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Analysis of MICE

Analysis of MICE. Chris Rogers 1 Imperial College/RAL Thursday 28 October, 2004. 1 With thanks to John Cobb. This talk. Comparison of G4MICE transport/Analysis against ICOOL - not full channel yet Start trying to understand how we analyse MICE Case study: no rf/absorbers

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Analysis of MICE

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  1. Analysis of MICE Chris Rogers1 Imperial College/RAL Thursday 28 October, 2004 1With 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 • Case study: no rf/absorbers • Full cooling channel • Scope: • work only in the transverse plane for now s(E)= s(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, <E>, <Pz>, 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: • Prove that we can achieve cooling • Do we have a robust measurement of “cooling”? • Is it good to ~10-3? • Is 10-3 appropriate? • Show how to achieve the best cooling • Different input beams • Input beta function, Lcan … • 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-linear1: Pz in terms of phase space variables 1Berg; Gallardo

  11. Emittance Growth 2 • Solution - use normalised trace space? • Equation of motion in drift • Take x’, y’ instead of px, py - 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. 4D Phase Space Emittance Low emittance beam - Phase Space Phase Space Emittance (p mm rad x 10-2)

  14. 4D Trace Space Emittance Low emittance beam - Trace Space Trace Space Emittance (p 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 Rms Emittance= Area (2D) Our particle SPE= Area (2D) Phase space density contour at 1 s

  16. SPE - Math • Or mathematically1 (in 4 Dimensions): Single Particle Emittance Rms Emittance Particle Phase Space Coordinate Vector Beam Covariance Matrix 1Holzer uses a slightly different definition but I want to keep units consistent

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

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

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

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

  21. 0.6 2D: 0.36 0.6 Why so few low Emittance Particles? • In 1 s we have ~ 60 % of particles: • In 4D we have O.362~15% of particles in 1 s • (Conclusion - we need beams with different emittance)

  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 Nin(V)/Nout(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. Transverse Phase Space Emittance Transverse Trace Space Emittance Cooling performance

  28. Single Particle Emittance SPE - Upstream SPE - Downstream Nevts

  29. Single Particle Emittance 2

  30. Holzer Acceptance Holzer - Upstream Holzer - Downstream

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

  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…

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