New Derivation of the Vacuum Breakdown Equation Relating Breakdown Voltage and Electrode Separation

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Abstract
An analysis of the published measurements of breakdown voltage for various gap lengths for uniform and approximately uniform fields shows that the results may be represented by the breakdown equation V = Cxα and that the values of α lie in the range 0.1 to 1.1 with a mode of 0.7. A theory is developed which leads both to a breakdown equation of the same form and to a general expression to account for the range of values of α. This expression is confirmed for gaps up to 0.075 cm by direct experiment. The development is based on the postulate that an electron beam is emitted from the cathode, diverges, and bombards the anode to cause breakdown when a critical power flux is reached. The factor C is shown to include the critical power flux and to be related to both field and electrode separation. In support of the theory, the radii of craters produced on the anode are measured and shown to be related to the radius of an electron beam at the anode. Calculation shows the current carried by the beam to be of the order of 10−4 amp. Values of the critical power flux obtained from the equation V = Cxα and from anode crater data, respectively, agree within a factor of 1.5 and are of the order of 108 w cm−2. To explain the observed phenomena, a multiple electron beam system is proposed.

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