1. 04/01/2006MICE Analysis Meeting1 MICE phase III M. Apollonio, J. Cobb (Univ. of Oxford)

2. 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!

3. 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

4. 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

5. 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)

6. 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

7. 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

8. 04/01/2006MICE Analysis Meeting8 absorbers Sketch of absorbers position in phase III

9. 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)

10. 04/01/2006MICE Analysis Meeting10  FLIP mode (in vacuum)  Evbeta calculation  ICOOL simulation Z (m)  (m) B z (T)

11. 04/01/2006MICE Analysis Meeting11  Non FLIP mode (in vacuum)  Evbeta calculation  ICOOL simulation  (m) Z (m) B z (T)

12. 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 (%)

13. 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 (%)

14. 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)

15. 04/01/2006MICE Analysis Meeting15 J. Cobb initial emittance emittance variation

16. 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)

17. 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

18. 04/01/2006MICE Analysis Meeting18  (cm rad)  (%) NO absorbers: emittance growth in vacuum

19. 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