Spheromak Power and Helicity Balance

This note addresses the division of gun power and helicity between the open line volume and the closed flux surface volume in a steady state flux core spheromak. Our assumptions are that fine scale turbulence maintains each region close to an axisymmetric Taylor state, {mu}{sub o}j = {lambda}B. The gun region that feeds these two volumes surrounded by a flux conserver is shown topologically below. (The actual geometry is toroidal). Flux and current from the magnetized gun flow on open lines around the entire closed surface containing the spheromak. The gun current flows down the potential gradient, the potential difference between the two ends of each line being the gun voltage. Here, the gun voltage excludes the sheath drops at each end. These volumes have different values of {lambda} in each region (open line volume V{sub 1} and closed spheromak volume V{sub 2}) and we want to calculate the efficiency of transferring the gun power to the spheromak to sustain the ohmic loss in steady state