CAIN SIMULATION STUDIES FOR e? e? COLLISIONS. Department of Physics, University of Tennessee, Knoxville, TN 37996

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1 CAIN SIMULATION STUDIES FOR e? e? COLLISIONS ACHIM W. WEIDEMANN y Department of Physics, University of Tennessee, Knoxville, TN Disruption eects in e? e? collisions at a future linear collider aect the attainable luminosity; the angular spread of the disrupted beam particles may present a background in a detector. In this paper, I present simulations of the beam-beam interaction with the simulation code CAIN of relevance for these questions. 1. Introduction In an e + e? collider such as the proposed Next Linear Collider, 1 (NLC) the mutual attraction of the opposite-charged beams leads to a self-focusing eect enhancing the obtained luminosity, whereas in e? e? collisions the mutual disruption of the beams will decrease the luminosity. Furthermore, the disrupted beam particles might scatter on masks and the elements of the exit beam line and thus introduce backgrounds in a detector. An introduction to disruption in e? e? collisions and its eect on the attainable luminosity have been given at a previous workshop; 2 here I present more detailed simulations using the particle-in-cell code CAIN 3 which since has become available. 2. Parameters and Method For this study of electron-positron collisions at at center-of-mass energies of 1.0 and 0.5 TeV I choose as beam parameters those proposed for `at' beams in the Next Linear Collider, 1 with parameters as shown in this table: NLC-IIa NLC-Ib Nom. CMS Energy (TeV) Beam Energy (GeV) Bunch charge (10 10 ) Horiz. beta function at IP x (mm) Vert. beta function at IP y (mm) Horiz. emittance at IP x (m? rad) 4 4 Vert. emittance at IP y (m? rad) x at IP (nm) y at IP (nm) z (m) Work supported by the U.S. Department of Energy under Contract DE{FG05{91ER y Mail Address: SLAC, MS 94, P.O.B. 4349, Stanford, CA

2 In this CAIN study, each beam is simulated by 5000 macroparticles, and the beam-beam elds calculated in a mesh of 64 by 64 bins. The beams are tracked from?2:5 z to +2:5 z in 200 steps. 3. Angular Distributions Figures 1 and 2 show the vertical and horizontal beam proles (top and bottom) at the beginning of tracking, as the beam pulses overlap maximally, and after the collision (left to right). (The apparent asymmetry in the middle top gure each is an artifact of the display, and not real); Figure 1 is for e + e? collisions, and Figure 2 for e? e? collisions, respectively, both for 500 GeV incoming beams. Fig. 1. Electron-positron collisions at 1 TeV. The upper row shows the vertical, the lower one the horizontal beam prole, (from left to right before and after collision). The horizontal scale of the plots is 1000, the vertical 250nm (y, top row) or 1000nm (x, bottom row). One can see, that the nal beam particle distributions are indeed more spread out in space, as expected. Figure 3 shows the angular distributions of the particles emerging after the collision. These distributions are of relevance to assess, if the spent beam can leave the interaction region without hitting any beam pipe, mask, or the face of the exit quadrupole. In both types of collisions, the distribution of spent beam particles in the less focused horizontal (x-)direction is fairly similar, cutting o at less than 500 rad; in the more focused vertical (y-)direction, the spent beam particle distribution cuts o at about 180 rad in the e + e? case, and at about 850 rad for e? e?. I also considered vertical osets between the two beams, as they might occur during a deection scan (widely used at the Stanford Linear collider). Such an oset will, of course, reduce the luminosity and increase the angular spread of the spent beam more in the case of like-charged beams. In the case of an oset of 1 y, the range of 286

3 Fig. 2. Electron-electron collisions at 1 TeV. The upper row shows the vertical, the lower one the horizontal beam prole. Fig. 3. Final-particle angle distribution. Top Row, e + e?, bottom row, e? e? collisions, both at 1 TeV. Left to right: Scatter plot of horizontal (X') and vertical (Y') angle (in rad), histogram of vertical (Y'), horizontal (X') angle. 287

4 nal-particle vertical angles increases up to about 350 rad for for e + e? and 1000 rad for e? e? collisions. (The luminosities decreased by about 10% and 60% from their values at head-on collisions.) For head-on collisions of 250 GeV beams, the vertical angle cuto similarly increases from about 230 rad for e + e? to 500 rad for e + e?, and are about the same, about 350 rad, in the horizontal direction. Considering that { as planned for NLC { the aperture of the exit quadrupole is two meters away and has an inner radius of 7.5 mm, one can conclude that the bulk of the spent beam even in e? e? collisions will still enter the exit quadrupole and leave the interaction region without causing a serious background problem in a detector. 4. Luminosities and Beamstrahlung Spectra One obvious consequence of the repulsion of like-sign beams and the resultant disruption is a lesser luminosity for e? e? collisions. This CAIN simulation nds that the e? e? -luminosity is reduced by a factor of 3 for 500 GeV beams, and by a factor of 2.7 for 250 GeV beams compared to the e + e? luminosity, for the at beams whose parameters are given above. It might well be possible to enhance the e? e? luminosity by considering dierent beam parameters, for example round beams, or beams of dierent bunch length, but in this study I focus on the properties of e? e? collisions in the NLC interaction region as designed for e + e? collisions. Only a fraction of actual collisions will occur at the nominal center-of-mass energy of a NLC. Among the factors producing a spread in the energy distribution of the luminosity are the spread in the delivered beam energy (as produced by the machine lattice, expected to be a 0.5% eect at NLC), initial-state radiation, which is an irreducible eect and has to be accounted for in any physics analysis (leading to an energy loss of about 5% average, 12% r.m.s at the NLC), and beamstrahlung. Beamstrahlung is emitted as one bunch of beam particles passes through the electromagnetic eld of the counter-moving bunch, and will be only be considered here, as it might in principle be dierent for e + e? and e? e? collisions. In collisions of opposite-charged particles, the particles move to the core of the beam and therefore experience the weaker elds there, whereas the particles in e? e? collisions move outwards where they experience a larger eld strength. This CAIN simulation however nds that in both cases a similar number of beamstrahlung photons are emitted (1.6 photons per electron/positron at 1 TeV center-of-mass energy, 0.96 at 0.5 TeV). The fairly similar beamstrahlung spectra from this CAIN simulation are shown in Fig. 4. The luminosity spectra including beamstrahlung are shown in Fig. 5, for e + e? and e? e? collisions as well as those of beamstrahlung photons with electrons or positrons, and beamstrahlung with beamstrahlung photons. The latter two spectra are of relevance for calculations of detector backgrounds, such as e + e? pairs created by Bethe-Heitler (e! e e + e? ) and Breit-Wheeler (! e + e? ) processes, or hadrons (`minijets') from two-photon scattering. While 288

5 Fig. 4. Beamstrahlung spectra. Top Row, e + e?, bottom row, e? e? collisions, left column at 1 TeV, right, at 0.5 TeV CMS energy. Fig. 5. Luminosity spectra. Top Row, e + e?, bottom row, e? e? collisions, both at 1 TeV. Left to right: Spectra of e + e? (e? e? ), e?, and? Luminosities (per 10 GeV bin). 289

6 the rst two processes are included in CAIN, they were not considered in the present study. However, that the spectra are fairly similar for e + e? and e? e? collisions assures us that there is no obvious large dierence in the expected rates for these backgrounds. 5. Conclusions In this paper, I considered some particle distributions of interest for background studies and compared them for e + e? and e? e? collisions, using the same beam parameters in both cases. While the increased disruption eects in e? e? collisions are certainly noticeable, and cause both a a loss of luminosity compared to e + e? collisions and a wider spread of spent-beam particles, these eects are not so large as to make it signicantly more dicult to operate a NLC in a e? e? collision mode, even if no steps are taken to change the interaction region and machine lattice from that currently optimized for e + e? collisions. Acknowledgments I thank Clemens Heusch and Nora Rogers for organizing a stimulating and enjoyable workshop on the physics of e? e? collisions, which gave rise to this study. References 1. Zeroth-Order Design Report for the Next Linear Collider, SLAC Report 474, LBNL- PUB-5425, UCRL-ID (1996). 2. P. Chen, A. Spitkovsky, A.W. Weidemann, Int. J. Mod. Phys. A, 11, 1687 (1996). 3. The CAIN code and a manual, written by K. Yokoya, can be obtained at It supersedes and enhances the previously used program, ABEL, described in K. Yokoya, KEK-Report-85-9 (1985). 290