Resistive wall interaction of axially moving field-reversed E layers or plasma rings

Calculations are performed of the interaction force between an axially moving current carrying plasma ring or E layer with a resistive wall for a variety of parameters relevant to various moving-ring fusion schemes and experiments. Various wall configurations are considered: (i) For a thin resistive wall, the interaction force Fr(vz) is found to be proportional to the axial speed vz or to (1/vz) for small or large velocities, respectively, and to be strongly dependent on the ratio of the effective ring radius R to wall radius Rw. In contrast, the force dependence on the ring thickness δR is found small when rings with similar external field distributions are compared. For fusion-relevant ratios R/Rw≲0.7, and L/R=1–2 (L=ring length), the energy losses for moving the rings an axial distance equal to L may amount to 25% of the rings’ magnetic self-energy. However, this energy can be strongly reduced by proper choice of parameters. (ii) The addition of a fully flux-conserving wall at a radius Rc≳Rw is also found to lead to significant reductions of Fr(v) in the low-velocity regime, dependent in size on the ratio α=Rc/Rw. (iii) A finite wall thickness mainly will lead to increases in Fr(v) at large vz, where the transit time of the rings tt?(R2w+L2)1/2/vz becomes shorter than skin-depth time of the wall. In this case, Fr(v) ∼v−1/2z is obtained.