Kilpatrick limit
Encyclopedia
In particle accelerators, a common mechanism for accelerating a charged particle beam is via copper
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.
The maximum E field achievable is limited by a process known as RF breakdown
. These limits were tested at various RF
frequencies in the 1950s by W. D. Kilpatrick who fitted a formula through the data points at which reliable operation can be achieved. This is known as the Kilpatrick Limit.
Here,
is the frequency
, and
is the Kilpatrick E field in megavolts per metre (MV/m).
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
resonant cavities in which electric and magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s form a standing wave
Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling...
, 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 E field achievable is limited by a process known as RF breakdown
Electrical breakdown
The term electrical breakdown or electric breakdown has several similar but distinctly different meanings. For example, the term can apply to the failure of an electric circuit....
. These limits were tested at various RF
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
frequencies in the 1950s by W. D. Kilpatrick who fitted a formula through the data points at which reliable operation can be achieved. This is known as the Kilpatrick Limit.
Here,
is the frequencyFrequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
, and
is the Kilpatrick E field in megavolts per metre (MV/m).