STATIONARY VOLTAGE-CURRENT CHARACTERISTICS OF A PLASMA

In this paper a one dimensional, relativistic model of a two component mono energetic plasma of electrons and ions is investigated. Given an applied electric potential Phi(A) the electron and ion currents j(e) and j(i) are calculated. The analysis is based on the associated Lagra nge functional. The model equation is a nonlinear ODE of order two in terms of the electric potential phi. Electron and ion current are unkn own parameters. This ODE is subject to four boundary conditions. it is shown that infinitely many solutions (phi,j(e),j(i)) exist but only o ne distinguished solution minimizes the Lagrange functional. The asymp totic voltage-current-characteristics in non realistic, relativistic a nd ultra relativistic settings are computed and rigorously justified.