Physics: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 electric field [math]\displaystyle{ E }[/math] achievable is limited by a process known as RF breakdown. The reliable limits for various RF frequencies [math]\displaystyle{ f }[/math] were tested experimentally in the 1950s by W. D. Kilpatrick.[1]
An approximate relation by least-square optimization of the data yields[2]
[math]\displaystyle{ 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]\displaystyle{ E_0 = 1 \mathrm{\frac{MV}{m}} }[/math] (megavolts 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. doi:10.1063/1.1715731. Bibcode: 1957RScI...28..824K. http://www.escholarship.org/uc/item/3rs8w601.
- ↑ Wangler, Thomas (2008). RF Linear Accelerators (2nd ed.). Wiley-VCH. ISBN 978-3-527-62343-3. https://books.google.com/books?id=OJdgVI-UrikC.. 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.
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