Abstract: Travelling wave tubes designed to operate interchangeably at low power cw and high pulsed power have grids to gate the pulses and to switch the peak beam current between two values. To preserve optimum beam-focus conditions, the beam diameter should be simultaneously switched. A grid covering the central region of a concave cathode draws the low-current, small beam for cw operation or the central part of a large pulsed beam. A second grid controls added pulsed emission from the surrounding annular region of te cathode. To provide the proper ratio of beam sizes and uniform cathode loading, the cathode has radially varying radius of curvature. A hyperboloid of revolution is a good shape.