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Landau阻尼和能量守恒

Landau damping and energy conservation

  • 摘要: Landau阻尼是线性Vlasov-Poisson方程所描述的无碰撞等离子体中静电振荡强度的衰减或增长.其物理本质在学术界至今一直存在争论,主流的观点认为Landau阻尼是波和粒子交换能量的结果.但是目前用来解释Landau阻尼的物理图像和线性Vlasov-Poisson方程是矛盾的,这是因为线性Vlasov-Poisson系统的动能是守恒的,电场的能量不能转化为动能.本文发展了和线性Vlasov-Poisson方程完全一致的能量关系,并证明这个能量关系在数学上就是Landau阻尼.这应该是Landau阻尼最准确的物理图像.

     

    Abstract: Landau damping is a collisionless dissipation process for electrostatic plasma waves governed by the linearized Vlasov-Poisson equations. Its physical mechanism is still being debated. It is commonly believed that Landau damping is caused by the energy exchange between waves and particles. However, this picture is not compatible with the linearized Vlasov-Poisson system, because the kinetic energy of particles in the linearized Vlasov-Poisson system is conserved, and the energy of the electrical field cannot be converted into the kinetic energy for the particles. We derived an energy relation that is fully consistent with the linearized Vlasov-Poisson system. It is shown that this energy relation is an exact statement of Landau damping, and thus the most accurate physical picture for it.

     

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