Ideal focusing in the theory of electrostatic spectrographs

The problem of synthesis of field structures, in which the spectrographic principle of separating charged particle flows is implemented and ideal angular focusing is simultaneously observed in the symmetry plane for each energy value, is formulated. The search for spectrographic media is effectively carried out with the help of inverse mechanical problems. Two approaches are proposed, one of which involves the reduction to the integral Abel equation and the other is based on the application of the Goursat theorem. The algorithms for the synthesis of spectrographic media with ideal focusing of flows are described in detail, and possible versions of solutions corresponding to representatives of two structural classes (with potentials homogeneous in the Euler sense and with homogeneous potentials with a logarithmic singularity) are indicated. The prospects of developing high-transmission spectrographs for energy analysis are outlined.