Analysis of the rarefaction wave in a screw pinch plasma configuration

The Big Red Ball (BRB) is a spherical multi-cusp plasma confinement vessel that generates plasmas to study magnetic reconnection. Our experiment investigates the nature of the rarefaction wave which is important in understanding the boundary conditions imposed on the magnetic reconnection layer. The Helmholtz coils in the BRB are turned on which creates a magnetic field in the longitudinal direction and plasma is injected into the vessel and then the magnetic field is reversed using the drive coils. The experimental configuration is screw-pinch with the current running through the Toroidal Field coil through the center of the BRB generating a magnetic field in the toroidal direction. This generates a rarefaction wave which we simulate computationally using Dedalus, a spectral PDE solver. We use the ideal MHD equations to formulate our equations for the simulation and then introduce a first order perturbation into the equations. The perturbation is a displacement vector depending only on the radius as the setup is symmetrical in the azimuthal and longitudinal coordinates. The opposing magnetic field lines result in magnetic reconnection and as the rarefaction wave hits the reconnection layer during its formation, there is a drop in the reconnection rate.