A tokamak with nearly uniform coil stress based on the virial theorem

A novel tokamak design with a new type of toroidal field (TF) coil and a central solenoid (CS) whose stress is reduced greatly to the theoretical limit determined by the virial theorem, has been devised, and plasma production and confinement experiments in a new small tokamak based on this design are presented. According to the virial theorem, the best TF coil for producing the strongest magnetic field under the weakest stress requires equal averaged principal stresses in all directions. Applying this condition to a helical coil, its pitch number is determined as a function of the aspect ratio. The helical winding according to this condition is modulated in such a way that the poloidal field exists only outside of the torus, which reduces the torsional force on the helical coil and makes plasma breakdown possible. Moreover, a helical coil with this modulation and a low aspect ratio is similar to CS and TF coil systems in conventional tokamaks since its helical winding is nearly vertical in the outer part of the torus. With the aspect ratio A = 2, our optimal coil theoretically reduces the working stress in the coil to about one-third less than that of conventional TF coils. On the basis of the design, a small prototype, 'Todoroki-II', with a major radius of 0.3 m, a minor radius of 0.08 m, toroidal magnetic field strengths of BT < 1.5 T and plasma currents of IP < 40 kA, was made. An external vertical field increased the plasma pulse length and the current to 1 ms and 11 kA, respectively, while they were restricted with no vertical field control. Using a Cauchy-condition surface method, the shape and displacement of the plasma boundary were reconstructed, and position control using the vetical field was confirmed.