Plasma flow and acceleration in the magnetic nozzle

Plasma flow and acceleration in the magnetic nozzle with converging-diverging configuration are important for applications in electric propulsion as well as in fusion systems such as open mirrors.  We report on some novel features of plasma acceleration in the magnetic nozzle that have been revealed in recent analytical and computational studies. We show that the non-monotonic magnetic field with a local maximum of the magnetic field is a necessary condition for the formation of the quasineutral accelerating potential structure resulting in  a unique velocity profile fully determined by the magnetic field.  The explicit form of the solution can be obtained in the form of the Lambert function.  The fluid model has been further extended to include the effects of warm ions with anisotropic ion pressure. It is shown that the perpendicular ion pressure enhances plasma acceleration due to the mirror force.  The fluid model predicts that the accelerating solution has a unique value v₀ at the entrance to the magnetic nozzle. Subsonic and supersonic solutions are possible below and above some critical values,  v₀ < v_a and v₀>v_b, respectively. The solutions in the gap region v_a < v₀ < v_b are multivalued and therefore do not exist in fluid theory.  Kinetic effects are investigated using the quasineutral hybrid model with kinetic ions and isothermal Boltzmann electrons. It is shown that for cold ions the velocity profile agrees well with the analytical theory.  A new mechanism of the instabilities is revealed due to the wave breaking, particle trapping, and reflections that occur for particles in the gap region v_a < v₀ < v_b .  Stationary turbulent fluctuations reflect  a fraction of ions. Nevertheless, the velocity profile for passing particles generally follows the accelerating velocity profile which emerges as a constraint on the plasma velocity in the magnetic nozzle.  The role of this constraint in the matching of the magnetic nozzle with the plasma source is discussed.