Whistler Wave Instabilities Research Articles

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

Low-frequency whistler waves driven by energetic electrons in plasmas of solely electron cyclotron wave heating

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts.

On whistler-wave instability driven by butterfly-like electron distribution in a mirror magnetic trap

When electron cyclotron resonance (ECR) plasma heating is operated at a frequency exceeding the minimum electron cyclotron frequency in an open trap, the power deposition zone is shifted from the trap center towards higher magnetic fields. In this case, ECR heating may result in the formation of ‘butterfly-like’ distribution functions of fast electrons characterized by holes in a velocity space formed by particles that can not reach the heating zone while moving adiabatically from the trap center. In this paper, we develop a basic three-dimensional (1d-real + 2d-velocity space) kinetic model that allows us to describe the effects of the butterfly-like distributions on the whistler wave instability. We calculate a linear amplification gain for a whistler wave propagating along the magnetic field in an essentially inhomogeneous plasma, and compare the results with the well-studied case of anisotropy-driven whistler instability. The proposed theory is primarily aimed at the interpretation of recent experimental data accumulated in laboratory studies of kinetic instabilities and stimulated emission of ECR plasma discharges in mirror traps.

Saturation Properties of Whistler Wave Instability in a Plasma With Two Electron Components

AbstractSaturation properties of whistler wave instability driven by electron temperature anisotropy in a plasma with two electron components are investigated using particle‐in‐cell (PIC) simulations. Most of the previous self‐consistent PIC simulations or quasi‐linear theory used a single bi‐Maxwellian distribution of electrons, which might apply to solar wind or magnetosheath. In the inner magnetosphere, however, there is frequently a cold and dense electron component, coexisting with a hot electron component. In this work, we investigate the relation between temperature anisotropy (A) and parallel plasma beta (β‖) at saturation. Our results agree well with the previous conclusion obtained from linear theory in most cases. However, We show that the inverse relation breaks when β‖ is larger than certain value , beyond which A increases with increasing β‖. We also investigated the dependence of the saturation wave intensity on plasma beta and the initial linear growth rate and show that the saturation amplitude can be modeled as a function of the maximum initial linear growth rate even in a plasma with two electron components. Our results might be useful to couple the microscopic wave excitation process with macroscopic global energetic electron dynamics and to understand whistler wave excitation in the inner magnetosphere.

The effects of kinetic instabilities on the electron cyclotron emission from runaway electrons

In this paper we show that the kinetic instabilities associated with runaway electron beams play an essential role for the production of high-level non-thermal electron–cyclotron-emission (ECE) radiation. Most of the non-thermal ECE comes from runaway electrons in the low-energy regime with large pitch angle, which are strongly scattered by the excited whistler waves. The power of ECE from runaway electrons is obtained using a synthetic diagnostic model based on the reciprocity method. The electron distribution function is calculated using a kinetic simulation model including the whistler wave instabilities and the quasilinear diffusion effects. Simulations based on DIII-D low-density discharge reproduces the rapid growth of the ECE signals observed in DIII-D experiments. Unlike the thermal ECE where radiation for a certain frequency is strongly localized inside the resonance region, the non-thermal ECE radiation from runaway electrons is nonlocal, and the emission-absorption ratio is higher than that of thermal electrons. The runaway electron tail is more significant for ECE with higher frequencies, and the ECE spectrum becomes flatter as RE population grows. The nonlinear behavior of the kinetic instabilities is illustrated in the oscillations of the ECE waves. The good agreement with the DIII-D experimental observations after including the kinetic instabilities clearly illustrate the significance of the scattering effects from wave-particle interactions, which can also be important for runaway electrons produced in disruptions.

Effects of cold electron density on the whistler anisotropy instability

We confirm results from a previous derivation of the linear growth rate of the parallel propagating whistler wave instability when both cold and hot populations are present, and extend previous equations to describe the spatial growth rate. For moderate plasma beta, there is always a peak in the linear growth rate of the dominant mode with respect to the ratio of total plasma density to the hot plasma density. There is a similar peak in the linear convective growth rate for high anisotropy Ahot = T⊥ hot/T∥ hot − 1 but not for low anisotropy. We present these results for a large range of physical parameters. Our results can be used to quickly determine whether the growth rate will increase or decrease with respect to cold plasma density, and we demonstrate this for an event observed recently. We explain the observation that greater cold plasma density leads to a drop in the central frequency of the waves. Model equations can be used to predict the optimal cold plasma density for maximum temporal and spatial growth rate. A relativistic electromagnetic plasma dispersion code is used to show that the analytical formulas are roughly correct in the vicinity of the optimal cold density unless the thermal velocity is highly relativistic ∼0.5 c, where c is the speed of light. Comparison with the electromagnetic dispersion code WHAMP shows that our formulas are adequate for β∥ hot < 1 for realistic anisotropy.

Effects of Electromagnetic Fluctuations along Shock Front on Electron Motions in an Oblique Shock Wave

The evolution of a large number of electrons in a shock wave propagating obliquely to an external magnetic field is analyzed by means of a two-dimensional electromagnetic particle code. Furthermore, the motions of the same number of test electrons in the electromagnetic fields averaged along the shock front are calculated, that is, in the equation of motion for the test electrons, two-dimensional electromagnetic fluctuations with finite wave numbers along the shock front are excluded. A comparison of the two groups of electrons shows that the two-dimensional electromagnetic fluctuations, which grow up to large amplitudes because of whistler wave instabilities excited by electrons trapped in the main pulse region of the shock wave, can cause the detrapping of energetic electrons from the main pulse and their subsequent acceleration to much higher energies. It is also found that two-dimensional fluctuations can contribute to the reflection of electrons near the end of the main pulse.

Repeated Acceleration of Thermal Ions by an Oblique Shock Wave and Associated Whistler Instabilities

A magnetosonic shock wave propagating obliquely to an external magnetic field can repeatedly accelerate thermal ions if θ0≈45°, where θ0 is the angle between the wave normal and the external magnetic field. The ion energy gains in this process are theoretically analyzed, and an expression for the maximum energy is derived. This theory is verified using a two-dimensional, electromagnetic particle code. Furthermore, whistler wave instabilities generated by the accelerated ions are studied. The simulation demonstrates that whistler waves are excited in both the upstream and downstream regions, but that the whistler waves in these two regions have different frequencies and wavenumbers. It is shown that the characteristics of these waves can be explained by linear theory.

Quasi-linear analysis of whistler waves driven by relativistic runaway beams in tokamaks

The presence of a whistler wave instability (WWI) excited by runaway electrons may be the reason for the observation that the number of runaway electrons produced during disruptions in large tokamaks depends sensitively on the magnetic field strength. Previous work has shown that the linear growth rates of these waves are such that they are stable for high magnetic field (so the runaway beam can form) but unstable for low magnetic field. Here, it is shown that the quasi-linear diffusion process due to the WWI represents a very efficient pitch-angle scattering mechanism for runaways and consequently may stop runaway beam formation in large tokamak disruptions.

Whistler wave instabilities in collisionless current sheet

Instability of whistler wave in collisionless current sheet is studied with numerical solution of the general dispersion relation obtained in Ref.[4] for the physical model A. As revealed by the results, the whistler wave can be directly absorbed by collisionless current sheets. On the neutral sheet ( z/ d i = 0) oblique whistler waves over a rather wide range of wave numbers can propagate, while they are basically stable. In the ionic inertial region ( z/ d i < 1), the obliquely propagating whistler wave is unstable. On the edge of the ionic inertial region ( z/ d i = 1), the whistler wave is still unstable, with an increase in the growth rate, and in the frequency of the unstable wave. The growth rate is larger for the whistler wave propagating towards the neutral sheet ( k zd i < 0) than away from the neutral sheet ( k zd i > 0).

Whistler Wave Instabilities in the Collisionless Current Sheet

通过数值求解文献[4]中物理模型A得到的一般形式的色散关系,讨论了无碰撞电流片低频波不稳定性问题.结果表明,哨声波能被无碰撞电流片直接激发.在中性片上(z/di=0),在较宽的波数范围内,斜哨声波是可以传播的,但它基本上是稳定的.在离子惯性区内(z/di＜1,电子惯性区外),斜传播的哨声波是不稳定的.在离子惯性区边缘(z/di=1),斜传播的哨声波仍然是不稳定的,增长率更大,不稳定的波频率范围更高.此外,朝向中性片方向传播(kzdi＜0)的哨声波比离开中性片方向传播(kzdi＞0)的哨声波有更大的增长率.

Effect of loss-cone distribution on the generation of whistler waves in the magnetosphere

An anisotropic kappa velocity distribution with loss-cones is used to investigate whistler wave instability occurring in the magnetosphere. The elements of the dielectric tensor and dispersion relation using modified plasma dispersion function Z κ ∗(ξ) with loss-cone angle have been obtained for the linear waves propagating exactly parallel to a uniform local magnetic field in a homogeneous and hot plasma. The modified plasma dispersion function and integrals have been expressed in power-series form for argument of ξ≫1. Temporal/spatial growth rates for whistler wave in the magnetosphere have been evaluated by the method of numerical techniques. The results of such a kappa loss-cone distribution function on the generation of whistler waves are compared with those obtained by Maxwellian loss-cone distribution. Calculations show that either a loss-cone or a thermal anisotropy in the hot plasma component of the magnetosphere can lead to the generation of incoherent emission of low-frequency whistler waves. This methodology could be easily extended to the study of low frequency emissions from planetary magnetospheres under suitable choice of models of density and magnetic field and other plasma parameters.

A microinstability code for a uniform magnetized plasma with an arbitrary distribution function

We have developed a very general computer code for studying microinstabilities in a uniform magnetized plasma. Employing a new algorithm to perform two-dimensional numerical integrals in the conductivity tensor, the code can handle an arbitrary distribution function given by either an analytical function or numerical values on a momentum space grid and solve the full dispersion relation for an arbitrary propagation angle in either a non-relativistic or relativistic plasma except for a highly relativistic plasma (energy ⪢ 1 MeV). The results for cyclotron-maser instability and whistler-wave instability are presented to illustrate the validity of the method.

Excitation of whistler mode instability due to slow cyclotron interaction in an inhomogenous beam–plasma System

The excitation of whistler wave instability due to slow cyclotron (m = – 1) interaction in an inhomogeneous plasma penetrated by an inhomogeneous beam of electrons is studied. Expressions are obtained for the elements of the plasma and beam dielectric tensors. It is shown that the inhomogeneity in both beam and plasma number densities affects the growth rate of the instability.