1. Diffuser Studies Chris Rogers, IC/RAL MICE VC 09 March 2005

2. Overview • Two Aims: • Aim to understand in detail position/thickness/material of diffuser • Also would like to move the lead outside of the Solenoid bore • This may be possible due to iron shield • Require to provide beams of • Different momenta? • Different emittances? (transverse, ?longitudinally?) • Or at least get enough statistics that we can select such a beam • Initial thoughts on how to approach the problem and a few plots • Will initially consider MICE Stage VI as this has the most stringent requirements • Relate this back to phase 1 later • This is all work in progress!

3. Transverse requirements • Transverse phase space - two requirements: • Require that we can produce a beam that completely fills the cooling channel to scraping • Require that we can produce a beam that looks like the input beam from a neutrino factory • Take the larger of the two? • Also need to consider different beta function requirements • Different b in absorbers ->different b in spectrometer? • Also require that we can produce a beam less than eqm emittance ~ 1-2 pi mm rad • Statistical arguments apply • And beams in between

4. G4MICE Acceptance of Cooling Channel • The acceptance of the cooling channel • Take grid of particles in 2D x-px phase space • Left is the phase space map of the particles that make it through the spectrometer • Right is phase space map of particles that make it through the cooling channel • All maps are plotted at z=-2750 (centre of LH2), pz = 200 MeV, beta = 420 mm in absorbers px X/mm X/mm

5. G4MICE Matched 12 pi beam • For reference, this is a matched, “Gaussian” 12 pi beam • Inserted in 4T region, draw phase space map at z = -2750 • Centre of LH2 • Left is all muons, right is muons which make it to z = 2750 • Transmission ~90% • Monochromatic beam X/mm X/mm

6. G4MICE Matched beam - beta func Use beta function defined by: • Again for reference, this is the beta function for a matched beam into MICE • Calculated numerically (hacked from JHC/UB’s code) • No diffuser/TOF, but semi-analytical solutions exist • Hope to have them soon • No iron shield/field thereof

7. Position of diffuser Current Diffuser Position This shows the current position of the diffuser It would be desirable to move it out of the solenoid bore This may be possible due to field effects from iron shielding Iron shield ~450 mm

8. G4MICE Baseline Design TOF • b(z) (left) and en(z) (right) with diffuser at -6014 mm • Taken turtle beam as input • Doesn’t include field mods due to iron shielding • Big drop in beta in materials… 1/emittance factor? • Does include kinematic cut 215 < E < 235 MeV/c^2 • Note that the input beam is not symmetric in x and y Diffuser Diffuser TOF

9. G4MICE Baseline Design - Diffuser at -6014 • Again, phase space map at entrance to cooling channel • Left is full beam; Right is beam with cut 215 < E < 235 MeV/c^2 • Doesn’t include new field map • Decent match • 6 pi emittance X/mm X/mm

10. G4MICE Diffuser at -6150 • Do the stupid thing and move the diffuser forward to -6150 mm • Predictably get a mismatch in spectrometer • This is with the same energy cut • Event rate higher by factor ~ 1.7 at z = -2750 • Need to iterate with coil currents in the beam line mismatch

11. Longitudinal Phase Space Requirements • Need to be able to produce beams of <pz> between 140 MeV and 240 MeV (TRD) • Also require s(E) ~ 25 MeV • Really this just means pz between ~100 and ~270 MeV • I won’t worry about timing

12. G4MICE Baseline - Longitudinal • Energy and Pz • ~ Fine for 200 MeV • But we lose a lot of statistics

13. Summary • The baseline solution for the diffusers is fine to a point • Needs some further work • This has begun… • Outline for route has been established • Need to try very hard to get the diffuser outside of the solenoid bore • Tools are under development!