Steady-state rotational dynamics of a weakly ionized hydrogen plasma under cross-field configuration

We study a novel device for generating a high-speed rotating plasma. The device weakly ionizes and accelerates a hydrogen gas in a co-axial cylindrical chamber via the perpendicular configuration of electrodes with a magnetic field generated by a superconducting magnet. It has been hypothesized that extreme velocities and plasma particle compression could be achieved under this configuration [Wong et al., Phys. Plasmas 31, 013101 (2024)]. This work develops a rigorous theoretical model of the bulk plasma dynamics under steady-state centrifugal operation. By exploiting the axisymmetry of the system and from the application of problem-specific governing assumptions, a steady-state 1D model for the rotational dynamics of the bulk plasma is derived. From here, we present fully analytical solutions for the radial profiles of the MHD model: (azimuthal velocity, particle densities, pressure) and a semi-analytical solution for the electric potential. Tables of self-consistent plasma parameters are computed to provide a comprehensive characterization of the bulk plasma state. The model can determine the peak velocities and plasma compression, and permits parametric studies to elucidate the complex and nonlinear relationships between operational device settings and the achieved steady-state plasma state condition. The new theoretical solutions, therefore, provide necessary insights into the viability of the novel device for high-energy-density plasma applications.