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The coronal electron density distribution determined from dual-frequency ranging measurements during the 1991 solar conjunction of the Ulysses spacecraft

Dual-frequency ranging and Doppler measurements were conducted in support of the Ulysses Solar Corona Experiment (SCE) at and around the spacecraft's first solar conjunction in 1991 August. The differential group delay time between range codes on the two downlink carrier signals at the wavelengths 13.1 and 3.6 cm, a direct measure of the total electron content between spacecraft and ground station, was used to derive the electron density distribution in the solar corona. Linear power-law representations of the coronal electron density were derived for the range of solar distances from 4 solar radii to 40 solar radii on both sides of the Sun. The corona was found to be very nearly symmetric; the radial falloff exponent being 2.54 +/- 0.05 for occultation ingress (east solar limb) and 2.42 +/- 0.05 for egress (west limb), respectively. The departure of these exponents from the inverse equare relation implies that significant solar wind acceleration is occurring within the radial range of the observations. The electron density level was found to be considerably lower than that observed during the 1988 December solar occultation of Voyager 2. Although the smoothed sunspot number R(sub z) (a standard indicator of solar activity) was almost the same in 1988 December and 1991 August, the mean electron density at 20 solar radii was found to be 1.7 +/- 0.1 x 10(exp 3)/cu cm during the Ulysses conjunction, a decline by almost a factor of 4 from the value obtained during the Voyager conjunction.

Bird, M. K.↗

Degradation of Leakage Currents and Reliability Prediction for Tantalum Capacitors

Two types of failures in solid tantalum capacitors, catastrophic and parametric, and their mechanisms are described. Analysis of voltage and temperature reliability acceleration factors reported in literature shows a wide spread of results and requires more investigation. In this work, leakage currents in two types of chip tantalum capacitors were monitored during highly accelerated life testing (HALT) at different temperatures and voltages. Distributions of degradation rates were approximated using a general log-linear Weibull model and yielded voltage acceleration constants B = 9.8 +/- 0.5 and 5.5. The activation energies were Ea = 1.65 eV and 1.42 eV. The model allows for conservative estimations of times to failure and was validated by long-term life test data. Parametric degradation and failures are reversible and can be annealed at high temperatures. The process is attributed to migration of charged oxygen vacancies that reduce the barrier height at the MnO2/Ta2O5 interface and increase injection of electrons from the MnO2 cathode. Analysis showed that the activation energy of the vacancies' migration is ~ 1.1 eV.

acceleration factors↗

Optically thick ablation fronts

The physical characteristics of optically thick ablation fronts such as interstellar clouds are analyzed. Attention is given to cold clumps in both planar and spherical geometries and modifications caused by accelerations in a gravitational field or by evaporation of the clumps when encountered hot gas. The effects of ablation on the appearance of the Rayleigh-Taylor instability are examined in both linear and nonlinear regimes. The results of the calculations are applied to the astrophysical phenomena of cold clumps immersed in a supersonic flow, optically thick jets, and ablation in stellar envelopes. Evaporation in an optically thick front is projected to be orders of magnitude larger than evaporation in electron-conduction fronts in optically thin conditions. The optically thick processes could then be useful for modeling flows from, e.g., newly formed stars and active galactic nuclei.

Konigl, A.↗

Electromagnetic electron beam instabilities - Hot, isotropic beams

This paper considers the linear theory of electromagnetic instabilities driven by an electron beam in a homogeneous, nonrelativistic, Vlasov plasma. The beam is relatively hot, isotropic in its own frame, and streams parallel or antiparallel to a magnetic field B. Numerical solutions of the full dispersion equation for propagation parallel or antiparallel to B are presented, and the linear properties of the whistler heat flux and electron beam firehose instabilities are exhibited and compared. Under a broad range of parmameters the former mode has the lower beam speed threshold, and the larger maximum growth rate. In addition, it is demonstrated that, for a sufficiently large relative beam density, relative beam temperature, and plasma beta the whistler heat flux instability has a much lower beam speed threshold than the electrostatic electron beam instability. The application of these instabilities to first-order Fermi acceleration of electrons at space plasma shocks is discussed.

Gary, S. P.↗

Physics of Rotation Powered Pulsars and Their Nebulae

This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.

Arons, Jonathan↗

The X-Ray Polarization View of Mrk 421 in an Average Flux State as Observed By the Imaging X-Ray Polarimetry Explorer

Particle acceleration mechanisms in supermassive black hole jets, such as shock acceleration, magnetic reconnection, and turbulence, are expected to have observable signatures in the multiwavelength polarization properties of blazars. The recent launch of the Imaging X-Ray Polarimetry Explorer (IXPE) enables us, for the first time, to use polarization in the X-ray band (2–8 keV) to probe the properties of the jet synchrotron emission in high-synchrotron-peaked BL Lac objects (HSPs). We report the discovery of X-ray linear polarization (degree Π x = 15% ± 2% and electric vector position angle ψ x = 35° ± 4°) from the jet of the HSP Mrk 421 in an average X-ray flux state. At the same time, the degree of polarization at optical, infrared, and millimeter wavelengths was found to be lower by at least a factor of 3. During the IXPE pointing, the X-ray flux of the source increased by a factor of 2.2, while the polarization behavior was consistent with no variability. The higher level of Π x compared to longer wavelengths, and the absence of significant polarization variability, suggest a shock is the most likely X-ray emission site in the jet of Mrk 421 during the observation. The multiwavelength polarization properties are consistent with an energy-stratified electron population, where the particles emitting at longer wavelengths are located farther from the acceleration site, where they experience a more disordered magnetic field.

acceleration of particles↗

Complex vestibular macular anatomical relationships need a synthetic approach

Mammalian vestibular maculae are anatomically organized for complex parallel processing of linear acceleration information. Anatomical findings in rat maculae are provided in order to underscore this complexity, which is little understood functionally. This report emphasizes that a synthetic approach is critical to understanding how maculae function and the kind of information they conduct to the brain.

Non-NASA Center↗

Simulated Galactic Cosmic Ray and Solar Particle Event Radiation Effects on Inflatable Habitat, Composite Habitat, Space Suit and Space Hatch Cover Materials

The effect of particle radiation representative of galactic cosmic ray (GCR) and solar particle event (SPE) radiation on polymeric materials used in deep space mission environments is largely unknown. For NASA, this uncertainty represents an unquantified mission risk. To better quantify this risk, selected polymeric materials used in inflatable habitats, composite habitats, space suits and space hatch covers are irradiated at the Brookhaven National Laboratory, after which changes in relevant end-use properties are measured. The irradiated materials are lightweight candidates having critical functions such as ripstops, permeation barriers, micrometeoroids and orbital debris (MMOD) shield layers and restraint layers.The effect of several types of particle radiation are evaluated. To evaluate GCR effects, high-energy (1 GeV) protons and iron nucleons are used. To evaluate SPE effects, intermediate energy (ca. 20 to 40 MeV) protons are used. In addition, two mission scenarios are evaluated: a Mars mission cycle (space suit materials) and a worst-case 50 year deep space mission cycle (all materials). Lastly, a common polymer (high density polyethylene (HDPE)) is subjected to accelerated aging and radiation exposure to determine if a combined physical aging/radiation effect exists.The level of radiation induced property change observed in this study after exposure of polymers to kGy levels of intermediate and high energy ions is often significant and is quantitatively comparable to the level of change reported for similar materials exposed to MGy levels of low energy protons, electrons and gamma-radiation. This suggests that intermediate and high energy ions encountered in space may cause more damage than low energy forms of radiation due to displacement and linear energy transfer (LET) effects. For these reasons, it is recommended that final approval for mission use be made by the appropriate NASA material and structural review boards to ensure radiation induced changes in candidate materials do not interfere with their engineering function in the intended mission application. Since the materials tested in this report received doses exceeding actual mission doses, the results are considered conservative as a first approximation. However, caution must be exercised when evaluating radiation effects in the absence of other secondary factors know to contribute to degradation. In the addition to radiation type and energy, the results presented in this study show that molecular composition, orientation, stress and physical aging can also contribute to or influence degradation. Other factors such as polymer formulation, secondary radiation effects, stress, exposure to elevated temperature, thermal cycling and exposure to ozone were not investigated here, but must be considered when performing a comprehensive evaluation of a polymeric materials suitability for service in a space radiation environment. Only when the total sum of these factors operating in concert with radiation are accounted for, can accurate assessments of a material's suitability be made.

Jess M. Waller↗

Micromachined TWTs for THz Radiation Sources

The Terahertz (THz) region of the electromagnetic spectrum (about 300 - 3000 GHz in frequency or about 0.1 - 1 mm free space wavelength) has enormous potential for high-data-rate communications, spectroscopy, astronomy, space research, medicine, biology, surveillance, remote sensing, industrial process control, etc. It has been characterized as the most scientifically rich, yet under-utilized, region of the electromagnetic spectrum. The most critical roadblock to full exploitation of the THz band is lack of coherent radiation sources that are powerful (0.001 - 1.0 W continuous wave), efficient (> 1%), frequency agile (instantaneously tunable over 1% bandwidths or more), reliable, and comparatively inexpensive. To develop vacuum electron device (VED) radiation sources satisfying these requirements, fabrication and packaging approaches must be heavily considered to minimize costs, in addition to the basic interaction physics and circuit design. To minimize size of the prime power supply, beam voltage must be minimized, preferably 10 kV. Solid state sources satisfy the low voltage requirement, but are many orders of magnitude below power, efficiency, and bandwidth requirements. On the other hand, typical fast-wave VED sources in this regime (e.g., gyrotrons, FELs) tend to be large, expensive, high voltage and very high power devices unsuitable for most of the applications cited above. VEDs based on grating or inter-digital (ID) circuits have been researched and developed. However, achieving forward-wave amplifier operation with instantaneous fractional bandwidths > 1% is problematic for these devices with low-energy (< 15 kV) electron beams. Moreover, the interaction impedance is quite low unless the beam-circuit spacing is kept particularly narrow, often leading to significant beam interception. One solution to satisfy the THz source requirements mentioned above is to develop micromachined VEDs, or "micro-VEDs". Among other benefits, micro-machining technologies provide superior high frequency wall conductivity as a result of superior surface smoothness compared with conventional mechanical or electric discharge machining approaches. Micro-VED technologies are already being applied to the development of millimeter-wave klystrons at Stanford Linear Accelerator Center and submillimeter-wave klystrons at the University of Leeds. We are investigating the use of micro-machining technologies to develop THz regime TWTs, with emphasis on folded-waveguide TWTs. The folded-waveguide TWT (FW-TWT) has several features that make it attractive for THz-regime micro-VED applications. It is a relatively simple circuit to design and fabricate, it is amenable to precision pattern replication by micro-machining, and it is has been demonstrated capable of forward-wave amplification with appreciable bandwidth. We are conducting experimental and computational studies of micro-VED FW-TWTs to examine their feasibility for applications at frequencies from 200 - 1000 GHz.

Booske, John H.↗

Evaluation of 10V Chip Polymer Tantalum Capacitors for Space Applications

Due to low ESR and safe failure mode, new technology chip polymer tantalum capacitors (CPTC) have gained popularity in the electronics design community, first in commercial applications, and now in hi-rel and space systems. The major drawbacks of these parts are high leakage currents, degradation under environmental stresses, and a relatively narrow temperature range of operating and storage conditions. Several studies have shown that a certain amount of moisture in polymer cathodes is necessary for a normal operation of the parts. This might limit applications of CPTCs in space systems and requires analysis of long-term exposure to deep vacuum conditions on their performance and reliability. High leakage currents and limited maximum operational temperature complicate accelerated testing that is necessary to assess long-term reliability and require new screening and qualification procedures for quality assurance. A better understanding of behavior of CPTCs as compared to traditional, MnO2, capacitors is necessary to develop adequate approaches for QA system for space applications. A specific of CPTCs is that different materials and processes might be used for low-voltage (10 V and less) and high-voltage (above 10 V) capacitors, so performance and degradation processes in these groups require separate analysis. In this work, that is a part of the NASA Electronic Parts and Packaging (NEPP) program, degradation of AC and DC characteristics under environmental stresses at different temperatures and voltages have been studied in nine lots of commercial and automotive grade capacitors rated to 10 V. Results of analysis of leakage currents, high temperature storage (HTS) up to 5000 hrs in vacuum and air at different temperatures, and Highly Accelerated Life Testing (HALT) in the range from 85 C to 145 C are presented. Temperature and voltage acceleration factors were calculated based on approximation of distributions of degradation rates with a general log-linear Weibull model. Mechanisms of degradation and failures, and requirements for screening and qualification testing are discussed.

Tantalum Capacitors↗

A First-Principles Model Based on Saturation of the Electron Cyclotron Drift Instability for Electron Transport in Hydrodynamics Simulations of Hall Thruster Plasmas

We present a computational model based on the hypothesis that the higher-than-expected electron mobility across magnetic field lines observed in Hall thrusters is due to the growth and eventual saturation of the electron cyclotron drift instability. The key improvement of this model with respect to previous work is that it decouples the saturation of the instability from the correlation that exists between mobility and magnitude of the wave perturbations in linear theory, thereby enabling first-principles simulations. The model has been incorporated in the 2-D (r-z) multi-fluids code Hall2De and simulations of the H6 thruster at 300 V, 20 A are numerically stable and achieve a steady-state solution at a computational cost that is not significantly higher than previous Hall2De simulations. The computed location of the acceleration region is found to be within 10% of the length of the acceleration channel compared to that inferred by experiments. The simulations also capture well the plasma gradients along the channel centerline of this thruster. To further establish the validity of this model, we plan to conduct simulations of other thrusters and/or operating conditions.

Lopez Ortega, Alejandro↗

Evaluation of Automotive Grade Resistors for Space Flight

Over the past decade, electronic, electrical, and electromechanical (EEE) parts for space applications have undergone significant changes, largely driven by CubeSat and commercial space developers pushing the boundaries on the utilization of commercial parts in space. Global product shortages and shipping delays are still impacting space flight project deadlines. Many projects have turned to automotive grade resistors as an alternate to their MILSPEC counterparts to fulfill requirements. In addition, automotive grade resistors may offer designers a wider range of parts to consider. A recent NASA study recommended the use of high-volume manufactured commercial components for space applications provided these components show evidence of stringent fabrication controls and thorough reliability monitoring practices. Automotive grade components have stringent qualification requirements per the Automotive Electronic Council (AEC). However, the end user usually does not have insight into the practices the manufacturer may use to reduce/eliminate infant mortality nor for compliance to all datasheet specifications. Screening, Life and Accelerated Life testing on a set of standard automotive-grade chip resistors is proposed to evaluate the reliability of these components. Requirements from both the AEC-Q (Automotive Electronic Council Qualification) and EEE-INST-002 (Instructions for EEE Parts Selection, Screening, Qualification, and Derating) for resistors is compared and discussed. The resistors have been tested by using a modified methodology from EEEINST-002 to evaluate their reliability for space flight projects. The findings of this study indicate that the underlying degradation mechanisms at rated temperature and power are best represented by power law models with a fitted exponent between 0 and 1. A linear model is more conservative which compensates for potential model uncertainty given the wide range of design and materials used in automotive resistors, while still providing useful long-term resistance drift estimates. No electrical anomalies or failures were observed throughout the 1000-hour Life Tests other than small in tolerance resistance drift aging. Degradation models were utilized to quantify and extrapolate the long-term resistance drift under operating conditions for the components. The models demonstrated that some automotive-grade resistors are likely to operate 10 years at nominal usage conditions while others might fail earlier.

Zainab Abdullahi↗

Type II Radio Bursts and Their Association With Coronal Mass Ejections in Solar Cycles 23 and 24

Context. Meter-wavelength type II solar radio bursts are thought to be the signatures of shock-accelerated electrons in the corona. Studying these bursts can give information about the initial kinematics, dynamics, and energetics of coronal mass ejections (CMEs) in the absence of white-light observations. Aims. We investigate the occurrence of type II bursts in solar cycles 23 and 24 and their association with CMEs. We also explore whether type II bursts might occur in the absence of a CME. Methods. We performed a statistical analysis of type II bursts that occurred between 200 and 25 MHz in solar cycles 23 and 24 and determined the temporal association of these radio bursts with CMEs. We categorized the CMEs based on their linear speed and angular width and studied the distribution of type II bursts with fast (≥500 km s−1 ), slow (<500 km s−1), wide (≥60◦), and narrow (<60◦) CMEs. We explored the dependence of type II bursts occurrence on the phases of the solar cycle. Results. Our analysis shows that during solar cycles 23 and 24, 768 and 435 type II bursts occurred, respectively. Of these, 79% were associated with CMEs in solar cycle 23, and 95% were associated with CMEs in solar cycle 24. However, only 4% and 3% of the total number of CMEs were accompanied by type II bursts in solar cycle 23 and 24, respectively. Most of the type II bursts in both cycles were related to fast and wide CMEs (48%). We also determined the typical drift rate and duration for type II bursts, which is 0.06 MHz s−1 and 9 min. Our results suggest that type II bursts dominate at heights ≈1.7−2.3±0.3 R . A clear majority have an onset height around 1.7 ± 0.3 R assuming the four-fold Newkirk model. Conclusions. The results indicate that most of the type II bursts had a white-light CME counterpart, but a few type II bursts lacked a clear CME association. There were more CMEs in cycle 24 than in cycle 23. However, cycle 24 contained fewer type II radio bursts than cycle 23. The onset heights of type II bursts and their association with wide CMEs reported in this study indicate that the early lateral expansion of CMEs may play a key role in the generation of these radio bursts.

Sun: activity↗

Evaluation of Automotive Grade Resistors for Space Flight

Over the past decade, electronic, electrical, and electromechanical (EEE) parts for space applications have undergone significant changes, largely driven by CubeSat and commercial space developers pushing the boundaries on the utilization of commercial parts in space. Global product shortages and shipping delays are still impacting space flight project deadlines. Many projects have turned to automotive grade resistors as an alternate to their MIL-SPEC counterparts to fulfill requirements. In addition, automotive grade resistors may offer designers a wider range of parts to consider. A recent NASA study recommended the use of high-volume manufactured commercial components for space applications provided these components show evidence of stringent fabrication controls and thorough reliability monitoring practices [1]. Automotive grade components have stringent qualification requirements per the Automotive Electronic Council (AEC). However, the end user usually does not have insight into the practices the manufacturer may use to reduce/eliminate infant mortality nor for compliance to all datasheet specifications. Screening, Life and Accelerated Life testing on a set of standard automotive-grade chip resistors is proposed to evaluate the reliability of these components. Requirements from both the AEC-Q (Automotive Electronic Council Qualification) and EEE-INST-002 (Instructions for EEE Parts Selection, Screening, Qualification, and Derating) for resistors is compared and discussed. The resistors have been tested by using a modified methodology from EEE-INST-002 to evaluate their reliability for space flight projects. The findings of this study indicate that the underlying degradation mechanisms at rated temperature and power are best represented by power law models with a fitted exponent between 0 and 1. A linear model is more conservative which compensates for potential model uncertainty given the wide range of design and materials used in automotive resistors, while still providing useful long-term resistance drift estimates. No electrical anomalies or failures were observed throughout the 1,000-hour Life Tests other than small in tolerance resistance drift aging. Degradation models were utilized to quantify and extrapolate the long-term resistance drift under operating conditions for the components. The models demonstrated that some automotive-grade resistors are likely to operate 10 years at nominal usage conditions while others might fail earlier.

Zainab Abdullahi↗

Plastic scintillator block as photon beam monitor for EGRET calibration

The EGRET (Energetic Gamma Ray Experiment Telescope) detector has been calibrated at SLAC (Stanford Linear Accelerator) and, to a lesser degree, at the MIT Bates Linear Accelerator Center. To monitor the photon beams for the calibration, a plastic scintillator block, 5 cm x 5 cm in cross section, 15 cm in length, and viewed by a single photomultiplier tube, was used for the entire beam energy range of 15 MeV to 10 GeV. The design operation, and method of analysis of the beam intensity are presented. A mathematical framework has been developed to treat the general case of a beam with multiphoton beam pulses and with a background component. A procedure to deal with the fluctuations of the beam intensity over a data-taking period was also developed. The photon beam monitor is physically sturdy, electronically steady, simple to construct, and easy to operate. Its major merits lie in its sheer simplicity of construction and operation and in the wide energy range it can cover.

Lin, Y. C.↗

A current disruption mechanism in the neutral sheet - A possible trigger for substorm expansions

A linear analysis is performed to investigate the kinetic cross-field streaming instability in the earth's magnetotail neutral sheet region. Numerical solution of the dispersion equation shows that the instability can occur under conditions expected for the neutral sheet just prior to the onset of substorm expansion. The excited waves are obliquely propagating whistlers with a mixed polarization in the lower hybrid frequency range. The ensuing turbulence of this instability can lead to a local reduction of the cross-tail current causing it to continue through the ionosphere to form a substorm current wedge. A substorm expansion onset scenario is proposed based on this instability in which the relative drift between ions and electrons is primarily due to unmagnetized ions undergoing current sheet acceleration in the presence of a cross-tail electric field. The required electric field strength is within the range of electric field values detected in the neutral sheet region during substorm intervals. The skew in local time of substorm onset location and the three conditions under which substorm onset is observed can be understood on the basis of the proposed scenario.

Lui, A. T. Y.↗

Long-term prediction test procedure for most ICs, based on linear response theory

Experimentally, thermal annealing is known to be a factor which enables a number of different integrated circuits (IC's) to recover their operating characteristics after suffering radiation damage in the space radiation environment; thus, decreasing and limiting long term cumulative total-dose effects. This annealing is also known to be accelerated at elevated temperatures both during and after irradiation. Linear response theory (LRT) was applied, and a linear response function (LRF) to predict the radiation/annealing response of sensitive parameters of IC's for long term (several months or years) exposure to the space radiation environment were constructed. Compressing the annealing process from several years in orbit to just a few hours or days in the laboratory is achieved by subjecting the IC to elevated temperatures or by increasing the typical spaceflight dose rate by several orders of magnitude for simultaneous radiation/annealing only. The accomplishments are as follows: (1) the test procedure to make predictions of the radiation response was developed; (2) the calculation of the shift in the threshold potential due to the charge distribution in the oxide was written; (3) electron tunneling processes from the bulk Si to the oxide region in an MOS IC were estimated; (4) in order to connect the experimental annealing data to the theoretical model, constants of the model of the basic annealing process were established; (5) experimental data obtained at elevated temperatures were analyzed; (6) time compression and reliability of predictions for the long term region were shown; (7) a method to compress test time and to make predictions of response for the nonlinear region was proposed; and (8) nonlinearity of the LRF with respect to log(t) was calculated theoretically from a model.

Litovchenko, V.↗

Electron Scattering by Low-frequency Whistler Waves at Earth’s Bow Shock

Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large (θ(sub Bn) approximately equal or greater than 70°). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude (δB/B ~ 0.3), low-frequency (approximately equal or less than 0.1 Ω(sub ce) where Ω(sub ce) is the cyclotron frequency), obliquely propagating (θ(sub kB) ~ 30°–60°, where θ(sub kB) is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.

Oka, M.↗