二维Bernstein-Greene-Kruskal模式的高分辨率粒子模拟
High-Resolution Particle-In-Cell Simulations of Two-Dimensional Bernstein-Greene-Kruskal Modes
AI总结：
本文通过高达2048^2网格的二维PIC模拟验证了二维BGK模式的解析稳态解，并发现其在强背景磁场下稳定、弱磁场下失稳，失稳表现为方位角静电波激发并演化为螺旋图案。
摘要：
我们展示了二维Bernstein-Greene-Kruskal（BGK）模式的二维（2D）particle-in-cell（PIC）模拟，这些模式是Vlasov-Poisson方程的精确非线性稳态解，位于垂直于背景磁场的二维平面上，并具有局域于该平面的圆柱对称电势。PIC模拟使用理论中的解析电子分布和电势进行初始化。我们使用高达2048^2的网格分辨率确认了这些解的有效性。我们表明，在保持模型其他参数不变的情况下，这些解在较强的背景磁场下是动力学稳定的，但当磁场强度低于某一特定值时变得不稳定。当一个模式变得不稳定时，我们观察到不稳定性始于方位角静电波的激发，最终形成螺旋图案。
英文摘要：
We present two dimensional (2D) particle-in-cell (PIC) simulations of 2D Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear steady-state solutions of the Vlasov-Poisson equations, on a 2D plane perpendicular to a background magnetic field, with a cylindrically symmetric electric potential localized on the plane. PIC simulations are initialized using analytic electron distributions and electric potentials from the theory. We confirm the validity of such solutions using high-resolutions up to a 2048^2 grid. We show that the solutions are dynamically stable for a stronger background magnetic field, while keeping other parameters of the model fixed, but become unstable when the field strength is weaker than a certain value. When a mode becomes unstable, we observe that the instability begins with the excitation of azimuthal electrostatic waves that ends with a spiral pattern.
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