Calculation of the equilibrium evolution of the ZaP Flow Z-Pinch using a four-chord interferometer

A four-chord interferometer and measurements from an array of surface-mounted magnetic probes were used in conjunction with equations of radial heat conduction and radial force balance to calculate the equilibrium evolution of a pinch plasma in the ZaP flow $Z$-pinch. A multiple shooting method was used to solve the nonlinear coupled differential equation system, with ohmic heating and bremsstrahlung radiation as sources and sinks, respectively. Data from a single ZaP pulse are reported including profiles of magnetic field and temperature and their evolution. Profiles are dominated by high thermal conductivity near the axis which quickly decreases with radius. This is due to the plasma being weakly magnetized near the axis which increases thermal conductivity and flattens the temperature profile, but strongly magnetized near the characteristic radius, significantly reducing thermal conductivity and resulting in a large temperature gradient. The equilibrium evolution indicates that plasmas in ZaP heat and compress with increasing current as a result of magnetic compression during the quiescent period.