MICE stages IV, V & VI

1. MICE stages IV, V & VI U. Bravar – Univ. of Oxford – 10 March 2004 • Questions: 1)Can we compare the performance of MICE Stages IV, V and VI? 2)Can we do all the physics of MICE with a ‘reduced’ MICE channel?

2. Stages

3. ICOOL simulations • Run simulations of Stages IV, V and VI of MICE, as taken from the MICE proposal to RAL (2003). • Geometry: Assume that Stages V & IV are obtained by removing one or two LH and one or two RF modules from the final structure of MICE. I.e.: 1) Longitudinal distances between channel elements don’t change. Essentially, Stages V and IV are 2.75 m and 5.5 m shorter than Stage VI. 2) Use the same coil currents for all three stages (except: change the sign in downstream spectrometer coils as appropriate). • Check transmission and cooling as a function of the longitudinal coordinate z along the MICE channel for Stages IV, V and VI. 1) As usual, use normalised transverse “x-px” emittancee^

4. Transmission • Stage VI (full MICE) • Stage V (2 LH + 1 RF) • Stage IV (1 LH + 0 RF) • Input emittances: e^in = 3,000 mm mrad, 6,000 mm mrad, 9,000 mm mrad & 12,000 mm mrad. • Start with 10,000 muons. Count number of muons that are left as a function of z along the MICE channel. 1) z = 0 in the middle of the upstream spectrometer. ICOOL runs all the way to the middle of the down-stream spectrometer, to z = 4.10 m (Stage IV), 6.85 m (Stage V) & 9.60 m (Stage VI).

5. Cooling • Stage VI (full MICE) • Stage V (2 LH + 1 RF) • Stage IV (1 LH + 0 RF) • Input emittances: e^in = 3,000 mm mrad, 6,000 mm mrad, 9,000 mm mrad & 12,000 mm mrad. m+ beam, <pz> = 200 MeV/c. • See note on next page!

6. e^in = 6,000 mm mrad • Stage V (2 LH + 1 RF) • Stage IV (1 LH + 0 RF) • Stage VI (full MICE) • Question: why is e^in (Stage IV) >> e^in (Stage VI) when e^in should be ~6,000 mm mrad in all cases? Answer: the input beams for all three stages have the same e^in. However the values of e^ are calculated by using ONLY those tracks that make it all the way to the middle of the down-stream spectrometer. Since muon loss is larger in stage VI than in stage IV, e^ at all z locations is calculated from a reduced subset of events. As a consequence, calculatede^in (Stage IV) > calculatede^in (Stage VI).

7. Summary of results 1) At all z locations, only muon tracks that make it all the way to the downstream spectrometer are used to calculate e^. 2) Transmission = number of muons that reach the middle of the downstream spectrometer, out of 10,000 initial. Muon decay is disabled. 3) De^ / e^ = (e^upstream – e^downstream) / e^upstream = cooling; e^ is measured in the middle of the upstream and downstream spectrometers.

8. Errors • Question: what are the errors in the table on the previous page? • Answer: the figure shows De^/e^ (y-axis) vs. transmission (x-axis) for Stage VI. • Each point corresponds to a different ICOOL run with a different randomly generated input beam. • Total of 20 input beams, each beam contains 10,000 events. • All beams are Gaussian, e^in = 6000 mm mrad. (On the x-axis, I am actually plotting the number of events that are lost in the MICE channel, i.e. Transmission = 10,000 – # on the x-axis). • Standard MICE channel with all the materials and RF in place. • MICE channel with LH only, no Al and Be windows. To check how much of a difference this makes.

9. Bz fields and b^ functions • Stage V (2 LH + 1 RF) • Stage IV (1 LH + 0 RF) • Stage VI (full MICE) • Expectations: i) Bz = 4 T uniform in spectrometers. ii) b^ should stay 33 cm uniform in spectrometers. iii) b^ should have a minimum of 42 cm in the centre of LH absorbers. • Observations: i) Bz behaves as expected. ii) b^ is not uniform in downstream spectrometer. iii) In full MICE (Stage VI) b^ has a minimum after the first LH and before the last LH.

10. Remarks • Discussion with Bob Palmer & Mike Green on 8/3/04 (UK) or 3/8/04 (US). Currents in MICE coils are optimized assuming long channel with ~100 cells, no LH & no RF. Fine tuning of currents in individual coils may become necessary in the case of MICE. Coil-by-coil changes of ~5% should not constitute a major problem. • Similar study on Stages IV, V and VI will be performed with G4MICE. Work has already begun.

11. Conclusions • MICE Stage V can demonstrate the feasibility of a muon ionisation cooling channel. • MICE Stage IV can prove ionisation cooling as well, but cannot prove the feasibility of a long cooling channel, since it includes no RF. • The goals of the full MICE experiment can be achieved with Stage V. • Event loss becomes more relevant as MICE becomes longer and e^in becomes larger. • For e^in = 3,000 mm mrad, cooling in Stage V appears to be better than in Stage VI. However, there is little cooling in both cases (very close to equilibrium emittance). Results for Stage VI are worse because distributions in the downstream spectrometer are ‘less’ Gaussian, which induces a bigger ‘error’ in the emittance calculated with current techniques.