Simulated real beam into simulated MICE 1

Simulated real beam into simulated MICE

Mark RaynerCM26

Simulated real beam into simulated MICE 2

Introduction

Various fancy reweighting schemes have been proposed But how would the raw beam fare in Stage 6?

TOF0 measures px and py at TOF1 given quadrupole field maps On Wednesday I described the measurement of a 5D covariance matrix

(x,px,y,py,pz)

In this talk, compare two monochromatic 6-200 beams in Stage 6 A matched beam in the tracker A measured beam at TOF1

Measured (x, px) and (y, py) covariances No dispersion

Simulated real beam into simulated MICE 3

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 pperp

2/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 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 pperp2/Bz0 really an adiabatic invariant in the MICE Stage 6 fields?

Simulated real beam into simulated MICE 4

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 zTOF1 – zTOF0

s leff + F + D

Track through through each quad,

and calculate

Add up the total pathS = s7 + s8 + s9 + drifts

Q5 Q6 Q7 Q8 Q9

TOF1TOF0

zTOF1 – zTOF0 = 8 m

Simulated real beam into simulated MICE 5

B field and beta lattice

matched in tracker

abs = 42cm

Simulated real beam into simulated MICE 6

Matched beam

Simulated real beam into simulated MICE 7

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 [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 MICE 8

Measured beam

Simulated real beam into simulated MICE 9

Matching time in the first cavity

Sigma pz = 24.5 MeV Beta = 0.857 to 0.904 (-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 1st RF to before the TOF:

L/Eref = 4423 mm / (230 MeV * 300 mm/ns) = 0.064 ns/MeV Sigma t RF = 500 ps Sigma t = sqrt( (0.5 ns)**2 + (1.568 ns)**2 ) = 1.645 ns Cov(t,pz) = –38.42 ns MeV

Simulated real beam into simulated MICE 10

Conclusion