Magnetic helicity balance in the Sustained Spheromak Plasma Experiment

The magnetic helicity balance between the helicity input injected by a magnetized coaxial gun, the rate-of-change in plasma helicity content, and helicity dissipation in electrode sheaths and Ohmic losses have been examined in the Sustained Spheromak Plasma Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, and R. H. Bulmer, Nucl. Fusion 39, 863 (1999)]. Helicity is treated as a flux function in the mean-field approximation, allowing separation of helicity drive and losses between closed and open field volumes. For nearly sustained spheromak plasmas with low fluctuations, helicity balance analysis implies a decreasing transport of helicity from the gun input into the spheromak core at higher spheromak electron temperature. Long pulse discharges with continuously increasing helicity and larger fluctuations show higher helicity coupling from the edge to the spheromak core. The magnitude of the sheath voltage drop, inferred from cathode heating and a current threshold dependence of the gun voltage, shows that sheath losses are important and reduce the helicity injection efficiency in SSPX.