1 Chris Rogers Imperial College 18 May 2006 TOF II Justification

2 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

3 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

4 RF Bucket 40 o Phase I plot t-t RF vs E-E ref 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 metres z=190 metres z=0 Contours in total energy

5 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  // ~ 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]

6 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

7 90 o Phase (Periodic SFoFo) MICE default is to have RF at 90 o phase Then there is no “bucket” May be possible to run at 40 o in MICE V But can still measure emittance growth due to energy straggling z=0 z=40 metres  // with RF at 40 o  // with RF at 90 o

8 MICE Channel Much harder to match MICE is fundamentally not periodic due to pz loss 40 o ) 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