m.apollonioCM17 -CERN- (22/2-25/2/2007)1 M. Apollonio – University of Oxford sizes for PID & shields

m.apollonioCM17 -CERN- (22/2-25/2/2007)2  Consider different optics for MICE  Consider the maximum radius a particle can reach in the tracker (TK) = 15 cm the absorber (ABS) = 15 cm the RF windows (RF) = 21.3 cm It can be shown that  ~  Propagate the radius throughout MICE according to  These curves represent the ENVELOPE of the beam which just touches the TK, the ABS, the RF and the diffuser == muons with a given amplitude == MIN size of diffuser MIN radii in the downstream region

m.apollonioCM17 -CERN- (22/2-25/2/2007)3 CAVEAT: Z_diff= m (corrected w.r.t. the original presentation given at a previous an.meeting)

m.apollonioCM17 -CERN- (22/2-25/2/2007)4 current diffuser position ideal minimum R D RD-TRK= 15.1 cm RD-ABS= 13.5 cm RD-RF= 11.9 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)5 Wang Z-downstream: shield-in shield-out SW TOF KL

m.apollonioCM17 -CERN- (22/2-25/2/2007)6 current diffuser position  inside TKs  inside ABS  inside RF ideal minumum R D Every  in the TKs will traverse both ABS and RF R D must be as large as possible 10 cm is definitely too small !!! RD-TRK= 15.2 cm RD-ABS= 13.8 cm RD-RF= 11.9 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)7 Wang (with energy loss) R grows linearly far from the solenoid (beta ~ z 2 )

m.apollonioCM17 -CERN- (22/2-25/2/2007)8 Wang RD-TRK= 15.1 cm RD-ABS= 14.8 cm RD-RF= 13.0 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)9 Wang

m.apollonioCM17 -CERN- (22/2-25/2/2007)10 NF RD-TRK= 15.2 cm RD-ABS= 13.5 cm RD-RF= 10.5 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)11 NF

m.apollonioCM17 -CERN- (22/2-25/2/2007)12 SFOFO RD-TRK= 15.3 cm RD-ABS= 22.1 cm RD-RF= 10.8 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)13 SFOFO

m.apollonioCM17 -CERN- (22/2-25/2/2007)14 SFOFO RD-TRK= 14.6 RD-ABS= 30.9 RD-RF= 11.5

m.apollonioCM17 -CERN- (22/2-25/2/2007)15 SFOFO-140-7

m.apollonioCM17 -CERN- (22/2-25/2/2007)16 Summary of min R – DIFFUSER (cm)

m.apollonioCM17 -CERN- (22/2-25/2/2007) Definition of MIN Radius for PIDs and SHIELD holes !!! NOT IN SCALE (but figures should be correct) TOF KL SW 750 solenoid end plate  max radius 650

m.apollonioCM17 -CERN- (22/2-25/2/2007)18 According to the defs given in previous slides these are the min radii (a) for the shield (to let every  pass) and (b) for the PIDs (to accept every  ) Within tolerances 1000x1000 mm 2 600x x700 mm 2 Slightly out ? tolerances Is it a problem? iron shield

m.apollonioCM17 -CERN- (22/2-25/2/2007)19 Wang Z-downstream: shield-in shield-out SW TOF KL like having a 20 cm shorter SW calorimeter But only for the outer muons

m.apollonioCM17 -CERN- (22/2-25/2/2007)20 conclusions the maximum radii for particles traversing MICE are propagated (from the max R in 3 different places) through the apparatus (TKs, ABS, RF) Considering several optics: min Radius (at fixed position z=-6010 mm) for the diffuser is defined: in order to have particles in the TKs it turns out Rd should be as large as possible (compatible with mechanical contraints) In any case R D =10 cm seems to be small ! min radii for downstream shield holes are computed upon the requirement of accepting every  from trackers min radii for PIDs are computed upon the requirement of having the maximal acceptance within the detector: this condition can be probably relaxed Real B field in the “shield area” should take into account real map. This is just an approximation whose purpose is giving some initial figures

m.apollonioCM17 -CERN- (22/2-25/2/2007)21 radial size for the diffuser M. Apollonio – University of Oxford

m.apollonioCM17 -CERN- (22/2-25/2/2007)22 Z=-6010 mm for the upstream face of the diffuser. This is a figure established long time ago (CR, CM14 Osaka )  I focussed on the radial size of it propagate muons back from centre tracker to the diffuser record x,y position and check whether they fall within the diffuser generate beams upstream with proper ALPHA/BETA and go through the diffuser compute emittances  check bias due to r_cut would like to convince you that R=10 cm is a bit tight and propose some solution

m.apollonioCM17 -CERN- (22/2-25/2/2007)23 ICOOL sim, Pz=200 MeV/c diffuser Z= m

m.apollonioCM17 -CERN- (22/2-25/2/2007)24 r=10 cm r=15 cm

m.apollonioCM17 -CERN- (22/2-25/2/2007)25  n (mm rad) R 0 (0.1%) (cm) R 0 (0.5%) (cm) R 0 (1%) (cm) Beam fraction within radius R0

m.apollonioCM17 -CERN- (22/2-25/2/2007)26 try to see it another way … generate (gaussian) beams BEFORE DIFFuser: 1- thickness of 7 mm inflation: 2.7  6.5 mm rad (BETA=76 cm / ALPHA=.20 ) 2- thickness of 12.7 mm inflation: 2.7  10 mm rad (BETA=127cm / ALPHA=.37 ) 3- thickness of 8 mm inflation: 1.9  10 mm rad (BETA=189 cm / ALPHA=1.14 ) 4- thickness of 14.2 mm inflation: 3.4  10 mm rad (BETA=128 / ALPHA=.4) calculate emi before/after diffuser for several radii (compare with a large radius case) Pz=209 MeV/c +/- 10% Pz=148 MeV/c +/- 10% Pz=267 MeV/c +/- 10%

m.apollonioCM17 -CERN- (22/2-25/2/2007)27 ICOOL sim diffuser Z=-6.010

m.apollonioCM17 -CERN- (22/2-25/2/2007)28 A tentative scheme for the diffuser trying to exploit all the radial space (15 cm) within the tin can envelope being compatible with mechanical contraints

m.apollonioCM17 -CERN- (22/2-25/2/2007)29 7mm 15.5cm Emi inflation in single layer lead diffuser: 2.8  6.1 mm rad 7mm emi(after diff)=6 mm rad Muons selected on the overall channel ideal disc

m.apollonioCM17 -CERN- (22/2-25/2/2007)30 7mm 5cm 15.5cm Emi inflation in a staggered lead diffuser: 2.8  6.1 mm rad 7mm realistic diffuser fixed annulus movable disc + support

m.apollonioCM17 -CERN- (22/2-25/2/2007)31 7mm 5cm 15.5cm Emi inflation with a single layer of lead (small radius): 2.8  5.3 mm rad 7mm

m.apollonioCM17 -CERN- (22/2-25/2/2007) mm 8 mm 7 to 14.2 mm Proposal to accommodate many configurations 6, 10 mm Pz=200 MeV/c 10 mm Pz=140 MeV/c 10 mm Pz=240 MeV/c …just a sketch (see Stephanie/Wing drawings) 24 to 27 cm 30 cm trackerdiffuser envelope Supports (outer can/disc support): Al Pb diffuser disc and outer annulus

m.apollonioCM17 -CERN- (22/2-25/2/2007)33

m.apollonioCM17 -CERN- (22/2-25/2/2007)34 emi(R)/emi(R=30 cm) R_diffEmittance bias as a function of R_diff (partial inflation) Pz=209 MeV/c, emi=10mm rad, B=4 T Pz=148 MeV/c, emi=10mm rad, B=2.9 T Pz=267 MeV/c, emi=10mm rad, B=4 T single disc staggered discs

m.apollonioCM17 -CERN- (22/2-25/2/2007)35 SUMMARY a diffuser with R=10 cm is too small. We should try to use all the space available the choice of R_diff can be inspired by the emi_bias plot, in which case you can choose between 12 and 13.5 cm the “staggered” solution provide uniform inflation (till R~15 cm) and is equivalent to the ideal full disc case. Important for high emittances and low momenta