具有奇异性的$κ$分布背景中的电子空穴
Electron Holes in a $κ$ Distribution Background with Singularities
摘要：
在非热或$κ$粒子分布函数背景下，应用赝势方法导出了不同的电子空穴结构。相关的分布函数Ancel再现了麦克斯韦（$κ\rightarrow \infty$）极限下\cite{Schamel2015}的Schamel分布，为超热电子无处不在的等离子体（如空间等离子体）提供了一个重要的推广。计算了赝势和非线性色散关系。研究了谱指数$κ$对非线性色散关系的作用，例如，在涉及波振幅的情况下。从泊松方程的能量一样的第一个积分被施加到分析不同类别的解决方案的属性：与被困电子的情况下，与非解析分布的被困电子，或与过剩的被困电子。因此，特别注意的非正统的情况下，电子分布函数具有很强的奇异性，是不连续的或非解析的。
英文摘要：
The pseudo-potential method is applied to derive diverse propagating electron hole structures, in a nonthermal or $κ$ particle distribution function background. The associated distribution function Ansatz reproduces the Schamel distribution of \cite{Schamel2015} in the Maxwellian ($κ\rightarrow \infty$) limit, providing a significant generalization of it for plasmas where superthermal electrons are ubiquitous, such as space plasmas. The pseudo-potential and the nonlinear dispersion relation are evaluated. The role of the spectral index $κ$ on the nonlinear dispersion relation is investigated, in what concerns the wave amplitude for instance. The energy-like first integral from Poisson's equation is applied to analyze the properties of diverse classes of solutions: with the absence of trapped electrons, with a non-analytic distribution of trapped electrons, or with a surplus of trapped electrons. Special attention is therefore paid to the non-orthodox case where the electrons distribution function exhibits strong singularities, being discontinuous or non-analytic.
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