1. Analysis of MICE Chris Rogers 1 Imperial College/RAL Thursday 28 October, 2004 1 With thanks to John Cobb

2. This talk Comparison of G4MICE transport/Analysis against ICOOL - not full channel yet Start trying to understand how we analyse MICE 1. Case study: no rf/absorbers 2. Full cooling channel Scope: work only in the transverse plane for now  (E)=  (t)=0 Assume we have pid; x,y,t; px,py,E of all particles at some plane in the upstream and downstream trackers Not thinking about experimental errors Assume we have a Gaussian input beam

3. G4MICE Analysis Package We can get: Phase space emittance Trace space emittance in 2, 4, 6 dimensions Beta function Transmission,,, z Single Particle Emittance Holzer Acceptance We can: Cut on transmission, position, momentum Apply statistical weights We can take inputs from: For003 For009 G4beamline G4MICE simulation G4MICE reconstruction

4. Status of Analysis using G4MICE G4MICE Simulation still has some issues Virtual planes not reliable Need to fill entire MICE volume Cause problems in G4 transport for low beta Effect materials in the cooling channel Emittance growth in absorbers Needs virtual planes first Mostly events from ICOOL but Analysis from G4MICE Try to be explicit about which one I’m using

5. Emittance (no RF/absorbers) G4MICE ICOOL + Ecalc9f Heating

6. Emittance (no RF/absorbers) G4MICE ICOOL + Ecalc9f Low beta regions near Absorbers

7. On-Axis Bz - G4MICE - ICOOL

8. What needs doing in MICE’s Analysis before data taking? Aims of MICE: 1. Prove that we can achieve cooling Do we have a robust measurement of “cooling”? Is it good to ~10 -3 ? Is 10 -3 appropriate? 2. Show how to achieve the best cooling Different input beams Input beta function, L can … It would be nice to know where to look…

9. Emittance not constant? Emittance is not constant in empty channel Emittance grows and shrinks - is this cooling/heating? Systematic Error? ~ 10 -1 Depending on what you want to know… “What is the increase in the number of muons I can get into my acceptance?” “What is the increase in the number of muons I can get into my acceptance beyond any magnetic field effects?” (Liouville) We should at least know where the boundaries of our understanding lie Case study for emittance analysis

10. Emittance Growth We see emittance growth (cf also Bravar). Perhaps this is to be expected Equation of motion in drift is non-linear 1 : P z in terms of phase space variables 1 Berg; Gallardo

11. Emittance Growth 2 Solution - use normalised trace space? Equation of motion in drift Take x’, y’ instead of p x, p y - then normalise (From now on we get events from ICOOL, analysis/plots from G4MICE Analysis)

12. Trace space emittance (magnets only) 4D Phase Space Emittance 4D Trace Space Emittance ?

13. Low emittance beam - Phase Space 4D Phase Space Emittance Phase Space Emittance (  mm rad x 10 -2 )

14. Low emittance beam - Trace Space 4D Trace Space Emittance Trace Space Emittance (  mm rad x 10 -2 ) Same scale as previous slide

15. Single Particle Emittance (SPE) We can see the heating as a function of emittance without using many beams of different emittance Define Single Particle Emittance (SPE) by Phase space density contour at 1  Our particle SPE= Area (2D) Rms Emittance= Area (2D)

16. SPE - Math Or mathematically 1 (in 4 Dimensions): 1 Holzer uses a slightly different definition but I want to keep units consistent Particle Phase Space Coordinate Vector Beam Covariance Matrix Rms Emittance Single Particle Emittance

17. SPE (magnets only) Why no particles in beam centre? 4D SPE (pi mm rad) N evts SPE - Upstream SPE - Downstream

18. Why so few low Emittance Particles? In 1  we have ~ 60 % of particles: 0.6

19. Why so few low Emittance Particles? In 1  we have ~ 60 % of particles: 0.6

20. Why so few low Emittance Particles? In 1  we have ~ 60 % of particles: 0.6 2D: 0.36

21. Why so few low Emittance Particles? In 1  we have ~ 60 % of particles: In 4D we have O.36 2 ~15% of particles in 1  (Conclusion - we need beams with different emittance) 0.6 2D: 0.36

22. “Heating” as a function of emittance - SPE

23. Constant heating across the beam??? It looks like there is constant heating across the beam! But we assumed this was only a fringe effect Further investigation…

24. Heating as a function of acceptance - Holzer Alternatively use Holzer Acceptance Measure the number of particles in a (4D) hyper-ellipsiodal phase space volume Plot N in (V)/N out (V) I assume Gaussian distributions

25. Holzer Acceptance Upstream and Downstream Holzer - Upstream Holzer - Downstream Consistently have more particles upstream than downstream

26. Holzer Acceptance Upstream vs Downstream - Heating Goes up to 12

27. Cooling performance Transverse Phase Space Emittance Transverse Trace Space Emittance

28. Single Particle Emittance SPE - Upstream SPE - Downstream N evts

29. Single Particle Emittance 2

30. Holzer Acceptance Holzer - Upstream Holzer - Downstream

31. Holzer Acceptance 2 Not enough statistics for low emittance particles - wanted to see centre heating Slight “heating” due to beam loss in fringe

32. Conclusions We need to understand what causes “heating” and “cooling” in the magnets only channel It appears to be constrained to the fringes ?Guess due to non-linear fields? We can plot emittance as a function of phase space volume Shouldn’t assume a Gaussian beam Needs more code!

33. Conclusions 2 A lot I haven’t touched Longitudinal emittance/dynamics I expect it to be more difficult than transverse How many events do we need to select the desired beam? What beams do we need to get full coverage of our phase space? Much more…