1. Chris Rogers, MICE CM16 Wednesday Plenary Progress in Cooling Channel Simulation

2. Overview Aim is to simulate and understand errors on tracking in G4MICE to level of much less than detector resolution Solenoid modelling accuracy RF field maps RF field map modelling accuracy Absorber window GEANT4 parameters? Physics material model (GEANT4.8.2) Then examine G4MICE 6D cooling performance (still in progress) Match beam using full 6D Linear Beam optics package for RF, Quads, Solenoids Longitudinal matching & optics (still no amplitude momentum correlation) Mostly updated material, some new stuff

3. Solenoid Tracking Accuracy Reminder: Solenoid modelled using infinitely thin concentric current carrying sheets Analytical solution written to a grid During simulation, field at some point is taken by interpolation from the grid Dominant error is grid spacing Plot grid spacing vs tracking error through MICE Assume high precision for a very fine grid z spacing r spacing z spacing r spacing  (r)  (pt)

4. RF Modelling Implemented RF field maps Read in a file generated by SuperFish Thanks to Rick Fernow for providing SuperFish files

5. RF Tracking Accuracy Look at grid size vs tracking accuracy Dominant error is in  (r) (!) Even a very fine map introduces noticeable errors (compare with detector resolution ~ 0.3 mm)

6. RF Tracking Accuracy Look at grid size vs tracking accuracy Dominant error is in  (r) (relative to detector resolution) Even a very fine map introduces noticeable errors (compare with detector resolution ~ 0.3 mm)

7. A concern about phasing Phase by calculating an approximation to the energy increase expected on traversing an RF cavity Turns out this approximation is not good enough Serious distortion of the RF bucket ~ 1 MeV, 100 ps over MICE6 Would like to fire several reference particles with slightly different phases to find the one where the phase is set correctly Cannot remove stochastic processes properly (bug in GEANT4 or G4MICE) I now have code to integrate the equations of motion for particle tracking in the Optics module (inc dE/dz from Bethe Bloch) Not yet implemented for phasing though

8. RF bucket distortion “Reference Particle” Repeating 2.75 m lattice with no material (i.e. energy gain)

9. Multiple Scattering G4MICE MSc model (GEANT 4.8.2) Points are ICOOL Fano model Shown to agree well with ELMS/MuScat Curves are Moliere model Histo is G4MICE LH 2 Al Be

10. dEdX Bethe Bloch curve has random looking fluctuations (dashed line is calculated Bethe Bloch) Each point represents 1e4 muons so may be statistical Also note the energy straggling curve (200 MeV/c muon) Points ICOOL Curve is Landau fit - Vavilov is a better model Histo is G4MICE

11. Window Model Implemented arbitrary shaped windows (polycones) Plots are of actual track hits in the simulation Left is hits in absorber window Right is thickness of absorber window vs r G4 implements z vs r_inner, r_outer so where dz/dr is small, interpolation will be less accurate

12. Beam Heating from Window Polycone (realistic) window Cylindrical window Points show beam heating (change in SPE) vs radius for two models - cylindrical window and “realistic” window Windows have similar heating in centre (a little thinner) But realistic window shows slightly more heating on the edge Note the different scales Surprising how modest the emittance growth is (5x thickness) Histogram shows number of muons vs radius (6 pi beam)

13. Longitudinal beta Linear calculation (full line) Longitudinal beta with small transverse emittance RF field map (dashed) vs pill box (dotted) Longitudinal beta with 6 mm rad transverse emittance Need to look at amplitude momentum correlation here What do we do at 90 o where non-linearities are much worse?  perp 6 mm rad

14. Conclusions Next step is to look at cooling performance in the knowledge that the simulation is accurate to a high precision Paves the way for the data challenge Really starting to have a tool worthy of the experiment in G4MICE Understanding the cooling channel to some precision Need to worry about amplitude momentum correlation and longitudinal emittance growth