Plasma flow and equilibrium in the magnetic nozzle

Axisymmetric cylindrical configurations of the magnetic field are used to confine and guide plasmas in fusion and electric propulsion devices, where plasma equilibria are established as a balance between plasma pressure, magnetic stress (pressure) and inertial forces due to azimuthal plasma rotation and axial flow rotation. Most generally, in an axially inhomogeneous case, plasma rotation and azimuthal magnetic field are related via Alfvén wave type coupling. We show that, for a special case of a current-free nozzle and, therefore, absence of the azimuthal plasma rotation, the plasma flow along the magnetic surface can be analysed independently of the exact shape of the magnetic surface. The velocity of the transonic plasma flow is determined by the magnitude of the magnetic field on the magnetic surface, while the actual shape of the magnetic surface is determined by the solution of the generalised Grad–Shafranov equation that includes the inertial forces. These analytical results are confirmed with numerical simulations that highlight the contribution of the inertial forces to plasma acceleration and equilibrium. Implications for the flows in the magnetic nozzle for the electric propulsion and open mirrors for fusion are discussed.