Validity of closed periodic magnetic focusing for sheet electron beams

Theoretical analyses and numerical calculations have demonstrated that a closed periodic cusped magnetic (PCM) field can effectively confine a sheet electron beam in two transverse directions (i.e., in the wide and narrow dimensions, simultaneously) for stable long distance transport in which the sizes of the beam cross section are set by referring to the present state of the art. Moreover, the method for matching the transverse magnetic focusing force and the inner space charge force in the wide dimension of the sheet electron beam is given, and the longitudinal periodic length and the cross sectional shape of the closed PCM focusing structure can be determined. Calculations also demonstrate that the optimum focusing state can be attained by adjusting the wide dimension on the transverse section of the closed PCM structure independently. The work presented in this paper indicates that the closed PCM structure is very promising for the confinement of the sheet electron beam, and it can be helpful for guiding practical engineering design.