Magnetohydrodynamic Equilibria in Sharply Curved Axisymmetric Devices

Ideal magnetohydrodynamic equilibria in current-carrying diffuse toroidal pinches of circular cross section (tokamaks) are studied numerically to determine possible limitations on β = 8πp/B2. Equilibrium considerations alone give no limitations even for β∼1 or βp≃βq2A2∼A2, but the stability requirement q>1 for magnetohydrodynamic kink modes does limit β. The best case found has β∼0.1 with q>1, A = 3, and βp∼2.