Electron-Cloud Build-up in the FNAL Main Injector

LBNL-62738 Electron-Cloud Build-up in the FNAL Main Injector ∗ M. A. Furman, † Center for Beam Physics, LBNL, Berkeley, CA 94720-8211, USA Abstract We present a summary on ongoing simulation results for the electron-cloud buildup in the context of the proposed FNAL Main Injector (MI) intensity upgrade [1] in a ﬁeld- free region at the location of the RFA electron detector [2]. By combining our simulated results for the electron ﬂux at the vacuum chamber wall with the corresponding measure- ments obtained with the RFA we infer that the peak sec- ondary electron yield (SEY) δ max is > 1.4, and the average electron density is n e > 10 10 m −3 at transition energy for the speciﬁc ﬁll pattern and beam intensities deﬁned below. The sensitivity of our results to several variables remains to be explored in order to reach more deﬁnitive results. Ef- fects from the electron cloud on the beam are being inves- tigated separately [3]. namely K = 8, 20 and 30 GeV, and only for one full rev- olution in each case (revolution period T 0 = 11.1 µs). For each value of K, we assume two representative values for the RMS bunch length. We assume a bunch ﬁll pattern made up of 6 batches, each having a train of 82 bunches followed by 4 empty buckets. The ﬁrst batch is a double- intensity batch, with N b = 10.3 × 10 11 , while the bunches in the remaining batches have a more standard intensity N b = 5.7 × 10 10 . There is a 76-bucket-long gap after the last bunch of the 6th train for a total of 588 buckets. The bunch spacing in time is t b = 18.8 ns. We simulate the electron cloud build-up only in the ﬁeld-free section where the RFA electron detector is in- stalled. At this location the chamber is cylindrical of radius R = 7.3 cm and the beta functions are (β x , β y ) = (20, 30) m. We assume a normalized 95% transverse emittance n,95% = 15π mm-mrad for all bunches for all cases we investigate here. The energy spread is small enough that the dispersion contributes negligibly to the transverse beam size. We further assume the stainless steel SEY model de- scribed in [5, 6], with the additional practical assumption that the SEY at 0 energy, δ(0), is proportional to δ max . This latter is the primary variable exercised in this set of simula- tions: we allow it to range in 1.3 ≤ δ max ≤ 1.7. However, we keep ﬁxed E max , the incident electron energy at which the SEY peaks, at 293 eV. Table 1 shows the RMS trans- verse beam sizes and other beam parameters. Other simu- lation details and variables such as grid size and number of macroparticles are discussed in [11]. INTRODUCTION An upgrade to the MI at FNAL is being considered that would increase the bunch intensity to N b ∼ 3 × 10 11 in or- der to generate intense beams for the neutrino program [1]. While such high intensities will require signiﬁcant hard- ware upgrades, the technique of slip-stacking routinely al- lows, at present, bunch intensities N b > 1 × 10 11 . Dur- ing 2006 an RFA-type electron detector was installed in a ﬁeld-free section of the MI, which shows a clear electron cloud signal close to transition energy at such beam inten- sities [2]. In response to these developments, we have been ex- amining, by means of simulations with the build-up code POSINST [4–7], the magnitude of the electron-cloud effect and the potential risks thereof at higher values of N b [8– 12]. The present RFA measurements allow a ﬁrst calibra- tion of our results and therefore a prediction for the elec- tron cloud density expected at higher intensity. This article summarizes Ref. [11] and slightly corrects and clariﬁes its conclusions. RESULTS Fig. 1 represents one example of the time development of the average electron cloud density n e during one machine revolution assuming δ max = 1.3. In this case n e grows ex- ponentially during the ﬁrst batch owing to the high value of N b , and then decays to a negligible level during the pas- sage of the rest of the beam. For higher values of δ max , n e reaches or exceeds the beam neutralization level, as dis- cussed below. Figs. 2 show the one-turn-average incident electron ﬂux J e at the wall of the chamber vs. δ max for the 6 cases con- sidered, as labeled. Figs. 3 show n e for the same condi- tions. Several other quantities related to the electron cloud, such as average electron-wall impact energy and local den- sity, are discussed in [11]. SIMULATED CONDITIONS The MI beam ramps from injection at a kinetic energy K = 8 GeV to extraction at K = 120 GeV in ∼ 0.5 s, corresponding to ∼ 45, 000 turns, crossing transition at K 20 GeV. Ideally, we would simulate the entire ramp, but this is wholly beyond our present-day computer capa- bilities. We have therefore simulated only 3 values of K, ∗ Work supported by the FNAL HINS R&D Effort and by the US DOE under contract DE-AC02-05CH11231. Proc. ECLOUD07 Workshop, Daegu (S. Korea, April 9-12, 2007), http://chep.knu.ac.kr/ecloud07 † mafurman@lbl.gov DISCUSSION An approximate proportionality between J e and n e is evident in our simulated data, not just for the one-turn av-