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04/01/2006MICE Analysis Meeting1 MICE phase III M. Apollonio, J. Cobb (Univ. of Oxford)
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04/01/2006MICE Analysis Meeting2 Simulation ICOOL code evbeta: numerical solution of optical functions differential equations PHASE III Two back to back tracker solenoids, no RF cavities Never studied in any detail Assumption: step 3 can be used to: Cross-calibrate solenoids and tracking Demonstrate capability of measuring an emittance change to 1% 1 st possibility of observing cooling with solid absorber(s) work in progress!
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04/01/2006MICE Analysis Meeting3 U.Bravar’s study on matching revisited Naive approach: take M. Green’s currents for step 6 w.o. cooling channel (just so) but … Not just a matter of taking the whole experiment and put the two spectrometers closer (~800 mm, to be checked) Coil matching is an important issue !!! Solenoids will operate differently in step 3 from steps [4,6] 1 st step: MATCHING Step VI Step III
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04/01/2006MICE Analysis Meeting4 If you keep the same coil currents you end up into troubles … Asymmetric beta functions Solution: optimize the match coil currents i.o.t. get a symmetric (well behaved) beta function (m) z (m) vacuum flip mode
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04/01/2006MICE Analysis Meeting5 evbeta + MINUIT Constraints used: = 33cm symmetrical in the solenoid regions in the solenoid regions == flat Force to be ~ 60 cm in the middle of the apparatus Find the new coil currents: Variation with respect to M. Green‘s starting currents I/I(min) ~ -30%, I/I(max) ~ +7% CAVEAT: check current densities!!! FLIP MODE (fm), NON-FLIP MODE (nfm)
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04/01/2006MICE Analysis Meeting6 1 -6.007 0.110 0.258 0.326 -145.400 2 -5.848 1.294 0.258 0.280 -146.900 3 -4.507 0.110 0.258 0.320 -136.800 4 -4.150 0.197 0.258 0.284 -112.539 5 -3.710 0.198 0.258 0.304 -157.036 6 -2.712 0.198 0.258 0.304 157.036 7 -2.271 0.197 0.258 0.284 112.539 8 -1.827 0.110 0.258 0.320 136.800 9 -1.670 1.294 0.258 0.280 146.900 10 -0.327 0.110 0.258 0.326 145.400 1 -6.007 0.110 0.258 0.326 -145.400 2 -5.848 1.294 0.258 0.280 -146.900 3 -4.507 0.110 0.258 0.320 -136.800 4 -4.150 0.197 0.258 0.284 -116.717 5 -3.710 0.198 0.258 0.304 -159.676 6 -2.712 0.198 0.258 0.304 -159.676 7 -2.271 0.197 0.258 0.284 -116.717 8 -1.827 0.110 0.258 0.320 -136.800 9 -1.670 1.294 0.258 0.280 -146.900 10 -0.327 0.110 0.258 0.326 -145.400 1 -6.007 0.110 0.258 0.326 -145.400 2 -5.848 1.294 0.258 0.280 -146.900 3 -4.507 0.110 0.258 0.320 -136.800 4 -4.150 0.197 0.258 0.284 -161.340 5 -3.710 0.198 0.258 0.304 -147.550 6 -2.712 0.198 0.258 0.304 147.550 7 -2.271 0.197 0.258 0.284 161.340 8 -1.827 0.110 0.258 0.320 136.800 9 -1.670 1.294 0.258 0.280 146.900 10 -0.327 0.110 0.258 0.326 145.400 M.Green file ‘just so’ (no coil currents optimization) flip mode non flip mode coil current files after optimization
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04/01/2006MICE Analysis Meeting7 After finding the new -matched- currents we can run ICOOL sim. + ecalc9 For several materials In this study: 2 slabs of different materials soon after the first spectro and just before the second spectro Study with central absorber still to be done Li, LiH, C, Polyethilene, Be (NO Liq. H) Thickness chosen in order to ensure a total 13% reduction in p (thicker slabs result in a funny beta behavior) With different values of initial emittance Plot of d / Cooling of 5% visibile in FLIP-mode (less cooling in NON FLIP-mode) 2 nd step: study of cooling performances
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04/01/2006MICE Analysis Meeting8 absorbers Sketch of absorbers position in phase III
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04/01/2006MICE Analysis Meeting9 Parameters used in simulation P z =207 MeV/c with a spread of 10% Initial emittances ranging from 0.1 to 1.0 (cm rad) 10000 generated muons per point (i.e. initial emittance) Lost muons: worse cases at high initial (=1.0 cm rad) 4% (LiH, C, non flip mode) 3% (C, flip mode)
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04/01/2006MICE Analysis Meeting10 FLIP mode (in vacuum) Evbeta calculation ICOOL simulation Z (m) (m) B z (T)
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04/01/2006MICE Analysis Meeting11 Non FLIP mode (in vacuum) Evbeta calculation ICOOL simulation (m) Z (m) B z (T)
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04/01/2006MICE Analysis Meeting12 FLIP mode (LiH) Initial emittances: =0.2 cm rad =0.25 cm rad =0.3 cm rad =0.6 cm rad Points taken at several initial emittance values Emittance ‘measured’ at the end of the II tracker Z (m) (m) B z (T) / (%) p/p (%)
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04/01/2006MICE Analysis Meeting13 Non FLIP mode Initial emittances: =0.2 cm rad =0.25 cm rad =0.3 cm rad =0.6 cm rad Z (m) (m) B z (T) / (%) p/p (%)
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04/01/2006MICE Analysis Meeting14 LiH, Li, Be, CH, C 0.22, 0.26, 0.38, 0.41, 0.57 (cm rad)0.22, 0.25, 0.35, 0.4, 0.6 (cm rad) Non-flip modeFlip mode equilibrium emittances / (%) (cm rad)
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04/01/2006MICE Analysis Meeting15 J. Cobb initial emittance emittance variation
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04/01/2006MICE Analysis Meeting16 NB: cooling of large emittance beam is less than expected for a given p/p / = p/p * (1- (eqm)/ ) Should reach p/p asymptotically for oo Worse behaviour in NON-FLIP mode Investigate by removing absorbers in ICOOL See 2-3% growth of emittance for large emittance beams w.o. absorbers We know from UB and BP et al that norm. emittance is NOT conserved in a drift |B| is low in drift region between 2 solenoids Emittance growth No simple model for this (unsatisfactory)
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04/01/2006MICE Analysis Meeting17 i =0.1 cm rad i =0.2 cm rad i =0.3 cm rad i =0.6 cm rad i =1.0 cm rad Emittance growth in vacuum: NO ABSORBERS
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04/01/2006MICE Analysis Meeting18 (cm rad) (%) NO absorbers: emittance growth in vacuum
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04/01/2006MICE Analysis Meeting19 Conclusions (very tentative) Step 3 needs a lot more study Simple demonstration of 1% emittance measurement capability of MICE may not be easy/possible in step III (i.e. not as easy as perhaps expected) It could be possible to observe some cooling with LiH or Li or Be absorbers, but may need correction from MC (unpleasant) To DO list Find optimum/better matches Investigate emittance growth Try placing a central absorber Optmize thickness for absorbers
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