and the previous one lies in that the 22 December 2008 event occurred during an extremely quietinterval: THEMIS-AE index maintained below 25 nT for ~8h preceding the event. Figure 8 shows theobservational geometry of FAST and TH-E in this event. According to the mapping via T89 model (Kp=0), theTH-E footprint is ~0.6h MLT east to the FAST meridian yet appears to be slightly southward of the latitudinalrange where a reversed-type ion precipitation boundary crossing is seen on FAST (during ~1059:25–1059:50 UT;see Figure 9a). We, however, point out that even though we have chosen the most relaxed version (with Kp=0)of T89 model series for the mapping, the model still seems to be overstretched, since it yields persistentlylower Bh and higher |Bv| values than realistic observations. Therefore, the actual ionospheric footprint of TH-E

Figure 8. (a) The satellite trajectory of TH-E on GSM X-Y plane during 1030–1130 UT on 2008-12-22. (b) The observationalgeometry in the ionosphere. A red line with dots indicates the trajectory of FAST. A black curve with time label at 11 UTmarks the ionospheric footprint of TH-E calculated from T89 model (Kp = 0). The contours of �65°, �70°, and �75° MLAT,and 4–6 h MLT at 1100 UT, are labeled according to IGRF10 model. (c) Comparison between the magnetic fields (in VDHcoordinates) from TH-E observations and those from T89 model (Kp = 0) at TH-E locations.



Figure 9. (a) FAST observations of the ion energy flux spectrogram in downgoing, perpendicular, and upgoing direc-tions. (b) TH-E observations. From top to bottom are the omnidirectional ion energy flux spectrogram, ion anisotropyat different energy levels, the FFT PSD of the parallel wave component and perpendicular wave components, andthe ellipticity of perpendicular waves, respectively. The gray curves in the third to fifth panels denote the ambientfcp and fcHe.



would be somehow higher in latitudes than that predicted by the T89 model, possibly overlapping with thelatitudinal range of the ion precipitation boundaries see on FAST.

Figure 9a shows the FAST data for the ~1100 UT pass across the southern auroral oval. A reversed-type ionprecipitation boundary crossing is clearly seen. Figure 9b shows the TH-E observations. Different from theprevious event, the ion anisotropy (second panel) in 12–25 keV energy range is weakly negative in this event,while the positive anisotropy still exists in the energy range 1–12 keV. We note that in this event the overall CPSion temperature appears to be lower than usual: the population with peak energy fluxes lie distinctly below10keV as seen in the first panel of Figure 9b (and it is also the case in FAST observations shown in Figure 9a),which may be due to the long-lasting quiet geomagnetic condition preceding the event. The main thermalpopulation of CPS ions at<10 keV still contain the favorable anisotropy to excite an EMIC instability in this event.

The third and fourth panels of Figure 9b present the parallel and perpendicular wave FFT spectrograms. Thereare noticeable narrowband wave activities within fcHe and fcp, though the wave power is substantially weakerthan in the previous event. One possible reason of the relatively weak wave amplitude might be the lowerenergy level of CPS thermal ions that contain a positive anisotropy, which in turn alludes to a weaker energysource of EMIC excitation. One other possibility lies in that TH-E might be located in the decaying edge of anEMIC wave region. The perpendicular waves are found as much stronger than parallel waves, indicating aquasi-parallel wavefront. The waves between ~1058 and 1100 UT are potentially related to the reversed-typeboundary crossing seen by FAST around ~1059:40 UT. For these waves of interest the ellipticity (fifth panel)is found as mainly negative. Evidences of H-band EMIC waves are thus inferred from the data, and a possiblelinkage between the EMIC wave and the reversed-type event is again supported in this event. We noticein Figure 9a that equatorward of the 10 keV IB the ion precipitations are sharply confined to <4 keV, and theupper energy limit of the precipitation is further reduced toward lower latitudes. As predicted by theories(see Figure 3c) the EMIC wave scattering rate decreases toward higher energies, such that the>4 keV protonsmight not be efficiently scattered, given the relatively low wave power in this event.

In the above we have presented two FAST reversed-type events. In the supporting information we alsopresent another reversed-type event observed by REIMEI, during a ~0925 UT pass across the northern auroraloval on 23 February 2009. The observed ion fluxes and the calculated isotropy ratios clearly indicate areversed energy-latitude dispersion of ion precipitation boundaries. To avoid inflating the paper to anunwanted size, we are not to present that event in detail but shall summarize a few key observations andfeatures of the event as follows. In the 23 February 2009 event TH-A/E/D were all within 1 h MLT east of theREIMEI meridian. THEMIS in situ observations, including summary plots of the magnetic field and particlemeasurements as well as the FGL wave survey, can be found on the official THEMIS website (http://themis.ssl.berkeley.edu). The event interval occurred during the expansion phase of a moderate substorm. Energeticion injections (>30 keV), a common signature of substorm expansion, are found to occur at around ~0925 UTon all three probes. Accompanying these ion injections, strong wave intensifications with frequencies upto local fcp arise on all three probes. Though in this event the probes (in particular TH-A and TH-E) are a bitoff equator, and there is a coexistence of other low-frequency compressional waves, clues of H-band EMICwaves can still be identified from the in situ observations.

3.3. Other Possible Mechanisms3.3.1. Heavy Ion ContributionsOne may question our proposal that the reversed-type events violate the FLC-scattering scenario, sincewe have not considered the contribution of heavy ions so far. Indeed, as compared to the protons, heavierions have larger gyroradius and thus can be more subject to the FLC scattering. The IBs of those heavy ionsare thus situated earthward (equatorward in the ionosphere) of the proton IB and may possibly lead to areversed-type dependence of ion precipitation boundaries, provided that those heavier ions possessnontrivial fluxes. To clarify this issue, we resort to the energy-anglemass spectrograph (TEAMS) data on boardFAST. Figure 10 presents the TEAMS flux data for the 15 December 2008 and 22 December 2008 eventsintroduced above. At the current status of TEAMS calibration, only omnidirectional flux survey data areavailable, without pitch angle information. Nevertheless, the data quality to date suffices for one to make anorder-of-magnitude evaluation of the ion compositions (E. Lund, private communication, 2014). To be morediscreet, we have browsed over the raw mass spectrum for our events and confirmed that there are peaksroughly at ~1, 4, and 16, an expected feature of H+/He+/O+ plasma. As can be seen in Figures 10a and 10b, the



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He+/O+ ions are rather weak in fluxes. More specifically, the omnidirectional energy fluxes (integrated overpitch angles) observed by ESA on the verge of the precipitation boundaries at energies>1 keV are generallywell above 106 eV/cm2/s/eV, while in such an energy range the He+/O+ ion fluxes are less than 105 eV/cm2/s/eV.This invalidates the possibility that the heavy ion precipitation be an effective mechanism of the observedreversed-type energy-latitude dispersion. We have looked into the TEAMS data for all FAST reversed-type eventswe identified so far (there is no energy-mass instrument on board REIMEI) and confirmed that in none of ourinvestigated events He+/O+ ions appear to have any appreciable contribution to ion precipitation at energies>1 keV—we, however, do notice in a number of events that the O+ contribution may become nontrivial atenergies <1 keV, an issue to be touched in section 3.3.3 later.3.3.2. Time-of-Flight Convective Dispersion of Ion PrecipitationOne other possible origin of the energy-latitude dispersion of ion precipitation lies in the time-of-flight convectiveeffect of precipitating ions. In principle, ions with different energies have different travel times and thus will end atdifferent latitudes, due to the E × B drift in the course of their precipitation. Such a mechanismwas often invokedto interpret the observations of multiple energy-dispersed ion bands [e.g., Hirahara et al., 1997], which alsopossess the dispersion feature of decreasing energy toward deceasing latitude. There are no ionospheric flowmeasurements surrounding the ion precipitation boundaries in any of our investigated events. We have checkedthe in situ electric fields from THEMIS observations in our events and noticed that the DC azimuthal E fields are, ingeneral, weak (<1mV/m) inmost of our events, except during substorm expansion intervals (e.g., the 23 February2009 event). It is well recognized that in the nightside CPS the earthward convective flows tend to be decelerated,diverted, or even at times “rebounded” by the strong magnetic field and pressure gradients contained in thenear-Earth magnetosphere [e.g., Lee et al., 2012]. There might be some strong and transient earthward flows

Figure 10. (a) FAST TEAMS observations for 2008-12-15 event. From top to bottom are the omnidirectional energy flux spectrogram of H+, He+, and O+ ions, respec-tively. A dashed circle marks the O+ ion structures possibly originating from ion accelerations on top of the ionosphere. (b) The same as Figure 10a but for 2008-12-22event. (c) ESA pitch angle spectrogram in the energy range 100–1 k eV (top) and 30–100 eV (bottom).



inside the inner CPS, e.g., associated with local magnetic dipolarizations during substorm expansion intervals, buttheir associated electric fields are largely induced (instead of potential) and transient in nature andwould notmapalong the entire field line. Consequently, the meridional flows are usually found as small in the equatorwardportion of the auroral ionosphere [e.g., Provan et al., 2004; Bristow, 2008].

In the following we shall perform a semiquantitative evaluation on whether the convective dispersioneffect can by itself sufficiently account for the observed reversed-type events. For this purpose we shallassume that there is no alternative scattering mechanism (such as EMIC waves) in the magnetosphereand that the IB is solely determined by the FLC. Since the FLC-scattering IB in the magnetosphere is atlarger radial distance for protons with lower energies, to overcome this trend and lead to a reversed-type event in the ionosphere, very strong earthward (southward in the ionosphere) convections arerequired. We test with a number of empirical magnetic field models (Tsyganenko series T89, T96, T02,and Yue et al. [2013] model), with different model parameters. We use Rc/ρi = 8 to determine the IBs inthe equatorial magnetosphere and calculate the latitudinal shift of ion precipitation assuming the radialflow mapping along the entire field line. We infer from the calculation results that to cause a ~0.4° MLATseparation between the 1 keV and 10 keV proton precipitation boundaries, which is generally achievedor even exceeded in our reversed-type events, southward flows >750m/s in the ionosphere, orequivalent westward E field >1.7mV/m within L< 11 in the magnetosphere, are required. Such strongDC azimuthal E fields are not evidenced in THEMIS data in most of our reversed-type events and wouldbe statistically rare in realistic observations, as can be inferred from either the meridional velocitystatistics in the equatorward portion of the auroral ionosphere [e.g., Bristow, 2008] or the azimuthalE field statistics in the inner magnetosphere [e.g., Matsui et al., 2003]. Furthermore, in terms of thestatistical pattern, the distinct evening-morning asymmetry of reversed-type events shown in Figure 2may not be easily explained by the convective dispersion effect. To conclude form the abovearguments, we doubt that the time-of-flight convective effect of CPS ions can by itself adequatelyaccount for the observed energy-latitude dispersion of ion precipitation boundaries in reversed-typeevents, though admittedly we may not precisely determine its role on the basis of available data sets.3.3.3. Ion Acceleration in the Topside IonosphereSo far in our discussions on the FLC-scattering and EMIC-scatteringmechanisms, we have assumed a CPS origin ofprecipitating ions. However, particle precipitation observed by LEO satellites certainly contains non-CPSpopulation as well. Those non-CPS ion population seen in LEO satellite observations usually owe their origin toaccelerated ions from within and/or on top of the ionosphere. Two major ion acceleration mechanisms are theparallel electric field (E//) [e.g., Ergun et al., 2001] and the transverse ion heating by wave-particle interactions [e.g.,André et al., 1998]. A downward E// leads to mass-independent acceleration with near-isotropic or weakly field-aligned pitch angle distribution, as evidenced in a survey of downgoing ion acceleration structures in Hultqvist[2002]. For the transverse ion heating, the accelerated ions usually move upward due to the magnetic mirrorforce and form the so-called ion conics in velocity space. The transverse ion heating itself is mass dependent.However, ion conics are often observed in conjunction with upgoing suprathermal electron beams, whichindicate a likely coexistence of downward E// [Elphic et al., 2000; Lund et al., 1999]. A combined effect of thedownward E// and the transverse ion heating may cause the ion conics to be partly “trapped” in the downwardE// region [Gorney et al., 1985] and can also relieve the mass dependence of the ion energization [Lund et al.,1999, 2001]. The upwelling ions may, however, fail to escape into the magnetosphere due to the gravitationalforce and a downward E// (if coexisting); those ions may then fall back to the ionosphere while convecting withE × B drift and appear as downgoing ions in LEO satellite observations [e.g., Lockwood et al., 1985].

It is beyond the scope of this paper to perform a dedicated and extensive investigation on the ion accelerationin the topside ionosphere. We shall, however, exemplify the potential existence and underlying mechanisms ofthe ion acceleration via the 15 December 2008 event. While in section 3.1 we have focused on the reversedenergy-latitude dispersion for the ion population with energies >1 keV, Figure 5a clearly indicates anoutstanding existence of the other ion population, with energies below 1 keV yet with fluxes even stronger thanthe higher-energy ion population. Such lower energy precipitating structures extend to lower latitudes than thehigher-energy CPS population, reinforcing the trend of reversed energy-latitude dependence of ionprecipitation boundaries. No evidence of such lower energy ion population is seen in the magnetosphericmeasurement (Figure 6). The above observations offer strong clues of a coexistence of the CPS and non-CPS ionpopulations. In Figure 10c we present the pitch angle spectrogram of those lower energy ions from ESA



measurements in this event. The low-energy ions are essentially isotropic with empty upgoing cone, similar toan electron inverted V, before ~1030:30 UT, while near the equatorward end (~1031 UT) of those ion structures,they shift to even lower energies (<100 eV) and feature a broad peak around 90° pitch angle. Referring tothe TEAMS data, it is interesting to notice that between ~1030:20 and ~1031 UT, the O+ ions show a trace ofstructures around 100eV as well, providing further evidences of their origin in the ionosphere. These O+

structures are initially at essentially the same energy band as the H+ structures at around ~1030:30 UT, yet whenthe O+ structures become more prominent at ~1031 UT, their peak-flux energy band tends to be moderatelyhigher than that of the H+. This together with the ESA observation of ~90° peaks of 30–100eV ion pitch angledistribution around the same time, hinting that a transverse ion heating process is possibly involved in theformation of those ion structures. There are, however, no imprints of upgoing ion conics in local observations,indicating that the transverse ion heating and its resulting ion upflows may occur elsewhere. Combining theabove observational clues, we suggest that (a) the lower energy ion structures before 1030:30 UT, which arenear isotropic, might be associated with downward E// [Hultqvist, 2002] and (b) the O+ structures observedduring later time interval likely owe their origin to ion conic upflows in the cusp, polar cap, or nightside auroralregion, which fail to escape and fall back to the ionosphere as they convect with E × B drift toward lower latitudes.There is also a possibility that the lower energy ions come from the outflows in the conjugate ionosphere.However, were it the case, the temporal/spatial separation between the H+ and O+ structures would presumablybe larger than that in realistic observations, since the time-of-flight convective dispersion of H+ and O+ woulddiffer substantially under trans-hemispheric motions [Winningham et al., 1984; Hirahara et al., 1997].

Clues of similar ion acceleration structures can also be hinted in other events presented in this paper. Onecommon feature we shall particularly point out is that those lower energy ion precipitation structures nolonger exist equatorward of the CPS electron precipitation boundary (see Figure 5a and 21 February 2008 eventin the supporting information, for example). Such a feature also reinforces the notion that those low-energyion structures owe their origin in the topside ionosphere, since if they are from the inner magnetosphere, thereis no reason they have to be demarcated by CPS electron precipitation. Our observation is also consistent withthe survey result by Hultqvist [2002] in that downward accelerated ions are observed predominantly whenprecipitated electrons from the plasma sheet are present.

Upon examiningHultqvist’s [2002] and Lund et al.’s [1999] survey results, one can infer that the core energy of ionacceleration mostly lies below or around ~1 keV. Even for a minor set of events that extend beyond 1 keV, theenergy band of the ion acceleration structures is found as limited (typically<1 keV) [Hultqvist, 2002]. Therefore, itis not likely that the downward ion acceleration itself can cause a persistent trend of reversed energy-latitudedispersion over the CPS ion energy range from >1 keV up to tens of keV. This is partly corroborated by theTEAMS observations that in none of our investigated FAST events, the O+ ions appear to have any nontrivialcontribution to the reversed-type ion precipitation at energies >1 keV. That said, a combination of the twomechanisms, namely, the ion acceleration on top of the ionosphere and the pitch angle scattering of ions in theCPS, may result in a variety of energy-latitude distributions of the overall ion precipitation. (1) The ionaccelerationmay be confined at latitudes higher than the precipitation boundaries of CPS ion population, e.g., asin the 7 February 2008 event shown in Figure 1a. (2) In case the ion acceleration occurs at latitudes lowerthan the precipitation boundaries of CPS ion population, there will be two more possibilities. If the CPS ionprecipitation features a normal-type energy-latitude dispersion, a mixed-type event would be formed, as onecan see in the 21 February 2008 event in the supporting information. Otherwise, if the CPS ion precipitation itselfis a reversed type, e.g., led by an EMIC-scatteringmechanism, the trend of reversed energy-latitude dependencewould be apparently reinforced, as the situation in the 15 December 2008 event. To summarize, the ionacceleration in the topside ionosphere can enhance the precipitation fluxes of mainly low-energy ions (≤1 keV).Its occurrence latitudes can be in arbitrary geometries with respect to the higher-energy CPS ion precipitationboundaries but are often delimited by the equatorward boundary of CPS electron precipitation [Hultqvist, 2002].

4. Discussion

Via investigating ion precipitation events with reversed energy-latitude dependence of precipitationboundaries, we explore viable mechanisms of ion precipitation other than the FLC scattering. We haveraised two major non-FLC mechanisms: the pitch angle scattering by EMIC waves in the equatorialmagnetosphere and the ion acceleration in the topside ionosphere. The former mechanism is more



highlighted. We first demonstrate theoretically that the H-band EMIC wave can effectively resonate withkeV protons in the CPS and lead to strong pitch angle diffusion of them, at places where the local FLCno longer supports their scattering. The EMIC-proton scattering rate tends to decrease with increasingproton energies, which is contrary to the trend of FLC scattering. The H-band EMIC wave thus looms asone viable mechanism leading to the precipitation of CPS thermal protons and to the reversed energy-latitude dependence of the precipitation boundaries.

To support the above proposal, we present a few reversed-type events with conjunctive observationfrom THEMIS. So far from our ongoing survey over FAST/REIMEI data during THEMIS tail seasons, wehave been able to identify seven reversed-type events that have conjunctive THEMIS observations withdesirable geometry and data availability (see criteria in section 2.2). In those events, the reversedenergy-latitude dependence of ion precipitation boundaries generally persists throughout the energyrange from >1 keV to the upper limit of particle instruments on board LEO satellites. Evidences of EMICwaves are found in five out of the seven events from THEMIS data using the procedures described in thepaper. Vice versa, though off our main research interest we have also checked four events with normal-type energy-latitude dispersion of CPS ion precipitation (>1 keV) and with conjunctive THEMISmeasurements (using the same geometry criteria), for example, the 7 February 2008 event shown inFigure 1a and 21 February 2008 event shown in the supporting information. In situ THEMIS data showno hint of the existence of H-band EMIC waves in those normal-type events. More extensive survey isstill undergoing. Our event pool so far may not be adequate for us to assert a statistical significance, butthe achieved results already enable us to tentatively conclude that the H-band EMIC wave is one of theleading mechanisms of the reverse-type event.

Based up the above theoretical and observational results, we are in a position to claim that the EMIC wave canact as one other major precipitationmechanism of CPS ions besides the FLC scattering. Such an EMIC-scatteringmechanism can operate in different ion energy range from the FLC scattering and may at times (such as inreversed-type events) behave as the leading mechanism of the ion precipitation in certain region of theinner CPS.

We, however, shall point out that not all H-band EMIC waves can result in detectable reversed-type events inpractical observations. Besides the wave parameters (power, frequency, etc.) which directly control thescattering rate, the spatial location of the EMIC wave region may also affect the measurability of reversed-typeevents. If the wave region is either too far away from the Earth (where the EMIC-scattering overlaps with or isoverridden by the FLC scattering), or too close to the Earth (where the EMIC minimum resonant energyapproaches or exceeds the upper energy limit of the particle instrument), no reversed-type event can bepractically detected. Therefore, reversed-type events are most likely observed when the EMIC waves regionexists moderately earthward of the FLC-scattering IB of higher-energy protons. In this regard, we shall attemptto compare the FLC-scattering IB of 12 keV proton inferred from Yue et al. [2013, 2014] model with the H-bandwave statistics in Min et al. [2012]. To aid the readers, the wave statistics in Min et al. [2012] are assembled inthe supporting information of this paper. For Yue et al.’s model with average geomagnetic and solar windconditions (Kp=2; Pdyn=1–2 nPa), the IB is located at R~8 RE in themidnight and extends to R~12 RE at |Y | ~ 10 REin both dawnside and duskside flanks (see Figure 3a). Comparing this geometry with the wave statisticsinMin et al. [2012], one can obtain the following inferences: (1) EMIC waves exist with moderate occurrencerate and wave power surrounding and earthward of the IB in the near-midnight (|Y|< 4 RE) sector, whichmay cause the reversed-type events there. (2) Toward the flanks, the waves tend to have much higher wavepower and occurrence probability in the morning sector than in the evening sector, which can naturally resultin a statistical prevalence of reversed-type events in the morning sector. There is a region with nontrivialoccurrence rate of EMIC waves in the duskside flank at X>�5 RE and R< 10 RE, but the associated wave poweris fairly weak there. In contrast, in the dawnside flank at X>�6 RE and R< 12 RE, both the wave occurrencerate and wave power are rather strong in a broad region earthward of the FLC-scattering IB. In a companionsimulation study (B. Ni et al., submitted manuscript, 2014), the authors adopt the wave statistics inMin et al.[2012] and find that with the averaged wave parameters (wave power, center frequency, etc.) in respectivesectors, keV CPS protons may not be effectively scattered in the evening sector yet can be stronglyscattered in the morning sector. The above comparisons and arguments explain the statistical MLTasymmetry of reversed-type events as revealed in Figure 2: the occurrence probability of reversed-typeevents is low in the evening sector yet much higher in the morning sector.



The research goal of this study is to make an initiative step toward the exploration of the non-FLC precipitationmechanisms of CPS ions and to raise a few principal candidates of them. We have purposefully chosen thereversed-type event as a “breakthrough” for the above research objective. Admittedly, a number of issues arestill open, such as a more quantitative investigation on both the FLC-driven and EMIC-driven protonprecipitation fluxes and their comparisons with actual LEO observations. The study can be advanced in a fewaspects in the future. First, even from our limited survey we have noticed that the ambient magnetosphericconditions and key parameters of EMIC waves (power, frequency, etc.) vary substantially from case to case, suchthat their role in scattering CPS ions is better examined via an event-oriented approach. Second, when the FLC-scattering mechanism and non-FLC mechanisms coexist, to better discriminate their respective roles, it isdesirable to estimate the local FLC from practical data, which is not done in this study but is achievable incertain events under favorable probe geometries [Liang et al., 2013]. Last but not least, for a more accurateevaluation of the scattering rate of EMIC waves upon CPS ions, it is essential to extend our model to a morerealistic, event-adaptedmagnetic field configuration (instead of a dipolar model used in this study). We are nowattempting to extend this study in a more event-oriented and quantitative way along the above directions;relevant results will be the content of publication in the near future.

5. Conclusion

In this study, we explore possible ion precipitation mechanisms other than the FLC scattering, byinvestigating ion precipitation events with a reversed energy-latitude dispersion pattern as compared tothat expected from the FLC-scattering scenario. We analyze two major non-FLC precipitationmechanisms: the pitch angle scattering of protons by H-band EMIC waves in the equatorial CPS and theion acceleration in the topside ionosphere. The former mechanism is more focused on and examinedvia theories and joint observations from LEO and THEMIS satellites. We propose that the H-band EMICwave may cause strong pitch angle scattering of CPS protons, preferentially in the keV energy range.Such an EMIC wave scattering mechanism may cause the ion precipitation in lower energy ranges tooccur at lower latitudes than the high-energy ion IB due to the FLC scattering, producing the reversedenergy-latitude dependence of ion precipitation boundaries seen on LEO satellites.

Appendix A

In this section we shall briefly introduce our procedures to calculate the quasi-linear pitch angle diffusioncoefficient. The entire procedures and computational code inherit from the studies of Summers and Thorne[2003] and Summers et al. [2007]. In our following presentation we shall basically use the same notionsand symbol systems as in Summers et al. [2007], except that a few expressions are reformed and converted fromGaussian to SI units. Readers who are interested in theoretical principles and more computational details arereferred to Summers et al. [2007]. Some key simplifications and assumptions contained in the procedures are thefollowing: (a) we consider only parallel-propagating waves; (b) we consider only the first-order gyroresonancewith protons; (c) we adopt a dipole magnetic field configuration; and (d) the R-mode branch, which might inprinciple exist in the frequency range of interest in amulti-ion plasma, is not considered in this study, since the Rmode tends to be damped in the presence of a positive anisotropy of hot protons [Horne and Thorne, 1994],which is found to exist in all of our investigated events.

The dispersion relation of a parallel-propagating EMIC wave in a H+/He+/O+ cold plasma can be written as

y2

x2¼ 1� 1

α�x1

1þ xþ εη1x � ε

þ εη24x � ε

þ εη316x � ε

� �; (A1)

in which

x ¼ ωΩej j ; y ¼ ck

Ωej j ; α� ¼ Ω2e

ω2pe

:

Here Ωe and ωpe denote the electron gyrofrequecy and plasma frequency, respectively; ε=me/mp denotesthe electron-to-proton mass ratio; and η1, η2, and η3 denote the density ratio of proton, He+, and O+,



respectively. On the other hand, the first-order gyroresonant condition with protons (when the relativisticeffect is included) can be written as

x � εγ¼ yβcosα; (A2)

in which γ= (1� v2/c2)� 1/2 and β = v/c are relativistic parameters and v and α denote the velocity and pitchangle of the proton. For given particle v and α, a combination of equations (A1) and (A2) yields a series ofsolutions of x and y (equivalentlyω and k), so-called the “resonant roots.” Theremay exist a maximum of threeresonant roots in H band (ε/4< x< ε), He band (ε/16< x< ε/4), and O band (0< x< ε/16), respectively.

We assume a Gaussian power spectral density (PSD) of the magnetic field of EMIC waves,

W ωð Þ ¼ Wmexp � ω� ωmð Þ2δω2

" #:

In a quasi-linear theory, the pitch angle diffusion coefficient can be calculated via

Dαα v; αð Þ ¼ πΩ2pWm

2γ2B20�Xj

1� xj cosαyjβ

� �2� dxdy

�� j

βcos α� dxdy

� �j

�� exp � ωj � ωm

� �2δω2

" #(A3)

where B0 is the ambient magnetic field. The summation is carried out over all resonant roots (xj, yj). dxdy

� �j

denotes the derivative of x over y (from the dispersion relation (A1)), calculated at the resonant root (xj, yj).

Equation (A3) gives the local diffusion coefficient at a space point with magnetic field B0. Under anonhomogeneous magnetic field, the particles undergo adiabatic bounce motion along the field line. Toeffectively evaluate the pitch angle scattering efficiency of precipitating particles, it is routine to average theDαα over the particle bouncing trajectory to achieve a “bounce-averaged” diffusion coefficient. Under adipolar field geometry, such a bounce-averaged pitch angle diffusion coefficient has the form

Dααh i v; αeq� � ¼ 1

1:3� 0:56αeq ∫λm

0Dαα v; α; λð Þ � cos α cos

7λcos2αeq

dλ (A4)

in which αeq is the equatorial pitch angle and α is the pitch angle at a magnetic latitude λ:

sin2α ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 3sin2λ

pcos6λ

sin2αeq (A5)

The upper limit of the integral λm denotes the mirror point where α=90°.

The above-outlined procedures will be used to evaluate the scattering efficiency of EMIC waves over a broadenergy range of protons. In this paper, for demonstration purpose we use the following model parameters inour example calculation in Figure 3c:Wm=0.5 nT2/Hz; ωm=0.6Ωp, δω=0.1Ωp for H-band EMIC (ωm=0.15Ωp,δω=0.03 Ωp for He-band EMIC); η1 = 90%, η2 = 5%, and η3 = 5%. The plasma number density (0.5–0.8 cm�3) isset to increase toward the Earth and labeled in the plot with corresponding L values. A more dedicatedsimulation, aiming to thoroughly examine the parameter dependences and more subtleties of the EMIC-protonscattering, is performed in a companion study (B. Ni et al., submitted manuscript, 2014).

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AcknowledgmentsWe are grateful to NASA for support ofTHEMIS and FAST missions. THEMIS andFAST data used for this study are obtainedvia the open data access provided by theUniversity of California, Berkeley. BinbinNi acknowledges the support fromthe NSFC grant 41204120 and from theFundamental Research Funds for theCentral Universities grant 2042014kf0251.We acknowledge J. McFadden, C. Carlson,D. Larson, and K.-H. Glassmeier for theirwork on THEMIS ESA, SST, and FGM. Wealso appreciate the data calibration worksand kind suggestions from J. McFadden(PI of FAST ESA), E. Lund (PI of FASTTEAMS), and K. Asamura (PI of REIMEIEISA). We thank for useful discussions withWen Li, Jichun Zhang, and Jeongwoo Lee.

Larry Kepko thanks Eric Lund and oneanonymous reviewer for their assistancein evaluating this paper.

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on an energy-latitude dispersion pattern of ion precipitation potentially associated with...

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