1. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 1 Use of TOFs for Beam measurement & RF phasing Analysis workshop, RAL 4 September 2008 Mark Rayner

2. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 2 Early beam diagnostics with the TOFs: For each muon… Use timing measurements at TOF0 and TOF1 to measure momentum –Sigma P = x MeV/c [CM21] Given knowledge of… –Quad geometry and currents –Beam line geometry –Muon momentum …predict the transfer matrix for the muon between TOF0 and TOF1 –Deduce using small amplitude particles in G4MICE –Verify by solving Hill’s equations –Try higher amplitudes –Find a simple procedure for matching transfer matrices to muons Use TOF position measurements and the transfer matrix to deduce x’ and y’ –Test this in G4MICE first of all using Monte Carlo truth positions… –…then using detector response simulation positions Finally, create a phase plane with these (x, x’) measurements and measure the emittance, and other optical parameters

3. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 3 Energy loss –10.1 +/- 1.4 MeV per TOF station –2.8 +/- 0.9 MeV in the Ckov –1.8 MeV in the 8m of air Scattering –1.8 +/- 1.1 degrees per TOF –1.4 +/- 0.8 degrees per Ckov Focussing –4.6 +/- 2.6 degrees in Q789 ~m   ┴ =1mm ~250 MeV/c realistic muon beam

4. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 4 Simple momentum reconstruction Data available from time of flight counters –Time of flight –Displacement Estimate p in the air between TOF0 and TOF1 Momentum losses from PDG dE/dx for minimum ionizing particles –Estimate p before TOF0 –Estimate p after TOF1 TOF0TOF1

5. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 5 TOF0 Cherenkov TOF1 (Inside cage to shield from tracker solenoid fringe fields) Tracker solenoid muon photon electron Quadrupole triplet ~250 MeV/c realistic muon beam G4MICE What is ? p air using truth – true p z before TOF0 p air using truth – true p z after TOF1 p air using recon. – true p z before TOF0 p air using recon. – true p z after TOF1 MeV/c

6. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 6 Deducing the transfer matrix from G4MICE Monte Carlo truth E.g. a 1150mm drift Cherenkov Quadrupoles

7. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 7 7 Gaussian 0.5mm Rectangular 1mm Gaussian 7.5mm Cherenkov ‘matrix elements’ X plane, 0.8m ‘drift’

8. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 8 G4MICE quad fields – transverse plane 23.6 cm 17.82 cm

9. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 9 TOF0  TOF1 transfer matrix as a function of momentum: Units: metres and MeV/c Two lines Red-solid: FDF plane Blue-dashed: DFD plane

10. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 10 TOF0  TOF1 transfer matrix as a function of momentum: Units: metres and MeV/c Two lines Red-solid: FDF plane Blue-dashed: DFD plane

11. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 11 Gaussian beam 7.5mm MC truth G4MICE detector simulation of TOF hits with x’ reconstructed using MC transfer matrix TOF 0TOF 1 x / m x’ x / m x’ x / m x’ x / m x’

12. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 12 Errors – some initial thoughts The question: can we use position measurements from two TOFs to measure transverse emittance? –Error = slab width / root 12 ~ 2 cm Error on x’?

13. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 13 TOF1 & cage Tracker Solenoid 1 Tracker 1 Photon Muon Electron Focus coil RF H2 absorber Extrapolating the time Time extrapolation to tracker reference plane (or RF cavity) required for –Defining a neutrino factory like bunched, stable beam –Measuring longitudinal emittance Necessary to track each muon on the basis of –Tracker (and TOF?) x, p x, y, p y, t, p z measurements –Magnetic (and electric) field maps –Energy loss models

14. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 14 Extrapolation of t, P z to TRP Time of flight  pz ~ intrinsic beam line  pz  t <500ps would be desirable in the tracker reference plane –Chris got 77ps using only the tracker pz (tracker 24ps, material 12ps, TOF 70ps) –A back of an envelope calculation suggests TOFs can achieve 30ps using TOF reconstructed p z with perfect tracking TOF  pz may be complementary to tracker  pz >6MeV/c when p t <10 MeV/c –38% of muons when there is no diffuser, E=200MeV/c,  n =2mm,  =33.3cm (John Cobb, CM19)  pz [MeV/c] Before TOF0 After TOF1 Intrinsic to beam line 2.83.5 Due to  TOF 4.44.7 Total5.25.8 Resolution of the tracker Smearing due to stochastic processes Both + 50ps TOF timing resolution Chris Rogers, Thesis

15. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 15 Extra slides

16. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 16 TOF 0  TOF 1 PDG calculations

17. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 17 Beam line parameters table from Kevin Kevin’s dataTrace space transfer matrix approximation ElementPosition Effective Length Field Strength s k = (e/p)*dB/dx [p=(250–11–3)~235MeV] Omega (phase advance) = s * Sqrt Mag k mmT/mmm -2 TOF0 centre20.8116 Drift 24.9637 – 20.8116 – 0.33 = 3.8221 Drift Space20.8624 CKOV121.0624 Drift Space21.5674 Q35 Qd - Q724.96370.660.88758QD0.661.1330.748 Drift Space25.6237Drift26.1237 – 24.9637 – 0.66 = 0.5 Q35 Qd - Q826.12370.66-1.34275QF0.66-1.7141.131 Drift Space26.7837Drift27.2837 – 26.1237 – 0.66 = 0.5 Q35 Qd - Q927.28370.661.14749QD0.661.4640.966 Drift Space.27.9437 Drift 28.8437 – 27.2837 – 0.33 = 1.23 TOF1 centre28.8437 Q35 dimensions: Pole tip radius (the radial distance between the central axis of the quadrupole and its pole tip) 17.82 cm Vertical ½ aperture 23.6 cm, Horizontal ½ aperture 23.6 cm

18. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 18

19. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 19 TOF1 Sigma X [m] and Sigma X’, 250 MeV/c, dp/p = 10% Initial beam –1 mm –alpha=0

20. Mark Rayner, Analysis workshop 4 September ‘08: Use of TOFs for Beam measurement & RF phasing, slide 20 -25 -20 -15 -10 -5 0 5 10 15 20 25 0123456789101112131415 Half width x / cm Half width y / cm TOF0 Diffuser norm. em. 7.1 mm after the diffuser z / m Clues on the probable beam just before TOF 0 Kevin’s assumptions at the target –Pions have mean Pz 444 MeV/c –Each variable is assume to have a top hat distribution due to scraping x 5.1 mm, x’ 0.033 y 2.0 mm, y’ 0.014 Pz 2.5% –Could use G4MICE to figure out the muon optical functions –Haven’t done this yet Average muon momentum / MeV? –Tune dipoles for 208.58 after diffuser –222.87 before diffuser –250 before TOF0 -11 in each TOF -3 in the Cherenkov -2 in the 8 m air CM15 Transport half width plot –Cov x’x’ = cov xx * (beta/Pz) 2 –Marco: beta before diffuser 83 cm (Half width) 2 / beta is constant Beta x TOF0 190 cm Beta y TOF0 332 cm –Gradients ~ 0 so alphas ~ 0 Kevin’s muon beam assumption –dp/p ~ 10%