Simulated real beam into simulated MICE1 Mark Rayner CM26

Simulated real beam into simulated MICE2 Introduction  Various fancy reweighting schemes have been proposed  But how would the raw beam fare in Stage 6?  TOF0 measures p x and p y at TOF1 given quadrupole field maps  On Wednesday I described the measurement of a 5D covariance matrix (x,p x,y,p y,p z )  In this talk, compare two monochromatic beams in Stage 6  A matched beam in the tracker  A measured beam at TOF1  Measured (x, p x ) and (y, p y ) covariances  No dispersion

Simulated real beam into simulated MICE3 Time in MICE  RF frequency = 200 MHz, period = 5 ns  Neutrino factory beam  Time spread is approximately 500 ps  Want < 50 ps resolution in cavities  Possible methods for tracking time from TOF1 to the upstream tracker  Use of the adiabatic invariant p perp 2 /B z0  The flux enclosed by the orbit of a charged particle in an adiabatically changing magnetic field is constant  Use of the linear transfer matrix for solenoidal fields  Multiply matrices corresponding to slices with varying B z0 and kappa  Tracking step-wise through a field map  Measured or calculated?  A Kalman filter  Implemented between the trackers  Static fields  None of these methods is particularly difficult  Nevertheless, there is merit in simplicity  This talk will investigate the first approach  Is p perp 2 /B z0 really an adiabatic invariant in the MICE Stage 6 fields?

Simulated real beam into simulated MICE4 Reconstruction procedure Estimate the momentum p/E = S/  t Calculate the transfer matrix Deduce (x’, y’) at TOF1 from (x, y) at TOF0 Deduce (x’, y’) at TOF0 from (x, y) at TOF1 Assume the path length S  z TOF1 – z TOF0 s  l eff +  F +  D Track through through each quad, and calculate Add up the total path S = s 7 + s 8 + s 9 + drifts Q5Q6Q7Q8Q9 TOF1TOF0 z TOF1 – z TOF0 = 8 m

Simulated real beam into simulated MICE5 B field and beta lattice matched in tracker  abs = 42cm

Simulated real beam into simulated MICE6 Matched beam

Simulated real beam into simulated MICE7 Beam 1  Beam 1: Runs 1380 – 1393  Kevin’s optics 6 mm – 200 MeV/c emittance-momentum matrix element  Analysis with TOF0 and TOF1 – the beam just before TOF1:  Covariances:  sigma(xp x ) = –610 mm MeV  sigma(yp y ) = +85 mm MeV  Longitudinal momentum  Min. ionising energy loss in TOF1 = MeV  pz before 7.5 mm diffuser (6-200 matrix element) = 218 MeV [Marco]  RF cavities have gradient 9.1 MV/m and 90 degree phase for the reference muon  Start with pz = N(230, 0.1) MeV before TOF1, centred beam, transverse optics as above

Simulated real beam into simulated MICE8 Measured beam

Simulated real beam into simulated MICE9 Matching time in the first cavity  Sigma pz = 24.5 MeV  Beta = to (-1  to +1  )  Time over L = 17.2 ns to 16.3 ns  Difference = 0.89 ns  RF period = 5 ns  Transfer matrix:  Work the covariance matrix back from the 1 st RF to before the TOF:  L/Eref = 4423 mm / (230 MeV * 300 mm/ns) = ns/MeV  Sigma t RF = 500 ps  Sigma t = sqrt( (0.5 ns)**2 + (1.568 ns)**2 ) = ns  Cov(t,pz) = –38.42 ns MeV

Simulated real beam into simulated MICE10 Conclusion