Beam-beam Simulations with the Gaussian Code Trs

We describe features of the soft-gaussian beam-beam simulation code “TRS” and present sample results for the PEP-II e+e− collider. 1 DESCRIPTION OF THE CODE A basic experimental observation in e+e− colliders in stable operation is that the particle distribution density at the beam core is approximately gaussian, while the density at large amplitudes (a few σ’s away from the center) is not gaussian and is much larger than the extrapolation from a gaussian fit to the core [1, 2]. The code TRS (Two-Ring Simulation) [3] is geared to study the beam core of colliding e+e− beams. Although it can be used to study large-amplitude tail distributions, it is very inefficient at doing so, since the vast majority of the CPU time is spent simulating the gaussian core. The “engine” of this code is similar to that in other codes [4, 5, 6, 7]. The code is written in FORTRAN 77, and is yet to be documented in detail. 1.1 Simulation technique In the simplest case each beam is represented by a single bunch traveling in a separate, distinct ring and collisions occur at only one interaction point (IP). The basic simulation technique consists in tracking a given number (typically 1000–50000) of macroparticles per bunch and computing, at every turn just before the collision, the centroids 〈x〉± , 〈y〉± and rms widths σx±, σy± of the distributions, where the subscript +(−) refers to the e+(e−) beam. For the purposes of computing the beam-beam interaction, the code assumes that the transverse distribution of the kicking bunch is gaussian, using the just-computed values of 〈x〉, 〈y〉, σx and σy in the Bassetti-Erskine formula [8] for the electromagnetic field of a gaussian distribution. This formula is then used to compute the kick on every macroparticle of the opposing bunch. The role of the two colliding bunches is then reversed, completing the computation of the beam-beam interaction. Each macroparticle is then tracked through its corresponding ring lattice, and the process is iterated for many turns, typically corresponding to 3–5 damping times. An aperture “lattice element” intercepts par∗Work supported by the US Department of Energy under contract No. DE-AC03-76SF00098. † [email protected] ticles at large amplitude, and these are removed from the simulation. The main output of the program is a file the with turn-by-turn values of 〈x〉±, 〈y〉±, σx±, σy± and the remaining number of macroparticles. Simple postprocessors can then compute the luminosity and the frequency spectra of 〈x〉±, 〈y〉±, σx± and σy±. The program can also output the x and y projections of the time-averaged macroparticle distributions in binned form.