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Chris RogersImperial College

18 May 2006

TOF II Justification

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TOF2 resolution justification The need for longitudinal emittance Detector resolution vs emittance resolution

Some parts of this talk may come up in the CM Plenary

Overview

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PDG

Energy Loss through LH2

In material beam (E) changes because of Energy straggling (dominant)

Width of energy loss distribution Curvature of dE/dx

Muons with lower energy lose more energy than the reference particle This is longitudinal emittance growth that we should measure

PDG

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RF Bucket 40o Phase

I plot t-tRF vs E-Eref for a single muon over a long beamline In longitudinal phase space, muons are contained in an “RF

bucket” Optical “aberrations” cause emittance growth over ~ 10s of cells

Random effects (energy straggling) from passing through material cause muons to get knocked out of the RF bucket

This is also longitudinal emittance growth

Energy straggling switched ONEnergy straggling switched OFF

Position of reference particle

z=0

z=275 metresz=190 metres

z=0Contours in total energy

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Longitudinal beta function (Periodic SFoFo)

Set up the beam so that the longitudinal phase space structure is periodic over a MICE 2.75 m cell

Define “longitudinal beta function” // ~ (t)/(E) Choose // ~ 0.025 ns/MeV for periodic “matched” //

Compare with a non-periodic structure Deliberately introduce a mismatch by choosing // ~ 0.05

ns/MeV initially

~Periodic (“matched”) //

Deliberately unmatched //

Energy straggling switched OFF

Repeating structure made up of 4 x 2.75 m SFoFo lattices

LH2

// [m]

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Longitudinal Emittance (Periodic SFoFo)

Slightly small (E) ~ 10 MeV, (t) ~ 0.25 ns Much larger and I start falling out of the bucket I haven’t cut on muons inside the bucket for this plot

Two effects to be measured Growth due to optical “aberrations” (quite significant) Growth due to energy straggling

Alternatively count directly the number of muons in the RF bucket

Energy Straggling

Optical aberrations

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RF @ 90o Phase (Periodic SFoFo)

MICE default is to have RF at 90o phase Then there is no “bucket” May be possible to run at 40o in MICE V

But can still measure emittance growth due to energy straggling

z=0

z=40 metres

// with RF at 40o

// with RF at 90o

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MICE Channel

Much harder to match MICE is fundamentally not periodic due to pz loss (RF @ 40o)

Difficult to prevent emittance growth No RF cavities in the tracker/matching section

But I should be able to do better than this with some more faff