Transverse profile of the electron beam for the RHIC electron lenses

The transverse profile of the electron beam plays a very important role in assuring the success of the electron lens beam–beam compensation, as well as its application in space charge compensation. To compensate for the beam–beam effect in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, we recently installed and commissioned two electron lenses. In this paper, we describe, via theory and simulations using the code Parmela, the evolution of the density of the electron beam with space charge within an electron lens from the gun to the main solenoid. Our theoretical analysis shows that the change in the beam transverse density is dominated by the effects of the space charge induced longitudinal velocity reduction, not by those of transverse Coulomb collisions. We detail the transverse profile of RHIC electron-lens beam, measured via the YAG screen and pinhole detector, and also describe its profile that we assessed from the signal of the electron-backscatter detector (eBSD) via scanning the electron beam with respect to the RHIC beam. We verified, in simulations and experiments, that the distribution of the transverse electron beam is Gaussian throughout its propagation in the RHIC electron lens.