A Simplified Model of Intrabeam Scattering*
K.L.F. Bane, SLAC, Stanford, CA 94309, USA
Abstract Note that Raubenheimer’s 1/Tp formula is the same, except that ½
Beginning with the General Bjorken-Mtingwa replaces g(a/b)H/ p; his 1/Tx,y formulas are identical.
solution, we derive a simplified model of intrabeam
scattering (IBS), one valid for high energy beams in
normal storage rings; our result is similar, though
more accurate than a model due to Raubenheimer. In
addition, we show that a modified version of
Piwinski’s IBS formulation (where 2x,y/ x,y has been
replaced by ) at high energies asymptotically
approaches the same result.
The function g() (solid curve) The ratio of local growth rates in
INTRODUCTION and the fit g=(0.021-0.044 ln) p as function of x, for b=0.1
(dashes). (blue) and b=0.2 (red) [ y=0].
Intrabeam scattering (IBS) tends to increase the beam phase space
volume in hadronic, heavy ion, and low emittance electron storage The plot on the right shows that, as long as is not too close to 1, the
rings. result is not sensitive to , and the model approaches B-M from above as
The two main detailed theories of IBS are ones due to Piwinski and Piwinski’s formulation depends on dispersion through 2/ only. If we
Bjorken-Mtingwa (B-M). modify his result so that 2/ is replaced by , then at high energies his
Solving IBS growth rates according to both methods is time consuming, result asymptotically approaches that of B-M.
involving, at each iteration step, a numerical integration at every lattice
Approximate solutions have been developed by Parzen, Le Duff,
Raubenheimer, and Wei.
Consider as example the ATF ring with no coupling; to generate vertical
errors, magnets were randomly offset by 15m, and the closed orbit was
HIGH ENERGY APPROXIMATION found; < >=17m, yielding a zero current emittance ratio of 0.7%. I=3.1
The B-M solution has integrals involving 4 normalized parameters a, b, x, y:
where =[2+(’ ½’)2]/ is the dispersion invariant, and
=’ ½’/. For our approximation we:
(1) assume a,b<<1, and (2) set x,y to 0
Steady-state local growth rates over ½ the ATF, for an example with
vertical dispersion due to random errors. Given are results due to
Bjorken-Mtingwa, modified Piwinski, and the high energy approx.
The approximate growth rates:
For coupling dominated NLC, ALS example (=0.5%) the error in steady-
state (Tp1,Tx1) obtained by the model is (12%,2%), (7%,0%).
Transverse growth rates:
 A. Piwinski, in Handbook of Accelerator Physics, (1999) 125.
 J. Bjorken and S. Mtingwa, Part. Accel., 13 (1983) 115.
 T. Raubenheimer, SLAC-R-387, PhD thesis, 1991.
 K. Bane, et al, Phys Rev ST-Accel Beams 5:084403, 2002.
* Work supported by DOE contract DE-AC03-76SF00515