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 [H. Schamel, Phys. Plasmas 22, 042301 (2015)] in the Maxwellian ($\kappa \to \infty$) 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.

中文翻译：

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具有奇点的 aκ 分布背景中的电子空穴

赝势方法用于在非热或κ粒子分布函数背景中推导出不同的传播电子 - 空穴结构。相关的分布函数 Ansatz 再现了 [H. 沙梅尔，物理。等离子体22 , 042301 (2015)] 在麦克斯韦 ($\kappa \to \infty$) 限制，为超热电子无处不在的等离子体提供了重要的推广，例如空间等离子体。评估赝势和非线性色散关系。研究了频谱指数κ在非线性色散关系上的作用，例如在波幅方面。泊松方程中类似能量的第一积分用于分析不同类型解的性质：没有被困电子、被困电子的非解析分布或被困电子过剩。因此，要特别注意电子分布函数表现出强奇异性、不连续或非解析性的非正统情况。