Eur. Phys. J. D (2026) 80: 43
https://doi.org/10.1140/epjd/s10053-026-01159-2

Research - Atomic and Molecular processes in Plasmas

Generalized Bohm criterion and sheath dynamics in magnetized plasma with super-extensive electrons, thermal ions, and secondary electron emission

¹ MASI Laboratory, Multidisciplinary Faculty of Nador, Mohammed I University, Nador, Morocco
² Laboratory of Physics of Matter and Radiation, Faculty of Science, Mohammed I University, Oujda, Morocco

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Received: 19 February 2026
Accepted: 31 March 2026
Published online: 24 April 2026

Abstract

In this work, we present a comprehensive theoretical and numerical investigation of a magnetized electropositive plasma sheath, accounting for the combined effects of secondary electron emission (SEE) from the wall, non-extensive primary electrons, and thermal ions. Using the Sagdeev potential formalism, a generalized Bohm criterion $M$ is derived, and the floating potential ${\psi }_w$ is obtained from the zero-net-current (flux conservation) condition at the wall. In addition, a generalized expression for the secondary electron density at the sheath edge $N_{s0}$ is determined under the quasi-neutrality assumption. A systematic parametric analysis is carried out to examine the influence of four key parameters: the secondary electron emission coefficient $\gamma$, the non-extensive parameter $q$, the ion to electron temperature ratio $T=T_i/T_e$, and the magnetic field inclination angle $\theta$. It is shown that increasing $\theta$ relaxes the Bohm criterion requirement and drives the floating potential toward more negative values. An increase in $\gamma$ reduces the negative wall charge, resulting in a less negative floating potential and a reduction in sheath thickness. Conversely, a decrease in the non-extensivity parameter $q$ enhances the potential drop and increases the sheath thickness. Increasing the temperature ratio $T$ strengthens ion penetration into the sheath, reduces the magnitude of the floating potential, and significantly enhances secondary electron production. Overall, these results highlight the crucial roles of non-extensive electron statistics, magnetic field effects, thermal ions, and secondary electron emission in accurately modeling plasma–wall interactions in magnetized plasma environments.