Magnetic mirror effects on a collisionless plasma in a convergent geometry

Several plasma thruster concepts, as well as ion engine chambers, use magnetic cusps to protect walls and to throttle electron flow to anodes. We present a kinetic model of the plasma in the vicinity of one cusp. Electrons, strongly confined by the electrostatic presheath and sheath, are assumed isotropic. Collisionless ions are either magnetically guided or completely nonmagnetized, thus bracketing conditions of interest. For magnetized ions, electrostatic and magnetic mirror forces compete, and the resulting self-consistent potential is found by imposing quasineutrality. A similar competition occurs for nonmagnetized ions, this time as a result of the convergence of equipotential lines. Analytical solutions are found for monoenergetic ions, and these are generalized to the case of an initially Maxwellian population, for which some numerical iteration is required. The presheath potential drop is in all cases of the order of 0.6–0.75 times the electron temperature, and ions enter the sheath at a sonic velocity, according to Bohm’s criterion. Contrary to intuition, the cusp does not reduce the ion flux (per unit area) to the wall, only the size of the wall area section that carries this flux by virtue of its connection to the distant plasma. These kinetic results are verified by checking the conservation of relevant moments of the ion distribution, including two new quantities that generalize the average magnetic moment and the total ion enthalpy by accounting for the nonzero ion heat fluxes.