Violation of adiabaticity in magnetic billiards due to separatrix crossings

We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance

Approximate analytical formulation of radial diffusion and whistler-induced losses from a preexisting flux peak in the plasmasphere

International audienceModeling the spatiotemporal evolution of relativistic electron fluxes trapped in the Earth's radiation belts in the presence of radial diffusion coupled with wave-induced losses should address one important question: how deep can relativistic electrons penetrate into the inner magnetosphere? However, a full modeling requires extensive numerical simulations solving the comprehensive quasi-linear equations describing pitch angle and radial diffusion of the electron distribution, making it rather difficult to perform parametric studies of the flux behavior. Here we consider the particular situation where a localized flux peak (or storage ring) has been produced at low L < 4 during a period of strong disturbances, through a combination of chorus-induced energy diffusion (or direct injection) at low L together with enhanced wave-induced losses and outward radial transport at higher L. Assuming that radial diffusion can be further described as the spatial broadening within the plasmasphere of this preexisting flux peak, simple approximate analytical solutions for the distribution of trapped relativistic electrons are derived. Such a simplified formalism provides a convenient means for easily determining whether radial diffusion actually prevails over atmospheric losses at any particular time for given electron energy E and location L. It is further used to infer favorable conditions for relativistic electron access to the inner belt, providing an explanation for the relative scarcity of such a feat under most circumstances. Comparisons with electron flux measurements on board the Van Allen Probes show a reasonable agreement between a few weeks and 4 months after the formation of a flux peak

Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves

International audience[1] Quantifying the loss of relativistic electrons from the Earth's radiation belts requires to estimate the effects of many kinds of observed waves, ranging from ULF to VLF. Analytical estimates of electron quasi-linear diffusion coefficients for whistler-mode chorus and hiss waves of arbitrary obliquity have been recently derived, allowing useful analytical approximations for lifetimes. We examine here the influence of much lower frequency and highly oblique, fast magnetosonic waves (also called ELF equatorial noise) by means of both approximate analytical formulations of the corresponding diffusion coefficients and full numerical simulations. Further analytical developments allow us to identify the most critical wave and plasma parameters necessary for a strong impact of fast magnetosonic waves on electron lifetimes and acceleration in the simultaneous presence of chorus, hiss, or lightning-generated waves, both inside and outside the plasmasphere. In this respect, a relatively small frequency over ion gyrofrequency ratio appears more favorable, and other propitious circumstances are characterized. This study should be useful for a comprehensive appraisal of the potential effect of fast magnetosonic waves throughout the magnetosphere. Citation: Mourenas, D., A. V. Artemyev, O. V. Agapitov, and V. Krasnoselskikh (2013), Analytical estimates of electron quasi-linear diffusion by fast magnetosonic waves

Kinetic equation for nonlinear wave-particle interaction: solution properties and asymptotic dynamics

We consider a kinetic equation describing evolution of the particle distribution function in a system with nonlinear wave-particle interactions (trappings into resonance and nonlinear scatterings). We study properties of its solutions and show that the only stationary solution is a constant, and that all solutions with smooth initial conditions tend to a constant as time grows. The resulting flattening of the distribution function in the domain of nonlinear interactions is similar to one described by the quasi-linear plasma theory, but the distribution evolves much faster. The results are confirmed numerically for a model problem

Charged particle nonlinear resonance with localized electrostatic wave-packets

A resonant wave-particle interaction, in particular a nonlinear resonance characterized by particle phase trapping, is an important process determining charged particle energization in many space and laboratory plasma systems. Although an individual charged particle motion in the nonlinear resonance is well described theoretically, the kinetic equation modeling the long-term evolution of the resonant particle ensemble has been developed only recently. This study is devoted to generalization of this equation for systems with localized wave packets propagating with the wave group velocity different from the wave phase velocity. We limit our consideration to the Landau resonance of electrons and waves propagating in an inhomogeneous magnetic field. Electrons resonate with the wave field-aligned electric fields associated with gradients of wave electrostatic potential or variations of the field-aligned component of the wave vector potential. We demonstrate how wave-packet properties determine the efficiency of resonant particle acceleration and derive the nonlocal integral operator acting on the resonant particle distribution. This operator describes particle distribution variations due to interaction with one wave-packet. We solve kinetic equation with this operator for many wave-packets and show that solutions coincide with the results of the numerical integration of test particle trajectories. To demonstrate the range of possible applications of the proposed approach, we consider the electron evolution induced by the Landau resonances with packets of kinetic Alfven waves, electron acoustic waves, and very oblique whistler waves in the near-Earth space plasma

Remarkable charged particle dynamics near magnetic field null lines

The study of charged-particle motion in electromagnetic fields is a rich source of problems, models, and new phenomena for nonlinear dynamics. The case of a strong magnetic field is well studied in the framework of a guiding center theory, which is based on conservation of an adiabatic invariant – the magnetic moment. This theory ceases to work near a line on which the magnetic field vanishes – the magnetic field null line. In this paper we show that the existence of these lines leads to remarkable phenomena which are new both for nonlinear dynamics in general and for the theory of charged-particle motion. We consider the planar motion of a charged particle in a strong stationary perpendicular magnetic field with a null line and a strong electric field. We show that particle dynamics switch between a slow guiding center motion and the fast traverse along a segment of the magnetic field null line. This segment is the same (in the principal approximation) for all particles with the same total energy. During the phase of a guiding center motion, the magnetic moment of particle’s Larmor rotation stays approximately constant, i.e., it is an adiabatic invariant. However, upon each traversing of the null-line, the magnetic moment changes in a random fashion, causing the particle choose a new trajectory of the guiding center motion. This results in a stationary distribution of the magnetic moment, which only depends on the particle’s total energy. The jumps in the adiabatic invariant are described by Painleve II equation

Electron pitch-angle diffusion: resonant scattering by waves vs.nonadiabatic effects

International audienceIn this paper we investigate the electron pitchanglediffusion coefficients in the night-side inner magnetospherearound the geostationary orbit (L 7) due to magneticfield deformation. We compare the effects of resonantwave–particle scattering by lower band chorus waves and theadiabaticity violation of electron motion due to the strongcurvature of field lines in the vicinity of the equator. Fora realistic magnetic field configuration, the nonadiabatic effectsare more important than the wave–particle interactionsfor high energy (> 1 MeV) electrons. For smaller energy,the scattering by waves is more effective than nonadiabaticone. Moreover, the role of nonadiabatic effects increases withparticle energy. Therefore, to model electron scattering andtransport in the night-side inner magnetosphere, it is importantto take into account the peculiarities of high-energy electrondynamics

Wave energy budget analysis in the Earth's radiation belts uncovers a missing energy

International audienceWhistler-mode emissions are important electromagnetic waves pervasive in the Earth's magnetosphere, where they continuously remove or energize electrons trapped by the geomagnetic field, controlling radiation hazards to satellites and astronauts and the upper-atmosphere ionization or chemical composition. Here, we report an analysis of 10-year Cluster data, statistically evaluating the full wave energy budget in the Earth's magneto-sphere, revealing that a significant fraction of the energy corresponds to hitherto generally neglected very oblique waves. Such waves, with 10 times smaller magnetic power than parallel waves, typically have similar total energy. Moreover, they carry up to 80% of the wave energy involved in wave–particle resonant interactions. It implies that electron heating and precipitation into the atmosphere may have been significantly under/over-valued in past studies considering only conventional quasi-parallel waves. Very oblique waves may turn out to be a crucial agent of energy redistribution in the Earth's radiation belts, controlled by solar activity

Kinetic equation for nonlinear resonant wave-particle interaction

We investigate nonlinear resonant wave-particle interactions including effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relation between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations

Charged particle dynamics in turbulent current sheet

We study dynamics of charged particle in current sheets with magnetic fluctuations. We use the adiabatic theory to describe the nonperturbed charged particle motion and show that magnetic field fluctuations destroy the adiabatic invariant. We demonstrate that the evolution of particle adiabatic invariant's distribution is described by a diffusion equation and derive analytical estimates of the rate of adiabatic invariant's diffusion. This rate is proportional to power density of magnetic field fluctuations. We compare analytical estimates with numerical simulations. We show that adiabatic invariant diffusion results in transient particles trapping in the current sheet. For magnetic field fluctuation amplitude few times larger than a normal magnetic field component, more than 50% of transient particles become trapped. We discuss the possible consequences of destruction of adiabaticity of the charged particle motion on the state of the current sheets