Asymmetric one-dimensional slow electron holes

Slow solitary positive-potential peaks sustained by trapped electron deficit in a plasma with asymmetric ion velocity distributions are in principle asymmetric, involving a potential change across the hole. It is shown theoretically how to construct such asymmetric electron holes, thus providing fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a wide variety of prescribed background ion velocity distributions. Because of ion reflection forces experienced by the hole, there is generally only one discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is unstable unless there is a local minimum in the ion velocity distribution, in which the hole velocity then resides. For stable equilibria with Maxwellian electrons, the potential drop across the hole is shown to be Delta\phi= 2/9 f''' (Te/e) (e\psi/m_i)^2 , where \psi is the hole peak potential, f''' is the third derivative of the background ion velocity distribution function at the hole velocity, and Te the electron temperature. Potential asymmetry is small for holes of the amplitudes usually observed, <~0.5Te/e.

等离子体中由俘获电子亏损维持、且离子速度分布不对称的慢孤立正电位峰，本质上为不对称结构，其空穴两侧存在电势变化。本文从理论上阐明了此类不对称电子空穴的构建路径，进而为多种给定的背景离子速度分布提供了一维弗拉索夫-泊松（Vlasov-Poisson）方程的完全自洽解。由于空穴会受到离子反射力的作用，通常仅存在一个离散的慢空穴平衡速度。此外，该平衡态不稳定，除非离子速度分布存在局部极小值，且空穴速度恰好处于该极小值位置。对于电子服从麦克斯韦分布的稳定平衡态，空穴两侧的电势差可表示为：Δφ = (2/9) f''' (Tₑ/e) (eψ/mᵢ)²，其中ψ为空穴的峰值电势，f'''为背景离子速度分布函数在空穴速度处的三阶导数，Tₑ为电子温度。对于常规观测到的振幅量级的空穴，其电势不对称性较弱，通常小于~0.5Tₑ/e。