The Design of the Poloidal Magnetic Configurations in Tokamaks

The aim of this paper is to present an optimization procedure for the design of the Poloidal Field (PF) coil system of a tokamak reactor. Starting from the target plasma shape, a simplified toroidal field (TF) coil shape is derived to satisfy the basic requirements of bending-free coil and maximum (usually about 1%) TF ripple at the plasma boundary. Then, the PF coils, which are mechanically attached to the TF, optimal number, and locations, are computed. This computation is done by optimally matching at the desired plasma boundary the external magnetic flux that keeps the plasma magneto hydro dynamic (MHD) equilibrium with the magnetic flux generated by the PF coils. The external magnetic flux is matched at the plasma boundary by optimally selecting the principal components of the modified mutual inductance matrix M* that minimize the plasma boundary deformation from its reference shape. Since the M* accounts for the plasma response through the linearization of the Grad-Shafranov equation, the solution found is correct to first order and it substantially simplifies the lengthy, nonlinear computations that are presently used to achieve the same goal.