Iron liquid-argon and uranium liquid-argon calorimeters for hadron energy measurement

NUCLEAR

INSTRUMENTS

AND

METHODS

141

(1977)

61-8o; ~q) N O R T H - H O L L A N D

PUBLISHING

CO.

I R O N L I Q U I D - A R G O N AND U R A N I U M L I Q U I D - A R G O N C A L O R I M E T E R S

FOR H A D R O N ENERGY M E A S U R E M E N T C.W.

F A B J A N , W. S T R U C Z I N S K I , W . J . W I L L I S

CERN, Geneva, Su,itzerktnd C. K O U R K O U M E L I S * ,

A.J. LANKFORD*

and P. R E H A K t

Yale University, New Haven, Connecticut, U.S.A. Received 4 October 1976 We studied with a specially designed h a d r o n calorimeter the contributions o f different m e c h a n i s m s affecting the energy resolution o f such instruments. It is s h o w n that in ordinary materials the resolution is d o m i n a t e d by " n u c l e a r fluctuations". Meas u r e m e n t s with a u r a n i u m calorimeter show that these fluctuations can be effectively c o m p e n s a t e d by the amplifying effect o f nuclear fission in u r a n i u m . T h e resolution at low energies is good (a = 9.6% for 10 GeV/c pions) a n d i m p r o v i n g with energy.

1. Introduction The use of a calorimeter to measure hadron energy is very attractive for many applications in highenergy physics experiments. By a calorimeter we mean a device which contains enough matter to absorb essentially all the energy of the hadron, and in which the absorbed energy is converted in some way into an electrical signal1). In principle, if all the steps in this sequence are linear, the signal will be proportional to the energy of the hadron. Such a device has the merit of measuring the energy of all hadrons, neutral as well as charged, as well as protons and electrons. The measurement is performed instantaneously, or at least on an electronic time-scale. Thus it is available for use in triggering other devices. If there are several hadrons in a nearby cluster, there is the possibility of measuring the total energy of the whole cluster. As the energy of the incident hadron is increased, the size of the calorimeter must increase to contain the hadron cascade, but only logarithmically, in contrast to detectors depending on deflection in magnetic fields. Finally, it is easy to cover very large solid angles with an array of calorimeters, which may be difficult to do with other techniques of energy measurement. Two factors have inhibited the use of these devices for hadron energy measurement. One is the fact that a hadron calorimeter of sufficient size represents a large mass of material. The other is that the calorimeters which have been built have given an energy resolution somewhat worse than that required for many * Partially s u p p o r t e d by the U S - A E C . t Present address: B r o o k h a v e n National Laboratory, Upton, LI, New York, U.S.A.

experiments. At first this could be, and often was, ascribed to the fact that the calorimeters were not large enough, and to the fact that instead of measuring all of the energy released in the block of absorber, they sampled the energy release between thick slabs of material, for example several centimeters of iron. A number of other effects have been suggested which might also limit the resolution, as will be mentioned below. The real nature of the ultimate limitations on energy resolution could not be made clear because a series of measurements which clearly identified the relative magnitudes of the different fluctuation processes in hadron cascades had been lacking. In this paper we wish first to describe the series of measurements which accomplished this goal, then to consider how the most serious limitations on energy resolution might be circumvented, and finally to describe measurements made with a device designed to eliminate the most serious fluctuations. Indeed we find substantially improved energy resolution. In these measurements we detect the ionization due to the energy loss of the particles in the hadron cascade by means of the liquid-argon ion chamber technique. The first liquid-argon ion chamber calorimeter was constructed by two of the present authors, but the size of that device was only sufficient to contain electromagnetic showers, induced by electrons or photons2). The detector described in this paper is of ample size for the detection of hadron showers as well. The liquid-argon ion chamber technique has a number of advantages for a study of this sort. In order to study the spatial distribution of the shower energy, event by event, our calorimeter is divided into about 80 different sections. The liquid-argon ion chamber

62

c . w . VABJAN et al.

technique allows an absolute and stable intercalibration of the many independent sections necessary for this purpose. An important possible fluctuation which may limit the energy resolution is that due to the sampling of the shower particles, and our technique allows us to measure that. directly. It also makes convenient the use of very fine sampling, i.e. very thin plates of absorber, and it guarantees a uniform response over the area of a detecting section. It makes possible a convenient choice of materials for the absorbing plates. Finally, this technique allows us to obtain outputs from an active volume buried in a three-dimensional array of such sections without introducing an appreciable dead volume in the d e t e c t o r - a difficult problem with detectors using scintillation light, for example. iron is the substance most commonly used in calorimeters and most of our measurements are made with thin steel plates. After studying the spatial distribution of the shower, we isolate the contribution of the fluctuation in our response due to each of a number of mechanisms. We find that the dominant one is due to the effects associated with the disruption of the iron nuclei by the hadron cascade. This then limits the ultimate resolution obtainable in this device. Experimental insight into this effect is gained by comparing the charge released by electrons and hadrons of the same energy. From a practical point of view the performance limitation due to nuclear fluctuations provides inadequate resolution for many high-energy physics applications, while our measurements show that the other fluctuations can be reduced to substantially smaller levels. Thus we were led to consider methods of attacking the problem of nuclear fluctuations. While the effect is intrinsic to the hadron cascade, there are a number of methods of compensation which might be considered. Data gathered on correlations in individual events show that it is possible to develop ways of compensating the data for the nuclear fluctuation, thereby improving the energy resolution and confirming our understanding of the source of this fluctuation. However, fluctuations in the correlations in individual events limit the accuracy of this compensation and the improvement in resolution which can be obtained. We sought a more effective method of compensation, which led us to make measurements of hadron cascades in 23SU plates3). We estimated that the additional signal generated in the aftermath of fission should compensate the nuclear fluctuation almost ideally, on an event-by-event basis. Also, uranium is an interesting substance for use in calorimeters because of the

TABt.E I Average fractional energy deposition by particle type for l0 GeV proton interactions in an iron-argon calorimeter". Type of energy deposition

Percent of total

Primary proton ionization Secondary proton ionization Secondary n -+ ionization i t + ionization Electromagnetic cascade Z - I ionization Residual nuclear exitation energy Neutrons with energy > 10 MeV transported to a radius ~ 2 interaction lengths Neutrons with energy -: 10 MeV Nuclear binding energy plus neutrino energy

2.3 31.6 8.2 0.05 21.0 2.4 3.7 4.9 3.9 20.6

~' T. A. Gabriel and W. Schmidt, ORNL/TM-5105 (1975).

very compact detectors which can thereby be made. Our estimates were confirmed by these measurements, both in that the energy is compensated in the mean, as seen by comparing electrons and hadrons, and in that the resolution is very considerably improved. 2. Factors which limit the resolution in hadron calorimeters

It may be useful to summarize briefly the processes which occur in a hadronic cascade. The hadron interacts with a nucleus after approximately one interaction length, generating typically several charged pions and several neutral pions, depending upon the incident energy, as well as a number of relativistic protons and a number of nuclear fragments. These last will be neutrons of energies of a few MeV and charged particles of very short range, including slow protons, deuterons, s-particles, and heavier fragments. The photons from neutral pions rapidly lead to electromagnetic showers which deposit all their energy by ionization of relativistic electrons. The charged pions and relativistic protons go about another nuclear interaction length and make further nuclear interactions which lead to the same kinds of particles in the final state. The nuclear fragments rarely interact again, but deposit their energy near the first interaction in the form of high ionization density tracks. The neutrons deposit their kinetic energy by elastic and inelastic collisions, and upon being captured by nuclei yield their binding energy of a few MeV in the form of photons, although this may happen at distances of many interaction lengths from the original

CALORIMETERS

FOR HADRON

source. Certain forms of energy are not visible in the absorber as ionization. These are: energy lost by neutrinos, mostly from pions at rest; high-energy muons from decays which have very long range; and that energy which is required to break up the nuclei, or nuclear binding energy. Most ionization detectors are also less than completely sensitive to particles of high ionization density, so that some of this ionization is effectively lost. In some absorbers it may be very difficult to retain all the energy of the neutrons. For example, in iron the interaction cross-section for neutrons of a few MeV energy is very small. Very careful Monte Carlo calculations of hadronic cascades have been made by an Oak Ridge Group¢). It is interesting to look at their results on the form in which ionization is eventually deposited, as shown in table I. It can be seen that the most important forms in which energy is deposited are due to the electromagnetic cascades from g°'s, as well as that due to slow particles. The fast pions deposit relatively little of the whole. It is also surprising what a large fraction of energy goes into nuclear binding energy. A useful simple picture of the cascades is to consider them as being made up of two components: an electromagnetic shower component due to the neutral pions, and another component associated with the nuclear fragments. The division of energy between these shown in table 1 is only true on the average, while individual events show a large fluctuation in the ratio of these two components because their contributions are determined largely by the nature of the very first interaction, where only a few particles are involved, particularly at low incident energies. The different response of a calorimeter to each of these two components proves to be the most important phenomenon affecting the performance of hadron calorimeters. In the light of the above discussion, we may list those fluctuations which limit the resolution of hadron energy measurement. I) Fhtctuations in the leakage o/' ionizing particles. This can be reduced by making the absorber sufficiently large, but the range of high-energy muons is such that they cannot possibly be contained. There is also a loss of particles out of the face of the absorber through which the incident particle enters, or albedo. This can be eliminated if we reject those events where the interaction is in the first interaction length of the absorber. However, if we are not willing to accept substantial inefficiencies, this effect remains to limit the energy resolution. 2) Fluctuations in the leakage o/'non-ionizing particles.

ENERGY

MEASUREMENT

63

Neutrinos will escape from any absorber. Hadrons are in principle retained, except for albedo, but in practice an absorber which is large enough to contain most hadrons still leaks neutrons of a few MeV, particularly when a material such as iron is used. 3) Fluctuations in nuclear binding energy necessary to disrupt the nuclei in the cascade. This energy is not directly detectable. 4) Fluctuations in the saturation o]' the detector response to particles of high ionization density. This saturation of response is present in almost every detector of ionizing radiation, but to different degrees. It can cause the effective loss of most of the energy corresponding to slow protons and heavier nuclear fragments. 5) Sampling fluctuations. These are the fluctuations associated with the fact that in most calorimeters not all of the ionization is measured, but only periodically sampled. Even in those few detectors which use a homogeneously sensitive detector, some dead regions in the absorber are unavoidable and therefore may contribute a fluctuation of this type. 6) Noise. This includes effects of photon statistics in scintillation detectors, amplifier noise, and signal distortions due to slow neutrons from previous events or pile-up of events occurring within the time resolution of the detector. 7) Fluctuations due to non-uniJorm response. This effect would be absent in an ideal detector, but many calorimeters which have actually been built clearly suffered to some degree from this effect. We include here such effects as the non-uniform response across a given section of the detector, and different responses due to errors in calibration between different sections of a detector. The requirements for a device to determine unambiguously the limits on calorimeter performance are not quite the same as those for a practical detector. For example, the device must be made larger than necessary in order to contain a sufficient fraction of the energy so that it can be confirmed that the performance is not degraded by reducing the length. For reasons of economy, most calorimeters have been made slightly smaller than was thought necessary for the very best performance, so that one cannot be sure that they were not more seriously affected by leakage effects than was intended. In the same way the sampling in the detector if sampling is required - - should be made sufficiently fine to obtain the limiting performance, otherwise one cannot be sure that other effects

64

c . w . FABJAN et al.

are not being obscured by sampling. As published data on calorimeters with different thicknesses of plates are insufficient to evaluate the influence o f sampling fluctuations on the energy resolution, there should be a provision for measuring the sampling fluctuation directly. This is possible by making, in effect, two independent calorimeters which are interleaved on a fine scale, so that two different measurements of energy may be made on a single event. The difference in these two measurements gives a measurement of the sampling fluctuation due to that plate thickness. The detector must be divided into m a n y read-outs, both longitudinally and transversely, to confirm that the detector is sufficiently large and to measure the effects o f albedo. This leads to a rather large number o f independent read-out sections, but this is also required in order that the correlations and energy deposited in different spatial regions can be investigated for individual events. As we shall show, this allows some particularly interesting studies to be made o f the factors which limit the calorimeter performance, as well as allowing use of the correlations to compensate for some of these effects and improve the energy resolution. It is most interesting to be able to vary the ionization saturation effect in the detection of densely ionizing particles, so as to be able to measure directly the

A

~pam

'73

~ see

~e~

Fig. 1. Schematic representation of the mechanical and electrical construction of the calorimeter.

effect on the resolution. Also, it is essential to be able to vary the absorber material so as to observe the effects of different nuclei and different radiation lengths. An essential practical feature is to ensure that the fundamental effects are not being obscured by instrumental ones. This means that the noise should be negligibly small and measurable, the response uniform over each detector section, and the many different sections have an accurate intercalibration. The device described in the next section meets all of these requirements.

3. Description of the calorimeter 3. I. ELECTRONICS The calorimeter consists of nested arrays o f stacks of hexagonal plates, as shown in fig. 1, together with some auxiliary sections. Longitudinally it is divided into six sections, referred to as A, B, C, D, E, F, which can be read out independently, while there are seven arrays of hexagonal plates to give the radial distribution. The dimensions of this structure and the nuclear properties are given in table 2. In the case of the iron plates, one cell, i.e. one plate plus one liquid-argon gap, represents 0.1 radiation length or an ionization loss of 2.7 MeV. From our previous measurements we know that this configuration gives a very good energy resolution for electromagnetic showers, about 7.4% divided by the square root of the electron energy. This sampling step is also about 10 times smaller than in previous calorimeters. The uranium plates are somewhat thicker in the relevant parameter, i.e. ionization loss through a cell, which is about 4 MeV in this case. This turns out to be large enough so that sampling begins to affect the energy resolution. Mounted in front of the central hexagon is an array of lead plates, 4 0 c m square. This was provided in order to investigate the hadron-electron separation in a high-Z material. These plates are made by cementing 0.15 mm thick lead sheets on each side of a 0.5 mm thick steel plate. It represents 0.36 interaction length of material. [Results on the separation of electrons and hadrons in iron were given in our earlier paper2). The separation using lead plates will be discussed in a paper in preparation 5).] Following the lead-plate array there is a thin layer of 10 strips, each 1 cm wide, placed there to observe the shower distribution of electrons and hadrons at this depth (see also ref. 5). All of these structures are immersed in the same bath of liquid argon which serves to measure the ionization

65

CALORIMETERS FOR HADRON ENERGY MEASUREMENT TABLE 2 Properties of calorimeter sections. Pb A Number of plates Material Thickness Density (g/cm 3) Radiation lengths/cell Energy loss/cell (MeV) Interaction length/cell Liquid-argon gap (ram) Density (g/cm 3) Radiation lengths/gap Energy loss/gap (MeV) Mean density (g/cm 3) Mean radiation length (mm) Mean interaction length (mm) Total energy loss (MeV) Total radiation lengths: Longitudinal Transverse from axis Total interaction lengths: Longitudinal Transverse Capacitance per stack (nF) r.m.s, electrical noise per stack (MeV) r.m.s, noise per stack, including radioactivity (MeV)

B

C

Iron D

E

F

40 75 75 100 100 100 150 /0.3 mm Pb Fe Fe Fe Fe Fe Fe /0.5 mm Fe 1.5 1.5 1.5 1.5 1.5 1.5 9.2 7.9 7.9 7.9 7.9 7.9 7.9 0.097 0.099 0 . 0 9 9 0 . 0 9 9 0 . 0 9 9 0 . 0 9 9 0,099 1.40 2.72 2.72 2.72 2.72 2.72 2.72 0.0091 0.015 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0.015 2 2 2 2 2 2 2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0.015 0.015 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0 . 0 1 5 0.015 0.44 0.44 0.44 0.44 0.44 0.44 0.44 4.88 4.2 4.2 4.2 4.2 4.2 4.2 29 35 35 35 35 35 35 308 240 240 240 240 240 240 56 204 204 272 272 272 408

A

23sU B

C

75 75 100 U U U 1.7 1.7 1.7 19.3 19.3 19.3 0.50 0.50 0.50 4.0 4.0 4.0 0.027 0 . 0 2 7 0.027 2 2 2 1.4 1.4 1.4 0.015 0 . 0 1 5 0.015 0.44 0.44 0.44 9.6 9.6 9.6 7.4 7.4 7.4 161 161 161 300 300 400

2.2 3.9

7.5 13

7.5 13

10 13

10 13

10 13

15 13

38 61

38 61

50 61

0.36 0.65 2xl9

1.13 1.9 2xl9

1.13 1.9 2xl9

1.5 1.9 2x25

1.5 1.9 2x25

1.5 1.9 2x25

2.3 1.9 2x27

1.73 2.49 2x19

1.73 2.49 2x19

2.3 2.49 2x25

13.0

13

13

15

15

15

18

25

25

29

13

13

13

15

15

15

18

70

70

80

of tracks crossing the gap between the plates, which is 2 mm in each case. A m i n i m u m ionizing particle deposits 8000 electrons on each millimeter o f its length. Al t ern at e plates have a voltage o f the order o f 2 kV with respect to the g r o u n d plates. All the g r o u n d plates are electrically connected, but alternate signal plates are read out separately to achieve the two interleaved i n d ep en d e n t ion chambers, l and II, necessary to measure the sampling fluctuations. This connection is shown in fig. 2. The mechanical structure o f the hexagonal arrays is provided by 10 m m d i a m e t e r steel rods traversing the length o f each stack t h r o u g h each o f the six corners o f the hexagon. These rods are insulated by shrinkable teflon tubing, tightly fitting over the rod, and tension is maintained by a spring behind a nut at the end. Mechanically there are three stacks t h r o u g h the longitudinal dimension o f the detector, but each stack is divided in two electrically, so that the total n u m b e r o f longitudinally i n d e p e n d e n t read-outs is 6. T he stacks are supported on thin (8 ram) fibre-glass spacers placed on the stack below. T h e b o t t o m stacks rest on

a rolling table so that the whole assembly can be rolled back and forth in its container. Th e 2 m m gaps are maintained by teflon rings a r o u n d the tie rods. N o o t h er spacers are necessary because the exact spacing is not critical: it is the total length o f liquid argon in a stack that determines the response. S o m e care must be given to the connections since we desire very low inductance to provide a fast response time, but at the same time we wish to maintain a very small dead-space between the different sections. The low i m p ed an ce is provided by strip-line cables running the length of stacks. Since there are two interleaved read-outs in each stack, there are two strip-line cables which are run side by side with a c o m m o n g r o u n d plate, as shown in fig. 2. Each g r o u n d e d hexagon is connected to the ground plate by means o f a short wire on one side o f the strip-line cable assembly. Th e connecting wire is welded to the steel plate and then soldered on to the strip-line cable. The alternate signal plates are connected to the strip-line cables on opposite sides of the strip-line cable array. Th e strip-line cable itself is made from a piece o f 1.6 m m thick fibre-glass

66

c.w.

FABJAN et aL

printed circuit b o a r d with a teflon filling, which provides lower electrical noise than that o f phenolic b o a r d , because o f smaller dielectric loss. A thin layer o f fibre-glass b o a r d underneath the strip-line cable assembly insulates it from the plates below, and a n o t h e r layer on the u p p e r surface insulates it from the stack placed i m m e d i a t e l y above. The thickness o f the whole assembly is only 8 ram, and is o f a density o f less than half that o f the stack arrays, so that the effective fraction o f the mass which is not sensitive to particles is small, a b o u t 1.5% each in the tie rods and

I

v

I

I

Fig. 2. Drawing of the connections in the detector stacks. The corner at the end of the stack has been cut away to show the different layers in the connection scheme. (A) Hexagonal plate of steel or uranium with a hole at each corner for 10 mm tie-bar. Connecting wires are welded to these plates. (B) Double-sided printed circuit board. The lower side carries the ground signals, the upper side carries the two strips at high voltage, for alternate signal plates. (C) Copper foil soldered to the lower conductor on the printed circuit board. The ground connection wires are soldered to this foil. (D) Insulating phenolic sheet. (E) Insulating phenolic-glass laminate bridge over the connection system, 8 mm thick on the sides. Another stack rests on top of this insulator. (F) Printed circuit board which provides the calibration capaci-tance and high voltage blocking, with the ground conductor shown facing outward, i.e. rotated downwards from the actual orientation. (G) Copper surface on printed circuit board which provides calibration capacitance through the board to the signal leads on the other side. (H) Copper shield for the calibration capacitance to prevent cross talk to other channels. (1) Signal pads, at high voltage, on the back of the printed circuit board. (J) High voltage blocking capacitor. (K) Signal conductor of one of the output strip cables. (L) Ground conductor of an output cable. (M) Two output strip cables,

in the stack interstices. T h e signal plates are b r o k e n in the middle o f the stack so that the electrical o u t p u t s are i n d e p e n d e n t at the two ends. A t the ends, the printed circuit b o a r d strip-line cable receives a printed circuit e d g e - c o n n e c t o r to carry away the signals. The connection to the amplifiers is m a d e by a flexible strip-line cable o f 3 ~ impedance, specially m a d e for this purpose. It consists o f two layers o f k a p t o n foil between c o p p e r foils of 0.1 mm thickness, with two further layers of m y l a r foil for insulation on the exterior. The length o f the connecting cable is a p p r o x i mately 3 m. The detector was first run with the connection described above, where the high voltage is brought in on the strip-line cables used for the signal. As it is more convenient not to have high voltage a p p e a r i n g near the preamplifiers, the system was modified by placing a blocking c a p a c i t o r i m m e d i a t e l y on the ion chamber. The c a p a c i t o r was placed on a piece o f printed circuit b o a r d attached to the edge-connector on the end o f the connection strip a n d lying in the plane o f and immediately adjacent to the end hexagonal plate, as shown in fig. 2. The c a p a c i t o r was a specially m a d e unit of m i c a - p a p e r construction*. Multiple stripleads allowed it to have a low inductance, 25 n i l , for a capacitance value o f 0.1 llF. it had a voltage rating of 3.5 kV and was quite c o m p a c t for those values. Ceramic capacitors cannot be used at low temperatures, but this unit showed no d a m a g e upon exposure to liquid-argon temperature. Out o f 100 units in use for a b o u t one half year, one unit failed, p r o b a b l y because o f a period in which high voltage was on the c h a m b e r s without the presence o f liquid, leading to s p a r k i n g and consequent voltage reversal on the capacitors. Since this detector was designed for m a x i m u m flexibility for different tests, the connecting leads are rather long. This, c o m b i n e d with the rather large area o f the plates, leads to natural values o f capacitance and lead inductance which give a limit for the rise-time z) which is consistent with the charge collection time in pure liquid argon with 2 mm gaps. W e knew from earlier measurements °) that the collection time could be reduced by a factor o f four by a d d i n g 1% methane, but this was not required with the rise-time (200 ns) chosen on the basis of the a b o v e considerations. A l t h o u g h the inductance in the connections has been m a i n t a i n e d at a sufficiently low value so that the rise-time is adequate, the transient voltage across that inductance and the presence of the blocking c a p a c i t o r * Custom Electronics, Inc., Oneonta, New York 13820, U.S.A.

67

C A L O R I M E T E R S FOR H A D R O N E N E R G Y M E A S U R E M E N T

make calibration at the preamplifier difficult to relate to charge on the chamber itself. Therefore we introduced the calibration charges directly upon the chamber. This is done by means of a capacitor introduced on the strip-lines connecting the individual plates. The capacitor consists of a printed circuit board placed on top of the two strip-line signal leads as shown in fig. 2. The calibration is most effective if the calibration charge is introduced in such a way that it has the same time-dependence as the charge collected in the liquidargon gaps. This shape has been illustrated in our previous paper2). The calibration is done by means of a voltage step function from a precision pulser. This arrives at the end of a long 100 ~2 cable, which must be properly terminated. The network which accomplishes this termination and produces the desired shape at the output is shown in fig. 3. The calibration capacitors have been measured with a three-terminal bridge to high precision, and the change in going from room temperature to liquid-argon t e m p e r a t u r e has been m e a s u r e d - - a 4% correction. In this way each section of the calorimeter has an absolute charge calibration. D a t a discussed later show that this calibration is accurate to 0.5% or better. The stainless-steel vessel which contains liquid argon also serves as an electrical shield for the detector. The

from Pulse~ - ~ IOOQ Cob[e

~

Q)

I00~ L

~- ~-cable ~ - Ccal

add

~ = t_L_r 3 tr

in L A = 3 O O n s

L .--,,-t = 100 n s = RC~ot = -~- --,,-

*

{

Cto~ = lOOOpF L

= 10 P.H

Ctot : C~dd Ccabte + CCC~ 1

If w e h a v e

C,ot > 1 0 0 0 p F

"-'~0(]~ Cable ~

,00o

b)

preamplifiers are placed in closed aluminium boxes which are attached to the dewar body so that they are effectively part of the same shielding system. We found that it was not necessary to prevent ground loops carrying current through the dewar system, for example, on the plumbing connections. On the other hand, care must be exercised on lines that penetrate this shield; for example, the high-voltage cables, calibration leads, and instrumentation leads such as thermocouples. These may inject charge into the detectors in the same way as does the calibration capacitance. The levels of concern may be expressed by noting that a I V signal on an unbalanced capacitance of a few picofarads to the signal leads gives a charge of the same magnitude as the signals due to particles. The same remark holds for leads penetrating the preamplifier box. These must be bypassed immediately at the point of entrance. The strip-line cable terminates with a low-induction connection to a transformer followed by a chargesensitive preamplifier which drives a long cable carrying the signal to the electronics trailer. This circuit is exactly the same as that described in our previous paper2), except for the addition of an output stage to drive the shielded twisted-pair cable. Further attention has been given to the question of protecting the preamplifier in the case of a spark in the detector. Fig. 4a shows the adopted configuration, which allows a spark to occur without destroying any of the components of the preamplifier. The circuit takes advantage of the inductance in the connecting cable and the saturation of the 3D3 core, and uses a diode which is capable of absorbing the current due to the spark. The additional capacitance introduced by this diode is 1.2 pF or 5%. In the electronics trailer, the signal from the preamplifier drives a differential amplifier for common-mode rejection, is given a bipolar shape, and is fanned out to

ntimes i ~

,00o

a ) FET- ProtectionCircuit H.T

I R = (n-l) xlOOf~ Cto ~ = n x 1 0 0 0 p g U~ = tJ P ~ t s e r n

CBko~,og

BAY72

FET

l CDete¢~ 3D3

Fig. 3. Network which terminates the calibration cable and creates from a step function a rise-time which imitates the charge collection curve in liquid argon. Two different networks are shown (a) and (b) depending on the value of Cto,.

Core Fig. 4. a) Circuit diagram for the FET-protection o f the preamplifier.

Fig. 4. b) Circuit

diagram of the shaping amplifier.

500NS SHAPING -AMP

CALORIMETERS

FOR H A D R O N

analog-to-digital converters (ADCs) and to an analog read-out system followed by a pulse-height analyser. l-he circuit of this amplifier is shown in fig. 4b. With this arrangement there is no observable noise pick-up between the preamplifier and the shaping amplifier. Yhe waveforms are shown in fig. 5, with the pole-zero cancellation adjustment made to minimize the very small third lobe of the output waveform. The ADCs are of a type intended for use in a charge integrating mode, but measure the voltage at the peak of our bipolar waveform by using a narrow gate positioned around the peak of the voltage waveform. This is feasible because there is no jitter in the calorimeter signal. These ADCs are connected via a C A M A C interface to an on-line computer, which produces plots for checking equipment performance and writes the data on magnetic tape. At the same time the signals are sent to an analog system consisting of a sequence of summing circuits allowing all parts of the calorimeter sections to be added. The most common mode of operation is shown in fig. 6. Recall that the sections are each provided with interleaved independent outputs which we call I and 11. Typically all tile I-signals throughout the whole calorimeter are added and all the If-signals are added separately. These go into a sampling circuit which can produce as output the peak value of either I+11 or ! - I 1 , the latter with an offset from zero. The output of this unit is then gated into a pulse-height analyser. In this manner the sampling fluctuations can be observed directly, by comparing the I - I ! and I+11 signals. By summing only certain portions of

ENERGY

69

MEASUREMENT

the detector, spatial distributions can be obtained rapidly, and by gating on a single-channel analyser connected to some portion of the calorimeter and displaying another sum on the pulse-height analyser, correlations can be observed. We find this ability to make analcg analyses a valuable complement to the computer analysis off-line. For calibration purposes the computer can trigger this system with no pulser input to obtain the pedestal, with a small value of the pulser output, or with a large pulser output. In this way the linearity of the system is continuously checked. Alternatively, the pulser is self-triggered and used to gate the pulseheight analyser. The analog system is calibrated by adjusting the gain of each shaping amplifier to deliver the same signal to the pulse-height analyser for the same charge input through the calibration system. It is not necessary to adjust the ADC gains because the calibration data are recorded on magnetic tape along with event data. It was observed that these calibrations are stable to 0.1%. 3.2. CRYOGENICS

The liquid argon is contained in a double-walled stainless-steel cryostat, with superinsulation of aluminized mylar layers. It consists of a cylinder, 3 m Segment of detector

Segment of detector

Au

B,

2 3 4 5 6

1 2 3 4 5 6

7 ~

7

I

BIt

1

2-7 Ct

1

Bt

~ ]

7

B[I

Ctt

TOT=

% 7

'53-

7

Ft:

DI~FF.( TOPHA Fig. 5. The wave forms: (a) at the calibration capacitor; (b) at the o u t p u t o f the preamplifier; (c) at the o u t p u t o f the s h a p i n g amplifier.

Fig. 6. The system o f s u m m i n g circuits a n d peak sampling device used to perform an analog analysis on the data.

70

C . W . F A B J A N et al.

long with an inside diameter of 1.3 m. The thickness of the walls on the beam axis is 3 mm for each of the two walls. Access to the interior is obtained by means of a central flange sealed by knife edges on a copper gasket. The liquid-argon temperature is maintained by a heat-exchanger made of 10 mm diameter stainlesssteel tubing at the top of the cryostat. A liquid nitrogen inflow is connected to the input of this heat-exchanger, while the output is controlled by a solenoid valve. The solenoid valve is in turn actuated by a pressure controller reading the argon vapour pressure. In this way, the argon vapour pressure is maintained above atmospheric by (0.4-1-0.05) bar. The cryostat is equipped with two capacitance-level gauges to control the filling operation, one covering the whole height of the cryostat, and another one covering only a few centimetres at the top for fine adjustment to the desired level, just above the ion chamber plates. An insulated liquidargon line was provided so that transfer to and from the storage cryostat could be carried out in the liquid phase. The time required to cool down and fill is about 48 h, and the same time is needed for warm-up by means of heaters attached to the inside of the cryostat. The liquid can be transferred out of the detector in about 2 h. About 3 m 3 of argon are needed to fill the detector. The storage cryostat is also equipped with a liquid nitrogen heat-exchanger so that the liquid can be preserved for long periods of time and transferred back and forth between the two cryostats. Indeed, the same liquid argon was used for all the measurements reported here, over a period of about nine months. The electrical feedthroughs penetrating the wall of the cryostat are made of standard vacuum-tight fittings, except for those where the strip-line cable passed through the argon-air interface. This was made by potting the bundle of strip cables with a glassfilled epoxy resin. There are three such feedthroughs, each containing 32 strip-cables and leading into the three preamplifier boxes. Low-power electrical heaters are used to keep these feedthroughs at ambient temperature despite the heat leak up the copper strips. It is important that the argon be maintained in a high state of purity, in order to allow the collection of free electrons2). The purity is monitored in three ways. First there is an electrolytic Hirsch cell which detects oxygen in the argon gas*. Secondly, we have a small liquid-argon test chamber connected to the argon gas system, which allows argon to be liquefied and the response to c~ and /~ radioactive sources to be deter* Hirsch Oxygen Meter MK 11, manufactured by Chemical Division, England.

Engelhard,

Ltd.,

Cinderford,

Gloucestershire,

mined. Thirdly, inside the detector volume itself there is a small test chamber with an c~-particle source. As shown in our earlier paper2), the ~-particle response is particularly sensitive to impurities. When we first received our liquid argon, our analyser showed about 0.7 ppm of oxygen. As we transferred it back and forth between the two cryostats, this number slowly increased to about 1.4ppm after 9 months. The detector cryostat is equipped with a diffusion pump which can produce a vacuum of better than 10 -5 tort, despite the large area of plates. However, we found that a mechanical pump vacuum is sufficient, as is careful flushing with argon gas. We provided the system with a purifier, shown in fig. 7, which is capable of removing oxygen, water, and other impurities. It was not necessary to use this purifier during the course of the measurements reported here, but it has been used subsequently and has performed as intended. The purification is done in the gaseous phase. The input stream of gaseous argon, at a rate of 40 m 3 per hour, is mixed with a few parts per million of hydrogen gas and passed through a Deoxo unit*) which catalyses the reaction between the hydrogen and impurity oxygen to form water. The gas stream then passes over a molecular sieve with 13 A aperturest. This removes water and many other gases, but allows the noble gases to pass through. The advantage of this purification scheme over that used in our previous work is that the purifier need not be regenerated and that the reactions proceed at room temperature. On the occasion when it was used, the input argon stream contained about 8 parts per million of oxygen. Adding hydrogen in somewhat more than the stoichiometric fraction, the output stream contained a hydrogen fraction well below 1 ppm. At the voltage we customarily use on the detector, 2 kV, it is advisable to keep the oxygen content below 2 ppm. 3.3. BEAM The measurements described here were made at the CERN Proton Synchrotron (PS). The momentum spread in the beam was approximately 1% fwhm and the maximum momentum was 10 GeV/c. Cherenkov counters were used to label electrons, pions, K-mesons, and protons or antiprotons. Muons were identified by a counter placed at the end of the calorimeter. There were a number of beam-defining counters, and a veto * Deoxo, manufactured by Chemical Division, Engelhard, Ltd., Cinderford, Gloucestershire. England. t Linde Molecular Sieves, manufactured by Union Carbide Corporation. Materials System Division, New York, NY, U.S.A.

z

d

Filling line for Argon

Liquid

3.0 m 3

//~!/I//li)I ~ I I~ '

Liquid Nitrogen

Fig. 7. A diagram of the argon purification and handling system.

~ir~///l,

Nitrogen

Uqu~d

m3

1.2

?-

®

Pilling line for Liquid Argon

Heot

exchonger

Min, Mox.-Monometer

Solenoid volw

Sofety voLve (max. pressure 1.5 ot )

Mongol volve

I><3---

z

m > r~

N

z

0 Z

©

> ©

72

c . w . FABJAN et al.

counter with a hole defining the beam after the last magnet but far from the detector so as to be insensitive to the albedo. The last deflecting magnet was about 6 m in front of the detector. A n array of scintillation counters with 3 mm resolution was used to determine the exact point of entry at the front of the calorimeter. Fifteen metres upstream of our detector, the beam passed through a 0.5 m hydrogen target used for another experiment. The rates in this beam were rather high, of the order of 106 particles per second. In order to avoid pile-up, it was necessary to provide a system of electronic protection which rejected those events where there was a particle within 1 Its preceding or within 500 ns following the event of interest. This lowered the rate considerably, but was found extremely effective in rejecting pile-up. The counter used to reject extra particles was a large one, so that scattered particles were rejected as well as additional particles in the beam. The time aperture during which a second particle nearly coincident with the first could be accepted was about 20 ns. This leads to a residual pile-up which is easily detectable as a peak of pulse height twice that of a single particle. By varying the rate during periods when this experiment had control over the beam, we verified that rate effects do not affect any of the conclusions in this paper.

4. Results for the iron plate calorimeter We establish the shape of the plateau as a function of high voltage for relativistic particles by selecting muons which traverse the calorimeter. The signature for a muon is a particle which is present in the beam, traverses a 5 0 c m absorber placed after the last deflecting magnet, and reaches a large scintillation counter placed after the calorimeter. This signal shows a behaviour, as a function of the current in the

last deflecting magnet, which demonstrates that it is a beam-like particle. Consequently, it represents muons with an energy near to 10GeV/c. This is relevant because in a very thick absorber the muon energy loss shows a relativistic increase, like the Iogartithm of the momentum, which is due to hard collisions. Even though we define the energy loss by the peak of the distribution, it still is greater than that for " m i n i m u m ionizing particles" for muons of this high energy. The distribution of charge deposited by these muons is displayed in fig. 8, which shows the characteristic tail due to large energy losses, but with a very sharp cut-off on the low side. The peak value is plotted in fig. 9, with a rapid increase to a nearly constant value, as a function of high voltage. The slight increase in apparent collected charge seen at high

~0

oB~-

g

06 ~

v

~ o2 1

0

2

3

High voltage (kV)

Fig. 9. The most probable charge signal from muons as a function of the high voltage on the calorimeter, showing the plateau for minimum ionizing particles.

800

Fig. 8. A distribution of the charge deposited by m u o n s traversing the entire length of the detector, with high voltage = 3 kV. The zero is marked on the abscissa by the small spike, a few channels wide.

J

1

Fe / LA

o

~o

20

(1 ,._,-,,..q

ao

ao

so

Go

vo chonne{s

Fig. 10. The distribution of charge deposited by 10 GeV/c pions incident on the iron plate calorimeter.

CALORIMETERS

FOR H A D R O N E N E R G Y

73

MEASUREMENI

TABLE 3 Charge distributions for IO GeV/c re- in iron plates. Radial section

Interaction point

High Z

A

Central Outer ring

All events

0.17

0.73 0.15

0.63 0.17

0.63 0.29

0.08 0.10

0.03 0.05

3.03

Central Outer ring

High Z

0.56

1.06 0.28

0.26 0.20

0, l0 0,18

0.015 0.07

0.00 0.03

2.73

Central Outer ring

A

0.05

1.21 0.16

0.84 0.23

0.24 0.26

0.02 0.08

0.00 0.03

3.10

Central Outer ring

B

0.03

0.14 0.06

1.24 0.16

0.88 0.42

0.04 0. I 0

0.00 0.04

3. I 1

Central Outer ring

C

0.03

0.09 0.04

0.12 0.05

1.71 0.34

0,30 0.19

0.14 0.11

3.15

voltages has been studied with greater care in a small chamber which is capable of going to much higher voltage. This increase seems to correspond not to a greater collection of charge but to a slight increase in electron drift velocity, which leads to a shorter collection time. As discussed in section 3, the calibration signal is made to have the same rise-time as the electron collection time at the normal running voltage. The dependence of output signal on rise-time is known as the ballistic deficit. For very high collecting voltages we have effectively overcorrected for this effect, leading to an increase in the apparent charge. The curve in fig. 9 is characteristic of argon containing about 1 ppm of oxygen. If the argon is much purer, the curve is not very different, because the loss of electrons is due to recapture by positive ions on or near the particle track, not to capture of electrons by oxygen as they cross the drift space7). Most of our data were taken with 2.5 kV on the calorimeter. Fig. 10 shows the charge distribution for 10 GeV/c pions incident on the detector. Fig. 11 shows the standard deviation of the peak as a function of particle type and available energy. The available energy is that energy which should, in the simplest model, appear in the absorber as ionization. For electrons and protons it is the kinetic energy. For mesons it is the total energy, while for antiprotons it is the total energy plus one proton mass. Using this variable, the different particles give nearly the same response. We have checked that these results can be obtained

Collected charge (pC) in section B C+ D E

Total charge

F

from off-line analysis of the ADC results as well as the analog method. They are also independent of beamrate, provided the pile-up protection system is used, and are reproducible over periods of many months,

r •

~ e

+

TL

100 --

50

~: 1 0 - -

P }

Fe / LA

U238/LA

- -

Resotution

---

Sampling fluctuation

Z~Z2-_,--

u_

L

r

0

5

10

AVAILABLEENERGY [GeV] Fig. I 1. The standard deviation of the distribution of the charge signal as a function o f particle type and available energy. Results for both the Fe/LA and the U/LA calorimeter are shown and the corresponding widths for the sampling fluctuations,

74

c . w . FABJAN et al.

with different fillings of liquid argon, etc. We therefore know that they are intrinsic properties of the calorimeter. Our task is now to identify the source of the fluctuations which give rise to this width. In table 3 we show the distribution of charge for incident pions of 10 GeV/c in a two-dimensional array. Rather little energy is deposited in the last sections. To show that the length is sufficient from the point of view of resolution, we give in fig. 12 the standard deviation as a function of the length of calorimeter included in the summation of charge. It can be seen that the asymptotic value is well defined. To estimate the asymptotic transverse size of the detector, we note that, using the centre hexagon only, a resolution of a = 22% is found for 10 GeV/c pions, compared to cr = 17% if the whole detector is used. Furthermore, from an inspection of the energy deposition we see that tripling the transverse dimensions increases the collected charge by only 25%. The shape of the radial energy deposition distribution is known from other measurements, allowing us to conclude that little energy is deposited outside our detectorS). When the beam was displaced to the axis of one of the stacks of the outer ring, the collected charge dropped by 10%, with only a slightly larger width. These arguments are suggestive, but they do not quite allow us to estimate the improvement of resolution from a further increase of the radius. Perhaps it is safe to say that in any practical calorimeter one would hesitate to attribute energy appearing very far away from the main shower to the particle of interest, so that there is a practical limit to the useful radius of a calorimeter, and any energy, for example carried by neutrons of a few MeV, that escapes that radius we would prefer to consider as part of the inevitable losses discussed below.

In order to study the albedo effect, the loss of energy back through the entrance face, we would like to compare particles which interact in the front of the calorimeter with those which interact deep inside it. The latter will not be subject to the albedo effect, because energy travelling backward will be absorbed. Of course, we may be confused between those cases that interact in the front section of the calorimeter and those which interact further in, but send a substantial amount of energy backward. However, this confusion is not very important because a large amount of energy is usually released near the first interaction, while the albedo effect involves a much smaller amount of energy. In any case, the effectiveness of our criterion for the interaction point is established by the observed effect on the resolution, the effect shown in fig. 13 where, indeed, a small improvement of resolution is shown for those interactions which occur in the later sections of the calorimeter. The albedo must be the cause of this effect. As we have explained, the sampling fluctuations are measured by comparing the signals in the interleaved sections I and II on individual events. We check, of course, that this difference is zero on the calibration signals. The accuracy with which this is true, and still more the accuracy with which the average of i - I 1 is zero on real events, is a demonstration of the accurate intercalibration of the different sections. When we examine the distribution of I - I 1 , we find that for electrons it is very accurately Gaussian, while for incident hadrons it is Gaussian near the peak but contains substantial tails at the level of 1 0 - 3 . This might be expected because hadron stars in nuclei can sometimes manage to deliver most of their energy into

protons 10 C-eVlc


--

b 10 o

LL 50

Equal weights

zx With optimal weights

0

l 1

I 2

I 3 Length

I 4

I 5

J 6

I 7

I 8

I 9

rintenacticx~ length]

Fig. 12. The standard deviation o f the charge distribution as a

function of the length of the calorimeter.

0

[ 1

I 2

I 3

I 4

1~ 5

I 6

~_ 7

I 8

I 9

Position of interaction i-interaction l e n g t h ]

Fig. 13. The standard of the charge distribution for 10 GeV/c pions as a function of the interaction point.

75

C A L O R I M E T E R S FOR H A D R O N E N E R G Y M E A S U R E M E N T

heavy nuclear fragments which deposit the energy very locally, while it is very difficult for an electromagnetic shower to do this. The results for the standard deviation of the sampling fluctuation distribution for different particles and different energies are shown in fig. l l. Here we see, as we found in our earlier paper2), that the sampling fluctuations are larger for hadrons than for electrons. We noted that all of the energy resolution for electrons was explained by sampling fluctuation. Now we are able to see that although the sampling fluctuations are larger for hadrons than for electrons, they still explain only a small part of the total width of the hadron energy distribution. At least that is the case for our very thin plates. Presumably the contribution of sampling goes approximately as the square root of the plate thickness, so that for plates of several centimetres thickness the contribution of the sampling fluctuations would be very important. This is consistent with the fact that our observed resolution is about half the width of that observed in calorimeters with plates of 3 cm iron. In fig. 14 we show a comparison of the charge delivered by electrons and hadrons as a |unction of energy. It will be noted that the charge delivered by electrons is accurately proportional to the energy of the electron, while the hadrons fall on a different line, with only a small difference according to particle type. If all the energy of a hadron appeared in the electromagnetic shower, the hadron would surely look like the electrons. We know, then, that the missing energy must somehow be associated with nuclear particles. An obvious candidate for an effect associated with

"

i

P I F e l LA

nuclear particles is the saturation effect at high ionization densities, since this is a very small effect for electromagnetic showers where the particles depositing energy are relativistic over almost all their path length. We are able to make a direct measurement of this effect by comparing the dependence on high voltage of the signal from electrons and the signal from hadrons. It is customary to measure the size of the saturation effect by comparing the signal given by 5 MeV or-particles with that given by 5 MeV electrons. For a detector which did not exhibit any saturation with ionization density, this ratio should be 1; for typical liquid scintillation counters, this ratio is about 0.1. In our previous paper 2) it was shown that by varying the high voltage this ratio can be changed from about 0.25 to 0.05 in liquid argon. Thus by studying the ratio of signals given by muons and hadrons as a function of high voltage, we can obtain direct insight into the importance of this effect for highenergy hadron cascades. Fig. 15 shows the muonhadron ratio and the hadron resolution as a function of high voltage. Only a small effect is seen in the electron-hadron ratio, while the effect in the resolution can be explained by the fact that the electronic noise starts to become important at low high-voltages where the signal is considerably reduced. We conclude that the missing signal for hadrons is due to leakage of neutrons and neutrinos and the loss of nuclear binding energy. It is difficult to determine the relative importance of these experimentally, but the total that we observe agrees with the Monte Carlo calculations. The fluctuation in this missing energy dominates the hadron resolution, if there is an event

~'~

. ~ 1 u~3a'~~'

~/

~o~_--o~°~

~o

iI

~/./i

/ j/J///n/"

g 0a

-o

-

_/oJ° ~

120 100 r~

u

06

o

T~ c h c l r g e / I 1 c h a r g e

•

~ width

80

60 t~

0.4 40

.o_ ~r 02 t

1

i

~

] ~ 5 AvChloble Energy [GeV]

t

1

t

l 10

0

20 I 1

__

I 2

High voLtoge

Fig. 14. Charge collected from hadrons and electrons in the Fe/LA and U/LA calorimeter. The charge is measured in arbitrary units, which are different for the two calorimeters resulting in a normalized response for electrons.

_ _ 1

3

(kV)

Fig. 15. The ratio o f t l e charge collected from m u o n s and pions at l0 GeV/c, normalized to one at the highest voltage (left scale). Also shown is the width of the n-charge distribution (right scale).

76

C.W.

F A B J A N et al.

TABLE 4 Weights which give the smallest relative width to the charge distribution: for events interacting in Section B. Radial section High Z

A

Weights for section B C+ D

E

F

Resolution r.m.s. (%)

Central Outer ring

1 I

I I

I 1

[ I

I I

I I

15.6

Central Outer ring

4.39

2. I I 0.00

1.00" 2.04

1.00 1.66

1.29 1.30

0.91 0.47

13.7

Interaction here.

which gives its energy mainly to neutral pions in the first interaction, there will be little missing energy since it will mostly appear as electromagnetic showers. On the other hand, if there are very few neutral pions but many charged pions and nuclear fragments in the first interaction, there will be much binding energy absorbed in the first and subsequent interactions and a substantial loss of low-energy neutrons and neutrinos. Since the missing energy is on the average about 30% of the total, a fluctuation in this number can easily account for the observed energy resolution. We can see evidence for this explanation in the data by examining the distribution functions of the total charge more carefully. In fig. 16 we show a logarithmic display of the charge deposited by 10 GeV/c pions. After the intensity has dropped somewhat more than an order of magnitude on the high side of the peak, which appears very broad on this scale, we see a break and then a much more rapid fall. This break occurs at the charge that would be deposited by an electron of the same energy. The natural conclusion is that the events which correspond to charge exchange or almost complete conversion of the hadron energy into one or more neutral pions are those which give the maximum possible energy. The shape of the distribution just beyond this energy is given by the sampling fluctuation for electromagnetic showers, which we have measured on the incident electrons. The average event contains only a fraction of its energy in neutral pions, and these events occur near the peak of the distribution. Further evidence in support of this interpretation is obtained by noting that this shoulder is much less evident in the distribution with incident protons, where there is much less probability of obtaining leading neutral pions. On the other hand, it is visible with incident antiprotons, as we expect. The fact that the different forms of missing energy giving rise to the nuclear fluctuation are all highly

correlated, allows the possibility of devising compensation mechanisms. The first of these which we shall discuss is based on the fact that the electromagnetic energy originating in neutral pions is confined to regions of the detector very near to the source of the neutral pions, because of the short radiation length in iron compared to the interaction length. This means that in those interactions which give their energy mainly to neutral pions, the energy is deposited mainly in the central sections where the beam enters, and mainly in the longitudinal section where the interaction first occurs; while in those interactions which contain few neutral pions, the low-energy neutrons, hadrons, and protons produced at wide angles carry energy into all the surrounding sections of the detector. We may expect to see a correlation then between the total charge deposited and the spatial extent of the cascade. This was investigated by selecting interactions which occur in a given central section. The total charge was then derived by allowing weights to vary for the different sections of the detector, with the weight in the section of the original interaction set equal to 1. The weights were determined by searching for values which minimized the relative width of the weighted charge distribution. The results are shown in table 4, and they are approximately independent of particle

Fig. 16. A display of the charge deposited by l0 GeV/c 7r- in the Fe/LA calorimeter on a logarithmic scale of six decades, showing the "charge exchange" break on the high energy side.

CALORIMETERS

FOR H A D R O N

ENERGY

MEASUREMEN]

77

type and energy. Allowing the weights to vary from I reduces the width of the distribution by about 14%. As expected, the weights are greater than I for the sections surrounding the interaction section, and incident electrons and incident hadrons then give approximately the same weighted signal (see also fig. 12). in conclusion, we have studied the hadron resolution in a detector of sufficient size so that the leakage of fast particles is not important. We find that the contribution of sampling and of the ionization saturation effect to the resolution is also small in this device. We demonstrate that the resolution is dominated by the nuclear fluctuations. Our next task is to find the means of compensating for the energy loss that causes these fluctuations. The key to this is to realize that there are a number of closely connected phenomena associated with these fluctuations. Careful Monte Carlo calculations support the conclusion of simple models that the number of neutrons, the fraction of heavily ionizing particles, the binding energy, and missing neutrons are all closely correlatedg). (See also footnote to table I). While the last two are unmeasurable, a good many methods can be thought of for measuring the first two. One method we have described above is based on the fact that the neutron component is spread over a larger volume of the absorber than the others. Thus a measurement of the spatial distribution of the energy affords a method of determining what fraction of it is carried by the neutrons. Since the separation of the neutron component in this way is not very clean, the compensation is very approximate, but we found evidence of a substantial effect. In the next section we describe our suggestion of a better method, and the verification that it is indeed more effective.

process. The common isotope of uranium, 238U, is fissionable by neutrons of energies above 1 MeV, which includes the greater portion of the evaporation neutrons from nuclear disruptions. Once a fission sequence is initiated, the neutrons resulting from the fission itself can cause additional fissions, etc., so that there is a net multiplication of the number of neutrons by a factor of about 2. Our detector samples the kinetic energy of these neutrons. Also, following the fission there are prompt 3,-ray decays of the residual nuclei which are detected in our ion chamber. The fission fragments themselves, of course, carry a very large amount of energy, but these are not detected because their range ends inside the uranium plates. Thus we may expect to see the desired effect of an increased energy deposit associated with the neutrons in the hadron cascade. A quantitative estimate of this effect may be made from numbers available from previous measurements. There are two measurements of the number of neutrons released by high-energy hadrons in uraniuml°). The authors find that there are approximately 34 neutrons per GeV of incident proton energy, emerging from a 10cm diameter Z38U target. This is to be compared with 20 neutrons per GeV from a lead target. Since lead and uranium are so close in atomic number, the difference of 14 neutrons per GeV must be associated with the fission process. The average number of neutrons produced in a fission of 238U is 2.625 11). Therefore the number of fissions in the target giving rise to the neutrons is approximately 5.3 per GeV. The spectrum of these neutrons has been confirmed to be essentially that of the fission spectrum~ °). Therefore the well-known 238U cross-section averaged over the fission spectrum ~~) can be used to predict that

5. Energy compensation by fission amplification

number of fissions = 0.713 number of neutrons incident,

It would seem that the best compensation method would be one that is intrinsic in the hadron cascade, not requiring some analysis correction or combination of different forms of information. We believe that the element of the hadron cascade which is most closely correlated with the nuclear fluctuation is the quantity of neutrons of a few MeV energy. These are almost absent if the shower is purely electromagnetic, and must be numerous in cases where there is a great loss of nuclear binding energy as well as being completely correlated with the neutron loss. We seek a method of increasing the response of the calorimeter to these neutrons. One obvious method is to insert in the calorimeter an amplifier of the number of these neutrons. We know of such an amplifier: the nuclear fission

so that, in a large uranium absorber, the number of fissions produced by the 34 neutrons emerging from the target region is 24.2, or the total number of fissions per GeV of incident energy is 29.5. Each of these releases, on the average, 206 MeV, of which we can expect to detect efficiently the 8.0 MeV in the form of prompt 7-rays~2), representing 236 MeV total. In addition, the fission neutrons make inelastic collisions, and those which do not make more fissions are captured by uranium nuclei which then emit y-rays. The amount of this energy has been tabulated as I1.1 MeV per fission 12). The total amount of energy in this form is then 19.1 MeV per fission, or 563 MeV per GeV of incident available energy. Most of this is

78

C.W. FABJAN et al.

TABLE 5 Charge distributions for 10 GeV/c 7r- in uranium-iron plates. Radial section

Central Outer ring Central Outer ring Central Outer ring Central Outer ring Central Outer ring

First int. point

All events A B After B Undefined (small in all c.s.)

Collected charge (pC) in section

No. of events

A

B

C

D

E

Total charge

0.627 0.146 0.885 0.158 0.145 0.073 0.115 0.061 0.364 0.459

0.319 0.133 0.199 0.138 0.828 0.129 0.120 0.075 0.060 0.192

0.134 0.092 0.038 0.069 0.181 0.145 0.745 0.125 0.018 0.090

0.022 0.016 0.0 0.021 0.0 0.027 0.218 0.082 0.0 0.014

0.003 0.052 0.0 0.045

1.544

80 000

1.524

51 211

1.596

17 122

1.725

7 543

1.236

4 119

0.52 0.089 0.094 0.0 0.050

Charge distributions for 5 GeV/c n + in uranium-iron plates. Radial section

Central Outer ring Central Outer ring Central Outer ring Central Outer ring Central Outer ring

First int. point

All events A B After B Undefined (small in all c.s.)

Collected charge (pC) in section

No. of events

A

B

C

D

E

Total charge

0.317 0.055 0.469 0.052 0.093 0.006 0.079 0.0 0.165 0,192

0.139 0.019 0.083 0.021 0.427 0.20 0.083 0.0 0.017 0.039

0.047 0.014 0.007 0.005 0.064 0.041 0.283 0.17 0.0 0.01 I

0.017 0.003 0.002 0.0 0.009 0.008 0.124 0.023 0.0 0.001

0.005 0.0 0.0 0.0 0.0 0.0 0.060 0.009 0,0 0.0

0,612

30 601

6.630

17 648

0.662

5 699

0.660

3 885

0.415

3 869

in the form o f p h o t o n s which have an energy near that o f the peak o f the p h o t o n energy in an e le c t r o m a g n e t i c shower in uranium, and thus should be sampled in a similar way in o u r detector. The fission process can then be expected to increase the a p p a r e n t energy release due to h ad r o n s by as much as 56%, while increasing the signal due to e l e c tr o m a g n e ti c showers by only a small a m o u n t because o f the small value o f the photofission cross-section. Fortuitously this factor is a p p r o x i m a t e l y that required to p r o d u c e the same energy response to hadrons as to electrons. Thus we will expect a reasonably close c o m p e n s a t i o n o f the nuclear effect in uranium. F u r t h e r m o r e , this c o m p e n sation should be closely correlated with the nuclear fluctuation, event by event, and thus should produce a decrease in these fluctuations and an i m p r o v e m e n t in the energy resolution. M o r e careful M o n t e C a rl o calculations confirm the a p p r o x i m a t e m a g n i t u d e o f the amplificationS).

6. Results with the uranium calorimeter T o test this idea we replaced the central hexagon of plates in sections A, B, and C by uranium plates with the properties given in table 2. N o t e that this is depleted uranium, with a smaller a m o u n t o f 235U ( ~ 0 . 3 % ) than in natural uranium, although we believe the results are not sensitive to the a m o u n t o f 235U. Fo r the neutron energy spectrum width which we have to deal, the 238U is suitable, and the 235U is undesirably radioactive. O u r uranium is still s o m e w h a t radioactive and there is a pile-up, due to small unresolved pulses, which effectively increases the r.m.s. noise. This is sensitive to the shaping time and could be decreased substantially with a shorter shaping time. The effect is shown in table 2. We did not find this to be a limiting factor in the resolution. When hadrons are incident upon the detector we find that a greater fraction o f the energy is contained within the central section than i~ the case of the iron

79

CALORIMETERS FOR HADRON ENERGY MEASUREMENT

calorimeter, but still a certain fraction of the energy is deposited in the outer iron sections. The spatial distribution of the deposited energy is shown in table 5. Here the relation of charge to deposited energy is that appropriate for energy loss by ionization in the appropriate stack, according to the figures given in table 2. It is interesting to estimate the response that would be obtained if the calorimeter were made solely of uranium. The signal in the outer sections might then be different. Fortunately the correction is small, particularly at 5 GeV/c. From those data, ignoring the small contribution from the outer ring, we conclude that the hadron response in uranium compared to iron is greater than that given by the ionization energy loss calibration by a factor of about 1.4. Since we wish to be certain not to overstate the enhancement of the hadron response in uranium, we estimate the effect of replacing the outer ring by uranium by increasing the signal in iron by a factor of 1.24-0.2, which then includes 1.00 in the range of error. Using this correction, a comparison of the signals due to electrons and hadrons is shown in fig. 14. The charge deposited by electrons is all in the centre section. For the uranium calorimeter, the electron spectrum was taken at only one energy, 3 GeV. It had been established in the iron calorimeter that energies between 1.5 and 10 GeV gave a linear signal deposited in the calorimeter. It is seen that the hoped-for compensation has been very nearly achieved, and given the conservative correction for the outer ring it may be that an all-uranium calorimeter is slightly overcompensated. Fig. 17 shows the shape of the 10 GeV pion charge distribution. The resolution is also greatly improved, as expected. The charge-exchange-like shoulder also disappears, presumably because the hadron peak now sits at the same position. The sampling fluctuation was measured and is shown in fig. 11, to be compared with that in iron. The relative width of this fluctuation is now no longer

negligible compared to the reduced width of the total charge distribution. This makes it interesting to unfold this contribution from the total width since, at least in principle, the sampling fluctuation may be reduced further by using thinner plates. The result is shown in fig. 18, where interactions occurring in the second calorimeter section have been used to eliminate also the contribution of the albedo. Albedo is small, but itis seen to influence the resolution by comparing the resolution measured for different interaction points in fig. 13. it is interesting to speculate on the sources of the remaining fluctuation and total charge deposited in the calorimeter. It is clear that although we may have succeeded in compensating the nuclear fluctuation on the average, the correlation between the amplified signal and the unseen signal is not complete. Furthermore, the number of fissions is certainly finite and may represent an appreciable fluctuation. Indeed, if we simply take a Gaussian distribution for the contribution of the fission energy, appropriate to the average number of fissions, we may expect a fluctuation from this source of about 3% for 10 GeV hadrons. We must also expect some fluctuation from the few percent of insensitive volume in our detector. Altogether we must say that the observed resolution is not much greater than that one would calculate optimistically. 7. Conclusions

We have built a calorimeter in which contributions of different mechanisms to the energy resolution can be separately studied. We show that in a carefully made device, each of these can be made small relative to one, which we call the nuclear fluctuation, that LI : : ~ / L A

10

GeV/c

T:

1000 ~

Counts

. . . .

SAMPLING

U'4F:;L DED

500

-x

II L

:

0

10

_

20

,

33

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~\ 7h ,

~

50

60

'

,

,

=

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.

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Fig. 17. The distribution of charge deposited by 10 GeV/c pions in uranium,

Fig. 18. The distribution of signal due to 10GeV/c pions in uranium, with the sampling fluctuations unfolded.

80

('. W.

FABJAN

d o m i n a t e s the energy resolution in ordinary materials. We also show how the effect o f the nuclear fluctuations may be partially c o m p e n s a t e d by studying the spatial distribution o f the h a d r o n cascade. In addition, we suggest a new mechanism for c o m p e n s a t i n g this effect m o r e exactly, the amplifying effect o f nuclear fission in uranium. M e a s u r e m e n t s on a uranium c a l o r i m e t er verify this c o m p e n s a t i o n and the considerable improvement in resolution it affords. O u r measurements show that a cal o r i m et er which gives good energy resolution in the region 5-10 G e V can be made. The resolution seems to i m p r o v e with increasing energy, as might be expected once the systematic nuclear fluctuation is removed, and if we extrapolate according to the square root of the energy we expect very good resolutions at higher energies. We are indebted to K. Ratz for his careful work in m o u n t i n g the plates and to J. Lindsay, J . C . Berset, V. Radeka, and B. Smith for their original contributions to the electronics. We have benefited from the kind assistance o f D. T h o m a s and M. Curatti o f Westfield College, R. O r r o f the R u t h e r f o r d L a b o r a t o r y , T. Ericson and R. H o g u e o f B r o o k h a v e n L a b o r a t o r y , and K. Winter o f C E R N . Program assistance was provided by Y. Perrin. We thank R. Palmer o f B N L for help in o b t ai n i n g some o f the uranium, and

et al.

T . A . Gabriel o f O R N L for special nuclear cascade co m p u t at i o n s.

References ~) A recent conference report gives a wide selection of papers on this technique, including the preliminary version of these results: Proc. Calorimeter Workshop, Batavia, May 1975 (ed. M. Atac; FNAL, Batavia, 111., U.S.A., 1975). 2) W.J. Willis and V. Radeka, Nucl. Instr. and Meth. 120 (1974) 221. 3) C. W. Fabjan, W. Struczinski, W. J. Willis, C. Kourkoumelis, A. J. Lankford and P. Rehak. Phys. Lett. 60B (1975) 105. 4) T.A. Gabriel and K. Chandler, Part. Acc. 5 (1973) 161; Nucl. Instr. and Meth. 116 (1974) 333. See also: T.A. Gabriel, Proc. Calorimeter Workshop, Batavia, May 1975 (ed. M. Atac; FNAL, Batavia, II1., U.S.A., 1975) p. 13. -~) C. W. Fabjan et al., in preparation. 6) j. Fischer and S, lwata, private communication (1973). "7) L. Onsager, Phys. Rev. 54 (1938) 554. s) E. B. Hughes et al., Nucl. Instr. and Meth. 75 (1969) 130. ~) T. A. Gabriel, private communication. ~o) W.A. Gibson, A. Zucker, R. E. Green, E. E. Gross, J. S. Fraser, J. W. Hilborn and J. C. D. Milton, in Electronuclear Division Annual Progress Report For Period Ending December 31, 1965 (ORNL-3940) (Oak Ridge National Lab., Tenn., May 1966) p. I10; L. R. Veeser, R. R. Fullwood, A. A. Robba and E. R. Shunk, Nucl. Instr. and Meth. 117 (1974) 509. ~) Fast neutron physics (eds. J. B. Marion and J. k, Fowler; Interscience Publ., New York, 1960) ch. 5. J2) M. F. James, AEEW-M863 (1969); W. H. Walker, AECL3109 (1968).