Global characteristics of plasma acceleration across the magnetic field: sonic point regularization and global profiles

We consider the one-dimensional problem of acceleration of quasineutral partially magnetized plasma across the magnetic field. The ions assumed to be unmagnetized, while magnetized electrons are considered in the drift diffusion approximation. Ionization processes are also included allowing finite velocity of neutrals as is typical for Hall thrusters. The electric field is created by the potential difference applied across the discharge. We show that resolving the sonic point singularity impose strong constraints on stationary solutions and plasma parameters profiles. We find a simple condition defining the range of plasma paramaters where the stationary solutions are possible identifying two separate branches. The stationary profiles for all plasma parameters are build starting from the sonic point. These solutions show that plasma profiles are very stiff (rigid) for a fixed potential difference and the whole problem should be considered as an eigen-value problem for the electron temperature (or equivalently for the ionization rate). The implications for the matching of the quasineutral plasma with the sheath region as well as for the breathing mode oscillations are discussed.