Anomalous Resistivity in Plasma Focusing Cells for Intense Electron Beams

The efficient focusing of electron beams generated from a pulsed-power-driven diode can produce a bright spot on a high atomic number bremsstrahlung converter for radiography. Pulsed-power diodes can reliably produce high doses with < 1-cm spot sizes. Because of its simplicity, gas cell focusing has been the method of choice for several decades. The electron beam enters the cell through a thin foil that separates the gas from the vacuum diode region. Ideally, the relativistic electron beam drives a gas breakdown that produces a highly conductive plasma. If the beam enters the cell with the correct focusing angle and the beam self fields are largely neutralized, the beam focuses ballistically onto a radiation converter (target). Plasma focusing cells (density approaching 10¹⁶ cm^-3) have a potential advantage over that of a neutral gas due to the large initial conductivity. The influence of micro instabilities and turbulence can degrade the classical resistivity of these cells for some parameters. Using the simulation code LSP, we have observed the onset of anomalous resistivity for low plasma densities and large embedded magnetic fields. The resistivity results from oscillations due to the Bernstein mode instability in the current-carrying plasma. Due to the Doppler effect, the frequency of the electron mode in the ion rest frame can be made sufficiently low to interact with the ions. The resulting oscillations have a growth rate that scales with the relative drift speed between the electrons and ions. Here we discuss the scaling of the instability derived from simulation and theory and its impact on the operation of a plasma focusing cell for radiography.