Time-dependent optimization of initiation phase of the outer PF coil-only inductive start-up of NSTX plasmas

Abstract

Dynamic modelling of the inductive plasma start-up utilizing only the outer poloidal field (PF) coils without using an in-board Ohmic solenoid was performed for the National Spherical Torus eXperiment (NSTX) based on the static calculation result. A time-dependent calculation using the two-dimensional axisymmetric dynamic code and the plasma evolution code enabled us to find the appropriate waveform of the NSTX PF coils that satisfied various start-up conditions, such as the formation and sustainment of field null, a significant amount of magnetic flux for further plasma current ramp-up, sufficient size of the E-t (.) B-t/B-perpendicular to = 0.1 kV m(-1) contour for successful breakdown, force balance condition, etc. Among many sets of solutions possibly satisfying the aforementioned conditions, the result introduced in this report also meets the requirement imposed by the power supply system. With the obtained current waveform of the PF coils, it is shown that the hexapole quality field null can be sustained for at least 6 ms with a reasonably large size. The available induction flux at the expected starting time of the breakdown period is as large as 0.15 Wb, with which the plasma current can ramp up to a few hundred kiloamperes, based on experience from the conventional in-board Ohmic solenoid start-up on NSTX. The size of the E-t (.) B-t/B-perpendicular to = 0.1 kV m(-1) contour, in which successful breakdown occurred in the presence of strong pre-ionization on DIII-D, is as large as more than 30 cm, and sustains for several milliseconds. An analysis for the force balance and the field index shows that the plasma produced can be stable for radial as well as vertical perturbations during the initial start-up phase.