Relativistic Bursian diode equilibria

Ender, A. Y.; Kuznetsov, V. I.; Schamel, H.
March 2011
Physics of Plasmas;Mar2011, Vol. 18 Issue 3, p033502
Academic Journal
A comprehensive study of steady-states of a planar vacuum diode driven by a cold relativistic electron beam is presented. The emitter electric field as a characteristic function for their existence is evaluated in dependence of the diode length, the applied potential V, and the relativistic beam factor at injection γ0. It is used to classify the different branches of possible solutions, which encompass electron flows that are (i) transmitted through the diode completely, (ii) partially reflected from a virtual cathode (VC) either within the diode region or at the collector side, and (iii) reflected totally. As a byproduct, the V and γ0 dependences of both bifurcation points of the minimum potential and of the transmitted current are obtained and the ultrarelativistic limit, γ0>1, is performed. In this highly relativistic regime, the density of electrons appears to be constant across the diode region except for a small area around the VC.


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