The physics of relativistic electron beams in rectangular and cylindrical geometries

The use of electron beams for the direct pumping of lasers for fusion applications requires the generation of large area beams in appropriate geometries. Two geometries which are of particular interest are rectangular electron beams with planar anodes and radially converging beams with cylindrical anodes. The generation of such beams requires the management of electron trajectories in a complex combination of applied and self-generated electric and magnetic fields. The beam's self-electric field limits the emitted current, and the deflection of the electron in the self-magnetic field (beam pinch) limits the beam area that can be generated from a single cathode. A simple analytic model is used to derive a scaling relationship for beam pinch in both geometries of the form V
^1/2
w/d = α, where V is the diode voltage, w the beam width, d the anode-cathode spacing, and α is a weak function of the geometry. Numerical calculations are presented to show the effects of nonuniform electric fields encountered in typical geometries together with supporting experimental measurements.