AN INVERSE FORMULATION FOR THE IDENTIFICATION OF MAGNETIC-FIELD PROFILES IN PLASMA LENSES

The knowledge and the control of the magnetic field profile is of majo r importance in the application of plasma discharges as magnetic lense s for charged particles beams, because of the complex dynamics of the plasma. Since conventional field measurements are quite difficult for high current plasma discharges, we propose an inverse formulation for the identification of the field profile directly from the focusing dat a. The problem is shown to be ill-posed, in general; therefore a regul arisation is needed. This is obtained, first, by means of a proper res triction of the observation space; second, by using an over determined data set, leading to a pseudo-inversion procedure. The numerical solu tion is illustrated, showing the procedure to be robust, at least for the practical applications range. In particular it is shown how the: p roposed method is effective in determining the amount of distortion of the field profile as compared to the reference linear one.