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A time domain discrete model for nonuniform transmission lines, based on a complementary formulation of the transmission line equations, is considered. By recasting the line equations in terms of flux and charge, one has to discretize alternatively only one of the two equations, the other being exactly verified. This approach has been widely used in electromagnetics to evaluate the discretization error. With reference to simple examples, we show how the error estimation can be used for a selective meshing of the line, leading to much better approximation with the same computational effort.

The knowledge and the control of the magnetic field profile is of major importance in the application of plasma discharges as magnetic lenses 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 data. The problem is shown to be ill-posed, in general; therefore a regularisation is needed. This is obtained, first, by means of a proper restriction of the observation space; second, by using an over determined data set, leading to a pseudo-inversion procedure. The numerical solution is illustrated, showing the procedure to be robust, at least for the practical applications range. In particular it is shown how the proposed method is effective in determining the amount o f distortion of the field profile as compared to the reference linear one.