Equilibrium of a toroidal plasma with noncircular cross section

The possibility of determining the cross-sectional form of a Tokamak plasma from measurements of the magnetic field outside the plasma is indicated. Two kinds of integral relation are obtained. The first, based on the equilibrium equations, gives an expression for the multipole moments of the generalized pressure in terms of a surface integral of quadratic combinations of the measured magnetic field. The second, based on the magnetic field equations, gives an expression for the analog of the multipole densities of the longitudinal current density in terms of a surface integral of linear combinations of the magnetic field measured outside the plasma. (auth)