Radiation damping in
accelerator physics
Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams ...
is a phenomenon where
betatron oscillations
Betatron oscillations are the fast transverse oscillations of a charged particle in various focusing systems: linear accelerators, storage rings, transfer channels. Oscillations are usually considered as a small deviations from the ideal reference ...
and longitudinal oscillations of the particle are damped due to energy loss by
synchrotron radiation
Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in some types ...
. It can be used to reduce the
beam emittance
In accelerator physics, emittance is a property of a charged particle beam. It refers to the area occupied by the beam in a position-and-momentum phase space.
Each particle in a beam can be described by its position and momentum along each of t ...
of a high-velocity
charged particle beam
A charged particle beam is a spatially localized group of electrically charged particles that have approximately the same position, kinetic energy (resulting in the same velocity), and direction. The kinetic energies of the particles are much lar ...
.
The two main ways of using radiation damping to reduce the emittance of a particle beam are the use of ''undulators'' and ''damping rings'' (often containing undulators), both relying on the same principle of inducing
synchrotron radiation
Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in some types ...
to reduce the particles' momentum, then replacing the momentum only in the desired direction of motion.
Damping rings
As particles are moving in a closed orbit, the lateral acceleration causes them to emit
synchrotron radiation
Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in some types ...
, thereby reducing the size of their momentum vectors (relative to the design orbit) without changing their orientation (ignoring the
quantum fluctuations of the radiation for the moment). In longitudinal direction, the loss of particle impulse due to radiation is replaced by accelerating sections (
RF cavities) that are installed in the beam path so that an
equilibrium
Equilibrium may refer to:
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* ''Equilibrium'' (film), a 2002 science fiction film
* '' The Story of Three Loves'', also known as ''Equilibrium'', a 1953 romantic anthology film
* "Equilibrium" (''seaQuest 2032'')
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is reached at the design energy of the accelerator. Since this is not happening in transverse direction, where the emittance of the beam is only increased by the quantization of radiation losses (quantum effects), the transverse equilibrium emittance of the particle beam will be smaller with large radiation losses, compared to small radiation losses.
Because high orbit
curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
s (low curvature radii) increase the emission of synchrotron radiation, damping rings are often small. If long beams with many particle bunches are needed to fill a larger
storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating, typically for many hours. Storage of a particular particle depends upon the mass, momentum, and usually the charge o ...
, the damping ring may be extended with long straight sections.
Undulators and wigglers
When faster damping is required than can be provided by the turns inherent in a damping ring, it is common to add
undulator
An undulator is an insertion device from high-energy physics and usually part of a larger
installation, a synchrotron storage ring, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. These ca ...
or
wiggler magnets to induce more synchrotron radiation. These are devices with periodic magnetic fields that cause the particles to oscillate transversely, equivalent to many small tight turns. These operate using the same principle as damping rings and this oscillation causes the charged particles to emit synchrotron radiation.
The many small turns in an undulator have the advantage that the cone of synchrotron radiation is all in one direction, forward. This is easier to shield than the broad fan produced by a large turn.
Energy loss
The power radiated by a charged particle is given by a generalization of the Larmor formula derived by LiƩnard in 1898
: