Shower shape analysis and longitudinal sampled electromagnetic calorimeters

486

Nuclear Instruments and Methods in Physics Research A237 (1985) 486-492 North-Holland, Amsterdam

SHOWER SHAPE ANALYSIS AND LONGITUDINAL ELECTROMAGNETIC CALORIMETERS H. G R A S S M A N N

SAMPLED

and H.G. MOSER*

CERN, Geneva, Switzerland

Received 8 November 1984

Possibilities to improve high energy electromagnetic calorimetry by means of suitable calorimeter segmentation are discussed. Some resulting improvements are examined concerning spatial resolution, photon-~r ° separation, electron-hadron separation and energy resolution as far as dominated by rear leakage. One way to realize such a calorimeter is discussed by a specific example.

1. Introduction Most calorimeters have segmentation transversal to the direction of the incident particles to provide spatial information. Some calorimeters also have longitudinal segmentation to improve electron-hadron separation. But with this exception the information from longitudinal shower development is commonly not used. This partially seems to be due to technical limitations which might be ovecome by new ideas. To show this we first mention an example how a high quality electromagnetic calorimeter could be constructed using recent developments in calorimetry. Then we discuss more in general some improvements which could arise from the use of longitudinally sampled calorimeters.

optically coupled crystal sections K1 and K2. One way to realize such a calorimeter should be the use of Csl scintillation crystals and photodiode readout. After the rediscovery of this material for calorimetry in 1983 the interesting properties of especially T1 doped CsI crystals have been shown for both energies in the MeV and GeV range. 2.1. How to prepare the active material

Using pure CsI crystals or crystals with dopants such as T1 or Na, one can achieve decay times between 0.5 and 3.0 /~s and different luminescence spectra (fig. 1)

[11. Several procedures to produce slabs consisting of two sections K1 and K2, which are optically coupled and

2. Suggestions for the construction of a fully active calorimeter with longitudinal segmentation. For example, one can imagine a fully active calorimeter with tower structure, whereby the active material consists of two longitudinal sections K1 and K2. The easiest way to get information from K1 and K2 is to separate K1 and K2 optically and to mount separate readout channels, preferably inside and outside the calorimeter. But this may be unsatisfactory because of problems concerning mechanical support, dead material, access, cooling if required and a lack of compactness. An alternative would be the use of crystals with different scintillation properties as decay times or emission spectra. Then information exists about the energy deposited in K1 and K2, respectively. There are several technical means to record this information explicitly. In the following, comments are made on a calorimeter with *RWTH, Aachen, Germany 0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

]

I

I

I

I

I

I

l

500

550

600

650

700

>,

C C

350

400

~+50

nm

Wavelength Fig. 1. Luminescence spectra of CsI with different dopants: (a) CsI(pure)~ (b) Csl(Na), (c) CsI(TI).

487

H. Grassmann, H.G. Moser / Calorimetry read out only at one side seem possible: 1) G!ueing together K1 a n d K2: We have very successfully operated with crystals which were coupled by optical grease without any p r o b l e m s [3]. 2) G r o w i n g a crystal from a melt of pure CsI and adding a d o p a n t material to the melt after the crystal has achieved a certain length. Over a wide range the luminescence intensity is nearly i n d e p e n d e n t of the T1 concentration and this may help to get a reasonably sharp b o u n d a r y between K1 and K2. But one has to examine this p r o b l e m in more detail [4]. 3) Forging together KI and K2 u n d e r high pressure [4].

2.2. Readout system and signal to noise ratio At all energies, the energy resolution is affected by calibration a n d intercalibration. At low energies the electronic noise becomes important, at high energies it has to be checked whether the uncertainty of the larger signal will d o m i n a t e the uncertainty of the small signal. If K1 emits a signal A~ a n d K2 a signal A 2 one can define two readout channels which produce signals S 1 a n d S 2 respectively by means of filters which only let pass a certain fraction of A 1 a n d A 2 in the following way: S 1 = all A1 + a12 A2, S2 =

a21 A 1 + a22 A2,

(1)

with aiy < I. With the help of some electronic circuit or software analysis one can get back A 1 and A 2 from S 1 and S 2. If S 1 a n d S 2 have some uncertainty A S 1, A S 2 this results in

aA

= [a./(a,,a.-

a.aj,)] 2 aS, 2

+ [ a,#( a,, a. - a.a;, )]2 aSj,2 In the following, some examples will show how such a filtering could be realized a n d how this will affect the signal to noise ratio.

2.3. Optical filters As shown in fig. 1 the luminescence spectra of CsI crystals with different d o p a n t s are quite different. A readout system as shown in fig. 2 would allow a system to be realized as postulated in the above section. A n optical filter at each p h o t o d i o d e limits its sensitivity to a certain range of wavelengths. As an example the light yield of a 2 x 2 × 30 cm 2 CsI crystal with one p h o t o d i o d e of 1 cm 2 sensitive area is estimated. CsI(TI) should emit a b o u t 5000 e - / M e V (A2), CsI(Na) a b o u t 1500 e - / M e V (A1) [2,3]. To get optimized signal to noise ratios one has to optimize the factors a,j. This would need a careful analysis of the luminescence spectra. Just to show a crude estimation,

FILTER l ~ KI

~(2

$2 AMPL.

CHARGE SENS. PREAMPL. Fig. 2. Possible readout for a crystal slab consisting of two optically coupled sections K1 and K2. KI and K2 have different luminescence spectra. Each filter suppresses either signals from K1 or K2 respectively. the aij may be chosen as all = 0 . 8 , a 1 2 = 0.2, a21 = 0.2, a n d a22 = 0.8. The electronic noise of a high quality preamplifier with one p h o t o d i o d e of a b o u t 75 n F capacitance at 3/zs shaping time is a b o u t 400 e [2]. This results in: AA~2 = AA~ = (0.33 AS1) 2 + (1.33 AS2) 2, a n d with A S = 4 0 0 e :AA=530e . F o r K1 this is equivalent to a noise of 110 keV, for K2 to 370 keV. For K2 this would be at the limit where calibration with radioactive sources in pulse mode is still possible at present. After a precise enough evaluation of the luminescence spectra it might turn out that the above m e n t i o n e d values for the different aij c a n not be realized. The resulting signal to noise ratio could be higher then. In spite of this, calibration with radioactive sources would remain possible if one of the channels S is switched off during calibration of the other. This procedure would also be necessary if the aij are not k n o w n to a high enough precision. M a n y electromagnetic showers will deposit very m u c h more energy in the front section K1 than in the rear section K2. Eq. (2) shows whether p h o t o n statistics of signal S 1 will cause a significant uncertainty in $2: T h e above m e n t i o n e d light yields and a t t e n u a t i o n factors will cause an uncertainty in $1 a n d S 2 of: A S 2 = 0.8 × 1500 E1 + 0.2 × 5000 E2, A S 2 = 0.2 X 1500 E 1 + 0.8 × 5000 E z. A S is the n u m b e r of electrons, E is in MeV. F r o m eq. (2) follows: ( A A 2 / A 2 ) 2 = 8.5 X I O - S E 1 / E 2 + 9 × 1 0 - 5 / E 2 . So even an energy deposit in K1 of 10 GeV and in K2 of 100 MeV will cause an uncertainty of a b o u t 1 MeV for A 2 only.

2.4. Electronic frequency filter The readout system is shown in fig. 3. Only one p h o t o d i o d e and one preamplifier are needed per crystal

488

H. Grassmann, H.G. Moser / Calorimetry

I

I<1

a I

K2

1

CHARGESENsJ_.J' . ~ ,,,,~S~PREAMPL. SHAP.AMPL.

A photodiode surface with increased refractive index would result in a higher signal, a decreased capacitance in a lower noise. Another interesting development are photodiodes which are sensitive to shorter wavelengths than is the case now. This could increase the light yield especially of CsI(Na) and CsI(pure).

Fig. 3. Possiblereadoutof two opticallycoupledcrystalswhich makes use of the different decay times of KI and K2. The shaping amplifiers work at different shaping times.

slab. The two shaping amplifiers work at different shaping times. The signals coming from K1 and K2 have different decay times. So each shaping amplifier will integrate a fraction of the signals from K1 and K2 respectively according to its shaping time and the decay time of the signal. Again eqs. (1) and (2) can be used, where aij is the fraction of the signal Aj with decay time "9 which is integrated by the shaping amplifier i with shaping time t i. With the approximation, that a shaping amplifier at shaping time t, will integrate a signal of decay time "9 over a time interval 2t,, a,j will be a,j= [1-

exp(-Zti/"9)]

(approximation).

In principle it would be of advantage to use one rather long and one rather short shaping time. But unfortunately the electronic noise increases with decreasing shaping time. Also a shaping time t with t << r would integrate only a small fraction of the signal. Again an estimation: If CsI(T1) is used (5000 e - / M e V , r = % = 0.9 ~s) and CsI(Na) (1500 e - / M e V , r = r 1 = 0.5 /ts) for the two sections, one would get at t 1 = 0.5 /xS and t 2 = 3 /~s: aA12 = 2 7 a S 2 + 12 a S 2. At 0.5/~s shaping time one has to expect about 1200 e - noise, at 3 >s about 400 e - . So k A 1 = 6400 e - and k A 2 = 5700 e-. In the CsI(T1) section this corresponds to a noise of 1.1 MeV, at the CsI(Na) section to 4.3 MeV. If one has to read out 9 slabs together this results in a noise of 3.3 Mev and 13 MeV, respectively. The energy uncertainty due to photon statistics also would increase compared to separated readout of K1 and K2. These values are only estimations but give a feeling of the expected behavior of such a device. Another possibility for the readout system would be the use of flash-ADCs. The signal/noise ratio would depend on the specific readout procedure and therefore is not discussed here. But a significant improvement of the signal/noise ratio is not expected.

3. Monte Carlo calculations

It is known that one can gain information from the energy dependent shape of a high energetic electromagnetic shower. Of course each individual shower will show statistical deviations from the average shower profile. However, correlations between different parts of the shower exist; for example a shower which starts late in the calorimeter material can be expected to give large rear leakage out of the calorimeter. This section is largely independent of the previous one; the following conclusions being true for all kinds of calorimeters as long as their intrinsic energy resolution is good enough. Therefore we have done all MC calculations with iron as calorimeter material. The program EGS4 has been used, which was available at C E R N for some weeks. As cutoff energy for electrons 5 MeV was chosen and for gammas 1 MeV. In order to check whether our results were dependent on this choice a small sample of 20 GeV electrons with cutoff energies of 1 MeV and 0.5 MeV for electrons and photons, respectively, was generated. These cutoff energies were also used for creating 1 GeV showers.

3.1. Two particle separation and space resolution By measuring the energy deposit within the first few radiation lengths of a calorimeter it might be possible to improve spatial information in some cases. More important would be an increased capability to separate two electromagnetic showers or a shower and a minim u m ionising particle. If only the total longitudinal projection of the deposited energy is observed, two showers have to have about a distance of one Moli6re radius to be separated. This distance will be smaller if information about the energy deposit within the first few radiation lengths exists. F r o m calculations which have been done for another purpose it is known that within the first 2.2 radiation lengths (X0) about 90% of the deposited energy are absorped within an area of 0.5X 0 x 0.5X 0 around the shower axis. In total only 40% of the energy is deposited within this area. This has been proved for energies between 1 GeV and 20 GeV [51.

2.5. Possible improvements

3.2. ~r°/ gamma separation

Photodiode readout of scintilation crystals is a rather new method and many improvements are still possible.

The two gammas from the decay of a high energetic rr ° cannot be separated if the ~r° energy exceeds a

489

H. Grassmann, H.G. Moser / Calorimetry 3.3. Energy resolution 80 a 60 50

40 3O 2O

10 0

0

100

200

300

400

500

600

ENERGY IN MEV

24

b

2o §,6 12

8 4

o

o

I oo

200

300

•

400

500

600

ENERGY IN MEV

Fig. 4. (a) Energy deposit of 20 GeV "y's within the first 2 X0 of a calorimeter. (b) Energy deposit of 20 GeV ~-°'s within the first 2 X0 of a calorimeter.

In the following it is assumed that energy resolution is dominated by fluctuations in rear leakage. A correlation exists between the total deposited energy and the energy deposit within a certain section of such a calorimeter. This is shown in fig. 5, where the horizontal axis shows the energy deposit (E(tot)) of 20 GeV electrons in a calorimeter of 16X 0 lenght. The vertical axis shows the corresponding energy deposit within the last 3X 0 (E(rear)). From this follows a correlation between the rear leakage out of the calorimeter and the energies E(rear) and E(tot). The information about E(rear) does not exists in conventional calorimeters or it is not used for this purpose. In those calorimeters only the projection parallel to the axis E(rear) of fig. 5 is visible. An evaluation of plots such as fig. 5 would enable one to correct partially for rear leakage fluctuations. From such a plot it also can be estimated how the correction would be influenced by some intrinsic energy resolution in the measurement of E(rear) and E(tot). If the energy has to be measured within a wide range, as it is the case in all experiments, energy dependent correction algorithms have to be used. A first order approximation to such an algorithm is a rotation in the (E(rear), E(tot)) plane around the point (0,0). This will be used in the following. Because the dependence between E(rear) and E(tot) is nonlinear this is only a crude correction which shall demonstrate

10

P,, 8

certain limit which is dependent on the experimental setup. But the shape of an electromagnetic shower of energy E is different from two overlapping showers of each energy E / 2 . This effect could be used to achieve some efficency in ~ 0 / . / separation. This principle works at very high energies, too. Because of the large fluctuations in the shower development this efficiency cannot be expected to be high. To examine this effect we have compared the overlying showers from two 10 GeV y ' s with the shower from a single 20 GeV y. Significant differences were only found between the energy deposits within the first few and the very last few (say 16X 0 to 20X0) radiation lenghts. In the mean part of the calorimeter the differences in energy deposit are very small compared to the corresponding fluctuations. Figs. 4a and 4b shows the energy deposit of 20 GeV y ' s and ~'°'s within the first two radiation lengths. For example, an energy cut at 60 MeV would leave 12% of the ~r°'s but 35% of the 7's.

6 - : \ .

4

- .:.. .-~: . ~ . ~ . • 'd~

.:. ~.2"~

2 0

I

5

16

17

I

I

18

19

2.r)

E(TOT)/C,EV Fig. 5. Energy deposit of an electromagnetic shower within a longitudinally sampled calorimeter. E(tot) = all energy which is absorbed in the calorimeter in total. E(rear)= energy deposit within the last few radiation lenghts of the calorimeter. The total calorimeter length chosen here is 16X0 and the rear part has a depth of 3X0 (from 13X0 to 16X0).

490

H. Grassmann, H.G. Moser / Calorimeto' 70

.10 18

6O

-

3

,•

14

z S0

12 4O

I0

o u

30

8

2O

6

10

4 ~

016

165 E

17. N

E

,4.

17.5 R G

~

Y

o

2

I

18.

•

18.5 t N

19

19.5 G E

20 V

0

I

I

l

I

I

I

I

0.

01

0 2

0.3

0.4

05

06

ROT ANGLE IN RAD. '-

,oo

Fig. 7. Energy uncertainty o of the corrected energy spectrum in dependence on the rotation angle of the described correction algorithm.

b

2: 80

O

60

40

2O I

016

165 E N

-I

17 E

-

i--

R

17.5 G

nh 18. Y

18.5 I N

19

19.5 G E

20 V

Fig. 6. (a) Energy spectrum of 20 GeV electrons in a calorimeter of 16X 0 length. The spectrum is fitted by an asymmetric Gaussian function with widths o ÷ and a . (b) Energy spectrum of fig. 6(a), corrected for rear leakage in first order. Calorimeter depth in total = 16X o, depth of the rear part = 3X 0.

t h e o p e r a t i o n principle. It will n o t result in o p t i m i z e d values. In figs. 6a a n d 6b a c o r r e c t e d a n d a n u n c o r r e c t e d e n e r g y s p e c t r u m is s h o w n for 20 G e V e l e c t r o n s in a

c a l o r i m e t e r o f 1 6 X 0 l e n g t h in total w h e r e b y t h e last 3 X 0 h a v e b e e n u s e d for t h e correction. F o r t h e s a m e c o n f i g uration the achieved energy resolution a (a=(a++ a ) / 2 , see fig. 6a) in d e p e n d e n c e o f t h e r o t a t i o n a n g l e is s h o w n in fig. 7*. T h e d e p e n d e n c e o f t h e e n e r g y r e s o l u t i o n o n the l e n g h t o f t h e rear c a l o r i m e t e r s e c t i o n is s h o w n in fig. 8a. Figs. 9a a n d 9b s h o w c o r r e c t e d a n d u n c o r r e c t e d s p e c t r a o f 20 G e V a n d 19.6 G e V e l e c t r o n s u n d e r t h e s a m e c o n d i t i o n s as in fig. 6. T a b l e ] gives a n o v e r v i e w for the a c h i e v e d c o r r e c t i o n s at d i f f e r e n t e n e r g i e s a n d c a l o r i m e ter lenghts. As mentioned above, these values are not optimized a n d give o n l y a n u p p e r limit. T h e table s h o w s t h a t t h e * We use in the following a = A E / E with J E = fwhm/2.35, so all values for a are in percent.

Table 1 Energy resolution a with and without correction ~. The errors for all values are about 10%. 1 Ge V electrons, in brackets the L,alues for 1 Ge Vphotons Calorimeter length: 10X 0 12X 0 a uncorrected (%) 3.3 (4.4) 1.6 (2.2) a corrected (%) 3.1 (3.8) 1.6 (1.8) 20 Ge V electrons, in brackets the values for 20 Ge V photons Calorimeter length: 12 X 0 14 X o o uncorrected (%) 4.8 (6.8) 2.5 (3.3) o corrected (%) 2.7 (3.0) 1.3 (1.6) 50 Ge V electrons Calorimeter length: a uncorrected (%) a corrected (%)

14X 0 3.6 1.5

16X o 2.1 0.9

15 Xo

1.8 (2.2) 1.0 (1.1)

16Xo 1.3 (1.6) 0.7 (0.9)

18X 0 0.7 0.4

18X 0 1.1 0.5

") For each correction procedure in this table optimized values were used for the rotation angle. The rear calorimeter section was either 2 X o or 3X 0 long.

491

H. Grassmann, H.G. Moser / Calorimetry

The behavior of each two particles in an em shower is statistically independent. The more particles are contained in a shower, the less will be the relative deviation of the shower d e v e l o p m e n t from an ideal mean. The principle discribed here can be used both to optimize rather long high energy calorimeters and to get a reasonable energy resolution from extremely short calorimeters.

1.4 1.2 1. 0.8 0.6 0.4 02 0.

I

I

0

1 2 3 4 5 xo LENGHT OF Rrde SEC~ON

I

I

I

Fig. 8. Energy resolution o after correction vs the length of the rear section of the calorimeter for 20 GeV electrons. The calorimeter length is 16X 0 in total.

3.4. Electron-hadron separation e / h separation could be improved with the information about longitudinal shower development compared to a calorimeter without sampling. But similar correlations between the different parts of a hadronic shower are to be expected as is the case for an electromagnetic shower. Those correlations, which are useful for em

correction is poor at energies in the range of 1 GeV and becomes better with increasing energy'. This might be understood by a phenomenological argument: o3 1 O0 I.z

8O

0 6O

~J

40

--

20

-n

0

~ 16.

~-- 120

0

~

n ,--J-Ln

17. E

N

17.5 E

LL]

R

18. G

18.5 Y

I

19. N

19.5 G

2P E

V

b

z 1

I~ 16.5

O0

80

0

6o

[

,o

[

I 1

n r-'0 16.

~1 16.5

~ I.-. 17. E

~m N

L' ---1 r " ~ u 17.5 18. E

R

G

I 18.5 Y

I

I 19.

hll 19.5

N

G

2D E

V

Fig. 9. Energy of spectrum of 20 OeV and 19.6 GeV electrons: (a) uncorrected, (b) corrected. The conditions are the same as in fig. 6.

492

H. Grassmann, H.G. Moser / Calorimetry,

calorimeters, cause a handicap for e / h separation: Some of the hadrons which are absorbed in the em calorimeter faking e - in this way will lose a large amount of energy also in the front part of this device. Because of this, the values for e / h separation from the total calorimeter and the front section separately cannot be multiplied to get the e / h separation value which can be expected from a combined analysis. The achievable e / h separation has therefore to be measured in an experiment or estimated by hadron MC calculations.

4. Further comments

We did not examine whether a sampling in more than two sections would result in further improvements. Neither did we examine the behavior of hadronic showers. Hadronic showers are subject to greater fluctuations than em ones. Also hadronic calorimeters have commonly not more than 5 to 6 interaction lengths. In spite of this it should be investigated whether a correction for leakage losses is possible for hadron calorimeters.

5. Conclusions

The readout of the first radiation lengths of an elctromagnetic calorimeter would improve spatial infor-

mation and allow the electromagnetic calorimeter to be built closer to the interaction point. The readout of the last radiation lengths would allow a relatively thin calorimeter to be built. Even if only one of these possibilities is realized this could result in an em calorimeter with smaller diameter. We want to thank E. Lorenz and H. Wegener who enabled us to start these investigations. K. Eggert and H. Faissner have helped us with interesting discussions. C. Cochet showed us where to get EGS programs from. Also J. Dorenbosch and T. Wyatt were involved in writing this paper.

References

[1] H. Grassmann, H-G. Moser and E. Lorenz, Forschungsbericht Univ. Erlangen, Phys. Inst. II (1984), to be published in Nucl. Instr. and Meth. [2] H. Grassmann et al., Max-Plack-lnst. Munich, MPIPAE/Exp. E1 131. [3] H. Grassmann, E. Lorenz, H-G. Moser and H. Vogel, Max-Planck-Inst. Munich, MP1-PAE/Exp. El. 136, to be published in Nucl. Instr. and Meth. [4] B. Sparrow, BDH Chemicals, private communication. [5] H. Vogel, private communication.