Relaxation of virtual cathode oscillations due to transverse effects in a crossed-field diode

Summary form only given, as follows. Recent studies of cylindrical and planar crossed-field diodes indicate the transverse dimension plays a role in delaying the onset of virtual cathode oscillations for currents injected above the theoretical limiting current. For 1d and 2d planar devices, the limiting current for the magnetized (B=B/sub Hull/) and unmagnetized diodes is examined for cold and thermal injection. A significant difference between the 1d and 2d smooth diodes is that the transverse direction gives an extra degree of freedom which is found to warm the electrons rapidly. The mechanism of this warming appears to be an instability in the transverse direction. The simulations show three different ´states´; laminar flow, virtual cathode oscillation and warm flow. Warm flow occurs when the electron have a spread of energy, either due to an instability or by thermal injection, when they pass though the potential minimum. Birdsall and Bridges (1966) showed that a small thermal spread of injected electrons damps virtual cathode oscillations. This warming effect allows ´warm flow´ to exist on the 2d state diagram (J/J/sub c/ versus B/B/sub Hull/) which is not found on the 1d state diagram for cold emission. Parameter space is explored on these state diagrams for B=0 and B=B/sub Hull/ for J near state transitions (J/spl sime/J/sub G/). In these PIC simulations, the particles are injected in such a way as to keep the transverse density as uniform as possible. This quiet particle injection algorithm was used so that particle noise does not cause numerical warming in the transverse direction.