Reduced model for direct induction startup scenario development on MAST-U and NSTX-U

Abstract

A reduced semi-empirical model using time-dependent axisymmetric vacuum field calculations is used to develop the prefill and feed-forward coil current targets required for reliable direct induction (DI) startup on the new MA-class spherical tokamaks, MAST-U and NSTX-U. The calculations are constrained by operational limits unique to each device, such as the geometry of the conductive elements and active coils, power supply specifications and coil heating and stress limits. The calculations are also constrained by semi-empirical models for sufficient breakdown, current drive, equilibrium and stability of the plasma developed from a shared database. A large database of DI startup on NSTX and NSTX-U is leveraged to quantify the requirements for achieving a reliable breakdown (Ip ~ 20 kA). It is observed that without pre-ionization, STs access the large E/P regime at modest loop voltage (Vloop) where the electrons in the weakly ionized plasma are continually accelerating along the open field lines. This ensures a rapid (order millisecond) breakdown of the neutral gas, even without pre-ionization or high-quality field nulls. The timescale of the initial increase in Ip on NSTX is reproduced in the reduced model provided a mechanism for impeding the applied electric field is included. Most discharges that fail in the startup phase are due to an inconsistency in the evolution of the plasma current (Ip) and equilibrium field or loss of vertical stability during the burn-through phase. The requirements for the self-consistent evolution of the fields in the weakly and fully-ionized plasma states are derived from demonstrated DI startup on NSTX, NSTX-U and MAST. The predictive calculations completed for MAST-U and NSTX-U illustrate that the maximum Ip ramp rate (dIp/dt) in the early startup phase is limited by the voltage limits on the poloidal field coils on MAST-U and passive vertical stability on NSTX-U.

Modelling of ohmic startup and runaway electron formation in support of JT-60SA initial operation

“…During the plasma breakdown, the electron density increases from the natural ionisation level to 10 15 -10 17 m −3 with an electron avalanche. Because the magnetic field lines are not closed initially, the electron energy is bounded by the free-streaming limit [6,51,52], E e = EL c /4 ≈ 250 eV for E = 0.5 V m −1 and L c = 2000 m. Only after the magnetic configuration is closed with a substantial plasma current, the electron can run away to relativistic energies. For the JT-60SA parameter, the typical plasma current after an electron avalanche is expected to be about 200 A, which increases to 10-15 kA at the time when hydrogen is fully ionised (burn-through).…”

“…where E is the electric field in V m −1 and p is the neutral pressure in Pa. The analyses of the breakdown time in NSTX [52] and KSTAR [87] have shown that the Townsend model of equation is insufficient for reproducing the timescale of experimental I p and n e rises, and a mechanism for shielding applied electric fields is required. Numerical studies using PIC simulations [87][88][89][90] have proposed that when ionisation proceeds, self-consistent electric fields formed by the charge separation of electrons and ions shield the applied electric field and retard the breakdown.…”

“…When the self-shielding field in equation (A.4) increases with the electron density, the mechanism can significantly retard the breakdown time. Although the effect of the self-shielding field requires self-consistent description of the potential formation [87,91,92] including the magnetic drift, the E × B drift, and the secondary electron emission from the wall, we here apply an ad hoc model considered by Battaglia et al [52], assuming that the applied electric field is shielded by up to 75% when E self in equation (A.4) exceeds E. We set the other parameter of equation (A.4) as γ ≈ 0.2-0.3 and T e = 1 eV in the simulation of this work. Another mechanism that breaks the assumption underlying the Townsend avalanche must be considered at low pressure.…”

Development of full electromagnetic plasma burn-through model and validation in MAST

“…This should be due to the feature in a spherical torus where E φ /p (kV m −1 Torr −1 ) is high. It was reported that free acceleration of electrons in a spherical torus could shorten the time of electron avalanche phase [20]. However, in the case there is a significant delay in the electron avalanche for some reasons e.g.…”

“…There are two plasma initiation scenarios in MAST, namely merging compression and direct induction [20,25]. Figure 2 shows the solenoid and poloidal field coils in MAST.…”