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

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

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

This relation is known as the Kilpatrick Limit.