Field analysis for a SMES magnet with radial force balance

The old concept of a radial force balanced coil is examined by calculating the magnetic force distribution from well known exact solutions of the quasi static magnetic field equations. The derived coil geometry is very nearly a torus of a circular cross section. The outside field has the distribution of a single poloidal line current which is a virtual image of a poloidal current sheet on the coil surface that terminates the outside field. The inside field is from a toroidal surface current that terminates the inside field. The J/spl times/B forces are all normal to the current sheets. The magnitudes of the current sheets are adjusted for radial force balance. For a radius ratio of 0.121, the resultant normal force is outward and uniform to about 4%. Thus a simple hoop structure around the minor circumference will support the coil. Vector addition of the two current sheets gives a helical surface current on the surface of the torus.<>