1. paul drumm, mutac jan 2003 1 MICE Beamline Optics Design Kevin Tilley, RAL, 12th June MICE Needs Generic Solution Pion Injection & Decay Section (a) Inputs (b) Solution Muon Transport (a) Inputs (b) Solution ε n Generation/Matching (a) Inputs (b) Solution Current & projected status.

2. paul drumm, mutac jan 2003 2 2 MICE Muon Beam - Generic Needs MICE Generic Needs:- –High flux muon beam (>600 muons thru-going MICE lattice / msec ) –High purity muon beam ( < 0.1 % contamination) –Muon momenta ~ 140 - 240 MeV/c –Muon emittances ~ 1 π mm rad - 10 π mm rad. –Beam matched into MICE Lattice –Also:- –Desirable muon momentum spread of at least dp/p=+/-10% full width.

3. paul drumm, mutac jan 2003 3 3 MICE Beamline Design - General Solution General Solution:- –Many similar requirements to Condensed Matter Pion-Muon Decay beamlines:- PSI uE4 TRIUMF muon beamlines RAL-RIKEN muon beamline –Thus we adopted to design a pion-muon decay beamline. –For us, demark into 4 functions: - pion injection decay muon transport ε n generation / matching

4. paul drumm, mutac jan 2003 4 4 MICE Beamline Design - General Solution

5. paul drumm, mutac jan 2003 5 5 MICE Beamline Design - General Solution Codes: TRANSPORT / DECAY TURTLE : –Why? Since both codes had extensive history / support. Both codes had been used to design all aforementioned pion-muon decay channels:- –PSI uE4 –TRIUMF muon beamlines –RAL-RIKEN muon beamline –How used? Pion injection & decay channel:- –Straightforward use of 2nd order TRANSPORT Muon transport –Muon source comes from DECAY TURTLE –Optical design using TRANSPORT to both:- »fit to desired conditions »sometime fit and find 'difference' for driving TTL to desired conditions. –Always iteration between TTL / TPT until rqd conditions met (as seen in Turtle) Pb. diffuser –Thickness set from scattering seen in DECAY TURTLE (uses REVMOC) Beamline materials (except Pb) –Modelling consistently in both codes with same Δp as G4Beamline but free

6. paul drumm, mutac jan 2003 6 6 Pion Injection & Decay Channel - Inputs/Constraints Geometry:- Target - Beamline Angle of ~20° chosen to allow high energy pion capture. Hence Target to Q1 centre shortest is 3.0m due to proximity to Synchrotron Hole Drilled ! (April 2004) z-position :- to avoid old HEP tunnel ? - to avoid Synchrotron electrical junction box Hence length of pion injection fixed, at Target - B1 centre ~ 7.98m B1 – Decay Sol distance set since Decay Sol to fit wall-hole geometry (hole ≈ 650mm)

7. paul drumm, mutac jan 2003 7 7 Pion Injection & Decay Channel - Solution Flux:- Maximise # pions into decay section -> maximises useful muon flux @ MICE –normally length (fixed) –magnets (limited) –optics Maximise accumulation of muons in decay section –highest decay solenoid field, consistent with controllable beam profile. Purity :- Chose always ~ highest pion momenta possible - to allow selection of 'backward' going muons for higher purity & higher fluxes. (Risk is assumption of accurate modelling of pion spectrum from target, but Target test in October'06 may tell us answer?):- Inclusion of C 2 H 4 'proton absorber' (ranges out protons greatly aids purity

8. paul drumm, mutac jan 2003 8 8 Almost all emittance, momenta cases use same pion optic above. (1 envisaged exception) C2H4 'Proton absorber' Pion Injection & Decay Channel - Solution C2H4 'Proton absorber'

9. paul drumm, mutac jan 2003 9 9 Pion Injection & Decay Channel - Solution 146086 46836 146086 Compares fairly well with RAL-RIKEN:- Injection efficiency ~ 0.82 RIKEN Efficiency of accumulating muons ~ 0.66 RIKEN (even though we have longer distance to Q1, longer quads, smaller aperture quads, and a longer pion injection than the RAL-RIKEN beamline. Also solenoid is shorter!) The pion injection & decay channel geometry & optic have remained unchanged since ~ CM8 in April 2004 :- under many different emittance and momentum designs. Sole changes have been scaling the fields of Q1-Q3, B1 & Decay Solenoid. May require small change for 10π,240MeV/c case 58.8 % Comparison with RAL-RIKEN pion injection & decay channel:-

10. paul drumm, mutac jan 2003 10 To provide beam for emittance generation & matching. Sufficient to deliver wide range of matched emittances into MICE. To include PID detectors & TOF0 – TOF1 Min Sepn 6.11m (deemed sufficient at CM9 for 6π / 200MeV/c case). Presence of upstream iron detector shield -> Q9 downstream mirror plate – Start / End Coil 1.1 distance no closer than 550.8mm. Not required to be achromatic but dispersion should be "small" ! (VC Jan 12 04!) Muon Transport, ε n generation & Matching: - Inputs/Constraints

11. paul drumm, mutac jan 2003 11 Flux:- Aimed at keeping B2 - Q4 distance as small as possible to capture maximum muon solid angle Aimed at keeping beamline length short to minimise beamsize growth due to PID detectors. Aimed at positioning PID detectors near beam foci to minimise emittance blowup. (both of the above competitive with keeping a minimum TOF0-TOF1 separation.) Purity:- Selection of backward going muons. Matching:- Scheme described in more detail in later slide, but:- Focus beam with a beamsize a function of desired emittance Triplet lattice, in order to facilitate:- ie. focus and same beamsize both planes at MICE Perform emittance generation immediately before MICE. Possible beam transport correction schemes. Muon Transport, ε n generation & Matching: - Solution

12. paul drumm, mutac jan 2003 12 Muon Transport - Solution example for 7.1π mm rad case given above

13. paul drumm, mutac jan 2003 13 ε n generation & matching into MICE - Solution The scheme. Place Pb Diffuser at MICE End Coil 1.1 -> (p/m o c)R.R'= ε n, rms R/R'=2p/qB= β match α=0= α match

14. paul drumm, mutac jan 2003 14 -> (p/m o c)R.R' ~ ε n, rms ~7.1π mm rad R/R'=2p/q ~ β match α ~ 0= α match Example achieves ~ matched 7.1π mm rad Example from 6π mm rad, 200MeV/c attempt ε n generation & matching into MICE - Solution Xrms ~ 3.55 cm, x’rms = 107 mrad, rxx'=0.04 yrms ~ 3.61 cm, y’rms = 102 mrad ryy'=0.13

15. paul drumm, mutac jan 2003 15 Current & projected status. Designs in TRANSPORT/TURTLE pp 11 66 10  240 Scale pion 200/1pi optic. New muon optic perfect focus beam at 1.3cm Just scale 200/6pi case Slight change to 200/10pi pion optic. Just scale 200/10pi muon optic 200 Scale pion 200/6pi optic. New muon optic perfect focus beam at 1.3cm ~ Done (7.1  Done 140 Scale pion 200/1pi optic. New muon optic perfect focus beam at 1.6cm Scale pion 200/6pi optic. New muon optic Scale 200/10pi optic. New muon optic (diffuser size though?) Red = dubious (without collimation) Green = projected to be possible