Formation and Stability of Virtual Electrodes in a Cylinder

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Abstract
Two-dimensional computer experiments have been performed to determine whether a stable virtual electrode can be formed inside an evacuated cylinder by the injection of charged particles from the outside. This question is important to the feasibility of certain inertial confinement schemes for fusion reactors. The charges are injected with constant velocity uniformly from the surface of the cylinder and directed at the axis. Above a certain current, depending on the injection velocity and dimensions, dc solutions exist corresponding to the formation of a virtual electrode at a calculable radius within the cylinder. Such analytic solutions involving virtual electrodes are not necessarily realized in practice as they were not in the one-dimensional computer experiments of Birdsall and Bridges on the short-circuited diode. The problem discussed here, although related to the diode, is different both in geometry and in the manner of injection. It is interesting that our computer experiments show the formation of a stable virtual electrode for a wide range of input current. Such variations of potential that do occur are transient and decay to less than ±2% after ten single-particle transit times. Experiments have also been conducted with the current injected from four separate guns. Stable virtual electrodes are formed in this case opposite each gun.