A power-balance model for local helicity injection startup in a spherical tokamak

摘要

A 0D circuit model for predicting I_p(t) in Local Helicity Injection (LHI) discharges is developed. Analytic formulas for estimating the surface flux of finite-A plasmas developed by Hirshman and Neilson (1986 Phys. Fluids 29 790) are modified and expanded to treat highly shaped, ultralow-A tokamak geometry using a database of representative equilibria. Model predictions are compared to sample LHI discharges in the A ~ 1 Pegasus spherical tokamak, and are found to agree within 15% of experimental I_p(t). High performance LHI discharges are found to follow the Taylor relaxation current limit for approximately the first half of the current ramp, or I_p ≤ 75 kA. The second half of the current ramp follows a limit imposed by power-balance as plasmas expand from high-A to ultralow-A. This shape evolution generates a significant drop in external plasma inductance, effectively using the plasma's initially high inductance to drive the current ramp and provide >70% of the current drive V-s. Projections using this model indicate the relative influences of higher helicity input rate and injector current on the attainable total plasma current.