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A first look at tracking the TOF1 time measurement through Stage 6

A first look at tracking the TOF1 time measurement through Stage 6. Mark Rayner 9 th March 2010. Introduction. Non-PID uses of the TOF1 50 ps resolution timing measurement: At what phase did the muon pass through the RF cavities? What energy must it have received?

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A first look at tracking the TOF1 time measurement through Stage 6

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  1. A first look at tracking the TOF1 time measurement through Stage 6 Mark Rayner 9th March 2010 Tracking time through Stage 6

  2. Introduction • Non-PID uses of the TOF1 50 ps resolution timing measurement: • At what phase did the muon pass through the RF cavities? • What energy must it have received? • What is the time in the upstream tracker? • Can we select a beam with appropriate initial longitudinal emittance? • What is the longitudinal momentum in the upstream tracker? • At sufficiently low amplitudes, via tracking, the TOFs can conceivably contribute a measurement of better resolution than the trackers • Possible methods for tracking time from TOF1 to the upstream tracker • Use of the adiabatic invariant pperp2/Bz0 • 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 Bz0 and kappa • Tracking step-wise through a field map – measured or calculated? • A Kalman filter • None of these methods is particularly difficult • Nevertheless, there is merit in simplicity • This talk will investigate the first approach • Is pperp2/Bz0 really an adiabatic invariant in the MICE Stage 6 fields? Tracking time through Stage 6

  3. 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(xpx) = –610 mm MeV • sigma(ypy) = +85 mm MeV • Longitudinal momentum • Min. ionising energy loss in TOF1 = 10.12 MeV • pz before 7.5 mm diffuser (6-200 matrix element) = 218 MeV [Apollonio] • RF cavities have gradient 7.3 MV/m and 90 degree phase for the reference muon • Start with pz = N(230, 25) MeV before TOF1, centred beam, transverse optics as above Tracking time through Stage 6

  4. Beam 2 • 6-200 element again • Matched in the upstream tracker • beta * kappa = 1 in the constant field region • Longitudinal dynamics • Initial pz = 207 MeV/c • Same Gaussian distribution with sigma(pz) = 25 MeV/c Tracking time through Stage 6

  5. The Stage 6 field map has been fixed Bz0 / MT z / mm matched in tracker babs = 42cm beta / mm z / mm Tracking time through Stage 6

  6. Longitudinal dynamics TOF1 Diffuser Beam 2 Tracker stations Tracker stations Beam 1 • Cuts • r < 150 mm in each tracker • A higher gradient is required for realistically large sigma(pz) Tracking time through Stage 6

  7. Mean square transverse momentum Tracking time through Stage 6

  8. The adiabatic invariant Tracking time through Stage 6

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