Theory of weak switching of arbitrary collector voltages in non-neutral plasma diodes

Abstract

The response function concept is used to describe analytically the dynamics of electrons in a non-neutral diode in which the collector voltage is switched on at t = 0 from zero to a weak but otherwise arbitrary time-dependent voltage. It generalizes previous investigations of simple switching (Akimov et al 2003 J. Appl. Phys. 93 1246; Ender et al 2004 Phys. Plasmas 11 3212), where the final voltage is assumed to be constant. Use is made of the Laplace transformation technique and a remarkably simple expression is found for the Laplace-transformed emitter electric field from which analytic solutions for the time-dependent, highly transient response of the diode can be obtained. As an application, the switching to a final harmonic collector potential called cos-switching is investigated and the usefulness of an approximative response function approach is demonstrated by a comparison of the approximative with the exact results. For diodes with different charge non-neutrality parameter and branches with no electron reflection various scenarios for cos-switching are explored, revealing the exact time behaviour of the emitter electric field and of the net current density. The amplitude A∞(ω) of the asymptotically driven oscillation as a function of the driven frequency ω is also presented. Of upmost importance is a novel resonance phenomenon we found in that part of the second zone of generalized Pierce diodes for which the non-reflecting equilibria are linearly stable against aperiodic and oscillatory eigenmodes. In a narrow band region A∞(ω) amplifies by a factor 50. This driven internal oscillation takes place on a high current level raising high promises e.g. for microwave generators and/or circuit current amplifiers as well as for diagnostic purposes.