Time-Dependent Simulations of Fast-Wave Heated High-Non-Inductive-Fraction H-Mode Plasmas in the National Spherical Torus Experiment Upgrade

30 MHz fast-wave heating may be an effective tool for non-inductively ramping low-current plasmas to a level suitable for initiating up to 12 MW of neutral beam injection on the National Spherical Tokamak Experiment Upgrade (NSTX-U). Previously on NSTX 30 MHz fast wave heating was shown to efficiently and rapidly heat electrons; at the NSTX maximum axial toroidal magnetic field (BT(0)) of 0.55 T, 1.4 MW of 30 MHz heating increased the central electron temperature from 0.2 to 2 keV in 30 ms and generated an H-mode plasma with a non-inductive fraction (fNI) ~ 0.7 at a plasma current (Ip) of 300 kA. NSTX-U will operate at BT(0) up to 1 T, with up to 4 MW of 30 MHz power (Prf). Predictive TRANSP free boundary transport simulations, using the TORIC full wave spectral code to calculate the fast-wave heating and current drive, have been run for NSTX-U Ip = 300 kA H-mode plasmas. Favorable scaling of fNI with 30 MHz heating power is predicted, with fNI ≥ 1 for Prf ≥ 2 MW.


Introduction
A Fusion Nuclear Science Facility based on the spherical tokamak concept needs to operate with little or no inductive drive from a central solenoid [1].A long-term research goal of the National Spherical Tokamak Experiment Upgrade (NSTX-U) [2] is to develop fully non-inductive plasmas, and the NSTX-U fast-wave heating system may be an effective tool for noninductively ramping low-current plasmas to a level suitable for initiating up to 12 MW of neutral beam injection [3].On NSTX, 30 MHz fast-wave heating efficiently and rapidly heated electrons; at the NSTX maximum axial toroidal field (B T (0)) of 0.55 T, 1.4 MW of fast-wave heating increased the central electron temperature (T e (0)) from 0.2 to 2 keV in 30 ms and generated an H-mode plasma (NSTX shot #138506) with a non-inductive fraction (f NI ) ~ 0.7 at a plasma current (I p ) = 300 kA [4].The NSTX-U fast-wave heating system will couple up to 4 MW of RF power (P rf ) and will operate again at 30 MHz, which is the 4 th harmonic of deuterium at the maximum NSTX-U B T (0) of 1 T. Predictive TRANSP free boundary transport simulations [5] have been run for NSTX-U I p = 300 kA H-mode plasmas in order to study the dependence of f NI on B T (0) and P rf .The TRANSP simulations used the TORIC full wave spectral code [6] to calculate the fast-wave heating and current drive.The transport in the simulations was benchmarked to the experimental results obtained on NSTX.This paper presents the results of these simulations and the implications for using 30 MHz power on NSTX-U to ramp I p non-inductively.

Predictive modelling assumptions
The thermal transport model used in the predictive TRANSP simulations was the Multimode MMM7.1 model [7].This model gave reasonably good agreement to plasma parameters (eg.f NI , T e (0) and plasma pressure) obtained experimentally during NSTX shot #138506 for a NSTX-U simulation with similar B T (0) and P rf .Effective charge, impurity, rotation and other profiles were taken largely from NSTX plasma shot #142305, a plasma that was part of an experimental campaign to support NSTX-U and next-step Spherical Tokamak devices [8].
All the simulations used a k // = 8 m -1 antenna phasing, the current drive antenna phasing used for shot #138506.The RF pulse was ramped up to the flat top level in 30 ms, starting at 100 ms.This RF power ramp rate was typical for experiments on NSTX.
In the simulations the electron density profile and central density (n e (0)) were initially chosen to be similar to shot #138506, which had n e (0) = 1.15x10 19 m -3 .The density in the simulation was ramped to this level in 100 ms, at that time a H-mode transition was imposed by flattening the density profile, as shown in figure 1. However when B T (0) > 0.75 T it was found that when using this relatively low density the plasma became unstable and the simulations terminated prematurely, EPJ Web of Conferences 157, 03052 (2017) typically only ~100 ms after the start of the RF pulse.
Increasing n e (0) to 1.43x10 19 m -3 resulted in stable plasma simulations up to P rf = 4 MW and B T (0) = 1 T. Simulations were run for P rf = 1.4,2, 3 and 4 MW, and for plasmas having B T (0) = 0.5, 0.65, 0.75, 0.89 and 1 T.      shows the area integrated current densities at 0.4 s. 90% of the RF-driven current is within r/a = 0.2, while 90% of the bootstrap current is generated within r/a = 0.5.Because the RF heating was strongly peaked near the axis this results in the development of a highly peaked T e (R) profile (figure 4(a)) which further increases the RF-driven current near the magnetic axis.This peaking of T e (0) and the RF-driven current at higher P rf , particularly at higher B T (0), caused the plasma simulation to become unstable in the first 100 ms of the RF pulse, prematurely terminating the simulation, as mentioned earlier.This behaviour was also seen in NSTX shot #138506.Although it didn't cause the plasma to disrupt it did result in a magneto-hydrodynamic reconnection in the plasma core that rapidly reduced the stored energy resulting in the plasma moving radially and briefly tripping the RF heating pulse.

Results
All the lower density, n e (0) = 1.15x10 19 m -3 simulations that didn't terminate by ~ 0.2 s reached a quasi-steady state condition by 0.4 s. Figure 5  Figure 6 shows the dependence of f NI at 0.4 s on B T (0) for the n e (0) = 1.15x10 19 m -3 simulations.Increasing B T (0) from 0.5 to 0.65 T is predicted to significantly increase f NI , particularly at the higher P rf .However, f NI   decreases above B T (0) = 0.65 T at all values of P rf .
For the n e (0) = 1.15x10 19 m -3 simulations fully noninductive operation is predicted with as little as 2 MW of RF power for a B T (0) = 0.65 T plasma, As mentioned earlier, increasing n e (0) to 1.43 x 10 19 m -3 provided stable plasma simulations up to P rf = 4 MW at B T (0) = 1 T. Figure 7 plots f NI at 0.4 s versus P rf for this slightly higher density case.f NI ≥ 1 is predicted for P rf ≥ 3 MW for the plasma simulations with B T (0) = 0.75 T. At P rf = 4 MW all the plasma simulations with B T (0) ≥ 0.65 predict fully non-inductive operation.Increasing P rf from 2 to 4 MW increased f NI by 1.6, 1.7, 1.8 and 1.4 for the 0.5 T, 0.65 T, 0.75 T and 1 T simulations, respectively.As expected, the somewhat higher density reduced the f NI achieved at a given P rf and B T (0) compared to the lower density simulations.
Figure 8 plots f NI at 0.4 s versus B T (0) for the n e (0) = 1.43 x 10 19 m -3 simulations.While f NI increases significantly when B T (0) is raised from 0.5 T to 0.65 T, f NI decreases when B T (0) increases from 0.75 to 1 T, as predicted for the n e (0) = 1.15 x 10 19 m -3 simulations.

Conclusions
The TRANSP simulation results presented here strongly support the possibility of achieving stable f NI ≥ 1 plasmas with P rf = 2-3 MW in an I p = 300 kA NSTX-U plasma.However while increasing P rf to higher levels than were achieved on NSTX shot #138506 is predicted to increase f NI the simulations also predict that the plasma may become unstable as P rf is increased, particularly at the highest B T (0) values achievable on NSTX-U.The simulations predict that increasing B T (0) to 0.65 T from 0.55 T, the value used in NSTX experiment, may significantly increase the achievable f NI .One caveat is that operationally it was difficult to control I p = 300 kA NSTX plasmas when fast wave power was coupled into the I p flattop, even at P rf = 1.4 MW.Coupling fast wave power at even higher levels will no doubt be challenging.But even more challenging will be coupling fast wave power immediately after start up in order to ramp I p up to 300-400 kA.These TRANSP simulation predictions must now await experimental validation in NSTX-U.

Figure 2
Figure 2 summarizes the predictive TRANSP simulation results for a NSTX-U plasma with the same

Figure 3 (
a) shows the time evolution of T e (0) reaches 5 keV.As shown in figure 3(b), the bootstrap current remains constant around 100 kA and the RF-driven current reaches 370 kA at 0.4 s. Figure 4(a) shows T e at the start of the RF pulse (dashed line) and at 0.4 s (solid line) for the case shown in figure 3. The T e profile becomes very peaked during the RF pulse (figure 4(a)).

Fig. 3 .
Fig. 3. Predictive TRANSP results for an I p = 300 kA, B T (0) = 0.65 T NSTX-U plasma with P rf = 4 MW.(a) Time evolution of n e (0), T e (0) and P rf .(b) Time evolution of various currents predicted by TRANSP.

Fig. 2 .
Fig. 2. Predictive TRANSP results for an I p = 300 kA, B T (0) = 0.5 T NSTX-U plasma with P rf = 1.4 MW.(a) Time evolution of n e (0), T e (0) and P rf .(b) Time evolution of various currents predicted by TRANSP.The predicted T e (0) and f NI are similar to NSTX shot #138506.
shows the dependence of f NI at 0.4 s on P rf for the n e (0) = 1.15x10 19 m -3 simulations.Also plotted in this figure is the f NI achieved during NSTX shot #138506.At P rf = 1.4 MW all the simulations have an f NI ~ 0.6, independent of B T (0), and in fairly good agreement with the f NI = 0.7±0.2achieved experimentally during NSTX shot #138506.Increasing P rf from 1.4 to 4 MW for the B T (0) = 0.5 T simulation approximately doubled f NI .For the B T (0) = 0.65 T and 0.75 T simulations f NI increased by 2.8 and 2.4, respectively.The B T (0) = 0.89 T simulation became unstable at ~ 0.2 s when P rf was increased above 2 MW and the B T (0) = 1 T simulations were all unstable early in the RF pulse.

Fig. 5 .
Fig. 5. f NI at 0.4 s versus P rf for plasma simulations with n e (0) = 1.15x10 19 m -3 .Also plotted in this figure is the f NI achieved during NSTX shot #138506 (grey filled circle with range during the shot indicated by the vertical bar).

Fig. 6 .
Fig. 6. f NI versus B T (0) for the n e (0) = 1.15x10 19 m -3 plasma simulations.Also plotted in this figure is the f NI achieved during NSTX shot# 138506 (grey filled circle with range during the shot indicated by the vertical bar).

Fig. 4 .
Fig. 4. (a) Electron temperature profile at 0.1 s, the start of the RF pulse (dashed line) and at 0.4 s (solid line).(b) Area integrated currents versus normalized minor radius for the case shown in figure 3 at 0.4 s. 90% of the RFdriven current is located inside r/a = 0.3.