Title: Why Cold BGK Modes Are So Cool: Dispersion Relations from Orbit-Constrained Distribution Functions Show Chinese title

Title: 为什么冷BGK模式如此出色：轨道约束分布函数的色散关系

Abstract: We derive analytic dispersion relations for cold, orbitally constrained systems governed by the Vlasov equation. For magnetized plasmas, we obtain the first explicit relation for two-dimensional anisotropic BGK modes with finite magnetic field, showing that only a finite number of angular modes can become unstable and identifying a magnetic-field threshold for stabilization. In the gravitational case, we establish a bound on the growth rate of core perturbations, set by the potential's curvature. These results clarify how orbital constraints shape the spectrum and growth of kinetic instabilities in cold, collisionless media. Show Chinese abstract

Abstract: 我们推导了受Vlasov方程约束的冷轨道受限系统的解析色散关系。 对于磁化等离子体，我们获得了二维各向异性BGK模式的第一个明确关系，该模式具有有限磁场，表明只有有限数量的角度模式可以变得不稳定，并确定了一个磁场稳定阈值。 在引力情况下，我们建立了由势能曲率决定的核心扰动增长率的界限。 这些结果阐明了轨道约束如何影响冷无碰撞介质中动能不稳定性谱和增长的方式。