Siminos Evangelos, Bénisti Didier, Gremillet Laurent
CEA, DAM, DIF, F-91297 Arpajon, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056402. doi: 10.1103/PhysRevE.83.056402. Epub 2011 May 12.
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 the 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 by Crawford and Hislop [Ann. Phys. (NY) 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.
我们将空间周期的非线性弗拉索夫 - 泊松平衡作为一个本征问题，在有限维(N)的傅里叶 - 厄米特基（分别在空间和速度变量中）下进行研究。当弗拉索夫方程中的对流项占主导时，特征值随(N)的收敛相当缓慢，限制了该方法的适用性。我们使用克劳福德和希斯洛普[《物理评论》（纽约）189, 265 (1989)]引入的谱变形方法，有选择地衰减与对流项相关的中性模连续谱，从而加速收敛。我们通过重现线性（空间均匀）平衡的动力学色散关系结果，来验证和基准测试我们方法的性能。最后，我们研究具有多个相空间涡旋的周期伯恩斯坦 - 格林 - 克鲁斯卡尔模的稳定性，将我们的结果与弗拉索夫 - 泊松系统的数值模拟进行比较，并表明初始不稳定平衡可能根据其被扰动的方式演化为不同的渐近状态。
