Measurements and Phenomenological Modeling of Magnetic FluxBuildup in Spheromak Plasmas

Internal magnetic field measurements and high-speed imaging at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper, L. D. Pearlstein, R. H. Bulmer, Nucl. Fusion 39, 863 (1999)] are used to study spheromak formation and field buildup. The measurements are analyzed in the context of a phenomenological model of magnetic helicity based on the topological constraint of minimum helicity in the open flux before reconnecting and linking closed flux. Two stages are analyzed: (1) the initial spheromak formation, i. e. when all flux surfaces are initially open and reconnect to form open and closed flux surfaces, and (2) the stepwise increase of closed flux when operating the gun on a new mode that can apply a train of high-current pulses to the plasma. In the first stage, large kinks in the open flux surfaces are observed in the high-speed images taken shortly after plasma breakdown, and coincide with large magnetic asymmetries recorded in a fixed insertable magnetic probe that spans the flux conserver radius. Closed flux (in the toroidal average sense) appears shortly after this. This stage is also investigated using resistive magnetohydrodynamic simulations. In the second stage, a time lag in response between open and closed flux surfaces after each current pulse is interpreted as the time for the open flux to build helicity, before transferring it through reconnection to the closed flux. Large asymmetries are seen during these events, which then relax to a slowly decaying spheromak before the next pulse