In this paper the space charge theory for a three-dimensional curvilinear beam-let with transversal initial velocity spread in electron guns composed of non-axisymmetric electron-optical systems is established.As a simple example of application
based on Kino’s plane space charge fluid theory
the space charge density of some three-dimensional curvilinear beamlet with transversal Maxwell initial velocity spread in a long Kino’ sgun is numerically calculated.