Instability development in the Bursian diode

Stability features of a Bursian diode (a vacuum diode with an electron beam) steady states in a mode with a negative potential difference between the collector and the emitter has been studied. Using linear theory, it is shown that solutions corresponding to the middle (overlap) branch are aperiodically unstable. The development of this instability at the nonlinear stage has been numerically investigated by a high-precision E, K code. It turned out that, depending on the phase of the perturbation, the process develops in opposite directions, and ends in stationary states lying on different branches of solutions. The process reaches solutions from the lower (normal) branch in an aperiodic manner, with a growth rate that matches the one predicted by linear theory. On the other hand, stationary solutions with reflection are affected by the process in an oscillatory manner. A general expression is obtained for the law of conservation of energy in the diode - external circuit system. In calculations of instability development, this law was carried out with high accuracy.