The Effect of Limiter Flux on Density Profile in FRC

TAE Technologies' device, C-2W, is a beam-driven field-reversed configuration (FRC) [1]. The FRC contains a closed field line region surrounded by the scrape-off layer (SOL) - an open field line region where plasma is confined by magnetic mirrors. The outer boundary of the SOL is defined by the first flux surface to touch the limiter, Ψ_lim. Outside the SOL, plasma density is expected to sharply reduce since plasma streams freely along field lines to the wall or limiters. The presented study evaluates the effect of the value of Ψ_lim on the radial position and profile of the edge plasma density in the mid-plane of the device. This task is especially difficult in FRCs because the magnetic field is largely created by plasma diamagnetic currents with an unknown distribution j(r,z). Here we propose a computationally light-weight method for reconstructing magnetic field using a plasma current parametrization similar to that of elongated Hill's vortex. Parameter optimization is used to find j(r,z), such that the flux at the wall matches experimentally measured magnetic flux. The maximum electron density gradient is calculated from the measured density profile, and the full procedure is run at shot times selected on a number of factors including data reliability, machine performance, and magnet currents. Results show a strong correlation between the radial location of the maximum plasma density gradient and radial location of the Ψ_lim surface at the mid-plane indicating that it plays a key role in determining FRC plasma edge.