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.
An approximate relation by least-square optimization of the data yields
This relation is known as the Kilpatrick Limit.
- Kilpatrick, W. D. (1957). "Criterion for Vacuum Sparking Designed to Include Both rf and dc". Review of Scientific Instruments. 28 (10): 824–826. Bibcode:1957RScI...28..824K. doi:10.1063/1.1715731.
- Wangler, Thomas (2008). RF Linear Accelerators (2nd ed.). Wiley-VCH. ISBN 978-3-527-62343-3.. 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.