Systems and methods establish plasma in a rotating magnetic field. An exemplary embodiment is a plasma thruster that establishes a first transverse magnetic field with respect to a system axis of a plasma propulsion system; establishes a second transverse magnetic field oriented orthogonally to the first transverse magnetic field, wherein the second transverse magnetic field is out of phase with the first transverse magnetic field; and establishes a magnetic field aligned with the system axis using a plurality of magnet elements oriented along the system axis. A plasma containment portion defines an interior region, wherein an interior region of a plasma containment portion accommodates a plasma that is established by a rotating magnetic field component that is cooperatively established by the first transverse magnetic field and the second transverse magnetic field, and wherein the plasma is accelerated out of the plasma containment portion by magnetic forces to generate a propulsion force.