Hall MHD Equilibrium of Accelerated Compact Toroids

We examine the structure and dynamics of the compact toroid's magnetic field. The compact toroid is dramatically accelerated by a large rail-gun Lorentz force density equal to $\mathbf{j \times B}$. We use magnetic data from the Compact Toroid Injection Experiment to answer the question of exactly where in the system $\mathbf{j \times B}$ has nonzero values, and to what extent we can apply the standard model of force-free equilibrium. In particular we present a method of analysis of the magnetic field probe signals that allows direct comparison to the predictions of the Woltjer-Taylor force-free model and Turner's generalization of magnetic relaxation in the presence of a non-zero Hall term and fluid vorticity.