Formation of a ribbon electron beam of a planar gyrotron in the end region and near the edge of the cathode

Abstract

The problem of formation of a ribbon beam with the cross section shaped as an elongated parallelogram, which is typical of electron-optical systems of planar gyrotrons due to the drift velocity along the cyclic coordinate, is solved. A local solution of the Laplace equation in the case of the temperature-limited emission near the cathode edge is constructed in the general case of 2D flows with nonuniform beam parameters. In contrast to arbitrary setting of the electrode geometry in this region, this solution does not violate the adopted hydrodynamic model of the flow. The results corresponding to typical parameters of a planar gyrotron are presented.