Design of force-balanced coils for high field tokamak reactors

New toroidal field (TF) coils theoretically optimized for high field tokamak reactors are designed. We had developed a tokamak with force-balanced coils (FBC´s) which are helical hybrid coils combining TF coils and a center solenoid (CS) for a reduction of the net electromagnetic force in the direction of major radius. Recently, the FBC concept was extended by the virial theorem of the magnetic field energy and working stress in the coils and their supporting structure. The poloidal rotation number N of the helical coil, which satisfies the uniform stress condition and is named as a virial-limit coil (VLC), is determined by the theorem while it requires a low aspect ratio A for strong toroidal fields. In order to minimize stray fields, the FBC winding is modulated so that its winding direction is nearly vertical and more horizontal in the outer and inner sides of torus, respectively. Thus the configuration of VLC with high elongation κ, large triangularity δ and low aspect ratio is similar to that of CS and TF coil systems in conventional tokamaks, while it can generate strong toroidal fields with much reduced volume of coils and their supporting structure. After the optimal procedure, the maximum working stress in VLC can be reduced to about one third of that in TF coils.