Abstract

In this paper a differential equation is obtained for the variation of the poloidal magnetic field along the cross section of the magnetic field surfaces in a tokamak. Toroidal axisymmetry is assumed. The coefficients of the differential equation depend on the curvature of the family of curves orthogonal to the magnetic field lines. Several shapes of magnetic field surfaces have been analyzed in detail as families of nested curves of circular, elliptic, and triangular elliptic shapes. Closed analytic solutions have been obtained in some cases. (C) 1998 American Institute of Physics.