相对论等离子体中共振不稳定性的波能量密度和增长率
The Wave Energy Density and Growth Rate for the Resonant Instability in Relativistic Plasmas
AI总结：
基于线性理论推导了相对论等离子体中任意传播角共振波的能量密度和增长率解析表达式，并以损失锥驱动不稳定性为例验证，为理解波不稳定性及结合准线性理论研究时间演化奠定了基础。
摘要：
在缺乏频繁碰撞的情况下，波不稳定性在天体物理等离子体中起着重新分配能量和动量的作用。存在许多不同类型的波，量化波能量密度和增长率对于理解在不同等离子体状态下可能发生何种波不稳定性非常重要。在整个宇宙中，存在许多等离子体包含大量相对论性粒子的情况。波能量密度和增长率的理论估计通常局限于场向传播角或非相对论性条件。基于线性理论，我们推导了在相对论等离子体中具有任意传播角的任意共振波的能量密度和增长率的解析表达式。为此推导，我们计算了相对论等离子体介电张量的厄米部分和反厄米部分。我们证明，我们的波能量密度解析表达式在增长率解析表达式为正（即驱动波不稳定性的波数范围）的波数范围内，表现出共振波能量的明确增加。作为具体示例，我们通过数值分析了损失锥驱动的不稳定性，在该不稳定性中，哨声模波在辐射带中将相对论性电子散射入损失锥。我们的解析结果进一步发展了线性理论基础，以更好地理解波不稳定性，并有望与准线性理论相结合，从而不仅能研究粒子动量分布函数的时间演化，还能研究通过不稳定性过程中的共振波特性。
英文摘要：
The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate for understanding what type of wave instabilities are possible in different plasma regimes. There are many situations throughout the universe where plasmas contain a significant fraction of relativistic particles. Theoretical estimates for the wave energy density and growth rate are constrained to either field-aligned propagation angles, or non-relativistic considerations. Based on linear theory, we derive the analytic expressions for the energy density and growth rate of an arbitrary resonant wave with an arbitrary propagation angle in relativistic plasmas. For this derivation, we calculate the Hermitian and anti-Hermitian parts of the relativistic-plasma dielectric tensor. We demonstrate that our analytic expression for the wave energy density presents an explicit energy increase of resonant waves in the wavenumber range where the analytic expression for the growth rate is positive (i.e., where a wave instability is driven). For this demonstration, we numerically analyse the loss-cone driven instability, as a specific example, in which the whistler-mode waves scatter relativistic electrons into the loss cone in the radiation belt. Our analytic results further develop the basis for linear theory to better understand the wave instability, and have the potential to combine with quasi-linear theory, which allows to study the time evolution of not only the particle momentum distribution function but also resonant wave properties through an instability.
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