A Monte-Carlo simulation of the equilibrium beam polarization in ultra-high energy electron (positron) storage rings

Abstract

a b s t r a c tWith the recently emerging global interest in building a next generation of circular electron-positron colliders to study the properties of the Higgs boson, and other important topics in particle physics at ultra-high beam energies, it is also important to pursue the possibility of implementing polarized beams at this energy scale. It is therefore necessary to set up simulation tools to evaluate the beam polarization at these ultra-high beam energies. In this paper, a Monte-Carlo simulation of the equilibrium beam polarization based on the Polymorphic Tracking Code (PTC) (Schmidt et al., 2002 [1]) is described. The simulations are for a model storage ring with parameters similar to those of proposed circular colliders in this energy range, and they are compared with the suggestion (Derbenev et al., 1979 [2]) that there are different regimes for the spin dynamics underlying the polarization of a beam in the presence of synchrotron radiation at ultra-high beam energies. In particular, it has been suggested that the so-called "correlated" crossing of spin resonances during synchrotron oscillations at current energies evolves into "uncorrelated" crossing of spin resonances at ultra-high energies.

Investigation of spin rotators in CEPC at Z-pole

“…9(c) shows the influence of higher-order spin resonances on equilibrium beam polarization, relative to the simulation results with SLIM. Here, depolarization effects of the higher-order spin resonances are simulated by a Monte-Carlo method based on PTC [35]. The spin resonance regions where the equilibrium polarization level is low becomes wider and higher-order synchrotron sideband spin resonances are visible.…”

Reevaluation of spin-orbit dynamics of polarized e+e− beams in high energy circular accelerators and storage rings: An approach based on a Bloch equation

“…All three approaches use (6) DK via (11) where τ −1 dep is not computed via (10) but via Monte-Carlo spin tracking and where the remaining terms in (11) are approximated by using then 0 -axis. 4 (iii) Compute τ −1 0 via (8) and τ −1 DK via ( 7) by linear approximation in orbit and spin variables via the so-called SLIM formalism. 19 Approach (ii) is the most practiced while approach (i) is only feasible if one can compute f andn as accurately as needed (which is not easy!).…”

“…In fact there is an alternative approach based on a Bloch-type equation for the polarization density 3 which we call 3 the Bloch equation (BE) and which we believe can deliver more information than the standard approach even if the latter includes potential correction terms. 4 So we aim to determine the domain of applicability of the Derbenev-Kondratenko formulas and the possibility in theory of polarization at the CEPC and FCC-ee energies. Of course both approaches focus on the equilibrium polarization and the polarization time.…”

Self-polarization in Storage Rings

“…SITROS evaluates τ p from the fit of P(t) and thus P ∞ from τ p τ BKS P BKS . More recently E. Forest Polymorphic Tracking Code [16] has been used for a modern implementation of this approach [17].…”