The chaotic interaction between electrons and whistler mode waves has been shown to provide a mechanism for enhanced diffusion in phase space. Pitch angle diffusion is relevant for the scattering of electrons into the loss cones, thus providing a source for auroral precipitating electrons. A single whistler mode wave propagating parallel to the background magnetic field has resonance with the electrons but the process is not stochastic. The presence of a second, oppositely directed whistler wave has been shown previously to introduce stochasticity into the system, thus enhancing phase space diffusion. Here we generalise previous work to include relativistic effects. The full relativistic Lorentz equations are solved numerically to permit application to a more extensive parameter space. We consider parameters scaled to intrinsic planetary magnetospheres, for electron populations with 'pancake' velocity distributions i.e. large anisotropies in velocity space. We show that the diffusion is rapid, occuring on timescales of the order of tens of electron gyroperiods, and is strongly sensitive to the wave amplitude, the wave frequency and the perpendicular velocity. Using Voyager 1 data we give an estimate of the whistler wave amplitude in the Io torus at Jupiter and show that the two whistler mechanism produces pitch angle diffusion of up to 10 degrees from an initial pancake distribution, on millisecond timescales.
A statistical study of the properties of large amplitude whistler waves and their association with few eV to 30 keV electron distributions observed in the magnetosphere by Wind
A Model for Generating Relativistic Electrons in the Earth's Inner Magnetosphere Based on Gyroresonant Wave-Particle Interactions
在磁暴的恢复阶段，内磁层（$3\le L \le 6$）中的相对论性（$>1$ MeV）电子通量增加到超过磁暴前的水平，在磁暴开始后约4天达到峰值。为了解释这些“杀手电子”的产生，提出了一个主要基于增强哨声模式合唱的电子随机加速的模型。在一个准线性的配方，动力学（福克-普朗克）方程的电子能量分布的推导，包括基于回旋共振电子哨声模式波相互作用和平行波传播的能量扩散系数;一个源项表示亚暴产生的（低能量）种子电子;和一个损失项表示电子沉淀由于俯仰角散射哨声模式波和EMIC波。稳态解的电子能量分布的构造，并拟合到一个victially推导出的相对论麦克斯韦分布的高能量的“硬”电子人口在地球同步轨道。该机制预计将是特别有效的一类小型和中型风暴拥有一个长期的恢复阶段，在此期间，许多亚暴发生。
Electron Heat Flux and Whistler Instability in the Earth's Magnetosheath
Swedish Institute of Space Physics（瑞典空间物理研究所）；Uppsala University（乌普萨拉大学）；Chalmers University of Technology（查尔姆斯理工大学）；Laboratory of Physics and Chemistry of the Environment and Space (LPC2E), OSUC, Univ Orleans, CNRS, CNES（环境与空间物理化学实验室（LPC2E）、OSUC、奥尔良大学、CNRS、CNES）；Laboratory for Atmospheric and Space Physics, University of Colorado（科罗拉多大学大气与空间物理实验室）；Imperial College London（帝国理工学院）
