1. OPTICS UPDATE Ulisse Bravar University of Oxford 3 August 2004

2. How to tune the MICE channel Baseline configuration: flip mode p = 200 MeV/c   = 42 cm in LH B z = 4 T in solenoids Steps: achieve minimum   as stated: FC & CC uniform B-field inside spectrometer (to 1%): EC uniform   inside spectrometer: MC

3. Software Matching code from Bob Palmer: written in QuickBasic, runs on Windows ICOOL + minimization routine ‘empty’ MICE channel paraxial tracks Numerical evolution of   by John Cobb: ‘empty’ MICE channel   from G. Penn, MuCool note 71: 2     ’’ – (   ’) 2 + 4   2  2 – 4 = 0 Work in progress: a)matching & minimization for Unix, ICOOL independent b)study of large amplitude tracks, with dE/dx & RF, p-spread

4. Present status of solutions For every set of coil configurations: a)Determine paraxial solutions for p = 200 MeV/c, flip and no-flip modes,   = 42, 25, 17, 7 cm in LH: 8 sets of currents b)Semi flip mode obtained by combining flip & no-flip: 4 more sets c)Stages IV and V of MICE obtained from stage VI d)p < 200 MeV/c: scale solutions from p = 200 MeV/c: (8 + 4) x 2 = 24 additional sets of currents e)p = 240 MeV/c: scale FC and CC, repeat matching: 12 more currents So far, have several of the solutions from first line. Also, solutions for reduced gaps: 400 mm, 500 mm…

5. Optical solutions (1) MICE proposal to RAL (2003): coil configuration from tab. 4.1 currents from tab. 4.2, case 1a p = 220 MeV/c p = 200 MeV/c p = 180 MeV/c MISMATCH for p = 200 MeV/c !!! z (m)   (m) B z (T)

6. Optical solutions (2) Currents from Bob Palmer’s note, Sept. 2003 Tab. 4 & 5 SFOFO   = 43 cm 200 MeV/c   looks OK:   = minimum in LH   = uniform in solenoid Mismatches at 180 and 220 MeV/c z (m) B z (T)   (m)

7. Optical solutions (3) Coil configuration from Mike Green and INFN-GE agreed upon at CERN 2004 meeting 600 mm GAP Currents determined with Bob Palmer’s minimization routine Again   at p = 200 MeV/c looks OK Note: big   increase in match coil region z (m) B z (T)   (m)

8. What happens at large amplitudes?   in the centre of LH cell Flip mode, p = 200 MeV/c From Bob Palmer, June 2004 Optical solutions with paraxial rays work fine for beams with   = 6  mm rad momentum (GeV/c)   (m)

9. What is wrong with the present coil configuration? 600 mm gap causes   growth. Possible consequences: beam scraping, smaller momentum acceptance 600 mm gap causes   increase. The beam that we are measuring is not the beam that we are cooling The smaller the gap, the better

10. Bob Palmer 9/2003 `M. Green 600 mm’  larger -- presumably due to increased spacing matching – focus coils and smaller B Smaller momentum acceptance: off momentum muons might scrape beam aperture Different here BzBz  Reminder

11.  functions @ 200 MeV/c, M. Green configurations, 400, 500, 600mm 400 mm500 mm600 mm New Old Green = - 5% solid -10% dashed Black = On momentum Red = + 5% solid +10% dashed Beta always > 1.8 metres in 2nd RF for p = 1.1 x p tune Decreased spacing helps beta-stability ‘400mm’ not as stable as Palmer solution (not buildable?)

12.  functions @ 240 MeV/c, M. Green configurations, 400, 500, 600mm 400 mm500 mm600 mm New 240 MeV/c looks ‘tidier’ Beta still rises in 2 nd RF – but less than at 200 MeV/c

13. Emittance growth in 600 mm gap MICE Note 49 (Bob Palmer, September 2003) Present coils (Mike Green et al., March 2004)   from ecalc9f increases in drift Quick fix: x-p x correlation in the Gaussian beam in the upstream solenoid PROBLEM z (m)   (  m rad)

14. Quick fix: x – p x correlation Note 49 MG coils with x-px correlation z (m)   (  m rad) x (m) p x (GeV/c)

15. dE/dx and acceleration From Bob Palmer, June 2004 Conclusion: Acceleration, dE/dx have no observable effect on MICE optics momentum (GeV/c)   (m)

17. MICE stages IV and V z (m)   (m) B z (T) Stage V Stage IV

18. MICE stage III z (m)   (m) B z (T)   (  m rad)

19. Flip and no-flip modes z (m)   (m) B z (T)

20. Conclusions Optical matching technique works fine, software upgrades in progress 48 optic solutions for every coil configuration, for stage VI only. Currents will be updated as necessary 450 mm gap looks better than 600 mm, but how good is good enough? Need decision on B-field in spectrometer when p < 200 MeV/c