Recently, observations from laboratory experiments have revealed amplitude modulation of whistlers by low-frequency perturbations. We here present theoretical and simulation studies of amplitude modulated whistler solitary waves (whistlerons) and their interaction with background low-frequency density perturbations created by the whistler ponderomotive force. We derive a nonlinear a nonlinear Schrodinger equation which governs the evolution of whistlers in the presence of finite-amplitude density perturbations, and a set of equations for arbitrary large amplitude density perturbations in the presence of the whistler ponderomotive force. The governing equations studied analytically in the small amplitude limit, and are solved numerically to show the existence of large scale density perturbations that are self-consistently created by localized whistlerons. Our numerical results are in good agreement with recent experimental results where the the formation of modulated whistlers and solitary whister waves were formed.
We consider the weak turbulence of whistler waves in the in low-β inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminis…
A range of nonlinear wave structures, including Langmuir waves, unipolar electric fields and bipolar electric fields, are often observed in association with whistler-mode chorus waves in the near-Earth space. We demonstrate that the three seemingly different nonlinear wave structures originate from the same nonlinear electron trapping process by whistler-mode chorus waves. The ratio of the Landau resonant velocity to the electron thermal velocity controls the type of nonlinear wave structures that will be generated.
Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth…
The resonant interaction of relativistic electrons and whistler waves is an important mechanism of electron acceleration and scattering in the Earth radiation belts and other space plasma systems. For low amplitude waves, such an interaction is well described by the quasi-linear diffusion theory, whereas nonlinear resonant effects induced by high-amplitude waves are mostly investigated (analytically and numerically) using the test particle approach. In this paper, we develop a mapping technique for the description of this nonlinear resonant interaction. Using the Hamiltonian theory for resonan…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic field topological structures consistent with the observations and our simulations in linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels dependi…
Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma immersed in an external solenoidal magnetic field and utilizing a technique known as the hydrodynamic substitution, a relativistic hydrodynamic system of equations governing the dynamics of various species has been obtained. Based on the method of multiple scales, a system comprising three nonlinear Schrodinger equation for the transverse envelopes of the three basic whistler modes, has been derived. Using the method of formal series of Dubois-Violette, a traveling wave solution of t…
We have studied the nonlinear dynamics of whistler waves in magnetized plasmas. Since plasmas and beam-plasma systems considered here are assumed to be weakly collisional, the point of reference for the analysis performed in the present paper is the system of hydrodynamic and field equations. We have applied the renormalization group method to obtain dynamical equations for the slowly varying amplitudes of whistler waves. Further, it has been shown that the amplitudes of eigenmodes satisfy an infinite system of coupled nonlinear Schrödinger equations. In this sense, the whistler eigenmodes for…
We consider the influence of the electron spin on the nonlinear propagation of whistler waves. For this purpose a recently developed electron two-fluid model, where the spin up- and down populations are treated as different fluids, is adapted to the electron MHD regime. We then derive a nonlinear Schrodinger equation for whistler waves, and compare the coefficients of nonlinearity with and without spin effects. The relative importance of spin effects depend on the plasma density and temperature as well as the external magnetic field strength and the wave frequency. The significance of our resu…
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear …
Properties of the electron mirror instability and its competition with the usually dominant whistler (electron cyclotron) instability driven by the electron perpendicular temperature anisotropy are investigated on the linear level using a Vlasov linear solver and on the nonlinear level using a two-dimensional full particle code. The simulation results show that the linearly subdominant electron mirror instability may compete on the nonlinear level with the whistler instability and may even become eventually the dominant mode that generates robust non-propagating sub-ion-scale coherent structur…
The nonlinear propagation of electromagnetic (EM) electron-cyclotron waves (whistlers) along an external magnetic field, and their modulation by electrostatic small but finite amplitude ion-acoustic density perturbations are investigated in a uniform quantum plasma with intrinsic spin of electrons. The effects of the quantum force associated with the Bohm potential and the combined effects of the classical as well as the spin-induced ponderomotive forces (CPF and SPF respectively) are taken into consideration. The latter modify the local plasma density in a self-consistent manner. The coupled …
Whistler-Alfvén turbulence in a non-neutral ultrarelativistic pair plasma
University of Wisconsin at Madison（威斯康星大学麦迪逊分校）；Space Science Institute（空间科学研究所）；University of Kansas（堪萨斯大学）；Massachusetts Institute of Technology（麻省理工学院）
The discovery of large-amplitude narrowband whistler-mode waves at frequencies of tenths of the electron cyclotron frequency in large numbers both inside ~.3 AU and at ~1 AU provides an answer to longstanding questions about scattering and energization of solar wind electrons. The waves can have rapid nonlinear interactions with electrons over a broad energy range. Counter-propagation between electrons and waves is not required for resonance with the obliquely propagating waves in contrast to the case for parallel propagation. Using a full 3d particle tracing code, we have examined interaction…
The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The moderately nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright- (pulses) or dark- (holes,…
An interesting characteristic of magnetospheric chorus is the presence of a frequency gap at $ω\simeq 0.5Ω_e$, where $Ω_e$ is the electron cyclotron angular frequency. Recent chorus observations sometimes show additional gaps near $0.3Ω_e$ and $0.6Ω_e$. Here we present a novel nonlinear mechanism for the formation of these gaps using Hamiltonian theory and test-particle simulations in a homogeneous, magnetized, collisionless plasma. We find that an oblique whistler wave with frequency at a fraction of the electron cyclotron frequency can resonate with electrons, leading to effective energy exc…
In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light pulses coupled to electron plasma waves in a relativistic cold plasma model. It is shown here that the instability can be understood on the basis of the stimulated Raman scattering phenomenon and the occurrence of density bursts in the trailing edge of the modulated structures are a manifestation of an explosive instability arising from a nonlinear phase mixing…
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature -- whistler drift modes that propagate along the electron drift as a Burger's shock, and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral -- are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the follow…
Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine the general electron energization, whereas electron scattering by waves relax anisotropy of electron distributions and produces small populations of h…
