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A (short) history of MICE – step III

A (short) history of MICE – step III. M. Apollonio – University of Oxford. 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?

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A (short) history of MICE – step III

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

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

  4. Step III: twoback 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 MICE CM - Fermilab, Chicago - (11/06/2006)

  5. FLIP mode (LiH) Initial emittances: e=0.2 cm rad e =0.25 cm rad e =0.3 cm rad e =0.6 cm rad Points taken at several initial emittance values Emittance ‘measured’ at the end of the II tracker MICE CM - Fermilab, Chicago - (11/06/2006)

  6. currents optimization: evbeta + MINUIT (in vacuum) simulation: ICOOL + ecalc9 Flip mode Non-flip mode LiH, Li, Be, CH, C De/e (%) De/e (%) e (cm rad) e (cm rad) 0.22, 0.26, 0.38, 0.41, 0.57 (cm rad) 0.22, 0.25, 0.35, 0.4, 0.6 (cm rad) equilibrium emittances MICE CM - Fermilab, Chicago - (11/06/2006)

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

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

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

  10. 1st 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 MICE CM - Fermilab, Chicago - (11/06/2006)

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

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

  14. Vacuum: e0=1.0 cm rad beta function in a.u. Fit to SPE: dN/de1=N0/4 e1/e2 exp(-e1/2e) Z (m) (GeV/c) (GeV/c) (GeV/c) (GeV/c) (m) (m) (m) (m rad) c2 contributions MICE CM - Fermilab, Chicago - (11/06/2006)

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

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

  17. warming in vacuum … why? Fit to SPE ecalc9 c2/dof 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 BZ=const+uniform and PZ=const the emittance growth is zero: this is fairly true in the solenoid regions where infact e~const • When you cross the flip region you have a rapid change in BZ BX, BY components: emittance grows up MICE CM - Fermilab, Chicago - (11/06/2006)

  19. e (m rad) ecalc9 Penn’s prediction Most of the effect explained Z (m) 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 planesalong the channel Start with the vacuum case... MICE CM - Fermilab, Chicago - (11/06/2006)

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

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

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

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

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

  26. LiH absorbers Z=2.95m Z=3.25m 20 22 Z=3.35m Z=3.25m 21 23 21 22 23 20 Intermediate region: cooling is spoiled (specially for high values of SPE) MICE CM - Fermilab, Chicago - (11/06/2006)

  27. LiH absorbers Z=3.45m Z=3.85m 24 26 Z=4.25m Z=3.45m 25 27 24 25 26 27 Cooling soon after 2nd LiH absorber: more effective on low SPEs MICE CM - Fermilab, Chicago - (11/06/2006)

  28. LiH absorbers 40 SPE(Z=5.5m) SPE(Z=0) 40 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 e1 • after all we want to INCREASE the phase space density, possibly • without caring about the tails of the SPE distribution MICE CM - Fermilab, Chicago - (11/06/2006)

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

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

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

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

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

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

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