Modeling magnetic fields measured by surface probes embedded in a cylindrical flux conserver

Abstract

Calculating magnetic fields at the surface of a flux conserver, perfect conductor, for displaced plasma currents is useful for understanding modes of a Z-pinch. The magnetic fields measured at the flux conserver are a sum of the magnetic fields from the plasma current and the eddy currents which form in the walls to keep the flux constant. While the magnetic field at the wall from the plasma current alone is easily calculated using the Biot-Savart law, finding the eddy currents in the flux conserver which satisfy the boundary conditions can be a tedious process. A simple method of calculating the surface magnetic field for a given Z-pinch displacement off-axis is derived for a cylindrical flux conserver. This relationship does not require the explicit calculation of the eddy currents, saving time when analyzing surface magnetic probe measurements. Analytic expressions can be used to describe the surface magnetic field which increase the understanding of the magnetic probe measurements.