1. MICE CM - Fermilab, Chicago - (11/06/2006) 1 A (short) history of MICE – step III M. Apollonio – University of Oxford

2. MICE CM - Fermilab, Chicago - (11/06/2006) 2 Motivations: can we observe an effect of cooling at an earlier stage ? First Results: they showed how emittance is not reduced as expected cooling not so effective. Why? What happens to emittance in vacuum? It grows. Why? Is the only quantity we want to use to characterize cooling? Or rather we want to use all the information we can get from the SPE distribution?

3. MICE CM - Fermilab, Chicago - (11/06/2006) 3 Parameters used in simulation (ICOOL) P z = 207 MeV/c Gaussian Beams 10000 muons per configuration selected sigma_p z =10% several emittances lost muons < 4% ERROR spotted: actual sigma_p z =3%

4. MICE CM - Fermilab, Chicago - (11/06/2006) 4  Step III: two back to back tracker solenoids and no RF cavities Step VI Step III  This operation requires some attention in redefining the currents of the coupling coils (matching)  Tried several techniques  MINUIT+evbeta (beta evolution equation in paraxial approximation)  MINUIT+ICOOL  They give approximately the same results for the optimised currents [MICE-CM-Osaka,28/2/2006] just so currents optimised currents

5. MICE CM - Fermilab, Chicago - (11/06/2006) 5 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

6. MICE CM - Fermilab, Chicago - (11/06/2006) 6 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) currents optimization: evbeta + MINUIT (in vacuum) simulation: ICOOL + ecalc9

7. MICE CM - Fermilab, Chicago - (11/06/2006) 7 Flip mode: 2 absorbers LiH, Li, Be, CH, C 2x7cm absorbers = 13% p z reduction 0.22, 0.26, 0.39, 0.4, 0.57 (cm rad) Optimisation: ICOOL+Minuit with non simm. currents

8. MICE CM - Fermilab, Chicago - (11/06/2006) 8 … and what do we get? What do we expect ?

9. MICE CM - Fermilab, Chicago - (11/06/2006) 9 current optimization schemes: evbeta+MINUIT ICOOL+MINUIT with 2 absorbers equilibrium asymptotic cooling

10. MICE CM - Fermilab, Chicago - (11/06/2006) 10  1 st observation: something is happening in the region between the two solenoids which spoils the emittance causing an undesired growth  What is the cause of this growth?  Is it due to the presence of material?  Does it happen in vacuum? Investigate a channel without absorbers

11. MICE CM - Fermilab, Chicago - (11/06/2006) 11  i =0.1 cm rad  i =0.2 cm rad Emittance growth in vacuum: NO ABSORBERS  i =0.3 cm rad  i =0.6 cm rad  i =1.0 cm rad

12. MICE CM - Fermilab, Chicago - (11/06/2006) 12 (%) Non Flip Mode Flip Mode  (cm rad) 2.3 % 2.8 %

13. MICE CM - Fermilab, Chicago - (11/06/2006) 13 Investigate emittance growth effort on understanding its origin vacuum Follow the beam along the channel at different Z Calculate the amplitude (single particle emittance) for each Z-plane NB if the beam is gaussian you can prove SPE follows a simple function [John’s note, in preparation] If V is the covariance of a multivariate gaussian distribution

14. MICE CM - Fermilab, Chicago - (11/06/2006) 14 Vacuum:  0 =1.0 cm rad  eta function in a.u. Fit to SPE: dN/d  1 =N 0 /4  1 /  2 exp(-  1 /2  ) (m) (GeV/c) (m rad) (GeV/c) (m) (GeV/c) Z (m)  2 contributions

15. MICE CM - Fermilab, Chicago - (11/06/2006) 15

16. MICE CM - Fermilab, Chicago - (11/06/2006) 16

17. MICE CM - Fermilab, Chicago - (11/06/2006) 17 ecalc9 Fit to SPE   /dof warming in vacuum … why?

18. MICE CM - Fermilab, Chicago - (11/06/2006) 18  G. Penn’s note 71: p.10, eq. (15)  Can be derived from the general expression of normalized emittance (4D)  Predicts an emittance growth in vacuum  Ideally if B Z =const+uniform and P Z =const the emittance growth is zero: this is fairly true in the solenoid regions where infact  ~const  When you cross the flip region you have a rapid change in B Z  B X, B Y components: emittance grows up

19. MICE CM - Fermilab, Chicago - (11/06/2006) 19 Z (m)  (m rad) ecalc9 Penn’s prediction Most of the effect explained

20. MICE CM - Fermilab, Chicago - (11/06/2006) 20 Is emittance growth uniform over the SPE spectrum or specific, i.e. some values more affected? Look at SPE distributions in different Z planes along the channel Start with the vacuum case...

21. MICE CM - Fermilab, Chicago - (11/06/2006) 21 Intermediate region: specific warming E(reg2) vs E(reg1, Z=0m) E(reg2) - E(reg1, Z=0m) vs E(reg1, Z=0m) vacuum 4 5 4 5 12 13 12 13 Z=0.61m Z=1.025m Z=1.925m Z=2.025m

22. MICE CM - Fermilab, Chicago - (11/06/2006) 22 vacuum 2021 Z=2.95m Z=3.25m Z=3.45m 24 20 21 24 25

23. MICE CM - Fermilab, Chicago - (11/06/2006) 23 SPE(Z=0) SPE(Z=5.5m) vacuum 40 Z=5.5m

24. MICE CM - Fermilab, Chicago - (11/06/2006) 24...continue with LiH (2 absorbers) LiH absorbers 4 4 5 5 Z=0.61m Z=1.025m

25. MICE CM - Fermilab, Chicago - (11/06/2006) 25 Cooling soon after 1 st LiH absorber Intermediate region: specific warming LiH absorbers 6 7 12 13 Z=1.025m Z=1.125m Z=2.025m Z=1.925m 6 12 13 7

26. MICE CM - Fermilab, Chicago - (11/06/2006) 26 Intermediate region: cooling is spoiled (specially for high values of SPE) LiH absorbers 2022 2321 Z=2.95m Z=3.25m Z=3.35m Z=3.25m 20 212223

27. MICE CM - Fermilab, Chicago - (11/06/2006) 27 Cooling soon after 2 nd LiH absorber: more effective on low SPEs LiH absorbers 2426 2725 Z=3.45m Z=4.25m Z=3.85m 2425 26 27

28. MICE CM - Fermilab, Chicago - (11/06/2006) 28 SPE(Z=0) SPE(Z=5.5m) LiH absorbers 40

29. MICE CM - Fermilab, Chicago - (11/06/2006) 29 The effect of warming up of overall emittance can be partly explained with the considerations seen in the vacuum case Yet the emittance growth in vacuum is just a fraction of the effect as seen with absorbers Emittance can be evaluated: as an average quantity (with some cautious cut): ecalc9 as a result of a fit on SPE distributions (seems to work well when world is gaussian) or considering the density of phase space for low values of  1 after all we want to INCREASE the phase space density, possibly without caring about the tails of the SPE distribution

30. MICE CM - Fermilab, Chicago - (11/06/2006) 30

31. MICE CM - Fermilab, Chicago - (11/06/2006) 31 Emi=1.0 cm rad beginning of channel end of channel end - beginning Emi=0.6 cm rad

32. MICE CM - Fermilab, Chicago - (11/06/2006) 32 Emi=0.4 cm radEmi=0.5 cm rad

33. MICE CM - Fermilab, Chicago - (11/06/2006) 33 Emi=0.3 cm radEmi=0.2 cm rad Emi=0.1 cm rad

34. MICE CM - Fermilab, Chicago - (11/06/2006) 34 current optimization schemes: evbeta+MINUIT ICOOL+MINUIT with 2 absorbers equilibrium asymptotic cooling phase space density for low SPE regions

35. MICE CM - Fermilab, Chicago - (11/06/2006) 35 Integral of events with emi<et Blue=cooled

36. MICE CM - Fermilab, Chicago - (11/06/2006) 36 Conclusions:  a review of step III has been shown  some better understanding of the emittance growth effect has been gained (Penn’s fmla)  a suggestion about a different definition of cooling based on SPE distribution has been introduced: this produces emittances in good agreement with the simple model Future things...  What happens when beam is not gaussian (real beam)?  Repeat studies with higher spread in Pz  Non-flip mode?