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 γ, including the Pierce (γ=1) and the Bursian (γ=0) diode as special cases. Physically such a study is of interest, e.g. in the transport problem of an electron beam in spatially bounded electronic devices. Similarity transformations are obtained which connect equilibrium solutions of different γʹs. This implies that by simple transformations one can infer from equilibria of the generalized Pierce diode to equilibria of nonneutral diodes. The regimes with partial and total reflection of electrons are studied in detail for the first time. A classification of nonuniform solutions for these regions as well as for the regime without reflection is presented. The equivalence between the Eulerian and the Lagrangian formulation of the diode dynamics is proved, and both, the aperiodical and oscillatory eigenmodes of the generalized Pierce diode are examined. New bifurcation points in the branches of dispersion relations are discovered.