High Internal Inductance for High $\beta_N$ Steady-State Tokamak Operation

An attractive scenario for steady-state tokamak operation at relatively high values of the internal inductance, $l_i$ $>1$, has been demonstrated at DIII-D. The more peaked current density profile leads to reduced core energy transport and higher ideal stability limits that could eliminate the need for n$\ge$ 1 active stabilization coils at $\beta_N\approx$ 4, or enable $\beta_N\approx$ 5 with wall stabilization. The scenario's potential is shown by discharges at $l_i$ $\approx$ 1.3 with high bootstrap current fraction $\mbox{f$_{BS}$ $\approx$ 0.8}$, high plasma pressure $\beta_N\approx$ 5 and excellent confinement H$_{98(y,2)}$ $\approx$ 1.8. This very high $\beta_N$ discharge with q$_{95}$ =7.5 has noninductive current fraction f$_{NI}$ $>1$ and too much bootstrap current in the H-mode pedestal, so $l_i$ decreases with time. To achieve a stationary current profile, the key is to maximize $\beta_N$ and f$_{BS}$ while maintaining $l_i$ high enough for stability through choice of q$_{95}$ or by reduced pedestal current. DIII-D modeling shows that with q$_{95}$ reduced to lower f$_{BS}$ to $\approx$ 0.5, a self-consistent equilibrium has $l_i$ $\approx$ 1.07 and $\beta_N\approx$ 4 (below the n=1 no-wall limit) with q$_{95} \approx$ 6. The remainder of the current can be externally-driven near the axis where the efficiency is high. Discharge tests with similar $l_i$ in the ITER shape at q$_{95}$=4.8 have reached f$_{NI}$=0.7, f$_{BS}$=0.4 at $\beta_N\approx$ 3.5 with performance appropriate for the ITER Q=5 mission, H$_{89} \beta_N$/q$_{95}^2$ $\approx$ 0.3. The $l_i$ was shown to increase further above 1, to enable higher self-consistent f$_{BS}$ and $\beta_N$, by reducing pedestal pressure and bootstrap current density through application of n = 3 resonant magnetic fields. With similar fields for ELM mitigation, and neutral beam and electron cyclotron current drive sources for near-axis current drive, the high $l_i$ scenario is a potential option for ITER. The increased core confinement can help mitigate the effect of reduced pedestal pressure.