Resonant electron-whistler interactions in the plasma sheet are investigated as possible explanations of the nearly isotropic fluxes of low-energy electrons observed above the diffuse aurora. Whistler mode waves, propagating near the resonance cone with frequencies near or larger than half the equatorial electron cyclotron frequency, can interact with low-energy plasma sheet electrons. A Hamiltonian formulation is developed for test particles interacting with the coherent chorus emission spectra. We consider the second-order resonance condition which requires that inhomogeneities in the Earth's magnetic field be compensated by a finite bandwidth of wave frequencies to maintain resonance for extended distances along field lines. These second-order interactions are very efficient in scattering the electrons toward the atmospheric loss cone. Numerical calculations are presented for the magnetic shell L -5.5 for wave amplitudes of .-• 10 -6 V/m, using different frequency and magnetospheric conditions. 1. Introduction The pitch angle scattering of energetic electrons by whistler waves in the the Earth's radiation belts is a long-standing research problem [Lyons and Williams, 1984, and references therein]. Whistler waves are responsible for the precipitation of electrons in both the plasmasphere and the plasma sheet [Bell, 1984]. As electrons scatter toward smaller pitch angles, they give up small quantities of energy, amplifying the waves to the point where the interaction becomes self-sustaining. The limit for stably trapped particle fluxes was first investigated by Kennel and Petschek [1966], and later in self-consistent quasi-linear diffusion models by Bespalov and Tvakhtengerts [1986], Villaldn et al. [1989], and Villa16n and Burke [1991]. Past studies have considered whistler waves for which the ratio between the wave and the electron cyclotron frequencies is 0•/•e << 1. In this case, only electrons whose energies are larger than or of the order of the magnetic energy per particle Ec, may interact with the waves. Normalized to the electron rest energy, Ec = (•e/0•p) 2. Here, •e and 0•p are the electron cyclotron and the plasma frequencies, respectively. As pointed out by Johnstone el al. [1993], in the outer plasma sheet the threshold energy for resonant interactions is Paper number 95JA01161. 0148-0227/95/95JA-01161 $05.00 the possibility of resonant interactions of whistler mode waves with electrons with energies well below 10 keV. For these interactions to take place, the wave frequency must be close to The diffuse aurora is formed by nearly isotropic fluxes of electrons, mostly with energies of <10 keV, that precipitate from the plasma sheet [Johnstone, 1983; Inan et al., 1992]. A number of studies have attempted to explain the diffuse aurora by the interaction of the electrons with electrostatic electron cyclotron harmonic (ECH) waves [Swift, 1981]. However, it does not that the amplitudes of ECH waves are large enough to account for the electron precipitation [Belmont et al., 1983; Roeder and Koons, 1989]. ...
The evolution of the bounce-averaged ring current/radiation belt proton distribution is simulated during resonant interactions with ducted plasmaspheric hiss. The plasmaspheric hiss is asstuned to be generated by ring current electrons and to be damped by the energetic prowns. Thus energy is transferred between energetic electrons and protons using the plasmaspheric hiss as a mediary. The problem is not solved self-consistently. During the simulation period, interactions with ring current electrons (not represented in the model) are assumed to maintain the wave amplitudes in the presence of damping by the energetic protons, allowing the wave specman to be held fixed. Diffusion coefficients in pitch angle, cross pitch angle/energy, and energy were previously calculated by Kozyra et al. (1994) and are adopted for the present study. The simulation treats the energy range, E > 80 keV, within which the wave diffusion operates on a shorter timescale than other proton loss processes (i.e., Coulomb drag and charge exchange). These other loss processes are not included in the simulation. An interesting result of the simulation is that energy diffusion maximizes at moderate pitch angles near the edge of the atmospheric loss cone. Over the simulation period, diffusion in energy creates an order of magnitude enhancement in the bounce-averaged proton distribution function at moderate pitch angles. The loss cone is nearly empty because scattering of particles at small pitch angles is weak. The bounceaveraged flux distribution, mapped to ionospheric heights, results in elevated locally mirroring proton fluxes. 0(30 5 observed order of magnitude enhancements in locally mirroring energetic protons at altitudes between 350 and 1300 km and invariant latitudes between 50 ø and 60 ø (Lundblad and Soraas, 1978). The proton distributions were highly anisotropic in pitch angle with nearly empty loss cones. The similarity between the observed distributions and those resulting from this simulation raises the possibility that interactions with plasmaspheric hiss play a role in forming and maintaining the characteristic zones of anisotropic proton precipitation in the subauroral ionosphere. Further assessment of the importance of this process depends on knowledge of the distribution in space and time of ducted plasmaspheric hiss in the inner magnetosphere. during this interaction with the energetic protons and then damped by thermal electrons during the course of their propagation through the inhomogenous magnetospheric environment [Cornwall et al., 1971]. The energy transferred to the thermal electron gas in the process leads to increased temperatures at the foot of these field lines and to an associated enhancement in 6300 ]• emissions characteristic of S AR arcs. magnitude less than locally mirroring ones. Protons that are However, in the ensuing time period, ion cyclotron waves have locally mirroring at these altitudes map to the equator near the been observed only rarely in the outer plasmasphere. During a edge of the atmospheric loss...
Abstract. Observations of Electric Field Distributions in the Ionospheric Plasma-A Unique Strategy (OEDIPUS C) was a tethered mother-son experiment that was launched northward from the Poker Flat rocket range at 0638 UT on November 7, 1995, across a sequence of a. uroral structures. During the flight's upleg the magnetically aligned tether was deployed to a separation of ,,•1.2 km and then cut at both ends. The forward payload contained a 50-kHz to 8-MHz steppedfrequency transmitter. Receivers were carried on both forward and aft payloads. The transmitter swept through the frequency range every 0.5 s. During each of the 3-ms steps the transmitter emitted only for the first 0.3 ms. The scientific complement also included multiangular electrostatic analyzers on both payloads that were sensitive to fluxes of electrons with energies from 20 eV to 20 keV. The durations of sampling and frequency steps were matched. During the flight the electron gyrofrequency was approximately twice the plasma frequency. When the transmitter swept through the lo½•1 gyrofrequency, the particle detectors on both payloads detected sounder-accelerated electrons (SAEs) independent of the energy steps being sampled. In addition, SAEs were detected at the aft payload out to separations of several hundred meters for wa,ve emissions at harmonics of the electron gyrofrequency as well as in the upper hybrid and whistler bands. As the vehicle separation increased, significant time differences developed between the wave-emission pulses a, nd the onsets/durations of SAE detections. The data indicate that electrons were heated through strong wa, ve-partic]e interactions. However, a simple resonant-interaction explana, tion •ppears inadequate. We outline requirements for any models purporting to explain OEDIPUS C measurements.
A detailed linear and nonlinear analysis of quasimode parametric excitations relevant to experiments in supplementary heating of tokamak plasmas is presented. The linear analysis includes the full ion-cyclotron harmonic quasimode spectrum. The nonlinear analysis, considering depletion of the pump electric field, is applied to the recent Alcator A heating experiment. Because of the very different characteristics of a tokamak plasma near the wall (in the shadow of the limiter) and inside, t-he quasimode excitations are studied independently for the plasma edge and the main bulk of tFle plasma, and for two typical regimes in overall d&nsity, the low (peak in density, ne = 1.5 x 1 0 H cM~?) and high (7o = _ x 10 ~M3) density regimes. At the edge of the plasma and for the low density regime, it is found that higher Pz 's (nz = c kz'o) than those predicted by the linear theory are strcngly excited. Inside the plasma,. the excitation of higher wave-numbers is also signiftcant. These results' indicate that a large amount of the rf-power may not penetrate to the plasma center, but will rather be either Landau-damped on the electrons or modeconverted into thermal modes, close to the plasma edge . Moreover, for sufficiently high peaks in density it is found that all the rf-power is modeconverted before reaching the plasma center. Inside the plasma the power density of the excited sideband fields is shown to be always very small in comparasion with their excitation at the plasma edge.
Whistler waves propagating near the quasi-electrostatic limit can interact with energetic protons (-•80 -500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate obliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker-Planck equation is integrated along the flux tube considering the contributions of multiple-resonance crossings. The quasi-linear diffusion coefficients in energy, cross energy/pitch angle, and pitch angle are obtained for second-order resonant interactions. They are shown to be proportional to the electric fields amplitudes. Numerical calculations for the second-order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments. IntroductionProton precipitation during controlled VLF transmission experiments occurs over a wide range of plasmaspheric L shells. Whistler waves transmitted from the ground propagate along the field lines to the magnetic equator where they become quasi-electrostatic [Koons, 1975[Koons, , 1977Kovrazhkin et al., 1983Kovrazhkin et al., , 1984, and interact with the protons in the energy range (-•80-500 keV). Furthermore, Bell and Ngo [1988] have shown that VLF electromagnetic waves commonly excite high-. amplitude electrostatic waves with the same frequencies but with much shorter wavelengths and that have the characteristics necessary to interact with the energetic protons. Lightning discharges [Burgess and Inan, 1990] also generate VLF waves that, after entering the magnetosphere, can become trapped bouncing back and forth between hemispheres. Some of these waves can also interact with energetic protons. The waves considered here are such that the ratios of the wave frequencies to the equatorial electron gyrofrequencies are 0.5 < a•/lqe(L) < 1. The argument L references the electron cyclotron frequency f•e to its equatorial values. The wave vectors k, form an angle •b with the background geomagnetic field Bo, which is assumed to be along the z direction. See Figure 1 for a representation of the geometry of the problem. Thus for most of their trajectories along the field lines • << f•e, •b ( 30 ø. Near the equator the waves propagate obliquely to the geomagnetic field with 0 ø ( •b ( 60 ø. The frequency range (0.5fee • f • fee)for the waves we propose to investigate has been observed in a number of experiments [Dowden et al., 1978; Koons, 1977; Kovrazhkin et al., 1984]. For purposes of illustration Plate 1 show...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.