Time evolution of the luminosity of colliding heavy-ion beams in BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider

R. Bruce,J. M. Jowett,M. Blaskiewicz,W. Fischer

doi:10.1103/physrevstab.13.091001

Abstract

We have studied the time evolution of the heavy ion luminosity and bunch intensities in the Relativistic Heavy Ion Collider (RHIC), at BNL, and in the Large Hadron Collider (LHC), at CERN. First, we present measurements from a large number of RHIC stores (from Run 7), colliding 100 GeV/nucleon Au beams without stochastic cooling. These are compared with two different calculation methods. The first is a simulation based on multi-particle tracking taking into account collisions, intrabeam scattering, radiation damping, and synchrotron and betatron motion. In the second, faster, method, a system of ordinary differential equations with terms describing the corresponding effects on emittances and bunch populations is solved numerically. Results of the tracking method agree very well with the RHIC data. With the faster method, significant discrepancies are found since the losses of particles diffusing out of the RF bucket due to intrabeam scattering are not modeled accurately enough. Finally, we use both methods to make predictions of the time evolution of the future Pb beams in the LHC at injection and collision energy. For this machine, the two methods agree well.

Highlights

During the design and operation of a heavy-ion collider, e.g., the Relativistic Heavy Ion Collider (RHIC) [1] or the Large Hadron Collider (LHC) [2], one of the main goals is to maximize the time integral of the luminosity L at the experiments
We cite [3,4,5,6] which are close to the applications of this paper. Many of these are based on the solution of systems of coupled ordinary differential equations (ODEs) that describe the time evolution of a few parameters characterizing the beam distributions, typically the intensities and the first- and second-order moments of the distributions
We focus on stores without stochastic cooling in order to make a comparison with the LHC

Summary

INTRODUCTION

During the design and operation of a heavy-ion collider, e.g., the Relativistic Heavy Ion Collider (RHIC) [1] or the Large Hadron Collider (LHC) [2], one of the main goals is to maximize the time integral of the luminosity L at the experiments. We cite [3,4,5,6] which are close to the applications of this paper Many of these are based on the solution of systems of coupled ordinary differential equations (ODEs) that describe the time evolution of a few parameters characterizing the beam distributions, typically the intensities and the first- and second-order moments of the distributions (beam centroids and emittances). Besides closing the system of equations, this can allow convenient analytical forms for some of the terms, e.g., those describing intrabeam scattering or the way in which the luminosity is modified by crossing angles at the interaction point This approach was applied to the evolution of heavy-ion luminosity in the LHC in Ref.

MEASURED LIFETIMES IN RHIC

PARTICLE TRACKING SIMULATION

Collisions

Interaction cross section

Intrabeam scattering

Radiation damping

Starting distribution

ODE SIMULATION

COMPARISON BETWEEN SIMULATIONS AND MEASUREMENTS IN RHIC

PREDICTIONS FOR THE LHC

Findings

CONCLUSIONS AND OUTLOOK