Collective diode dynamics: An analytical approach

An analytical study of the plasma states in nonneutral plasma diodes and of their stability is presented for an arbitrary neutralization parameter gam ma, including the Pierce (gamma = 1) and the Bursian (gamma = 0) diode as s pecial cases. Physically such a study is of interest, e.g. in the transport problem of an electron beam in spatially bounded electronic devices. Simil arity transformations are obtained which connect equilibrium solutions of d ifferent gamma's. This implies that by simple transformations one can infer from equilibria of the generalized Pierce diode to equilibria of nonneutra l diodes. The regimes with partial and total reflection of electrons are st udied in detail for the first time. A classification of nonuniform solution s for these regions as well as for the regime without reflection is present ed. The equivalence between the Eulerian and the Lagrangian formulation of the diode dynamics is proved, and both, the aperiodical and oscillatory eig enmodes of the generalized Pierce diode are examined. New bifurcation point s in the branches of dispersion relations are discovered. (C) 2000 Elsevier Science B.V. All rights reserved.