Theoretical aspects of the use of pulsed reflectometry in a spheromak plasma

Abstract

Pulsed reflectometry using both ordinary (O) and extraordinary (X) modes has the potential of providing time- and space-resolved measurements of the electron density, the magnitude of the magnetic field, and the magnetic shear as a function of radius. Such a diagnostic also yields the current profile from the curl of the magnetic field. This research addresses theoretical issues associated with the use of reflectometry in the Sustained Spheromak Physics Experiment spheromak experiment at the Lawrence Livermore National Laboratory. We have extended a reflectometry simulation model to accommodate O- and X-mode mixed polarization and linear mode conversion between the two polarizations. A Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) formula for linear mode conversion agrees reasonably well with direct numerical solutions of the wave equation, and we have reconstructed the magnetic pitch–angle profile by matching the results of the WKBJ formula with the mode conversion data observed in simulations using a least-squares determination of coefficients in trial functions for the profile. The reflectometry data also yield information on fluctuations. Instrumental issues, e.g., the effects of microwave mixers and filters on model reflectometry pulses, have been examined to optimize the performance of the reflectometry diagnostics.