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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 electric field $E$ achievable is limited by a process known as RF breakdown. The reliable limits for various RF frequencies $f$ were tested experimentally in the 1950s by W. D. Kilpatrick.^[1]

An approximate relation by least-square optimization of the data yields^[2]

$f=1.64\,\mathrm {MHz} \cdot \left({\frac {E}{E_{0}}}\right)^{2}\cdot \exp \left(-8.5{\frac {E_{0}}{E}}\right),\quad$ with $E_{0}=1\mathrm {\frac {MV}{m}}$ (mega volts per metre).

This relation is known as the Kilpatrick Limit.

References

^ 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.

[1] 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.

[2] 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.

[1]

[2]

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Kilpatrick limit

References

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