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| In [[particle accelerators]], a common mechanism for accelerating a charged particle beam is via [[copper]] [[Resonator#Cavity_resonators|resonant cavities]] in which electric and [[magnetic field]]s 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.
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| The maximum electric field <math>E</math> achievable is limited by a process known as RF [[Electrical breakdown|breakdown]]. The reliable limits for various [[Radio Frequency|RF]] frequencies <math>f</math> were tested experimentally in the 1950s by W. D. Kilpatrick.<ref>{{cite doi | 10.1063/1.1715731 }}</ref>
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| An approximate relation by least-square optimization of the data yields<ref>{{cite book
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| |title= RF Linear Accelerators
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| |last1= Wangler |first1= Thomas |authorlink1=
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| |coauthors=
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| |editor1-last= |editor1-first= | editor1-link=
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| |edition= 2nd
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| |date= 2008
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| |publisher= [[Wiley-VCH]]
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| |location=
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| |isbn= 978-3-527-62343-3
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| |pages=
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| |url= http://books.google.de/books?id=OJdgVI-UrikC&printsec=frontcover
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| }}. This form apparently comes from a [[Los Alamos National Laboratory|Los Alamos]] note:
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| : T. J. Boyd, Jr., ''Kilpatrick's criterion'', Los Alamos Group AT-1 report AT-1:82-28, February 12, 1982.</ref>
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| <math>f = 1.64\,\mathrm{MHz} \cdot \left(\frac{E}{E_0}\right)^2 \cdot \exp\left( -8.5 \frac{E_0}{E} \right), \quad </math> with <math>E_0 = 1 \mathrm{\frac{MV}{m}}</math> ([[Mega-|mega]][[volts]] per metre).
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| This relation is known as the '''Kilpatrick Limit'''.
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| == References ==
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| {{Reflist}}
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| [[Category:Accelerator physics]]
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