Variational analysis of a plasma-arc armature inside a railgun solid-hydrogen-pellet accelerator for fueling fusion reactors

The physical properties of a plasma-arc armature inside a hydrogen-pellet injector composed of a two-stage electromagnetic railgun are calculated by solving appropriate governing equations under simplifying assumptions. A variational method is employed to solve the temperature equation with the constraints that the variational integral must be minimized for a given plasma arc current and that the global enthalpy must be conserved. The magnetic field and the propulsive force of the railgun are calculated by modeling each current path as a composite of straight lines. The resulting railgun force is compared with the data from a recent hydrogen-pellet acceleration experiment at the University of Illinois, with reasonable agreement.