Time-independent states of a non-neutral plasma diode when emitted electrons are partially turned around by a transverse magnetic field

Abstract

An analytical study is presented on the steady states of a plasma diode that is uniformly occupied by infinitely massive ions of constant density and driven by a cold electron beam in the presence of an external transverse magnetic field. In contrast to our previous work [Pramanik et al., Phys. Plasmas 23, 062118 (2016)], here, we investigate the case when electrons are reflected back to the emitter by the magnetic field for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions have been evaluated for the specific values of the diode gap, applied voltage, neutralization parameter, and magnetic field strength. It was found that unlike vacuum diodes (e.g., the Bursian diode), steady state solutions also exist for negative values of the emitter field strength. In case of the Bursian diode, only a single type of solutions (Bursian branches) was observed. However, for the Pierce diode, the new family of solutions appeared along with the Bursian ones. In the absence of the external magnetic field as well as when it is weak, the potential distribution shows a wavy nature. However, when the Larmor radius was ten times the beam Debye length, the wavy potential profile and non-Bursian branches disappeared. Based on this phenomenon, a non-neutral diode can be used to operate fast electronic switches.