论文标题
电子孔横向不稳定性的多模理论
Multimode theory of electron hole transverse instability
论文作者
论文摘要
我们介绍了最初平面电子孔结构的Vlasov-Poisson 3-D线性稳定性分析，该分析通过沿未扰动的轨道进行整合来求解分布功能。在绝热泊松操作员的本征函数中扩展了非鼻肌电势扰动形状（平行于$ b $），从而概括了平衡的刚性偏移的先前假设。我们表明，然后通过第二个离散模式将ShiftMode修改，并在波浪状模式的连续体上进行积分。严格的处理表明，可以通过满足外波色散关系的单个模式来有效地近似连续体，从而使扰动成为三种模式的加权总和。我们从数值上找到了复杂不稳定性频率的解，以及确定扰动本特征模式的相应三个模式振幅。该多模分析优化了先前单模式结果的准确性，从大多数参数中的增长率略高，如额外的模式自由度所预期的那样。邻近稳定边界的振荡模式具有较大的模式扭曲，这有助于解释PIC模拟，这些模拟可观察到不稳定的$ \ sim20 $ \％以外的shiftmode阈值，并缩小了扰动。在高磁场，多模分析预测已经较小的生长速率降低。
We present Vlasov-Poisson 3-D linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain PIC simulations that observe instability up to $\sim20$\% beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.
