electrically coupling a pair of electrodes to a power source, in which each electrode is mated with a corresponding electrically conductive arm of the monolithic graphite heater, each electrically conductive arm having an electrode mount at a proximal end, a thermal apex at a distal end, and a transitional region between the electrode mount and the thermal apex, and in which each electrically conductive arm is structured to support a cathode mount electrically and mechanically coupling each thermal apex to form a maximum Joule-heating region at or adjacent the cathode mount and decreasing Joule heating along each transitional region; and

applying an electrical current to the pair of electrodes and through the electrically conductive arms of the monolithic graphite heater for operation of the monolithic graphite heater in a vacuum environment to reach an operating temperature through localized heating at the maximum Joule-heating region and thereby facilitate thermionic emission from the thermionic electron cathode fit in the cathode mount.