Tracking time through Stage 6 1

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

Mark Rayner9th 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 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

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

z / mm

z / mm

beta

/ m

mBz0

/ M

T

matched in tracker

abs = 42cm

Tracking time through Stage 6 6

TOF1

Diffuser

Tracker stations Tracker

stations

Beam 1

Beam 2

Longitudinal dynamics

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