Ideal MHD stability limits of low aspect ratio tokamak plasmas

The ideal magnetohydrodynamic (MHD) stability limits of low aspect ratio tokamak plasmas are computed numerically for plasmas with a range of cylindrical safety factors g., normalized plasma pressures β, elongations κ and central safety factors q(0). Four distinct regimes are optimized, namely: (a) low-q, plasmas with q(0) = 1.1 with and without a stabilizing wall, (b) low-q, plasmas with no wall and 1.1 < q(0) < 2, (c) high-β, high bootstrap fraction plasmas at moderate κ requiring a wall and edge current drive and (d) high-β, very high bootstrap fraction plasmas with moderate to high κ requiring a stabilizing wall but little external current drive. A stable equilibrium is found at an aspect ratio of A = 1.4 and an elongation of κ = 3.0, with 99.3% of the current provided by the plasma pressure and β = 45%. Special attention is paid to the issues of numerical convergence and the proper definition of bootstrap current fraction.