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Beginning with the General Bjorken-Mtingwa 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 In addition, we show that a modified version of Piwinski’s IBS formulation (where 2x,y/x,y has been replaced by ) at high energies asymptotically approaches the same result.
A Simplified Model of Intrabeam Scattering*
K.L.F. Bane, SLAC, Stanford, CA 94309, USA
The function g() (solid curve) and the fit g=(0.021-0.044 ln) (dashes).
The ratio of local growth rates in p as function of x, for b=0.1 (blue) and b=0.2 (red) [y=0].
HIGH ENERGY APPROXIMATION
The B-M solution has integrals involving 4 normalized parametersa, 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:
 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.
Transverse growth rates:
* Work supported by DOE contract DE-AC03-76SF00515