Intrabeam scattering is an effect in accelerator physics

Accelerator physics

Accelerator physics deals with the problems of building and operating particle accelerators.The experiments conducted with particle accelerators are not regarded as part of accelerator physics. These belong to particle physics, nuclear physics, condensed matter physics, materials physics, etc...

 where collisions between particles couple the beam emittance

Beam emittance

The beam emittance of a particle accelerator is the extent occupied by the particles of the beam in space and momentum phase space as it travels. A low emittance particle beam is a beam where the particles are confined to a small distance and have nearly the same momentum...

 in all three dimensions. This generally causes the beam size to grow. In proton accelerators, intrabeam scattering causes the beam to grow slowly over a period of several hours. This limits the luminosity

Luminosity

Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

 lifetime. In circular lepton accelerators, intrabeam scattering is counteracted by radiation damping

Radiation damping

Radiation damping in accelerator physics is a way of reducing the beam emittance of a high-velocity beam of charged particles.There are two main ways of using radiation damping to reduce the emittance of a particle beam—damping rings and undulators—and both rely on the same principle...

, resulting in a new equilibrium beam emittance with a relaxation time on the order of milliseconds. Intrabeam scattering creates an inverse relationship between the smallness of the beam and the number of particles it contains, therefore limiting luminosity

Luminosity

Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

.

The two principal methods for calculating the effects of intrabeam scattering were done by Anton Piwinski in 1974 and James Bjorken

James Bjorken

James Daniel "BJ" Bjorken is one of the world's foremost theoretical physicists. He was a Putnam Fellow in 1954, received a BS in physics from MIT in 1956, and obtained his PhD from Stanford University in 1959...

 and Sekazi Mtingwa in 1983. The Bjorken-Mtingwa formulation is regarded as being the most general solution. Both of these methods are computationally intensive. Several approximations of these methods have been done that are easier to evaluate, but less general. These approximations are summarized in Intrabeam scattering formulas for high energy beams by K. Kubo et al.

Intrabeam scattering rates have a dependence. This means that its effects diminish with increasing beam energy. Other ways of mitigating IBS effects are the use of wigglers

Wiggler (synchrotron)

A wiggler is an insertion device in a synchrotron. It is a series of magnets designed to periodically laterally deflect a beam of charged particles inside a storage ring of a synchrotron...

, and reducing beam intensity. Transverse intrabeam scattering rates are sensitive to dispersion.

Intrabeam scattering is closely related to the Touschek effect. The Touschek effect is a lifetime based on intrabeam collisions that result in both particles being ejected from the beam. Intrabeam scattering is a risetime based on intrabeam collisions that result in momentum coupling.

Bjorken-Mtingwa formulation

The betatron growth rates for intrabeam scattering are defined as,

,

,

.

The following is general to all bunched beams,

,
where , , and are the momentum spread, horizontal, and vertical are the betatron growth times.
The angle brackets <...> indicate that the integral is averaged around the ring.

Definitions: is the classical radius of the particle is the speed of light is the number of particles per bunch is velocity divided by the speed of light is energy divided by mass and is the betatron function and its derivative, respectively and is the dispersion function and its derivative, respectively is the emittance is the bunch length is the momentum spread and are the minimum and maximum impact parameters. The minimum impact parameter is the closest distance of approach between two particles in a collision. The maximum impact parameter is the largest distance between two particles such that their trajectories are unaltered by the collision. is the minimum scattering angle.

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