Mhd Calculations of Anode Plasmas

We have performed a series of idealized MHD calculations of the response of an anode plasma layer to the rising magnetic field in an applied-B ion diode. The purposes of this study were to consider Joule heating of the plasma layer, which could pose potential problems for lithium ion diodes, and the leakage of flux behind the ion-emitting surface, which is related to impedance collapse. We find that, as induced JxB forces move the plasma toward the wall, the entrained, initial field is compressed until it just equals the rising external field. Achieving such equilibrium decreases both Joule heating and flux leakage into the plasma. For relatively thin (1 mm) plasma layers at moderate densities (1016 lol7 cm-3) we calculate that this equilibrium is achieved quite rapidly, leading to acceptably low levels of both flux penetration and Joule heating. Introduction In a recent paper Slutzl concluded that Joule heating resulting from a rising diagmagnetic current in an applied-B ion diode would be sufficient to quickly bring the anode plasma to a multi-keV temperature. This would, for densities above 1016 lead to a considerable fraction of collisional ionization of Li+ to Li++ and Li+++. Thus, it was concluded that ideal initial conditions for such an anode plasma would be a relatively thick (to allow a sufficient supply of ions) layer of low density (< lo16cm-3) plasma. We have found from a series of idealized MHD calculations, however, that, if the anode surface has a conducting substrate, then much of the diagmagnetic current can flow there, flattening the magnetic field distribution in the anode plasma. This shunting of diagmagnetic current to the wall, shown to be more effective for thinner plasma layers, considerably reduces Joule heating. Furthermore, Desjarlais2,3 has shown that impedance collapse may be related to the rate of flux loss across the ionemitting surface, which would also be altered by reduced field gradients in the plasma. 1-D MHD Calculations A series of idealized 1-D MHD calculations was performed utilizing the following approximations: 1) A plasma of uniform density, no, temperature, To, extending a distance ro from the anode was assumed; ablation of new material from the substrate was ignored, as was the ionization of any neutrals that might be present in the gap. 2) An ideal gas equation of state for singly ionized Li was used. 3) An initially uniform, Bo = 5 T external magnetic field was applied, rising exponentially (time constant = 40 ns) to 10 T in 30 ns. Note that the rising component of field is here assumed to be in the same direction as the applied field, whereas experimentally, it may have a perpendicular component. 4) A highly conductive substrate was assumed, but heating and blow-off from this layer were ignored. 5) Erosion of ions from the plasma surface was ignored. The worst of these approximations is probably the first, since a non-uniform density and temperature distribution, a flux of material ablated off the anode surface, or the ionization of a significant number of 959 pre-existing neutrals would be required to give thP observed late time expansion of plasma away from the anode3. Nevertheless, results of calculations employing these approximations are instructive in that they point to the existence of an effect that must h· considered in more detailed models. ,... >< > 1C/) z w 0