Ecloud Build-Up Simulations for the FNAL MI for a Mixed Fill Pattern: Dependence on Peak SEY and Pulse Intensity During the Ramp

CBP Note 868 (Dec. 11, 2010) Ecloud Build-Up Simulations for the FNAL MI for a Mixed Fill Pattern: Dependence on Peak SEY and Pulse Intensity During the Ramp* M. A. Furman,* Center for Beam Physics, LBNL, Berkeley, CA 94720, and CLASSE, Cornell University, Ithaca, NY 14853 Abstract We present simulation results of the build-up of the electron-cloud density n in three regions of the F N A L Main Injector (MI) for a beam fill pattern made up o f 5 dou- ble booster batches followed by a 6th single batch. We vary the pulse intensity in the range N = ( 2 - 5) x 1 0 , and the beam kinetic energy in the range Ek = 8 - 1 2 0 GeV. We assume a secondary electron emission model qualitatively corresponding to T i N , except that we let the peak value of the secondary electron yield ( S E Y ) <J vary as a free pa- rameter in a fairly broad range. e t max Our main conclusions are: (1) At fixed N there is a clear threshold behavior of n as a function of S in the range ~ 1.1 — 1.3. (2) At fixed S , there is a threshold behavior of n as a function of A provided <S,„ is sufficiently high; the threshold value of N is a function of the characteristics of the region being simulated. (3) The dependence on Ek is weak except possibly at transition energy. 6th batch is always 50% of that in the first five). Detailed parameter values for each case are explained below. Pre- liminary results were presented at the PAC09 [6]. The results were obtained with the 2 D program POSINST, which simulates the electron-cloud build-up and decay in a specific region of the chamber under the action of a prescribed beam fill pattern [7-10]. A l l results here are based on the simulation for only one full machine revolu- tion; this is sufficiently long for the electron cloud to reach steady state, which typically occurs within the first ~ 2 //s following beam injection into an empty chamber. t e ASSUMPTIONS max max r c ax t Most o f these results were informally presented to the relevant M I personnel in A p r i l 2010. INTRODUCTION The desire to assess the impact of the electron-cloud ef- fect on the M I upgrade [1] has motivated the measurement of the incident electron flux J on the walls of the M I vac- uum chamber by means of a R F A electron detector installed in a field-free region [2] for various high-intensity beam fill patterns [3], and of the measurement of the semi-local av- erage of the volumetric electron-cloud density n by means of the microwave dispersion technique [4,5]. e c In this note we present simulation results for n in three different regions o f the chamber, which we label edel, bend, and FFellip. The first one, edcl, rep- resents a round-pipe field-free region where the R F A is installed. The other two represent regions where the m i - crowave transmission measurements have been performed: bend represents a dipole bending magnet, and FFellip a field-free region, both having elliptical chamber cross sec- tion. Table 1 provides the assumed values for the relevant parameters. e In the exercises considered here vary Ek, bunch inten- sity Ni, and S in the range specified in Table 2, but not in all possible combinations (here Ni, is the bunch inten- sity in any of the first 5 batches; the bunch intensity in the max * Work supported by Ihc F N A L MI upgrade R & D effort and by the US D O E under contract DE-AC02-05CH11231. t niafurnian@lbl.gov We assume a beam fill pattern similar to what has been used in the corresponding measurements, consisting of 6 batches in which the first 5 are obtained by slip-stacking booster batches; the 6th batch bunch intensity is 50% of that in any of the first five. Owing to an initial misunder- standing, we used two slightly different patterns for differ- ent sets o f simulation runs (see Fig. 2). The difference in the results for these two is expected to be negligible; for the sake of the record, however, we specify in the results below which pattern was used in which case. Although the beta functions and the transverse R M S beam sizes are different in the three sections, we set them equal for the purpose of the exercises carried out in this note. The bunch sizes quoted in Table 1 for Ek = 8 G e V correspond to a normalized 95% emittance £95,,, = 15 x 1 0 7 m-rad. For higher Ek we simply scale these T a's in proportion to 7 / , where 7 is the usual relativistic factor for the beam. In actuality, the longitudinal bunch shape, at least in the first 5 batches, is fairly flat as a result of the stacking pro- cess; however, to simplify things, we have assumed that the shape is gaussian with an R M S bunch length (in time) °t = 95/4, where r is the 95% bunch duration plotted in Fig. 1. Simulations comparing gaussian vs. flat longi- tudinal bunch profiles for the L H C [11], as well as for the M I (unpublished), showed very small differences in similar parameter regimes. Finally, we have assumed that the three R M S bunch sizes are the same for all bunches in the ring. r The electron-cloud build-up is seeded by ionization of residual gas. The ionization electron creation rate (elec- trons generated per proton per unit length of beam traver- sal) quoted in Tab. 2 is computed from the formula ri [ m ] = 3.284CT, [Mbarn] x P [Ton] x — — (1)