Kilpatrick limit

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.

$f(MHz)\; =\; 1.64\; E^2\; e^\{-8.5/E\}$

Here, $f$ is the frequency, and $E$ is the Kilpatrick E field in megavolts per metre (MV/m).

References

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: [http://link.aip.org/link/?RSINAK/28/824/1 Downloadable from AIP] (may require subscription).