The Electrodynamic Mechanism of Collisionless Multicomponent Plasma Expansion in Vacuum Discharges: From Estimates to Kinetic Theory

Abstract

This paper is devoted to the study of collisionless multicomponent plasma expansion in vacuum discharges. Based on the fundamental principles of physical kinetics formulated for vacuum discharge plasma, an answer is given to the following question: What is the main mechanism of cathode plasma transport from cathode to anode, which ensures non-thermal metallic positive ion movement? Theoretical modeling is provided based on the Vlasov–Poisson system of equations for a current flow in a planar vacuum discharge gap. It was shown that the non-thermal plasma expansion is of a purely electrodynamic nature, caused by the formation of a “potential hump” in the interelectrode space and its subsequent movement under certain conditions consistent with plasma electrodynamic transportation. The presented results reveal two cases of the described phenomenon: (1) the dynamics of single-component cathode plasma and (2) multicomponent plasma (consisting of multiple charged ions) expansion.

The kinetic theory of cathode plasma expansion in a spatially non-uniform geometric configuration of a vacuum diode

“…where Z e,i are the particle charge sign, q is the electron charge, m e,i are the rest masses of the electron and ion, respectively, ε 0 is the vacuum dielectric permittivity, and n e,i are electrons and ions number densities, respectively. The system of equation (1) represents a considerably more complex form of the Vlasov-Poisson equations system than in the previously employed one-dimensional model in [13], as describing the plasma expansion process in an axially symmetric diode requires transitioning to a cylindrical coordinate system. Unlike the one-dimensional kinetic equation in Cartesian coordinates used in [13], the 1.5D equation (1) contains terms pφ 2 me,ir f e,i and (− p r pφ me,ir )f e,i , corresponding to the contributions of centrifugal and Coriolis forces, respectively.…”

“…The system of equation (1) represents a considerably more complex form of the Vlasov-Poisson equations system than in the previously employed one-dimensional model in [13], as describing the plasma expansion process in an axially symmetric diode requires transitioning to a cylindrical coordinate system. Unlike the one-dimensional kinetic equation in Cartesian coordinates used in [13], the 1.5D equation (1) contains terms pφ 2 me,ir f e,i and (− p r pφ me,ir )f e,i , corresponding to the contributions of centrifugal and Coriolis forces, respectively. These terms arise as a consequence of the coordinate transformation of the Vlasov equation in the conservative form.…”

“…Given the diversity of hypotheses concerning this phenomenon, preference is given to models that rely on the minimum number of initial assumptions. One such theory of cathode plasma expansion is the previously proposed 'minimal' kinetic model, based on the Vlasov-Poisson system of equations for a planar (one-dimensional) vacuum gap, where the cathode plasma emission under the application of the anode potential is simulated by specifying simple boundary conditions [13,14]. This model has provided answers to the fundamental question of why anomalous ion acceleration occurs.…”

“…This paper presents further development of the kinetic theory of cathode plasma expansion previously given in [13,14]. The main improvement here lies in the use of a 1.5dimensional kinetic description, where the Vlasov equations, formulated in cylindrical coordinates, include one spatial coordinate r and two components of momentum p r and p φ , corresponding to the radial and azimuthal directions, respectively.…”

Kinetic simulation of vacuum plasma expansion beyond the "plasma approximation"

“…In this paper, the system of partial differential equations (3) was solved numerically on a rectangular uniform phase-space grid (x, p) having 5000 per 2001 grid points for electrons and ions. The Vlasov equations have been solved by using the high-order Cheng-Knorr semi-Lagrangian method similar to that previously used (Zubarev et al, 2020, Kozhevnikov et al, 2021. The numerical solution algorithm was implemented in Mathworks MATLAB exploiting the embedded high-performance CPU capabilities.…”