Ideal and quasi-ideal time focusing of charged particles

Deals with the problem of the determination of scalar and vector potentials of electromagnetic fields providing time focusing of strongly diverging packs of charged particles (specific values of relative energy spread being about 100%, angular spread attaining tens of degrees). The problem is solved within the framework of static non-relativistic corpuscle optics. A theory of ideal time and space-time focusing encompassing and systematizing all known particular cases of such focusing is developed. Necessary and sufficient conditions of isochronous motion and requirements for inner symmetry of motion (the latter increasing with the growth of the quality of focusing) are determined. It is shown that the obtained results make it possible to realize an adequate choice of harmonic fields for constructing the time-of-flight apparatus. They can also be used to determine the accuracy of field sustaining according to the known time-focusing properties.