Monte Carlo methods are often employed to numerically integrate kinetic equations, such as the particle-in-cell method for the plasma kinetic equation, but these methods suffer from the introduction of counting noise to the solution. We report on a cautionary tale of counting noise modifying the nonlinear saturation of kinetic instabilities driven by unstable beams of plasma. We find a saturated magnetic field in under-resolved particle-in-cell simulations due to the sampling error in the current density. The noise-induced magnetic field is anomalous, as the magnetic field damps away in continuum kinetic and increased particle count particle-in-cell simulations. This modification of the saturated state has implications for a broad array of astrophysical phenomena beyond the simple plasma system considered here, and it stresses the care that must be taken when using particle methods for kinetic equations.

中文翻译：

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动力学模拟中噪声引起的磁场饱和

Monte Carlo 方法通常用于对动力学方程进行数值积分，例如用于等离子体动力学方程的细胞内粒子法，但这些方法会在解中引入计数噪声。我们报告了一个关于计数噪声修改由不稳定等离子体束驱动的动力学不稳定性的非线性饱和的警示故事。由于电流密度的采样误差，我们在分辨率不足的细胞内粒子模拟中发现了饱和磁场。噪声引起的磁场是异常的，因为磁场在连续动力学和增加的粒子计数粒子细胞模拟中衰减。这种饱和状态的改变对除了这里考虑的简单等离子体系统之外的广泛的天体物理现象有影响，