Modeling Laboratory Sheared Plasma Arcade Equilibria

Plasmas in a force-free equilibrium appear in numerous astrophysical and laboratory contexts. One such class of equilibria includes the sheared magnetic arcade, which can be found on the solar corona or in the Wheaton Impulsive Reconnection eXperiment (WIRX). We develop an analytical model with Bessel functions to describe cylindrically symmetric constant 𝛼 force-free arcade equilibria, where 𝛼 is the force-free parameter given by J = 𝛼B. Our model constrains the current within a cylindrical shell. We use the MHD code AMRVAC to investigate the evolution of the equilibrium in the presence of a magnetic field which is azimuthally inhomogeneous and more similar to the actual experimental magnetic field. We generate predictions for experimentally measurable profiles of magnetic field line shearing angles. Finally, we develop a method to numerically solve for the nonlinear force-free field in arcades where 𝛼 varies with radius within the shell.