Wide Operational Windows of Edge-Localized Mode Suppression by Resonant Magnetic Perturbations in the DIII-D Tokamak

Edge-localized mode (ELM) suppression by resonant magnetic perturbations (RMPs) generally occurs over very narrow ranges of the plasma current (or magnetic safety factor $q_{95}$) in the DIII-D tokamak. However, wide $q_{95}$ ranges of ELM suppression are needed for the safety and operational flexibility of ITER and future reactors. In DIII-D ITER similar shape plasmas with $n=3$ RMPs, the range of $q_{95}$ for ELM suppression is found to increase with decreasing electron density. Nonlinear two-fluid MHD simulations reproduce the observed $q_{95}$ windows of ELM suppression and the dependence on plasma density, based on the conditions for resonant field penetration at the top of the pedestal. When the RMP amplitude is close to the threshold for resonant field penetration, only narrow isolated magnetic islands form near the top of the pedestal, leading to narrow $q_{95}$ windows of ELM suppression. However, as the threshold for field penetration decreases with decreasing density, resonant field penetration can take place over a wider range of $q_{95}$. For sufficiently low density (penetration threshold) multiple magnetic islands form near the top of the pedestal giving rise to continuous $q_{95}$ windows of ELM suppression. The model predicts that wide $q_{95}$ windows of ELM suppression can be achieved at substantially higher pedestal pressure in DIII-D by shifting to higher toroidal mode number ($n=4$) RMPs.

Figure 1

The evolution of (a)–(c) log of Lyman alpha $D_{\alpha }$ signals and $n=3$ $I$-coil current for three plasmas of varying pedestal density vs $q_{95}$, (d) electron pedestal density $n_{e,\mathrm{ped}}$ for discharge 145380 (blue), discharge 132741 (red), and discharge 157303 (black). The windows of ELM suppression are shaded in yellow.

Figure 2

tm1 simulation of the penetration of the $m/n=10/3$ RMP and its effect on the electron pressure at different $q_{95}$ for discharge 145380: (a) $q$ profiles at different times from Fig. 1, (b) electron pressure profile from tm1 (solid) vs measurement (dashed) for each $q$ profile from $t_1$ to $t_5$, (c) island width $W_{10/3}$ from tm1, and (d) change in pedestal pressure $\mathrm{\Delta }{P}_{e,\mathrm{ped}}$ from tm1 vs RMP strength and $q_{95}$, showing the five different times as black dots. The experimental pressure profiles before ELM suppression (black dashed) is shown in Fig. 2.

Figure 3

Comparison of the pedestal pressure vs $q_{95}$ from experiment (blue), eped prediction (black) and tm1 simulation (red) at (a) high density (discharge 145380) and (b) intermediate density (discharge 132741).

Figure 4

(a) Comparison of the pedestal pressure vs $q_{95}$ from experiment (blue), eped prediction (black) and tm1 simulation (red) at low plasma density (discharge 157303), and (b) Poincaré plot of the magnetic flux surfaces overlaid with the tm1 predicted pressure profile (white) and original pressure profile (blue) for $q_{95}=3.225$, indicated in Fig. 4.

Figure 5

tm1 simulation of the pedestal pressure change $\mathrm{\Delta }{P}_{e,\mathrm{ped}}$ vs resonant field strength $B_r(G)$ and $q_{95}$ for (a) $n=3$ RMP and (b) $n=4$ RMP at high plasma density for discharge 145380 [Fig. 1]. The blue solid line corresponds to a 15% reduction in $P_{e,\mathrm{ped}}$, and the purple dashed line in Fig. 5 corresponds to a 15% reduction in the pedestal pressure for the intermediate density discharge 132741 [Fig. 1].