Modeling of plasma behavior in a plasma electrode Pockels cell

We present three interrelated models of plasma behavior in a plasma electrode Pockels cell (PEPC), In a PEPC, plasma discharges are formed on both sides of a thin, large-aperture electro-optic crystal (typically KDP). The plasmas act as optically transparent, highly conductive electrodes, allowing uniform application of a longitudinal field to induce birefringence in the crystal. First, we model the plasma in the thin direction, perpendicular to the crystal, via a one-dimensional fluid model. This yields the electron temperature and the density and velocity profiles in this direction as functions of the neutral pressure, the plasma channel width, and the discharge current density, Next, we model the temporal response of the crystal to the charging process, combining a circuit model with a model of the sheath which forms near the crystal boundary. This model gives the time-dependent voltage drop across the sheath as a function of electron density at the sheath entrance. Finally, we develop a two-dimensional MHD model of the planar plasma, in order to calculate the response of the plasma to magnetic fields. We show how the plasma uniformity is affected by the design of the current return, by the longitudinal field from the cathode magnetron, and by fields from other sources. This model also gives the plasma sensitivity to the boundary potential at which the top and bottom of the discharge are held, We validate these models by showing how they explain observations in three large Pockels cells built at Lawrence Livermore National Laboratory.