Scaling laws with current for equilibrium momentum spread and emittances from intrabeam scattering and electron cooling rates

Emittance growth due to intrabeam scattering (IBS) is a major limitation for high energy high density accelerators. The reachable maximum particle density depends strongly on how IBS can be compensated for by electron cooling (EC). Hence calculations of the growth rates of the horizontal and vertical emittances
̇h,v/ h,v and of the (longitudinal) momentum spread
̇ / due to IBS are necessary for estimates of the final beam quality. For that purpose the standard theory of the IBS rates based on classical Coulomb scattering has been developed by Piwinski [1], Bjorken and Mtingawa [2], and Martini [3]. Lateron various approximations which make the theory applicable and solvable for practical purposes have been applied by Wei [4], Rao and Katayama [5], Piwinski [6], and Parzen [7]. All these IBS heating rates can be cast into the form