Relativistic Beam-Wave Interactions

The results of the special theory of relativity have been used to modify the nonlinear interaction equations for linear-beam devices to account for relativistic mass changes when the electron velocity is a significant fraction of the velocity of light. The effect of these mass changes on gain and efficiency is evaluated and it is found that the gain is reduced and the efficiency increases rapidly as ke approaches one. The velocity spread in the stream is independent of the voltage. The harmonic current amplitudes and optimum drift distances are calculated for a relativistic klystron and one finds that as ke approaches one the klystron behaves according to a ballistic theory.