Krafft C, Volokitin A
Laboratoire de Physique des Plasmas, Ecole Polytechnique, University Paris-Sud, 91128 Palaiseau Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):053107. doi: 10.1103/PhysRevE.87.053107. Epub 2013 May 17.
Horseshoe distributions are shell-like particle distributions that can arise in space and laboratory plasmas when particle beams propagate into increasing magnetic fields. The present paper studies the stability and the dynamics of wave packets interacting resonantly with electrons presenting low-energy horseshoe or shell-type velocity distributions in a magnetized plasma. The linear instability growth rates are determined as a function of the ratio of the plasma to the cyclotron frequencies, of the velocity and the opening angle of the horseshoe, and of the relative thickness of the shell. The nonlinear stage of the instability is investigated numerically using a symplectic code based on a three-dimensional Hamiltonian model. Simulation results show that the dynamics of the system is mainly governed by wave-particle interactions at Landau and normal cyclotron resonances and that the high-order normal cyclotron resonances play an essential role. Specific features of the dynamics of particles interacting simultaneously with two or more waves at resonances of different natures and orders are discussed, showing that such complex processes determine the main characteristics of the wave spectrum's evolution. Simulations with wave packets presenting quasicontinuous spectra provide a full picture of the relaxation of the horseshoe distribution, revealing two main phases of the evolution: an initial stage of wave energy growth, characterized by a fast filling of the shell, and a second phase of slow damping of the wave energy, accompanied by final adjustments of the electron distribution. The influence of the density inhomogeneity along the horseshoe on the wave-particle dynamics is also discussed.
马蹄形分布是一种壳状粒子分布，当粒子束在空间和实验室等离子体中传播到不断增强的磁场中时可能会出现。本文研究了在磁化等离子体中与呈现低能马蹄形或壳型速度分布的电子发生共振相互作用的波包的稳定性和动力学。线性不稳定性增长率是根据等离子体频率与回旋频率之比、马蹄形的速度和张角以及壳的相对厚度来确定的。使用基于三维哈密顿模型的辛算法对不稳定性的非线性阶段进行了数值研究。模拟结果表明，系统的动力学主要由朗道共振和正常回旋共振处的波粒相互作用主导，高阶正常回旋共振起着至关重要的作用。讨论了粒子在不同性质和阶数的共振处同时与两个或多个波相互作用时动力学的具体特征，表明这种复杂过程决定了波谱演化的主要特征。用呈现准连续谱的波包进行的模拟提供了马蹄形分布弛豫的全貌，揭示了演化的两个主要阶段：波能量增长的初始阶段，其特征是壳的快速填充；以及波能量缓慢衰减的第二阶段，伴随着电子分布的最终调整。还讨论了沿马蹄形的密度不均匀性对波粒动力学的影响。
