Title: Studies of the beam-beam interaction for the LHC
Abstract: LBNL-43061, CBP Note 308 STUDIES OF THE BEAM-BEAM INTERACTION FOR THE LHC # S. Krishnagopal ∗ , Centre for Advanced Technology, Indore, INDIA M. A. Furman and W. C. Turner, LBNL, Berkeley, CA, USA Abstract We have used the beam-beam simulation code CBI to study the beam-beam interaction for the LHC. We find that for nominal LHC parameters, and assuming only one bunch per beam, there are no collective (coherent) beam- beam instabilities. We have investigated the effect of sweeping one of the beams around the other (a procedure that could be used as a diagnostic for head-on beam-beam collisions). We find that this does not cause any problems at the nominal current, though at higher currents there can be beam blow-up and collective beam motion. possible beam-size blow-up and distortion consequence of quadrupole collective effects. as a 2 RESULTS 2.1 Nominal LHC Parameters LHC parameters used in the simulations are given below in Table 1. Table 1: Parameters for the LHC simulations. Parameter Energy (TeV) Revolution period (µs) Emittance (nm-rad) Beta function (m) Tunes (H, V) Nominal bunch current (mA) Number of bunches Value 1 THE CODE CBI The code CBI (for C ollective B eam-beam I nteractions) is a self-consistent code that models the transverse beam-beam dynamics of beams of arbitrary distribution and ellipticity. It is a Particle-in-Cell (PIC) code that calculates the beam- beam force on a two-dimensional (transverse) Cartesian grid. The code is evolving and presently has the following features: (a) there is only one bunch per beam and there is only one collision point; (b) the beams are ultra-relativistic; (c) longitudinal dynamics is not modeled; (d) arc transport is linear; (e) radiation damping and fluctuations are put in once a turn and at one point in the ring; (f) there is no crossing angle; (g) transverse dimensions and distributions of the beams can be completely arbitrary. Details of the code can be found in Refs. 1 and 2. The code, as described above, is a strong-strong beam- beam code that is best suited for studying collective beam- beam effects in storage-ring e + e – colliders, particularly quadrupole effects (that affect the beam sizes). To our knowledge, quadrupole collective effects have never been studied for hadron colliders, and it seemed interesting and relevant to undertake this study for the Large Hadron Collider (LHC). In particular, in light of a proposal for sweeping one beam around the other as a diagnostic for head-on collisions [3], it seems relevant to look at As can be seen from Table 1, the simulations use the nominal LHC parameters [4], except for the fact that we assume one bunch per beam, and therefore do not model parasitic beam-beam collisions. This is a feature we hope to incorporate into the code in the future. We first ran our simulation for nominal LHC parameters, with the nominal bunch current of 0.2 mA, and with an idealized feedback system that takes out all collective dipole effects (centroid motion). For reasons of computer time, the simulations were run for only 90,000 turns. Figure 1a shows the rms beam sizes for the last 20,000 turns of the simulation: it is clear that for nominal LHC parameters there are no collective quadrupole effects that could affect the performance. Beam sizes are pretty much equal to their nominal value, and there is no sizable beam blow-up. When the current is increased to 1 mA (Fig. 1b) there is some beam blow-up, but all beam sizes are the same, and there is no indication of collective behavior. Work supported by the US Department of Energy under contract No. DE-AC-03-76SF00098. Presented at the PAC99, New York City, March 29-April 2nd, 1999. Email: [email protected]
Publication Year: 1999
Publication Date: 1999-03-01
Language: en
Type: article
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Cited By Count: 2
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