Evolution Of Electron Distribution Function Research Articles

Одномерное квазилинейное уравнение для описания генерации токов увлечения в плазме токамака геликонами

A quasi-linear equation which allows describing evolution of electron distribution function and generation of non-inductive currents by helicons is obtained. It is shown that in the analysed case the Fokker-Planck equation can be approximated by a one-dimensional equation in the longitudinal electron velocity space with a diffusion coefficient proportional to the helicon power absorbed by electrons due to Landau damping.

Drift Resonance Between Particles and Compressional Toroidal ULF Waves in Dipole Magnetic Field

AbstractWe examine the drift‐resonant particle dynamics for toroidal ultralow frequency (ULF) waves in a pure dipole background geomagnetic field. We confirm that the resonant condition originally believed to apply only for poloidal ULF waves, , also applies for compressional toroidal waves. The predicted phase relationships have been confirmed from Van Allen Probes observations. Their good agreement provides the first observational evidence for the drift resonance condition controlled by the compressional toroidal ULF wave. Moreover, we extend the drift resonance theory into a nonlinear regime. The resulting particle motion can be described by a modified pendulum equation with solutions depending on the wave number . For high‐ toroidal waves, the resonant islands become asymmetric to perturb the particle trajectories within each potential well and consequently increase the trapping widths in both energy and L‐shell. We further carry out test‐particle simulations to show the evolution of electron distribution functions when they interact with either toroidal or poloidal waves. These findings demonstrate that toroidal ULF waves, like their poloidal counterparts, play an important role in magnetospheric particle dynamics.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

Accurately modelling and forecasting of the dynamics of the Earth’s radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave–particle resonant interaction. Energetic electron acceleration or scattering into the Earth’s atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave–particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Electron acceleration during three-dimensional relaxation of an electron beam-return current plasma system in a magnetic field

We investigate the effects of acceleration during non-linear electron-beam relaxation in magnetized plasma in the case of electron transport in solar flares. The evolution of electron distribution functions is computed using a three-dimensional particle-in-cell electromagnetic code. Analytical estimations under simplified assumptions are made to provide comparisons. We show that, during the non-linear evolution of the beam-plasma system, the accelerated electron population appears. We found that, although the electron beam loses its energy efficiently to the thermal plasma, a noticeable part of the electron population is accelerated. For model cases with initially monoenergetic beams in uniform plasma, we found that the amount of energy in the accelerated electrons above the injected beam-electron energy varies depending the plasma conditions and could be around 10-30% of the initial beam energy. This type of acceleration could be important for the interpretation of non-thermal electron populations in solar flares. Its neglect could lead to the over-estimation of accelerated electron numbers. The results emphasize that collective plasma effects should not be treated simply as an additional energy-loss mechanism, when hard X-ray emission in solar flares is interpreted, notably in the case of RHESSI data.

Inverse bremsstrahlung absorption with full electron-electron collisions operator

A two-dimensional Fokker-Planck program is developed, in which full e-e collisions are taken into account self-consistently with arbitrary anisotropy of electron distribution function (EDF), to investigate inverse bremsstrahlung and the evolution of EDF. The numerical results show that e-e collisions will enhance inverse bremsstrahlung absorption. The evolution of EDF can be divided into two stages distinguished by different absorption rates. During the first stage, an initially Maxwellian EDF transforms rapidly into an anisotropic one with two temperatures. With the increase of anisotropy, the absorption rate decreases dramatically while the contribution ratio of e-e collisions increases rapidly. In particular, we find that with the increase of ion charge state Zi the contribution ratio of e-e collisions increases in the high laser frequency regime, while it decreases in the low frequency regime.

Stochastic Analysis of Anomalous Skin Effect for Linearly Polarized Intense Laser Light

A new method, based on a theory of a stochastic process, to study the mechanism of the anomalous absorption of an intense laser light in an overdense plasma is presented. A basic process of the anomalous skin effect is treated as a stochastic process in the time scale of electron Lamour motion in the laser field, i.e., microscopic scale. A diffusion equation in momentum space which describes the time evolution of electron distribution function is derived. The distribution function evolves to anisotropic in momentum space. The absorption coefficient and skin depth are analytically extended to the relativistic intensity regime by taking into account the time evolution of the electron distribution function.

Numerical Calculation on a Mechanism of Current Sustainment during LHCD

We study time evolution of electron distribution function with a long tail during applying of lower hybrid waves for the purpose of effective current sustainment. We solve numerically two dimensional Fokker-Planck equation combining with the quasi-linear diffusion effects due to both the applied lower hybrid waves and the excited plasma waves of \(\omega{=}\omega_{\text{pe}}\cos\varTheta\). We find that the plasma waves excited due to the resonances with electrons near above the thermal velocity play an important role of a recovery of the flat tail against the destroy of it due to the Coulomb collisions; the quasi-linear diffusion effects are strengthened in the velocity region of the inverse Landau damping. We discuss the possibility of the effective current sustainment making use of this mechanism.