Nov 9, 2002 Rajendran Raja, MIPP Collaboration Meeting 1

Designing the Time of Flight System

Rajendran Raja

Fermilab

MIPP Collaboration meeting

November 9, 2002

Nov 9, 2002 Rajendran Raja, MIPP Collaboration Meeting 2

Preamble

We consider a time of flight array of dimensions hdx,hdy,hdz = (230.0,120.0,2.5) cm, where hdx,hdy and hdz are the half lengths in x,y and z. The direction x is horizontal., y vertical and z is the beam direction. Each scintillator has hdx=2,5 cm. There are 92 counters in all in this array. The radiation length of scintillator in Geant is 42.2 cm and the interaction length is 88.7 cm. 5cm of scintillator in the beam direction is equivalent to 0.118 radiation lengths and 0.056 interaction lengths. The midpoint of the array is placed at –283.699 cm in z in the mother volume, the target being at –832.55cm and the center of the Jolly Green Giant being at –739.998 cm. The distance from the target to the center of the ToF system is 548.851 cm. The time taken by light to travel this distance is 18.307 ns. An accuracy of 150 ps in ToF measurement is thus a 0.819% measurement of the ToF.

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E r r o r a n a l y s i s T h e m o m e n t u m p o f t h e p a r t i c l e i s r e l a t e d t o i t s r e s t m a s s b y t h e f o r m u l a

. D i f f e r e n t i a t i n g t h i s l e a d s t o

2

0

0

p

p

m

m . S i n c e i s m e a s u r e d b y

m e a s u r i n g t h e t i m e t t a k e n t o t r a v e l t h e l e n g t h L , i . e .

ct

L , t h i s l e a d s t o

)(2

0

0

t

t

L

L

p

p

m

m

. T h e s e i n d i v i d u a l t e r m s

a d d i n q u a d r a t u r e t o g i v e t h e p e r c e n t a g e e r r o r i n m a s s

224

22

0

0

t

t

L

L

p

p

m

m

cmp 0

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MIPP Radiation lengths

C u m u lative R ad iation L ength vs d istan ce a lon g b eam

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Figure 2

Cumulative Interaction length vs distance along beam

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2 as a function of momentum for the three particle types

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E r r o r i n t h e m a s s a s a f u n c t i o n o f m o m e n t u m

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Mass hypothesis assignment contours. Red denotes pion, cyan denotes Kaon and yellow denotes proton. Horizontal lines are the nominal ,K p masses. Gaussian distributions in mass assumed

Nov 9, 2002 Rajendran Raja, MIPP Collaboration Meeting 9

Error in m0

2 as a function of momentum

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Mass hypothesis assignment contours. Red denotes pion, cyan denotes Kaon and yellow denotes proton. Horizontal lines are the nominal ,K p masses. Gaussian distributions in mass2 assumed

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Number of 's the equal likelihood contours are away from the mass hypotheses

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Figure shows the acceptance of the ToF system as a function of momentum

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M ass2 as a funct ion o f mo m entum w ith perfect tim e and length o f flight measurem ents. T hree bands are seen fo r the , K and p hypotheses. T he flatness o f these curves is an ind icat ion o f the co rrectness o f the G eant tracking a lgo rithm

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S a m e a s p re v io u s fig u re , bu t w ith T o F re so lu t io n o f 1 5 0 p s

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Efficiency curves for the three particle species as a function of momentum, ToF resolution=150ps

Purity Curves for the three particle species as function of momentum, ToF resolution=150ps

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Efficiency curves for the three particle species as a function of momentum, ToF

resolution=100ps

Purity Curves for the three particle species as function of momentum, ToF

resolution=100ps

Nov 9, 2002 Rajendran Raja, MIPP Collaboration Meeting 18

T h e v e r t e x o f o r i g i n o f a l l e + e - p a i r s . P r i m a r y v e r t e x i s a t – 8 3 2 . 5 c m . T h e u p s t r e a m e n d ( r e d ) a n d t h e d o w n s t r e a m e n d ( b l u e ) o f t h e C e r e n k o v , T o F a n d R I C H a r e

s h o w n .

T h e v e r t e x o f o r i g i n o f e + e - p a i r s w i t h e n e r g y > 0 . 3 G e V . P r i m a r y v e r t e x i s a t – 8 3 2 . 5 c m . T h e u p s t r e a m e n d ( r e d ) a n d t h e d o w n s t r e a m e n d ( b l u e ) o f t h e C e r e n k o v , T o F a n d R I C H a r e s h o w n .

Nov 9, 2002 Rajendran Raja, MIPP Collaboration Meeting 19

Optimizing the number of counters The counters in the center have a large number of background tracks. The (signal/signal_background) ratio for the center counters is ~0.02 where as the loss in acceptance of tracks less than 2.5 GeV by removing one counter in the middle is ~ 0.01, assuming a roughly flat distribution in Figure 27. If one were to remove the center 6counters, this would leave a 25cm gap which will cause a 6 loss in acceptance in the ToF. This would ameliorate the photon conversion problem significantly. In addition, the average charged multiplicity of tracks in counters with |x|>100cm is < 0.02, if one increases the width of the counters to 10cm for |x|>100cm, then the average multiplicity of tracks in these counters will be <0.04. The number of counters would go from 92 to 66 with this modification. If one were to remove the central 6counters, we can get by with 60counters in all. This would represent a reduction in total number of phototubes from 194 to 120 i.e a reduction of 38% in phototube costs.

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