Shielding effect estimation of a toroidal magnetic field winding on a control magnetic field in tokamaks

The possibility of distortion of controlling (vertical) magnetic field in tokamaks due to the shielding effect of the winding of longitudinal (toroidal) field at the disposition of current-carrying ''controlling'' turns outside of the longitudinal field winding is investigated. The extreme case is considered. It is supposed that the normal component of the controlling field in the vicinity of the longitudinal winding conductor surface is completely compensated by the field of induced eddy currents, i.e. normal component of the composite field is equal to zero. So the problem is to determine the eddy current field with further determination of the composite field. The problem is solved by the method of successive approximations, i.e. the solutions of the auxilary external Neuman problems are found. On the basis of this method, a calculation program for the BESM-6 computer is written, and the calculations are made for the tokamak model with the longitudinal field winding, consisting of 24 sections of toroidal configuration. The big radius of the winding Rsub(o) was supposed to be equal to 250 cm, l and a were equal to 130 cm and 13 cm, respectively. The external controlling magnetic field antiBsub(o) was taken to be uniform. It is clear from the calculation results that in the range of R change, where the longitudinal winding is situated (150-320 cm), the magnetic field B is 6%-2% weaker than the magnetic field Bsub(o), but it surpass Bsub(o), outside of these limits (< 150 and > 320 cm)