Cranberg Hypothesis of Vacuum Breakdown as Applied to Impulse Voltages

If the Cranberg hypothesis for breakdown in vacuum is valid, measurements made using impulse and dc voltages may yield different results depending in part upon the rate of rise of the impulse and the nature of the attachment of the clumps to the parent electrode. It is assumed that metallic clumps are instantaneously detached from an electrode surface at a voltage dependent upon gap length as described by Cranberg. Consideration of the rise in impulse voltage occurring during the transit time of the clump to the opposing electrode yields the following results. For an over‐volting impulse of constant rise rate the breakdown voltage of a vacuum gap depends upon the ⅚ power of the gap length in the limiting case of large gap length and clump radii, and fast rise impulses. For the same limiting conditions, with an impulse of constant rise time, breakdown voltage was found to be related to the $\frac{5}{2}$ power of the gap length. A brief comparison of calculated results with experimental data in the literature indicates limited, although not conclusive, support for the Cranberg hypothesis in its application to impulse breakdown in vacuum.