Intrabeam scattering formulas for fast numerical evaluation
Open Access
- 30 June 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Special Topics - Accelerators and Beams
- Vol. 8 (6), 064403
- https://doi.org/10.1103/physrevstab.8.064403
Abstract
Small-angle multiple intrabeam scattering (IBS) emittance growth rates are normally expressed through integrals, which require a numeric evaluation at various locations of the accelerator lattice. In this paper, I demonstrate that the IBS growth rates can be presented in closed-form expressions with the help of the so-called symmetric elliptic integral. This integral can be evaluated numerically by a very efficient recursive method by employing the duplication theorem. Several examples of IBS rates for a smooth-lattice approximation, equal transverse temperatures and plasma temperature relaxation are given.Keywords
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