Stable equilibria for bootstrap-current-driven low aspect ratio tokamaks

Low aspect ratio tokamaks (LATs) can potentially provide a high ratio of plasma pressure to magnetic pressure β and high plasma current $I$ at a modest size. This opens up the possibility of a high-power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current, which requires operating at high ${\beta }_p.$ A high value of the Troyon factor ${\beta }_N$ and strong shaping is required to allow simultaneous operation at a high-β and high bootstrap fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both ${\beta }_N$ and β are defined in terms of the vacuum toroidal field. Equilibria with ${\beta }_N\text{⩾8}$ and β∼35%–55% exist that are stable to $n$ =$\infty$ ballooning modes. The highest β case is shown to be stable to $n$ =$\text{0,1,2,3}$ kink modes with a conducting wall.