Analysis of Ideal Stability Limits in DIII-D Discharges with High $\beta_N$ and $l_i$

Broad pressure profiles in DIII-D discharges with high $l_i$ enable stable access to high plasma pressure. As $\beta_N$ increases, the pressure peaking factor $f_p=P(0)/\langle P\rangle$ decreases, from $f_p\approx 3.7$ at $\beta_N\approx 2.9$ to $f_p\approx 2.4$ at $\beta_N>4.5$. Simultaneously, the ideal low-n stability limits calculated with a conducting wall increase from $\beta_N\approx 3.6$ to nearly 6, so that $\beta_N$ remains below the limit. In addition, $f_p$ decreases as $l_i$ is increased. Thus, the high $\beta_N$ stability limits result from both increased $l_i$ and decreased $f_p$. In a steady-state discharge, though, increased $\beta_N$ will limit the practical value of $l_i$ because of the increase in the bootstrap current density, particularly in the H-mode pedestal. Reducing the pedestal pressure with an n=3 magnetic perturbation increases $l_i$ but also increases $f_p$ so there is no net increase in the $\beta_N$ limit. A change in the discharge shape to reduce the pedestal pressure, to the single-null divertor ITER shape from a double-null, results in an $\approx$15\% drop in the $\beta_N$ limit.