标题： 非线性Vlasov-Poisson平衡的稳定性通过谱变形和傅里叶-埃尔米特展开 显示英文标题

标题： Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion

摘要： 我们研究空间周期性非线性Vlasov-Poisson平衡的稳定性，将其作为有限维傅里叶-埃尔米特基（分别在空间和速度变量中）中的特征值问题，$N$。 当Vlasov方程中的对流项占主导时，特征值随着$N$的收敛相当缓慢，限制了该方法的适用性。 我们使用[ J. D. Crawford 和 P. D. Hislop, Ann. Phys. 189, 265 (1989) ]中引入的谱变形方法，选择性地阻尼与对流项相关的中性模态连续谱，从而加速收敛。 我们通过重现线性（空间均匀）平衡的动能色散关系结果来验证和基准化我们方法的性能。 最后，我们研究具有多个相空间涡旋的周期性Bernstein-Greene-Kruskal模的稳定性，将我们的结果与Vlasov-Poisson系统的数值模拟进行比较，并表明初始不稳定的平衡可能根据扰动方式演化为不同的渐近状态。 显示英文摘要

摘要： We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, $N$. When the advection term in Vlasov equation is dominant, the convergence with $N$ of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced in [J. D. Crawford and P. D. Hislop, Ann. Phys. 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase space vortices, compare our results with numerical simulations of the Vlasov-Poisson system and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.