particle accelerators A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...

, a common mechanism for accelerating a charged particle beam is via

copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkish ...

resonant cavities in which electric and

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...

s form a

standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...

, the mode of which is designed so that the

E field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

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. An approximate relation by least-square optimization of the data yields. 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.

f = 1.64\,\mathrm \cdot \left(\frac\right)^2 \cdot \exp\left( -8.5 \frac \right), \quad

with

E_0 = 1 \mathrm

(

mega Mega or MEGA may refer to: Science * mega-, a metric prefix denoting 106 * Mega (number), a certain very large integer in Steinhaus–Moser notation * "mega-" a prefix meaning "large" that is used in taxonomy * Gravity assist, for ''Moon-Eart ...

volts The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827). Defi ...

per metre). This relation is known as the Kilpatrick Limit.

References

{{Reflist Accelerator physics