m.apollonio MICE Analysis meeting 23/1/2007 1

M. Apollonio – University of Oxford

Radius of diffuser and sizes for PID

m.apollonio MICE Analysis meeting 23/1/2007 2

Let’s 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 ~ <R2>

Propagate the radius throughout MICE according to

These curves represent the ENVELOPE of the beam whichjust touches the TK, the ABS, the RF and the diffuser == muons with a given amplitude ==

MAX size of diffuserMAX radii in the downstream region

00

XX RR

CAVEAT: field in the downstream region is approximate, neglectingthe presence of the shield!!!

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current diffuser position

ideal minimum RD

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Wang-200-42

Z-downstream: shield-in shield-out SW

TOF KL

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current diffuser position

inside TKs inside ABS inside RF

ideal minumum RD

Every in the TKs will traverse both ABS and RF

RD must be as large as possible10 cm is definitely too small !!!

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Wang 207-200-193 (with energy loss)

R grows linearly far fromthe solenoid (beta ~ z2)

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Wang-240-42

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Wang-240-42

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NF-200-42

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NF-200-42

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SFOFO-170-15

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SFOFO-170-15

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SFOFO-140-7

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SFOFO-140-7

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Summary of min R – DIFFUSER (cm)

optics min RD (TK) min RD (ABS) min RD (abs)wang 207-200-193-42 16.2 14.8 12.8wang 200-42 16.2 14.6 12.8wang 240-42 15.8 15.5 13.6NF (TRD) 200-42 16.2 14.4 11.9SFOFO 170-15 16.4 23.6 11.6SFOFO 140-7 16.3 34.9 12.8

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6399.5 6499.5 6574.5 6649.5 6729.5 7429.5 6524.5 6599.5 6689.5

250

250

100 100 50

50

40

40700

Definition of MIN Radius for PIDs and SHIELD holes!!! NOT IN SCALE (but figures should be correct)

TOF

KL SW

max radius

800

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optics R input hole R output hole R-TOF R-KL R-SWwang 207-200-193-42 246.5 295.5 272.1 324 587wang 200-42 246.5 296.6 272.1 323 587wang 240-42 223.2 262.5 243.3 284.5 507.3NF (TRD) 200-42 240.2 288 271 314.7 576.5SFOFO 170-15 243.3 291.2 268.9 317.9 576.5SFOFO 140-7 247.6 294.5 271 320 567

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 mm2

600x600 700x700 mm2

Slightly out ? tolerances

Is it a problem?

m.apollonio MICE Analysis meeting 23/1/2007 18

Wang-200-42

Z-downstream: shield-in shield-out SW

TOF KL

like having a 20 cmshorter SW calorimeter

But only for the outermuons

m.apollonio MICE Analysis meeting 23/1/2007 19

conclusions

the maximum radii for particles traversing MICE are propagated (from the max R in3 different places) through the apparatus (TKs, ABS, RF)

Considering several optics: min Radius (at fixed position z=-6150 mm) for the diffuser is defined: in order to have particles in the TKs it turn out Rd should be as large as possible

(compatible with mechanical contraints) In any case RD=10 cm is too small !

min radii for downstream shield holes are computed uponthe requirement of accepting every from trackersmin 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