Self-similar solutions for resistive diffusion, Ohmic heating, and Ettingshausen effects in plasmas of arbitrary <i>β</i>

Magneto-inertial fusion (MIF) approaches, such as the MagLIF experiment, use magnetic fields in dense plasma to suppress cross-field thermal conduction, attempting reduce heat loss and trap alpha particles achieve ignition. However, field can introduce other transport effects, some of which are deleterious. An understanding these processes is thus crucial for accurate modeling MIF. We generalize past work exploiting self-similar solutions describe planar geometry compare model radiation-magnetohydrodynamics (MHDs) code Chimera. solve 1D extended MHD equations under pressure balance, making no assumptions about ratio pressures plasma. The resulting ordinary differential equation (ODE) boundary value problem solved using a shooting method, combining an implicit ODE solver Newton–Raphson root finder. show that Nernst effect dominates over resistive diffusion high β plasma, but its significance reduced decreases. On hand, we find Ettingshausen Ohmic heating effects dominant low be observable even order unity though presence strong temperature gradient conduction remains dominant. then present test will useful validate codes effects. also observe plays role preventing separation when strong. Neglecting this term may lead overestimates electron at vacuum–plasma interface, edge z-pinch. developed used provide problems with arbitrary conditions magnetohydrodynamics ability freely switch on terms their individual implementations.