Intrabeam Scattering

TL;DR

This paper surveys intrabeam scattering (IBS) as a Coulomb-driven mechanism for emittance growth within particle bunches. It develops and compares multiple theoretical frameworks—starting from a simple gas model, through Piwinski’s and Martini’s formalisms, to the Bjorken–Mtingwa approach—and discusses high-energy simplifications for efficient computation. The growth rates depend intricately on lattice functions, dispersion, and a Coulomb logarithm, requiring ring-averaging to yield practical predictions. Across diverse machines (SPS, CELSIUS, RHIC, Fermilab Recycler, and FERMI FEL), the theories generally agree with measurements, validating IBS as a key factor in beam quality, especially under high-density, ultra-low-emittance conditions. The work underscores ongoing efforts to develop fast, accurate approximations to support design and operation of future high-brightness accelerators.

Abstract

Intrabeam scattering refers to the effects of the Coulomb interaction acting between pairs of charged particles within a bunch in an accelerator. One of the main consequences of intrabeam scattering is a change in the emittances of a bunch: in some circumstances (in particular, in hadron storage rings operating above transition), the transverse and longitudinal emittances may grow over time without limit. This may restrict the performance of machines for which maintaining low beam emittance is an important requirement. In this note, we describe some of the models used to analyse the effects of intrabeam scattering, and present in particular the Piwinski formulae for the emittance growth rates. We compare the predicted changes in emittance with measurements in a number of machines operating in different parameter regimes.

Figures (12)

• Figure 1: Longitudinal and transverse emittance growth in the SPS gareyte1984. The left-hand plot shows longitudinal charge density measurements of proton and antiproton bunches (left-hand and right-hand sides of the plot, respectively) made every 30 minutes, with successive measurements aligned from the bottom to the top of the plot. There is a larger increase in the bunch length for protons than antiprotons because of the larger bunch population (of order $10^{11}$ protons compared to $10^{10}$ antiprotons). The middle and right-hand plots show (respectively) the growth in longitudinal and transverse emittance over time for proton bunches with different bunch populations.
• Figure 2: Transverse emittance growth in CELSIUS raohermansson2000. Each plot shows the charge density in a 400 MeV proton bunch in the storage ring as a function of horizontal position within the bunch. The protons are first accumulated and then accelerated to 400 MeV with beam cooling turned on. For purposes of the measurements shown, the cooling is turned off after the bunch has reached equilibrium at 400 MeV, following which measurements are made at intervals for a total time of 92 seconds. Circles show measured data, and the lines show Gaussian fits.
• Figure 3: Longitudinal and transverse emittance growth in the CESR storage ring ehrlichman2013. Plots show the equilibrium horizontal (left) and vertical (middle) beam sizes and bunch length (right) as functions of bunch population for electron and positron bunches. Points show measurements and bands show theoretical predictions, taking into account uncertainties in the beam conditions. The vertical emittance can be controlled by adjusting the coupling using skew quadrupoles. Lower vertical emittances lead to larger equilibrium horizontal emittance and bunch length because of the effects of intrabeam scattering.
• Figure 4: Longitudinal motion of particles in a storage ring (a) below transition and (b) above transition. In both cases, a higher-energy particle (represented by the red dot on the orange outer path) follows a longer trajectory than a lower-energy particle (green dot on the blue inner path). Below transition, the higher velocity associated with higher energy more than compensates the increase in path length over one turn, so the revolution period falls with increasing energy. Above transition, particles are relativistic so that the increase in velocity with energy is negligible, and because of the larger path length, higher-energy particles take longer to complete each turn than lower-energy particles.
• Figure 5: In a collision between two particles, observed in a frame in which one particle is initially at rest, the impact parameter ($b$ in the figure) measures the perpendicular distance between the initial trajectory of the moving particle and the initial position of the stationary particle.