测地声模波包调制不稳定性
Modulational instability of Geodesic-Acoustic-Mode packets
AI总结：
本文利用非线性薛定谔方程和 ORB5 回旋动理学模拟研究测地声模波包的调制不稳定性，揭示朗道阻尼对高谱分量的抑制会显著阻碍不稳定性发展。
摘要：
孤立的、无阻尼的测地声模（GAM）波包已被证明遵循（聚焦型）非线性薛定谔方程（NLSE）[E. Poli, Phys. Plasmas 2021]。该方程预言了 GAM 波包对调制不稳定性（MI）的敏感性。本文利用 NLSE 模型对这一不稳定性所需的必要条件进行了分析和数值研究。将 NLSE 的预言与使用全球粒子模拟程序 ORB5 进行的回旋动理学模拟进行了比较，在这些模拟中，GAM 波包由轴对称径向电场 $E_r$ 的初始扰动产生。无论是在施加初始扰动的情况下，还是在不稳定性自发发展的情况下，都观察到 GAM 波包相对于调制的不稳定性。然而，在 NLSE 与回旋动理学模拟之间，小尺度动力学行为存在显著差异。这些差异主要源于非线性项强度的径向依赖性（我们在 NLSE 的求解中未保留这一依赖性）以及高谱分量的阻尼。高 $k_r$ 分量作为非线性效应的结果而发展，其阻尼可以用朗道阻尼来理解。本文研究了离子拉莫尔半径 $ρ_i$ 以及扰动波矢 $k_{\ ext{pert}}$ 对这一效应的影响。对于本文所考虑的参数，上述阻尼机制显著阻碍了 MI 过程充分发展，并且足够强以稳定一些（根据无阻尼 NLSE 模型）不稳定的波矢。
英文摘要：
Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schrödinger equation (NLSE) [E. Poli, Phys. Plasmas 2021]. This equation predicts susceptibility of GAM packets to the modulational instability (MI). The necessary conditions for this instability are analyzed analytically and numerically using the NLSE model. The predictions of the NLSE are compared to gyrokinetic simulations performed with the global particle-in-cell code ORB5, where GAM packets are created from initial perturbations of the axisymmetric radial electric field $E_r$. An instability of the GAM packets with respect to modulations is observed both in cases in which an initial perturbation is imposed and when the instability develops spontaneously. However, significant differences in the dynamics of the small scales are discerned between the NLSE and gyrokinetic simulations. These discrepancies are mainly due to the radial dependence of the strength of the nonlinear term, which we do not retain in the solution of the NLSE, and to the damping of higher spectral components. The damping of the high-$k_r$ components, which develop as a consequence of the nonlinearity, can be understood in terms of Landau damping. The influence of the ion Larmor radius $ρ_i$ as well as the perturbation wavevector $k_{\text{pert}}$ on this effect is studied. For the parameters considered here the aforementioned damping mechanism hinders the MI process significantly from developing to its full extent and is strong enough to stabilize some of the (according to the undamped NLSE model) unstable wavevectors.
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