US LHC Accelerator Research Program bnl fnal lbnl
US LHC Accelerator Research Program bnl - fnal- lbnl - slac PS 2 ecloud build-up studies: update 19 March 2009 Miguel A. Furman LBNL mafurman@lbl. gov LARP PS 2 ecloud 19 March 2009 1
Caveats 1. These results are preliminary 2. Obtained with 2 D build-up code POSINST • Similar to ECLOUD except in details 3. Need to check for numerical convergence • However, I believe I am not too far from it 4. Looked thus far only at: • Dipole bending magnet • Peak SEY=1. 3 • Injection and extraction energies (but not in between) • “LHC 25” beams (25 ns bunch spacing) 5. Previous results presented at: • LUMI 2006 (report no. LBNL-61925) • ECL 2 (report no. LBNL-61925 -update) My present results for average EC density are within a factor ~2 of Giovanni’s (15 Jan. 2009). More work is needed to understand the discrepancies LARP PS 2 ecloud 19 March 2009 2
Goals of PS 2 ecloud studies (as I see them now) 1. Predict as closely as possible the EC density ne and distribution 2. If a SC option is considered for the PS 2, quantify the power deposition on the chamber walls from the EC 3. Use ne and its distribution as inputs to understand effects on the beam 4. If an SPS-like instability is predicted, assess the possibility of a feedback system 5. Combine EC studies with space-charge • EC provides a local, dynamical, neutralization of the beam 6. Maintain an ongoing side-by-side comparison against MI upgrade • Measurements and code validation at the MI are likely to bolster PS 2 studies 7. Other? ? ? please provide suggestions LARP PS 2 ecloud 19 March 2009 3
Assumptions (almost all the same as G. Rumolo’s talk 15 -jan-09) 1. C=1346. 4 m, h=180 2. Elliptical chamber cross sect. , semi-axes (a, b)=(6, 3. 5) cm 3. Peak SEY=1. 3 4. KEinj=4 Ge. V, KEextr=50 Ge. V but not in between 5. Dipole bending magnet only thus far; B=0. 136 T (inj. ), B=1. 7 T (extr. ) 6. Beam: “LHC 25” (168 full + 12 empty buckets), sb=25 ns 7. Bunch length: st=3 ns (inj. ), st=1 ns (extr. ) 8. Nb=4. 2 x 1011 (nominal); but I also looked at smaller values 9. ex=ey=6. 5 x 10– 6 m-rad (RMS, normalized) 10. (bx, by)=(30, 26) m at dipole magnet (neglect bunch dispersive width) 11. Gaussian, parabolic or flat transv. and longit. bunch shapes • but not in all combinations 12. Computational params. : • • • macrop=20, 000 max. integration time step: Dt=3 x 10– 11 s sp. ch. grid=64 x 64 (just enough to cover (2 a)x(2 b) area) LARP PS 2 ecloud 19 March 2009 4
Build-up at inj. and extr. in dipole bend, Nb=4. 2 e 11 sensitivity to tr. bunch profile and SEY spectrum § § § Gaussian, parabolic or flat tr. profile Gaussian long. profile Conclusions: • Transverse profile not a significant variable • Rediffused vs. no-rediffused secondary electrons: significant variable - We don’t know exactly what is the % of rediffused in the actual vac. ch. • EC density ~(7 -8)x 1011 m– 3 at saturation, either at inj. or extr. N. B. : deep fluctuations due to “virtual cathode” phenomenon; although average ne is probably okay LARPNeeds PS 2 ecloud fixing, 19 March 2009 5
Build-up at inj. and extr. in dipole bend, Nb=4. 2 e 11 sensitivity to long. bunch profile § § § Gaussian or flat long. profile Gaussian tr. profile Conclusion: • Longitudinal profile not a significant variable • !!!? LARP PS 2 ecloud 19 March 2009 6
Average ne vs. bunch intensity Nb (tri-gaussian bunch profile) § Strong nonlinear behavior of ne vs. Nb • § § Partially explained by electron-wall impact energy: crosses 300 e. V at Nb~2 e 11 Curious non-monotonicity at 50 Ge. V Gröbner beam-induced multipacting condition similar to MI upgrade • Comparison will provide value in understanding LARP PS 2 ecloud 19 March 2009 7
Conclusions § These are preliminary results § Numerical convergence • I feel a bit uncomfortable; I expected a more significant dependence on longitudinal bunch profile § Looks like expected EC average density is ne~(0. 1– 1)x 1012 m– 3 • “average” means here: averaged both over time and space within the dipole chamber • Consistent with Giovanni’s results • Corresponds to ~(1– 10)% average beam neutralization • Beware: ne has large fluctuations near the beam, and is strongly time dependent § Discrepancies with Giovanni’s results need to be straightened out • On the scale of a factor ~2 • But there are qualitative differences as well (eg. , injection vs. extraction results) • We have not (yet) done exactly the same calculation, so not a big concern at this point § Next: examine numerics, “LHC 50” option, other regions of the chamber, build -up during the ramp (especially around bunch coalescing time), SEY model, MI upgrade, … LARP PS 2 ecloud 19 March 2009 8
LARP PS 2 ecloud 19 March 2009 9
Flat and Gaussian longit. beam profiles § The “gamma” flat profile is defined in LBNL-61925 § NB: for the transverse flat profile, I used a truly flat density function LARP PS 2 ecloud 19 March 2009 10
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