Tokamak Equilibrium

Axisymmetric hydromagnetic equilibria are obtained from an ideal fluid model by means of an asymptotic expansion in the inverse aspect ratio. The calculation is carried sufficiently far so that the equilibrium condition J×B = ≇p is satisfied to second order. This provides expressions for the eccentricity of the constant pressure surfaces as well as for their displacements, and for both the magnitude and the curvature of the external field that must be provided to support the equilibrium. Scaling considerations are invoked to show how the external field must be altered to compress the plasma to a smaller major radius and thus obtain additional heating. Elementary hydromagnetic considerations indicate that the configuration may be stable with respect to modes which have the symmetry of the equilibrium. Application is made to a specific compression heating experiment.