Modulation Of Electron Flux Research Articles

Implications of Asymmetric Loss Cone Distribution on Whistler‐Driven Electron Precipitation at Mercury

AbstractMercury has a large loss cone difference in its two hemispheres due to the northward shifted magnetic dipole. The precipitation difference of energetic electrons in both hemispheres is poorly understood. We show that the northern precipitation is 2.5‐times higher than for a symmetric loss cone due to the effects of the enhanced whistler instability at the southern hemisphere with the larger loss cone. Simulations including nonlinear pitch angle scattering by the whistler‐mode waves show rapid (tens of milliseconds) electron flux modulation related to the wave subpacket structures by repeated interactions within a discrete wave element. The difference in the nonlinear whistler instability in the two hemispheres should enhance the electron precipitation, which, along with the direct impact effects of solar wind, contributes to Mercury's surface–magnetosphere coupling. Electrons hitting the planet's surface may be a possible factor in the formation of water through the formation of hydroxyl groups.

Arase Observation of Simultaneous Electron Scatterings by Upper‐Band and Lower‐Band Chorus Emissions

AbstractThis study reports a relation between electron flux modulations and chorus emissions by using correlation analysis. On April 18, 2017, Arase observed an enhancement of electron fluxes and intensification of banded chorus emissions at the same time. A result of the analysis shows that both the upper‐band and lower‐band chorus emissions have good correlations with field‐aligned electron fluxes that satisfy their resonance conditions. This indicates simultaneous interactions with both the emission bands and electrons, resulting in electron pitch‐angle scattering toward the magnetic field direction. In addition, low‐energy electron fluxes in the perpendicular direction also show positive correlations with the chorus intensities, probably because the chorus emissions are modulated by a fluctuation of perpendicular low‐energy electron fluxes.

Simultaneous Observations of Localized and Global Drift Resonance

AbstractIn this study, we present Van Allen Probe observations showing that seed (hundreds of keV) and core ( 1 MeV) electrons can resonate with ultra‐low‐frequency (ULF) wave modes with distinctive m values simultaneously. An unusual electron energy spectrogram with double‐banded resonant structure was recorded by energetic particle, composition, and thermal plasma (ECT)‐magnetic electron ion spectrometer (MagEIS) and, meanwhile, boomerang stripes in pitch angle spectrogram appeared at the lower energy band. A localized drift resonance with m = 10 wave component was responsible for the resonant band peaked at ∼200 keV while a global drift resonance with m = 3 component gave rise to the upper band resonance peaked at ∼1 MeV. Time‐Of‐Flight on boomerang stripes suggested that the localized drift resonance with ∼200 keV electrons was confined within the plasmaspheric plume. Electron flux modulations were reproduced by numerical simulations in good consistency with the observations, supporting the scenario that localized and global drift resonance could coexist in the outer belt electron dynamics simultaneously.

Origin of Electron Boomerang Stripes: Localized ULF Wave‐Particle Interactions

AbstractUltralow frequency (ULF) wave‐particle interactions play a significant role in the radiation belt dynamic process, during which drift resonance can accelerate and transport energetic electrons in the outer radiation belt. Observations of wave‐electron drift resonance are characterized by quasiperiodic straight or “boomerang‐shaped” stripes in the pitch angle spectrogram. Here we present an ULF wave event on 1 December 2015, during which both kinds stripes were observed by Van Allen Probes A and B, respectively. Using the time‐of‐flight technique based on the pitch angle dependence of electron drift velocities, the “boomerang‐shaped” stripes are inferred to originate from straight stripes at the time and location covered by Probe B. Given that straight stripes were indeed observed by Probe B, our observations strongly support the charged particle interacting with azimuthally localized ULF waves. A new method is provided to identify the location of ULF wave‐particle interaction on the basis of remote observations of electron flux modulations.

BeiDa Imaging Electron Spectrometer observation of multi-period electron flux modulation caused by localized ultra-low-frequency waves

Abstract. We present multi-period modulation of energetic electron flux observed by the BeiDa Imaging Electron Spectrometer (BD-IES) on board a Chinese navigation satellite on 13 October 2015. Electron flux oscillations were observed at a dominant period of ∼190 s in consecutive energy channels from ∼50 to ∼200 keV. Interestingly, flux modulations at a secondary period of ∼400 s were also unambiguously observed. The oscillating signals at different energy channels were observed in sequence, with a time delay of up to ∼900 s. This time delay far exceeds the oscillating periods, by which we speculate that the modulations were caused by localized ultra-low-frequency (ULF) waves. To verify the wave–particle interaction scenario, we revisit the classic drift-resonance theory. We adopt the calculation method therein to derive the electron energy change in a multi-period ULF wave field. Then, based on the modeled energy change, we construct the flux variations to be observed by a virtual spacecraft. The predicted particle signatures well agree with the BD-IES observations. We demonstrate that the particle energy change might be underestimated in the conventional theories, as the Betatron acceleration induced by the curl of the wave electric field was often omitted. In addition, we show that azimuthally localized waves would notably extend the energy width of the resonance peak, whereas the drift-resonance interaction is only efficient for particles at the resonant energy in the original theory.

Remote Detection of Drift Resonance Between Energetic Electrons and Ultralow Frequency Waves: Multisatellite Coordinated Observation by Arase and Van Allen Probes

AbstractWe report the electron flux modulations without corresponding magnetic fluctuations from unique multipoint satellite observations of the Arase (Exploration of Energization and Radiation in Geospace) and the Van Allen Probe (Radiation Belt Storm Probe [RBSP])‐B satellites. On 30 March 2017, both Arase and RBSP‐B observed periodic fluctuations in the relativistic electron flux with energies ranging from 500 keV to 2 MeV when they were located near the magnetic equator in the morning and dusk local time sectors, respectively. Arase did not observe Pc5 pulsations, while they were observed by RBSP‐B. The clear dispersion signature of the relativistic electron fluctuations observed by Arase indicates that the source region is limited to the postnoon to the dusk sector. This is confirmed by RBSP‐B and ground‐magnetometer observations, where Pc5 pulsations are observed to drift‐resonate with relativistic electrons on the duskside. Thus, Arase observed the drift‐resonance signatures “remotely,” whereas RBSP‐B observed them “locally.”

Interactions of energetic electrons with ULF waves triggered by interplanetary shock: Van Allen Probes observations in the magnetotail

AbstractWe present in situ observations of a shock‐induced substorm‐like event on 13 April 2013 observed by the newly launched Van Allen twin probes. Substorm‐like electron injections with energy of 30–500 keV were observed in the region from L∼5.2 to 5.5 immediately after the shock arrival (followed by energetic electron drift echoes). Meanwhile, the electron flux was clearly and strongly varying on the ULF wave time scale. It is found that both toroidal and poloidal mode ULF waves with a period of 150 s emerged following the magnetotail magnetic field reconfiguration after the interplanetary (IP) shock passage. The poloidal mode is more intense than the toroidal mode. The 90° phase shift between the poloidal mode Br and Ea suggests the standing poloidal waves in the Northern Hemisphere. Furthermore, the energetic electron flux modulations indicate that the azimuthal wave number is ∼14. Direct evidence of drift resonance between the injected electrons and the excited poloidal ULF wave has been obtained. The resonant energy is estimated to be between 150 keV and 230 keV. Two possible scenaria on ULF wave triggering are discussed: vortex‐like flow structure‐driven field line resonance and ULF wave growth through drift resonance. It is found that the IP shock may trigger intense ULF wave and energetic electron behavior at L∼3 to 6 on the nightside, while the time profile of the wave is different from dayside cases.

Van Allen Probes observation of localized drift resonance between poloidal mode ultra‐low frequency waves and 60 keV electrons

We present NASA Van Allen Probes observations of wave‐particle interactions between magnetospheric ultra‐low frequency (ULF) waves and energetic electrons (20–500 keV) on 31 October 2012. The ULF waves are identified as the fundamental poloidal mode oscillation and are excited following an interplanetary shock impact on the magnetosphere. Large amplitude modulations in energetic electron flux are observed at the same period (≈ 3 min) as the ULF waves and are consistent with a drift‐resonant interaction. The azimuthal mode number of the interacting wave is estimated from the electron measurements to be ~40, based on an assumed symmetric drift resonance. The drift‐resonant interaction is observed to be localized and occur over 5–6 wave cycles, demonstrating peak electron flux modulations at energies ~60 keV. Our observation clearly shows electron drift resonance with the fundamental poloidal mode, the energy dependence of the amplitude and phase of the electron flux modulations providing strong evidence for such an interaction. Significantly, the observation highlights the importance of localized wave‐particle interactions for understanding energetic particle dynamics in the inner magnetosphere, through the intermediary of ULF waves.

Pulsating auroral electron flux modulations in the equatorial magnetosphere

In this study, we present the first in situ continuous measurements of electron flux modulations in the near‐equatorial magnetosphere correlated with pulsating aurora (PA) observations. The contested conjecture that the source of these electrons originates near the equator, made decades ago using sounding rocket data, has now been confirmed using this data. We compared the frequencies of equatorial electron flux pulsations and PA luminosity fluctuations at their ionospheric footprint, using simultaneous satellite‐ and ground‐based data from GOES 13 and Time History of Events and Macroscale Interactions during Substorms (THEMIS) instrumentation. Observations of PA were obtained on 15 March 2008 using a THEMIS All‐Sky Imager (ASI) located in northern Canada. The field line footprint of the geostationary GOES 13 satellite, mapped down to the ionosphere at ∼100 km, falls within the field‐of‐view of the ASI. We examined electron flux data from the Magnetospheric Electron Detector (MAGED) on GOES 13, in the energy range of 30 to 50 keV, by computing an array of the correlation coefficients between the pixel luminosity for each individual pixel of the ASI images and the flux measurements at the satellite. The results reveal a direct correlation between diffuse luminosity fluctuation periods near the ground and particle pulsation periods. The time variance between the two data sets was examined in order to explore the validity of the equatorial source region premise. The resulting time lag of < 1 s in the PA measurements is consistent with this claim. We also report on a preliminary quantification of the loss cone using the MAGED telescope response functions.

Simultaneous observations of quasi‐periodic ELF/VLF wave emissions and electron precipitation by DEMETER satellite: A case study

We present results of case studies of quasi‐periodic (QP) ELF/VLF hiss emissions detected onboard the DEMETER satellite. Three events with simultaneous periodic modulation in VLF wave intensity and energetic electron precipitation are found. In each event we observe exact coincidence of one or two busts of VLF wave intensity with energetic electron precipitation peaks. To our knowledge, such observations made onboard satellites have not been reported earlier. All events are observed at fairly quiet geomagnetic conditions (Kp <3). The dynamic spectrum of the VLF waves in these QP events was characterized by a regular frequency increase in each burst, and the repetition period was less than or about 20 s. These features allow us to suggest that the observed events belong to the QP2‐class, i.e., events which are not associated with geomagnetic pulsations. We also analyze energetic electron data from NOAA‐17 spacecraft which has helio‐synchronous circular orbit similar to DEMETER spacecraft and measured in the same region of the magnetosphere within 30 min for the analyzed events. NOAA‐17 data confirm that the QP emissions were detected by DEMETER in the region of isotropization of energetic electrons, which is typically associated with the development of the cyclotron instability. Modulation of electron flux with a period close to the QP emission period is observed in two events. Based on the observed correlation between bursts of wave intensity and energetic particle flux, we estimate the location and spatial extent of the source region for QP emissions.

Photoemission measurements of temperature in pulsed laser heating of various materials

The possibilities for the photoemission method of measuring the temperature of various materials heated by millisecond laser pulses have been investigated. The temperature of graphite, tungsten, tantalum, silicon plates, and silicon dioxide films was determined experimentally with a time resolution of 1 μs within the range 1200-2900 K. Introduction. Measurement of the temperature of fast processes is a complex problem in itself, and it is fur- ther aggravated if the temperature of an object changes from room to 3000 K at a rate of 10 8 K ⁄ s and there is no possibility of taking account of the accompanying change in the emissivity. In this case, to measure the temperature of the object, use can be made of the photoemission method in which modulation with a high-frequency electronic flux rather than a low one is produced, and one can compare the energy distribution of photoelectrons in two broad spec- tral intervals, one of which being part of the other, with the difference between the measured temperature and the ther- modynamic one turning out to be insignificant. The procedural error of such measurements does not exceed 0.3% at a surface emissivity approximately equal to 0.4. This property was revealed experimentally (1) and later confirmed theo- retically (2, 3). Measurement of the temperature of an object by the photoemission method from the spectra of photoelec- trons released by thermal radiation is based on the dependence of the energy distribution of photoelectrons of the ex- ternal photoeffect on the energy distribution in the object's radiation spectrum. In this case the gas of photoelectrons near the emitting body surface is the thermometric substance, and its temperature can be determined from the cut-off voltage of the volt-ampere characteristics of a photoelectronic device, for example, a photomultiplier for light fluxes normalized by the photocurrent (1) or by the change in the energy distribution of photoelectrons as a function of temperature (2, 3). As the body temperature increases, the maximum of the spectral energy distribution of its radiation is dis- placed to the side of short wavelengths (the Wien displacement), with the maximum of energy distribution of photo- electrons being displaced to the side of high energies. In this case, the body temperature is determined by the parameter k, which is the ratio of the photocurrent I 0 measured in the absence of the retarding field to the partially blocked photocurrent I bl measured in the presence of the retarding field in the cathode region of the photomultiplier. Since the relative content of electrons of different energies in this region is independent of the magnitude of the light flux arriving at the device, within the boundaries of linearity of its light characteristic k = f(T) (3). The process of measuring the body temperature is reduced to the recording of a two-level oscillogram of the amplitude of the voltage pulse at the photomultiplier anode U(t) in the process of electron flux modulation in the cath- ode region of the photomultiplier by rectangular pulses that are negative relative to the photocathode. Using these lev- els of the photomultiplier signal, the function k(T) is calculated in each period of the modulated signal, and using the calibrating function T(k) obtainable with the use of the standard thermal radiation, one determines the dynamics of the temperature of the investigated body T(t). The simplicity of the electron flow modulation in the cathode region of the photomultiplier with a frequency of 1 MHz allows one to make such measurement with a time resolution of 1 μs. The possibilities of the indicated method in measuring the temperature of fast thermal processes is illustrated below using several examples. Using an FMK-01 pulse photoemission pyrometer, we measured the temperature of sev-

Observations at geosynchronous orbit of a persistent Pc5 geomagnetic pulsation and energetic electron flux modulations

Abstract. A long lasting narrow-band (4–7 mHz) Pc5 fluctuation event at geosynchronous orbit is presented through measurements from GOES-8 and GOES-10 and the response of energetic electrons with drift frequencies close to the narrow-band pulsation frequency is monitored through a spectral analysis of flux data from the LANL-SOPA energetic electron instrument. This analysis shows electron flux modulations at the magnetospheric pulsation's frequency as well as at various other frequencies in the Pc5 range, related to the particles' drift-frequencies and their harmonics. A drift resonance effect can be seen, with electron flux modulation becoming more evident in the energy channels of electrons with drift frequencies closer to the wave frequency; however no net increase or decrease in energetic electron flux is observed, indicating that the net energy transfer and transport of electrons is not significant. This Pc5 event has a long duration, being observed for more than a couple of days at geosynchronous orbit over several traversals of the two GOES satellites, and is localized in azimuthal extent. Spectral analysis shows that most of the power is in the transverse components. The frequency of the narrow-band event, as observed at geosynchronous orbit shifts during the time of the event from 7±0.5 mHz to about 4±0.5 mHz. On the ground, CARISMA magnetometers record no distinct narrow-band fluctuation in the magnetic field, and neither does Geotail, which is traversing the outer magnetosphere a few RE further out from geosynchronous orbit, at the same UT and LT that GOES-8 and -10 observe the pulsations, suggesting that that there is no connection to external fluctuations originating in the solar wind. An internal generation mechanism is suggested, such as could be provided by energetic ring current particles, even though conclusive evidence could not be provided for this particular event. Through a statistical study, it is found that this event belongs to a class of similar events, occurring predominantly in the post-noon region in the inner magnetosphere.

Ultralow frequency modulation of energetic particles in the dayside magnetosphere

Energetic electron and ion (electrons: 30 keV to 500 keV, protons: 30 keV to 1.5 MeV) flux variations associated with ultralow frequency (ULF) waves in the dayside magnetosphere were observed during the CLUSTER's perigee pass near 0900 MLT on Oct. 31, 2003. The ULF modulation terminated where higher frequency fluctuations appeared, as the CLUSTER spacecraft entered the plasmasphere boundary layer (PBL) where the plasma ion density was elevated. In the region from L ∼ 5.0 to 10, the periods of the ion flux modulation and the electron flux modulation are same but out‐of‐phase. The observed magnetic ULF pulsations are dominated by the toroidal mode, along with a relatively weaker poloidal wave. A 90° phase shift between the radial electric field and the azimuthal magnetic field indicates that dominating toroidal standing waves observed at the southern hemisphere are a fundamental harmonic. This study shows that the modulation of the electron flux is dominated by the toroidal mode in the region of L > 7.5. The observations made in this analysis suggest the excitation of the energetic electron drift resonance at around 127 keV.

Modulation of the growth of auroral kilometric radiation by electromagnetic ion cyclotron waves

The role of electromagnetic ion cyclotron (EMIC) waves in the stimulation of auroral kilometric radiation is addressed in this study. Observations of the modulation of electron flux and energy due to EMIC/electrostatic ion cyclotron waves within the auroral kilometric radiation (AKR) source region have been reported in the past. These modulations produce in turn oscillations of the electron phase space density and therefore lead to fluctuations of AKR growth rate that may translate along the magnetic field line at the group velocity of the stimulating waves. For a model electron “horseshoe” distribution function, we use the theory of the cyclotron maser instability to investigate how this process might influence the AKR wave spectrum and fine structure.

Further study of flickering auroral roar emission: 1. South Pole observations

Hughes and LaBelle (2001) reported a single example of a new geophysical phenomenon: ∼10 Hz modulation of auroral radio emissions near twice the auroral ionospheric electron gyrofrequency. They called this phenomenon flickering auroral roar and suggested that it is related to flickering aurora, which results from ∼10 Hz modulation of the precipitating auroral electrons. Observations at South Pole Station during 2003 using a new high‐bandwidth receiving system have yielded 10 examples of flickering roar emissions. Although 10 examples is still a small number for statistics, these observations considerably extend previous knowledge of this phenomenon which was based on a single example. On the basis of the 2003 South Pole data set, flickering auroral roar accounts for only about 1–2% of auroral roar in number of seconds, but ∼20% of auroral roar events have some flickering feature. The observed modulation frequencies range from ∼3 to 30 Hz. The 10‐ to 20‐Hz modulations, which correspond to about 65% of the time when flickering roar occurs, are much more common than the higher‐frequency 20‐ to 30‐Hz modulations, which correspond to about 20% of the time when flickering roar occurs. These frequencies compare favorably with optical observations of auroral emissions, rocket observations of electron flux modulations, and modeling results. If these frequencies correspond to the oxygen gyrofrequency where electrons and ion cyclotron waves interact, the 3‐ to 30‐Hz frequency range would imply sources at altitudes of 1500–10,500 km. Six of the ten flickering roar examples occurred during substorm expansion phase as defined from local magnetometer data, in contrast to flickering aurora, which is usually observed after the onset of auroral breakup.

Further study of flickering auroral roar emission: 2. Theory and numerical calculations

Two recent papers report ground‐based observations of ∼3–30 Hz pulsations in the amplitude of 2fce auroral roar radio emissions. These pulsations occur in groups which last for ∼1 s with adjacent pulsation groups spaced from one to several seconds. We put forth that these pulsations reflect periodic modulation of precipitating auroral electron fluxes, which could include periodic downward field‐aligned bursts (FABs) and periodically modulated inverted‐V electron precipitation, similar to those that could account for flickering aurora. We calculate time and frequency variations in the growth rate of Z‐mode waves in the ionosphere for two different models of time‐varying electron distribution functions, one corresponding to acceleration by electromagnetic ion cyclotron waves (EMIC) and the other corresponding to a simple time‐varying accelerating potential (TVP). On the basis of these numerical calculations, the reported characteristics of ∼10 Hz flickering roar appear consistent with modulations induced in the electron distribution function via interaction with EMIC waves, since the modulation associated with EMIC waves results in flickering of only the lower portion of the auroral roar frequency band, as in most of the observations. The few observed cases of higher‐frequency flickering roar, at ∼20–30 Hz, fall above the O+ cyclotron frequency for the altitude range on interest, and may represent a different source of electron flux modulation such as a varying electrostatic potential. The radio observations provide an additional means of probing flickering phenomenon and in particular may put constraints on the form of modulations of the electron distribution function at the auroral roar source height of a few hundred kilometers.

A possible generation mechanism of temporal and spatial structures of flickering aurora

Optical observations of flickering aurora by a high‐speed imaging photometer system were carried out at Syowa Station in 1998. A comparison between observed parameters of flickering aurora and theoretical values of dispersive Alfvén waves indicates that observed flickering aurora would be produced by electron flux modulations by electromagnetic ion cyclotron waves or inertial Alfvén waves in the auroral acceleration region located over the altitude range of ∼2000–5000 km. Interference wave patterns of two dispersive Alfvén waves in a resonance cone can explain the observed temporal and spatial structures of flickering aurora; flickering columns (or spots) remain in almost the same location during their lifetime and that their shapes become indistinguishable every half flickering period at the timing of the interchange of the bright and dark columns (or spots).

Direct comparison of pulsating aurora observed simultaneously by the FAST satellite and from the ground at Syowa

We have made a direct comparison of a pulsating aurora observed simultaneously from the ground at Syowa in Antarctica and onboard the FAST satellite (∼3100 km altitude). The auroral form appeared as east‐west‐aligned bands consisting of two different types: a poleward moving pulsation and a standing mode pulsation, each with a period of ∼5 sec. The aurora occurs within the region of an inverted‐V structure of lower energy (0.1–1 keV) electron precipitation. The two different types of pulsating aurora are separated in space by a narrow gap in the inverted‐V potential structure. Spatial and temporal variations of the down‐going high‐energy (>5 keV) electron flux show a one‐to‐one correspondence with the optical pulsating aurora. The down‐going high‐energy (1–10 keV) ion flux modulation is out of phase (anti‐correlated) with the high‐energy electron flux modulation. These features suggest that the precipitating high‐energy electrons, which produce the pulsating aurora, are modulated by the oscillation of the field‐aligned electric field located above FAST.

Periodic variations of magnetosheath energetic electron flux associated with global Pc5 pulsations

Measurements from the Wind spacecraft in the solar wind, the Geotail spacecraft in the magnetosheath, and multiple magnetometers on the ground are combined to study a unique electron flux modulation event in the magnetosheath that occurred during an interval of global Pc5 waves. The electron event is characterized by a Pc5‐band oscillation occurring in the magnetic‐field‐aligned component of the electron flux (energy > 38 keV) while the local magnetic field and plasma density remained unperturbed. During this event the whole magnetosphere oscillated as inferred from magnetic field recorded at the CANOPUS, IMAGE, and 210° MM chains. At the ground stations that are mapped to the dayside and duskside magnetosphere, we find a one‐to‐one correspondence of the peaks in the horizontal component to those in the electron flux. At the stations mapped to the dawnside magnetosphere the observed frequency is twice that of the electron flux oscillation. The time‐lagged solar wind density and velocity at Wind were constant, which leads us to exclude the possibility that the waves were driven by ram pressure variations upstream of the bow shock. The Kelvin‐Helmholtz (K‐H) instability on the magnetopause is the more probable source of the Pc5 waves because (1) the solar wind velocity was ∼730 km s−1, well above the average value; (2) the ground‐based observations show that the Pc5 amplitude decreases with distance from the magnetopause; and (3) the dawnside and duskside magnetospheric flanks show oppositely polarized waves. The electron flux oscillation in the magnetosheath can be explained by intermittent magnetic connection between the spacecraft and the dawnside pulsating magnetopause. The ∼60 keV protons are continuously streaming throughout the whole interval, providing evidence for a continuously active source and permanent leakage through a tangential magnetopause discontinuity. It is worth noticing that at progressively higher energies the energetic particle angular distributions are gradually more isotropic because at higher energies the particles are strongly scattered in the magnetosheath.

Beam‐induced electron modulations observed during TSS 1R

We report on modulations of electron fluxes at megahertz frequencies measured by the Shuttle Potential and Return Electron Experiment (SPREE) during fast pulsed electron gun (FPEG) beam experiments conducted after the tether break event of the Tethered Satellite System Reflight. Six intervals of sustained modulations were identified while FPEG emitted a 100 mA beam of 1 kev electrons. During five events the beam pitch angle αB was near 90° and the modulations were near even or odd half harmonics of the electron gyrofrequency ƒce. In the sixth event with 60° ≥ αB ≥ 45°, electron modulations were near estimated values of the electron plasma frequency ƒpe and 2ƒpe. Whenever SPREE detected beam electrons modulated at a given frequency, secondary electrons were also modulated at the same frequency over a broad range of energies. Occasionally, some secondary electrons were modulated simultaneously at a second frequency. Multiple frequencies were related as ratios of low integers. In one case the beam electrons were simultaneously modulated at 0.8 MHz and 1.25 kHz. SPREE measurements suggest that the beam electrons propagate in cylindrical shells whose inner edge is marked by steep spatial gradients in fluxes at 1 keV [Hardy et al., 1995]. Inside the shell, electron distribution functions have positive slopes ∂ƒ/∂v⊥ > 0 at velocities near that of the beam. Velocity space gradients act as free‐energy sources to drive cavity modes that alter the instantaneous guiding centers of electrons causing SPREE to sample alternating parts of the beam cylinder's inner edge. Associated time‐varying electric fields also modulated the fluxes of secondary electrons reaching SPREE. Other cavity modes may be excited through nonlinear processes [Calvert, 1982], With αB far from 90°, electrons in the beam cylinder evolved toward bump‐on‐tail distributions to excite large‐amplitude Langmuir modulations at ƒpe and its harmonics [Klimas, 1983]. Low‐frequency modulations are attributed to electron interactions with ion acoustic‐like waves generated as the beam moved across magnetic field lines in the ionosphere at supersonic speeds.