Stability and energetics of Bursian diodes

Abstract

We present an analysis of the stability, energy, and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of equilibrium solutions for the same boundary conditions, one solution is found to be stable and the other unstable to linear perturbations. Following the linearly unstable solutions into the nonlinear regime, we find they relax to the stable equilibrium. A description of this process in terms of kinetic, potential and boundary-flux energies is given, and the relation to a Hamiltonian formulation is commented on. A nonlocal torque integral theorem relating the prescribed boundary data to the average current in the domain is also provided. The results will be useful for numerical verification purposes, and understanding Bursian diodes in general.