In particle accelerators, a common mechanism for accelerating a charged particle beam is via copper resonant cavities in which electric and magnetic fields form a standing wave, the mode of which is designed so that the E field points along the axis of the accelerator, producing forward acceleration of the particles when in the correct phase.
The maximum E field achievable is limited by a process known as RF breakdown. These limits were tested at various RF frequencies in the 1950s by W. D. Kilpatrick who fitted a formula through the data points at which reliable operation can be achieved. This is known as the Kilpatrick Limit.
f(MHz) = 1.64E2e − 8.5 / E
Here, f is the frequency, and E is the Kilpatrick E field in megavolts per metre (MV/m).
The formula as shown in this page is from:
Thomas Wangler, RF Linear Accelerators (1998), p.160.
This form apparently comes from a Los Alamos note:
T. J. Boyd, Jr., Kilpatrick's criterion, Los Alamos Group AT-1 report AT-1:82-28, February 12, 1982.
However, the original work by Kilpatrick, which includes the formulae in a different form is the reference below.
W. D. Kilpatrick, Criterion for Vacuum Sparking Designed to Include Both rf and dc, Rev. Sci. Instrum. 28, p.824 (1957); DOI:10.1063/1.1715731
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