Scaling relations for a needle-like electron beam plasma from the self-similar behavior in beam propagation

Abstract

Scaling relations of the main parameters of a needle-like electron beam plasma (EBP) to the initial beam energy, beam current, and discharge pressures are presented. The relations characterize the main features of the plasma in three parameter space and can provide great convenience in plasma design with electron beams. First, starting from the self-similar behavior of electron beam propagation, energy and charge depositions in beam propagation were expressed analytically as functions of the three parameters. Second, according to the complete coupled theoretical model of an EBP and appropriate assumptions, independent equations controlling the density and space charges were derived. Analytical expressions for the density and charges versus functions of energy and charge depositions were obtained. Finally, with the combination of the expressions derived in the above two steps, scaling relations of the density and potential to the three parameters were constructed. Meanwhile, numerical simulations were used to test part of the scaling relations.