Simultaneous Precipitation of Sub‐Relativistic Electron Microburst and Pulsating Aurora Electrons

We have identified for the first time an energy‐time dispersion of precipitating electron flux in a pulsating aurora patch, ranging from 6.7 to 580 keV, through simultaneous in‐situ observations of sub‐relativistic electrons of microburst precipitations and lower‐energy electrons using the Loss through Auroral Microburst Pulsation sounding rocket launched from the Poker Flat Research Range in Alaska. Our observations reveal that precipitating electrons with energies of 180–320 keV were observed first, followed by 250–580 keV electrons 0–30 ms later, and finally, after 500–1,000 ms, 6.7–14.6 keV electrons were observed. The identified energy‐time dispersion is consistent with the theoretical estimation that the relativistic electron microbursts are a high‐energy tail of pulsating aurora electrons, which are caused by chorus waves propagating along the field line.

Theoretically, the chorus waves can scatter relativistic/sub-relativistic electrons when they propagate to high latitudes along the field line because the resonance energy of chorus waves becomes higher (Horne & Thorne, 2003;Miyoshi et al., 2010Miyoshi et al., , 2015aMiyoshi et al., , 2020)).Microbursts and chorus waves have similar time scales and spatial distributions in L-value and MLT (e.g., Nakamura et al., 2000).Chorus waves and microbursts were also simultaneously observed on nearby magnetic field lines or same satellite (Breneman et al., 2017;Oliven & Gurnett, 1968).
Pulsating aurora is a type of diffuse aurora that exhibits intermittent modulation of luminosity whose period is typically several seconds.The precipitation of several to tens of keV electrons scattered by the chorus waves causes the pulsating auroral emission in the Earth's auroral ionosphere (e.g., Grono & Donovan, 2019, 2020;Hosokawa et al., 2020;Kasahara et al., 2018;Miyoshi et al., 2010Miyoshi et al., , 2015aMiyoshi et al., , 2021a;;Nishimura et al., 2020;Ozaki et al., 2019).A few Hz internal modulations are sometimes embedded in the main pulsation of the pulsating aurora.This time scale is very similar to that of rising tone elements of chorus waves (Miyoshi et al., 2015a) and a single burst of a microburst.The energy of electron precipitation associated with pulsating auroras has been studied by observations using ground-based auroral cameras, incoherent radars, and riometers (Grandin et al., 2017;Partamies et al., 2019;Tesema et al., 2020;Yang et al., 2019).For higher-energy electrons, Sandahl et al. (1980) observed precipitations of about 140 keV electrons into the ionosphere during pulsating aurora by a sounding rocket experiment.Radar observations also indicated that relativistic/sub-relativistic electrons precipitate into the middle atmosphere in association with pulsating auroras (e.g., Miyoshi et al., 2015bMiyoshi et al., , 2021a;;Oyama et al., 2017).However, direct observational evidence on the relationship between microbursts and pulsating auroral electrons has not yet been obtained.
Recently, based on the theory; the Miyoshi-Saito model (Miyoshi et al., 2010;Saito et al., 2012), Miyoshi et al. (2020) proposed a model in which chorus waves propagating along the field line cause electron scattering in a wide energy range, and both pulsating aurora electrons and relativistic/sub-relativistic electron microbursts are the same origin caused by the propagation of chorus waves.Kawamura et al. (2021) and Shumko et al. (2021a) reported that relativistic electron microbursts occurred with the pulsating auroral emission, which is consistent with the model proposed by Miyoshi et al. (2020).Another clue to confirm the Miyoshi-Saito model is the characteristic energy-time dispersion of the precipitating electron fluxes.The Miyoshi-Saito model predicts "inverse" energy-time dispersion of the precipitating electron fluxes; electrons with energies a few hundred keV arrive at the ionosphere before higher-energy (MeV) electrons.This feature is caused by the propagation delay of chorus waves from the magnetic equator to higher latitudes, increasing the resonance energy of electrons due to increased background magnetic field strength along the wave propagation path, and elongation of the travel distance of electrons from the scattering point to the ionosphere.Kawamura et al. (2021) reported this inverse energy-time dispersion of precipitating electron fluxes in a patch structure of pulsating aurora by using simultaneous observations of high-energy electrons and auroral emissions with the FIREBIRD-II satellite and ground-based auroral imagers.Shumko et al. (2023) has identified the inverse energy dispersion of relativistic electron microbursts as predicted by the Miyoshi-Saito model.However, they showed no direct observations of lower-energy electrons causing the pulsating aurora.This paper reports the first in-situ observation of the energy-time dispersion of precipitating electrons of microbursts and pulsating auroras obtained by the Loss through Auroral Microburst Pulsation (LAMP) sounding rocket experiment.We analyzed the precipitating electron data covering from 6.7 keV up to MeV range.We successfully detected the timing differences of the electron precipitations for different energies in a pulsating auroral patch.We also performed a model calculation about the energy-time dispersion of electron fluxes, taking into account the interactions between chorus waves and electrons, and compared it with the LAMP observations.

Instrumentation
The LAMP mission is a US-Japan sounding rocket experiment designed to observe the microburst electrons and the pulsating auroras simultaneously.We used the data obtained by a high-energy electron detector (HEP: High Energy Particle detector), a low-energy electron detector (EPLAS: Electron PLASma detector), auroral imagers (AIC: Auroral Imaging Camera), and a magnetometer (MIM: Magneto-Impedance Magnetometer HEP is an improved version of the detector installed in a previous sounding rocket experiment (Namekawa et al., 2021).HEP consists of a mechanical collimator, eight-layered silicon semiconductor detectors (SSDs), and an anti-coincidence sensor used to remove the effects of cosmic rays.HEP can measure 975 keV electrons from 207 Bi radiation source with an energy resolution ΔE = 53.5 keV.The anti-coincidence sensor consists of a plastic scintillator and four avalanche photodiodes (APDs).A part of cosmic rays penetrating through the SSDs emit photons inside the plastic scintillator surrounding the SSDs, and the APDs detect these photons.Then, the contribution of cosmic rays can be eliminated by the detection signals generated by the APDs.HEP was mounted on the top of the rocket so that the center of the field of view of HEP was parallel to the thrust axis of the rocket, which was controlled to be parallel to the local geomagnetic field.
EPLAS is an electron energy spectrum analyzer that covers 5 eV to 15 keV with 42 energy steps.EPLAS has a 360-degree planar field of view divided by 36 angular bins.The sampling time of EPLAS for one energy step is 1 ms, providing a 2-D velocity distribution function every 42 ms.AIC consists of two high-speed CMOS monochromatic imagers.We used images obtained by Sensor 1 of AIC (AIC S1) that was sensitive to photons of N 2 1PG emission of auroras with a 20 nm bandpass filter centering at 670 nm with a frame rate of 9.5 Hz.N 2 1PG emission is the typical permitted line of auroral emission in the ionospheric E-region.The field of view and angular resolution of AIC S1 are 27° × 27° and 0.5° × 0.5°, respectively.MIM is a triaxial magnetometer based on the magneto-impedance effect.We calculated the pitch angles of observed electrons using MIM data.

Observation
A ground-based all-sky EMCCD imager operated at Venetie, which is located near below the magnetic footprint of the apex of the rocket trajectory, observed an auroral patch at 236 s from the launch of LAMP (Figures 1a-1d).Red dashed lines in Figures 1b and 1d indicate the contour of the auroral patch.Figures 1a and 1b correspond to the off-phase of the patch, and Figures 1c and 1d correspond to its on-phase.The footprint of LAMP (red dot) was located within this patch, and the rocket was flying at an altitude of 388 km.The L-value was 7.0.Figures 1e and 1f show the count rate of precipitating electrons observed by HEP plotted in 10 ms intervals, with running averages over 50 ms.The center of the field of view of HEP pointed to 2.1 degrees off the opposite direction of the local geomagnetic field.Since the field of view of HEP is 45.2° × 45.2°, the electrons with pitch angles between 0° and 32.6° could be detected.We apply labels HEP-H (HEP-High) and HEP-L (HEP-Low) for observed electron count rates of energy channels 250-580 keV and 180-320 keV, respectively.Figures 1g-1i show the count rate of precipitating electrons observed by EPLAS with a time resolution of 42 ms, where the count rate is summed over all the azimuthal channels of the instrument.Again, we apply labels EPLAS-H (EPLAS-High), EPLAS-M (EPLAS-Medium), and EPLAS-L (EPLAS-Low) for electron count rates of energy channels 12.5-14.6keV, 9.1-10.7 keV, and 6.7-7.6 keV, respectively.Figure 1j shows the auroral emission intensity (wavelength at 670 nm) at the magnetic footprint of the rocket, observed by AIC S1 with a time resolution of 105 ms.Since AIC S1 looked downward from the rocket, reflected photons from the ground surface were also detected.The photon count rate due to the reflection has been estimated and subtracted in Figure 1j.The black dotted lines in Figures 1e-1j correspond to the observation times of the auroral images shown in Figures 1a  and 1b and Figures 1c and 1d, respectively.The red dotted box in Figures 1e and 1f corresponds to the time range when a microburst train was observed, and the red dotted box in Figures 1g-1j corresponds to the time range when a pulsating auroral patch and a low-energy electron precipitation train were observed.
Figures 1g-1j show that the EPLAS-H/M/L electron counts increase with the auroral intensity enhancement.These electrons contribute to the main pulsation of the pulsating aurora (Miyoshi et al., 2015b).In Figures 1g-1i, modulations are embedded in the electron count enhancements of EPLAS-H/M/L.It is clear from Figures 1e-1i that the increases in HEP-H/L electron counts preceded those of EPLAS-H/M/L electrons.Figures 1e and 1f also show that several spiky enhancements with a short duration, that is, microbursts, are embedded in the microburst train.The electron counts observed by EPLAS show an energy-time dispersion that is similar to typical flux variations of pulsating auroral electrons reported in the previous studies (Miyoshi et al., 2010(Miyoshi et al., , 2015b;;Nishiyama et al., 2011).
Here, we identify the difference in the arrival timing of the same microbursts observed by HEP-H/L in a more objective way.Figures 2a and 2c show the electron count rates (same as Figures 1e and 1f) together with smoothed values by applying 110 ms window sliding average.Figures 2b and 2d show the second time derivatives of the smoothed count rates, and the standard deviations of the second time derivatives for HEP-H/L, respectively.By using the second time derivative, the background can be subtracted without arbitrariness, and the locations of the peaks can be determined from the locations of their local minima.We applied the Savitzky-Golay method (Savitzky & Golay, 1964) to calculate the smoothing, its second derivatives, and the standard deviations of the second derivatives.The standard deviations of the second time derivatives plotted in Figures 2b and 2d are sign-reversed for comparison with the local minima of the second time derivatives.The arrival timings of microbursts observed by the HEP-H/L were determined as the timings when the second time derivatives take local minima, and their absolute values are greater than the standard deviations.Only bursts with 0.6 counts per 10 ms or more were used in this analysis.The blue and red dotted lines show the timing of the microbursts at the HEP-L (Figures 2a and 2b) and the HEP-H (Figures 2c and 2d), respectively.More bursts in HEP-L than in HEP-H are consistent with higher energy electrons being scattered less frequently because it is more difficult for waves to reach higher magnetic latitudes.We identified seven events in which the microburst at the HEP-H appears in close proximity to the microburst at the HEP-L.Red triangles in Figure 2c show the appearance timings of the identified seven microbursts of HEP-H.The HEP-L microbursts precede the HEP-H microbursts by 13.3 ms on average over six events out of the seven events (as shown with red triangles).Note that the time lag between the microbursts is unclear in the remaining event.Assuming a normal distribution with an average of 13 ms and a variance of 307 ms 2 as the occurrence distribution of time differences between microbursts at HEP-L and HEP-H, it was found that 78% of microbursts at HEP-L appeared before those at HEP-H.Correlation coefficients on time profiles of microbursts between HEP-H and HEP-L were calculated to demonstrate the relevance of each burst.The correlation coefficients were calculated with a sliding window 600 ms wide, successively moved by 10 ms during the period from 235 to 237 s after the launch of LAMP.The HEP-H data were shifted with respect to the HEP-L electron data within ±100 ms to examine changes in the correlation coefficients.Figure 3a shows the calculated correlation coefficients.The vertical axis shows the shifted time of the HEP-H electron data, and the horizontal axis is the start time of each correlation coefficient calculation window.A positive time shift of the HEP-H data indicates that HEP-L precedes HEP-H.Figure 3a demonstrates that the significant correlation coefficients appear when the HEP-H data are positively shifted in time, indicating that HEP-L tends to precede HEP-H at 235.0-237.0s after the launch of LAMP.Particularly large correlation coefficients (>0.5) are obtained when the HEP-L data precedes by 30 ms at 235.0-235.3s and by 0-10 ms at 235.3-235.7 s.This characteristic is consistent with that of the analysis by simple identification of the appearance  3b and 3c.
timings of the HEP-H and HEP-L microbursts described in Figure 2. Note that there is a drop of time difference around 235.25 s due to higher count rate bursts with shorter time differences in the window.
A superposed epoch analysis was applied to bursts detected by both HEP-H and HEP-L to accurately estimate the appearance time lag between them.In this analysis, the reference time (t = 0) is set as the timing when peaks of microbursts are identified in the HEP-H data, which is indicated by the red triangles (t0As) in Figure 2c.The result of the superposed epoch analysis is shown in Figure 3b.The time range of superposition is ±70 ms from the reference timing.A significant enhancement of HEP-L precedes that of HEP-H, with a time lag of 10 ms between the appearance of the maxima of their count enhancements.Red and black dotted lines in Figure 3b indicate when the count enhancements of HEP-H and HEP-L reach the midpoint between their own maxima and minima, respectively.These values for HEP-L appear at 18.3 and 25.4 ms before those of HEP-H, respectively.This result also suggests that most of the microbursts at the HEP-L appear before the microbursts at the HEP-H, indicating the inverse energy dispersion feature of the observed microburst.
It is difficult to detect individual bursts detected by EPLAS because lower-energy electron precipitations are expected to have a longer energy-time dispersion and to be observed spread out over time (Miyoshi et al., 2020).Then, a superposed epoch analysis was also performed on the EPLAS-H/M/L data to investigate the average precipitation timing of lower-energy electrons relative to those of microbursts at the HEP-L and HEP-H within an auroral patch.The reference time is set as the timing when peaks of microbursts at the HEP-L are identified (blue triangles (t0Bs) in Figure 2a).The microbursts at the HEP-L selected as t0Bs are obtained during the time when bursts with a count rate of more than 1.5 counts per 10 ms were present.Figure 3c shows the results of the analysis.An increase in count rates appears in the order of EPLAS-H, EPLAS-M, and EPLAS-L.The time lags from t0Bs are 546, 672, and 840 ms for the maximum peaks of EPLAS-H, EPLAS-M, and EPLAS-L, respectively.In all cases, the error is calculated from the square root of the counts.

Discussion
Here, we compare the energy-time dispersion of the precipitating electron fluxes observed by LAMP with those deduced from numerical simulations.Based on the Miyoshi-Saito model about pitch angle scattering of pulsating aurora and microbursts (Miyoshi et al., 2010(Miyoshi et al., , 2015a(Miyoshi et al., , 2015b(Miyoshi et al., , 2020;;Saito et al., 2012), we calculated the elapsed time from the generation of chorus waves at the equatorial magnetosphere to the arrival of precipitating electrons.For the generation of chorus waves, we launched a single rising tone element of chorus waves at the equator with a frequency sweep rate of 2 kHz/s.The generated chorus waves propagate parallel to the dipole magnetic field lines.In the simulation, the background electron density in the magnetosphere is assumed as 2.95 cm −3 , which is uniformly distributed along the magnetic field line using the empirical model of Sheeley et al. (2001).
Figure 4 shows the arrival timings of precipitating electrons at the ionospheric altitude as a function of electron energies.Orange, blue, and red lines show calculated timings by the test particle simulation, where the frequency of waves at the wave launch (ω) is 0.2, 0.3, and 0.42 f c,eq (f c,eq is electron cyclotron angular frequency at the equator where the waves are launched), respectively.On the other hand, black dots indicate the observed timings which are plotted so that the peak timing of microbursts at the HEP-L matches the calculated timing of the electron precipitation with energies of 240 keV based on the simulation for ω = 0.2 f c,eq .Note that dots for the where the frequency of waves at wave launch (ω) is 0.2, 0.3, and 0.42 f c,eq , respectively.A black line shows calculated timings assuming electrons of all energies depart from the magnetic equator at the same time.Note that the timings obtained by the observation are plotted so that the peak timing of the HEP-L microbursts matches the calculated timing of the electron precipitation with energies of 240 keV based on the simulation for ω = 0.2 f c,eq .microbursts at the HEP-L and HEP-H are plotted at energies of 380 and 240 keV, respectively.In the plot, we take 20 ms for the time lag between the appearance of the microbursts at the HEP-L and HEP-H.The inverse energy-time dispersion observed by HEP is in good agreement with the numerical simulation for ω = 0.2 f c,eq , and the observed peak timings of electron flux enhancement around 10 keV are consistent with the simulation for ω = 0.42 f c,eq .This mixture of multiple results is caused by the rising tone element of chorus waves which has certain frequency bandwidth at the same time (e.g., Santolík et al., 2003).There may have been some ambiguities in the results from the time-variations of the frequency chirping rate of the rising tones and amplitude fluctuations during the frequency chirping and phase discontinuities.The differences in arrival timings of the observed electrons with energies around 10 keV were longer than those with energies of 380 and 240 keV.This feature suggests that a flux enhancement of electrons with energies around 10 keV has a longer time scale than that of electrons with energies of a few hundred keV.These are consistent with the simulation results of Miyoshi et al. (2020) and Chen et al. (2020).
The black line shows the timings assuming electrons of all energies with a pitch angle of 0° depart from the magnetic equator at the same time.This assumption corresponds to the case that the pitch angle scatterings of all energy electrons take place at the magnetic equator.In this case, the 380 keV electrons are shown to arrive before the 240 keV electrons, which is not consistent with the observed energy-time dispersion.

Conclusions
The energy-time dispersion of precipitating electrons in the pulsating auroral patch was identified by in-situ observations with the energy range from 6.7 to 580 keV range for the first time.At energies above 180 keV, the observed microbursts show the inverse energy-time dispersion.The observed energy-time dispersion is consistent with the theoretical model.This observation is consistent with the Miyoshi et al. (2020) model that relativistic electron microbursts are a high-energy tail of pulsating aurora; the pitch angle scattering of electrons by chorus waves generates the microburst precipitation of relativistic/sub-relativistic electrons as well as the precipitation of lower-energy electrons which is responsible for the photon emission of pulsating auroras.

Figure 1 .
Figure 1.(a)-(d) Mosaic image of all-sky imagers captured at Poker Flat Research Range (PFRR), Fort Yukon (FKN), and Venetie (VEE).Red dots indicate the footprint of the rocket at 100 km altitude.Red dashed lines indicate the contour of the auroral patch.Yellow lines indicate the trajectory of the footprint of the rocket.The mapped altitude was 100 km.(e)-(f): Count rate of precipitating electrons observed by HEP.(g)-(i): Count rate of electrons measured by EPLAS.(j) Emission intensity of photons (670 nm) at the magnetic footprint (altitude of 100 km) of the position of the rocket obtained by AIC S1.The black dotted lines on panels (e)-(j) correspond to the observation times of panels (a)-(d).The red dotted boxes on panels (e)-(j) correspond to the time range when a microburst train, a pulsating auroral patch and a low-energy electron precipitation train were observed.

Figure 2 .
Figure 2. (a) and (c): The electron count rates (HEP-L and HEP-H, the same as those in Figures 1e and 1f) together with the smoothed values with time windows of 110 ms.(b) and (d): The second time derivatives of the smoothed count rate and their standard deviations assuming randomness and independence of each count rate data.The blue and red dotted lines show the appearance timings of identified bursts.The red and blue triangles (called t0As and t0Bs) indicate reference timings of the superpositions shown in Figures 3b and 3c.

Figure 3 .
Figure 3. (a) Correlation coefficients between HEP-H and HEP-L calculated every 10 ms with a time window of 600 ms.The contours are also plotted every 0.05.(b) Calculated HEP-H (red) and HEP-L (black) by the superposed epoch analysis.The reference time (t = 0) is set as t0As in Figure 2. Red and black dotted lines indicate when the enhancements of HEP-H and HEP-L reach the midpoint between their maxima and minima, respectively.(c) Calculated EPLAS-H (red line), EPLAS-M (black line), and EPLAS-L (blue line) by the superposed epoch analysis.The reference time (t = 0) is set as t0Bs in Figure 2.

Figure 4 .
Figure 4. Arrival timings of precipitating electrons at the ionospheric altitude as a function of electron energies.Black dots show the timings obtained by the observations.Orange, blue, and red lines show timings based on the Miyoshi-Saito model, where the frequency of waves at wave launch (ω) is 0.2, 0.3, and 0.42 f c,eq , respectively.A black line shows calculated timings assuming electrons of all energies depart from the magnetic equator at the same time.Note that the timings obtained by the observation are plotted so that the peak timing of the HEP-L microbursts matches the calculated timing of the electron precipitation with energies of 240 keV based on the simulation for ω = 0.2 f c,eq .