Abstract: In an electron beam machine for e.g. beam welding, the beam current I.sub.em is stabilized by negative feedback applied to the grid of the electron gun. The optimum cathode heating current is ascertained by causing the cathode heating current I.sub.H to decrease steadily from a maximum value. The beam current is kept constant by the feedback, which adjusts the grid voltage U.sub.W to offset the decrease in cathode temperature caused by the decreasing heating current; the rate of change of the grid voltage U.sub.W is monitored, and when this rate of change exceeds a threshold, the decrease in heating current is arrested, and the heating current is maintained at the thus established optimal value or preferably set at a slightly higher value, which secures an extended length of life of the cathode. This setting of the cathode heating current is repeated after a predetermined interval of time to establish a new value in response to a change of the condition of the cathode.