Intrabeam scattering (IBS) is an effect in accelerator physics where collisions between particles couple the beam emittance 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 lifetime. In circular lepton accelerators, intrabeam scattering is counteracted by radiation damping, 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.
The two principal methods for calculating the effects of intrabeam scattering were done by Anton Piwinski in 1974[1] and James Bjorken and Sekazi Mtingwa in 1983.[2] 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.[3]
Intrabeam scattering rates have a
1/\gamma4
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.
The betatron growth rates for intrabeam scattering are defined as,
1 | |
Tp |
\stackrel{def
1 | |
Th |
\stackrel{def
1 | |
Tv |
\stackrel{def
1 | |
Ti |
=4\piA(\operatorname{log})\left\langle
infty | ||
\int | dλ | |
0 |
λ1/2 | |
[\operatorname{det |
(L+λI)]1/2
Tp
Th
Tv
(\operatorname{log})=ln
bmin | |
bmax |
=ln
2 | |
\thetamin |
A=
| ||||||||||
64\pi2\beta3\gamma4\epsilonh\epsilonv\sigmas\sigmap |
L=L(p)+L(h)+L(v)
L(p)=
\gamma2 | ||||||
|
\begin{pmatrix} 0&0&0\\ 0&1&0\\ 0&0&0\end{pmatrix}
L(h)=
\betah | |
\epsilonh |
\begin{pmatrix} 1&-\gamma\phih&0\\ -\gamma\phih&
\gamma2{lH | |
h}{\beta |
h}&0\\ 0&0&0\end{pmatrix}
L(v)=
\betav | |
\epsilonv |
\begin{pmatrix} 0&0&0\\ 0&
\gamma2{lH | |
v}{\beta |
v}&-\gamma\phiv\\ 0&-\gamma\phiv&1\end{pmatrix}
{lH}h,v=
2 | |
[η | |
h,v |
+(\betah,vη'h,v-
1 | |
2 |
\beta'h,v
2]/\beta | |
η | |
h,v |
\phih,v=η'h,v-
1 | |
2 |
\beta'h,vηh,v/\betah,v
2 | |
r | |
0 |
c
N
\beta
\gamma
\betah,v
\beta'h,v
ηh,v
η'h,v
\epsilonh,v
\sigmas
\sigmap
bmin
bmax
\thetamin
IBS can be seen as a process in which the different "temperatures" try to equilibrate. The growth rates would be zero in the case that
\sigma\delta | |
\gamma |
=\sigmax'=\sigmay'
\gamma
\gamma
One may also the express conservation of energy in IBS in terms of the Piwinski invariant
\epsilonx | |
\betax |
+
\epsilony | |
\betay |
+ηs
\epsilonz | |
\betaz |
ηs=
1 | |
\gamma2 |
-\alphac
In the case of a coupled beam, one must consider the evolution of the coupled eigenemittances. The growth rates are generalized to
1 | = | |
\tau1,2,3 |
1 | |
\epsilon1,2,3 |
d\epsilon1,2,3 | |
dt |
Intrabeam scattering is an important effect in the proposed "ultimate storage ring" light sources and lepton damping rings for International Linear Collider (ILC) and Compact Linear Collider (CLIC).Experimental studies aimed at understanding intrabeam scattering in beams similar to those used in these types of machines have been conducted at KEK,[6] CesrTA,[7] and elsewhere.