Modeling and measurement of toroidal currents in the HSX stellarator

A set of magnetic diagnostics, including Rogowski coils, diamagnetic loops and two poloidal 'belts' of 3-axis pick-up coils measure the magnetic field at several locations around HSX. The two belts are separated by ≈1/3 of a field period and measure the local magnetic field vector at 16 poloidal locations at the two toroidal angles. With the VMEC [1] and PENTA [2] codes, a calculation of the Pfirsch-Schlüter (PS) and bootstrap currents is performed. The 3-D equilibrium reconstruction code V3FIT [3] is then used to calculate the expected response of the magnetic diagnostics. The sensitivity of the diagnostic set to features in both the PS and bootstrap current is explored. Because of the lack of toroidal curvature, the dipole PS current has a helical rotation and nearly reverses at the two toroidal locations. The bootstrap current in HSX is in the opposite direction compared to that in a tokamak. Compared to a tokamak, the relative magnitude of each current is reduced by a factor of the effective transform (≈3) [4]. The PS current reaches steady state quickly, whereas the bootstrap current rises throughout the discharge on a 50-500 ms timescale. In most cases, the toroidal current is still rising at the end of the discharge, reaching 0.4-0.6 kA. A 3-D model that relies on the calculation of the susceptance matrix [5] is used to calculate the time evolution of the toroidal current.