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A scintillation counter hodoscope for low energy light ions
NUCLEAR
INSTRUMENTS
AND
METHODS
I41
(~977)
263-272;
CC~ N O R T H - H O L L A N D
PUBLISHING
CO.
A S C I N T I L L A T I O N COUNTER H O D O S C O P E FOR LOW ENERGY L I G H T IONS* J . V . G E A G A , G . J . IGO, J. B. M c C L E L L A N D , M . A . NASSER, S. SANDER**, H, S P I N K A t . D. A. T R E A D W A Y ti"
Physics Department, UniversiO, of CaliJbrnia, Los Angeles, Cal~[brnia 90024, U.S.A. J. B. CARROLL§, D. FREDR1CKSON§§, V. P E R E Z - M E N D E Z and E . T . B . W H I P P L E
Lawrence Berkeley Laboratory, Berkeley, CaliJbrnia 94720, U.S,A. Received 9 November 1976 A 10-counter plastic scintillator hodoscope to measure pulse height, timing and position is described. The spatial, timing and pulse height resolutions were measured in a number of tests, and the mass resolution is discussed. The spatial resolution using the time-difference technique (0.7 cm fwhm for 100 MeV ~-partic[es) is roughly a factor of 1.8 better than the resolution using the ratio-of-pulse-height method for these counters.
1. Introduction
Studies of proton-nucleus elastic scattering have recently been extended into the region above 2 GeV/c. Below this region, the differential cross sections are usually measured by observing the scattered proton in a conventional magnetic spectrometer or by observing the recoil nucleus in a solid state counter telescope. At higher momenta, a high resolution spectrometer or a solid state counter telescope with good angular resolution (and thus poor solid angle) are required in order to reject inelastic events. An alternate method is to use a "low resolution'" spectrometer to obtain the momentum and angle of the scattered proton and a detector for the recoil nucleus. This last approach was chosen for measurements of p + 4 H e elastic scattering up to 5.75 GeV/c at the Lawrence Berkeley Laboratory Bevatron. The magnetic spectrometer has an angular resolution of better than 2 mrad (standard deviation) and a momentum resolution of 0.7% fwhm (full width at half maximum). This is not small enough to resolve elastic events. The recoiling light nuclei are detected in a 10-element *
Work supported in part by the United States Energy Research and Development Administration. ** Present address: Department of Environmental Health Engineering, California Institute of Technology, Pasadena, California 91109, U,S.A. ? Present address: High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. t ? Present address: Hughes Aircraft Company, El Segundo, California 90245, U.S.A. § Present address: Department of Physics, University of California, Los Angeles, California 90024, U.S.A. §§ Present address: Stanford Medical Center, Stanford, California, U.S.A.
scintillator hodoscope, which is the subject of this paper. The energy deposited in the hodoscope ranges from a few MeV to about 100 MeV. Using a reference time derived from a scintillator in the spectrometer, and assuming that the events originate at the target (a 6.3 mm thick copper collimator was used), the energy, scattering angle and mass of the recoil particles can be computed. A comparison of the recoil angles from the hodoscope and the forward angles from the magnetic spectrometer (tests of coplanarity and opening-angle) is very helpful in identifying elastic events. In order to be able to reject inelastic events during the data analysis, it is important to achieve the best possible timing, pulse height and spatial resolutions from the hodoscope scintillators. The performance of the hodoscope is described in this article. Section 2 gives details of the hodoscope construction. Next, two methods of measuring the position along the scintillators are discussed, the first using pulse heights (section 3) and the second using timing (section 4). Results for measurements of timing, pulse height and spatial resolutions are given in section 5. Section 6 contains a discussion of the mass resolution of the hodoscope and the conclusions. The construction of the hodoscope is shown in fig. 1. One coordinate of a particle's position in the hodoscope is given by which hodoscope element was struck by the particle. The orthogonal coordinate (position along the scintillator) can be obtained from the pulse heights measured in the photomultipliers at the two ends of the counter, as recently described by Arens et al.l'2). The ratio of pulse heights should depend only on position and not on the energy deposited in the scintillator, In addition, the pulse height
264
J.v. GEAGA et al.
resolution for such a detector is improved because independent measurements of the pulse heights can be made with the two phototubes. A position-dependent correction to these pulse heights improves the pulse height resolution even more, especially for large scintillators (for example, see refs. 3-8). An alternate method of obtaining the position along the scintillator is to measure the difference in the time of arrival of the light at the two ends of the counter. The time-difference technique was first discussed by Charpak et al.9), who achieved a spatial resolution of 5 cm fwhm for a collimated 9°St source. Charpak et al. also noted that the sum of the arrival times at the two phototubes on the ends of the detector is approximately independent of position along the scintillator. Thus the timing resolution for this type of detector is better than that of a scintillator with a single phototube, for which the timing depends on position. They also pointed out that summing the light output from the two phototubes (after properly adjusting the gains) gives a pulse height response more nearly independent of position than the output from either phototube alone. The time-difference technique of Charpak et al. was subsequently used by a number of groups (for example, see refs. 10-13). The scintillators were usually used to detect neutrons, and the quoted spatial resolution was the same as ref. 9 within about a factor of two. Improvements in the timing resolution with the use of two photomultipliers per scintillator were noted in refs. 3, 12, 14, 15. A significant improvement in the spatial resolution obtained from the time-difference technique was observed by Bollini et a1.16). They found that the spatial resolution was a function of the distance between phototubes. As the distance increases, the number of photons reaching the photomultiplier cathodes decreases, and the spatial resolution is poorer. A resolution of 0.35 cm fwhm was achieved with a 540 MeV proton beam incident on a counter of length 8 cm, height 2 era, and thickness 3 cm along the beam coupled directly to the phototubes. Bollini et al. also found better spatial resolution (but poorer timing resolution) with leading-edge discriminators than with zero-crossing discriminators. They explained this result in terms of light attenuation in the scintillator and timing walk in the leading-edge discriminators (see section 5). 2. Hodoscope construction and tests
The NE 102A scintillator used for the detectors was cut and polished by the manufacturer (Nuclear
Enterprises, Inc., San Carlos, California). The scintillator dimensions of 0.63 x 5.1 × 38 cm 3 were chosen for the elastic scattering experiments. Two pieces of ultraviolet transmitting lucite are epoxied together to form the light guide. One piece (0.63 x 5.1 x 10cm J) is epoxied directly to the scintillator and the other is a 5.1 cm diameter by 13 cm long lucite cylinder. An air gap of about 1-2 mm is present between the light guide and phototube, though a glue joint between them might improve the pulse height and timing resolutions. The scintillator and light guide are wrapped in a single layer of 25 pm of aluminum foil. The foil is covered with black masking tape except on the side of the detector that faces the experimental target. All tests were conducted with the particles entering the scintillator through the aluminum foil. RCA 8575 phototubes are used since they were found to give better spatial resolution using the time-difference method than other tubes tested (RCA 6810 and Amperex 56 DVP photomultipliers). The phototubes are wrapped in copper foil, which is maintained at the photocathode potential (about 2000-2400 V), then in mylar foil, and finally in magnetic shielding. The copper extends about 5 cm beyond the photocathode and it is insulated from both the lucite light guide and the aluminum foil wrapping. The hodoscope was designed to accept a wide range of pulse heights, from those produced by minimum ionizing protons up to those from alpha particles with an energy loss of about 100 MeV. Each phototube is operated with enough gain so that the anode pulses from the minimum ionizing particles trigger the
g.-----
!':
z
Fig. I. Diagram of the scintillator hodoscope,
SCINTILLATION
~']'~ ~
LTTOc H-.¢.~-~'~"~ ~r ANODE
COUNTER
HODOSCOPE
265
TO ANODE_ PMR,I~DYNODE r ~. . . . f "--'PLATCH PMR,2~ l ~ ~ _ _
PM''I PML,2[
"~ (TL)
TO LATCH
lU'~l -~ANODE |PML'IO[ f
---,!,.JDYNODE
PMRIIO ANODE "
r ' ~
~Ul::;uJ
TO LATCH
TRIGGERSCINT. TO
T-O TDC TDC STOP START Fig. 2. Schematic of the electronics used during tests of the hodoscope. Charge sensitive A D C s were employed. The T D C was actually an Ortec time-to-amplitude converter and an ADC. The latch (coincidence register), A D C and T D C information was collected by a C A M A C system and was stored on magnetic tape. Later it was analyzed as described in the text.
discriminators (the pulses are about 0.2 V). In order to avoid saturation effects in the last stages of the photomultiplier, the analog information is taken from the 11 th dynode. The response has been tested to be linear over the desired dynamic range in pulse height of about 100. The hodoscope electronics is shown in fig. 2. Chronetics 101 discriminators with leading-edge timing are used. This scheme requires substantially less equipment than if each hodoscope element has its own time-todigital converter (TDC) and two analog-to-digital converters (ADC) though the latter scheme would be necessary at high count rates. In addition to the leftright time difference, the left and right arrival times are measured relative to one of the magnetic spectrometer scintillators for the elastic scattering experiment. The hodoscope was tested with a I°6Ru source and with beams of 120MeV aHe, 120MeV 4He, and 50 MeV protons from the Lawrence Berkeley Laboratory 88" cyclotron. A I ° 6 R u fl-source (endpoint energy 3.5 MeV) was used to measure the pulse height and timing response as a function of position along the scintillator. A trigger scintillator was placed behind the hodoscope counters to insure that the fl-particles counted were nearly minimum ionizing when passing through the scintillators. With this coincidence requirement a peak could be observed in the pulse height distribution from the l°6Ru source. For one test with the 120 MeV alpha beam there was no trigger counter: only a left-right coincidence was
required. In all other tests with the cyclotron beams, a trigger scintillator was used to define the position of the beam particles entering the hodoscope. The main purpose of the cyclotron tests was to measure the light output as a function of energy for proton, 3He and alpha beams. A series of aluminum sheets were inserted into the beam upstream of the hodoscope to degrade the beam energy. The beam intensity was about 103-104 particles per second. The results for one counter are given in fig. 3. The energies have been corrected for losses in the beam pipe exit window, degraders, air, trigger scintillator, and aluminum foil on the hodoscope counters. A number of different energy loss tabulations were used to determine the degraded beam energy (refs. 17-19). A correction for the nonlinearity of the analog-todigital converters was applied; it affected only the largest pulse heights. The error bars in fig. 3 reflect uncertainties in the nonlinearity correction, the pulse height, the degrader thicknesses, and the energy loss calculations. A number of other tests were performed, mainly with the alpha beam. These include the variation of pulse height and timing with position, and the dependence of the spatial, timing, and pulse height resolutions upon the amount of light emitted in the scintillator. The use of degraders allowed the data to be collected rapidly and without changes to the cyclotron or beam line operating conditions. However, the degraders introduced multiple scattering and energy
266
J.v.
G E A G A el al.
straggling to the beam particles, which affected the resolution measurements. These are discussed further in section 5.
3. Position from pulse heights As a simple model o f a scintillation counter with a phototube at each end, assume that measurements are made o f the pulse height frorn each photomultiplier (PH u, PH R these are actually assumed to be pulse areas, because charge sensitive A D C ' s were used in the measurements described) and o f the time o f arrival of each pulse relative to some reference time (T u, Tr). Light attenuation in the light guide and scintillator will be assumed purely exponential. Let x be the distance along the scintillator from the center of the counter (see fig. 4). Then the pulse heights are
200
PHL = GILo e x p [ - (s+x)/D],
(I)
PH R = GRL o e x p [ - ( s - x ) / D ] ,
(2)
where L 0 is the light produced in the scintillator by the charged particle, GL and G R are the photomultiplier gains, 2s is the scintillator length, and D is the light attenuation distance. Fig. 5a gives light attenuation curves measured for four o f the hodoscope counters using a I°6Ru source. As can be seen, the light attenuation curves are not truly exponential. However, an exponential was fitted to the data from each o f the ten counters. The average value of D from the ten fits is about 8 0 c m with a standard deviation o f 31%. This variation is present even though the NE 102A scintillators were all purchased and polished at the same time, and the counter construction techniques were identical for all counters. Combining the two eqs. (1) and (2) above, one obtains x
= ~ D In(PHR/PHL) + C I ,
Lo = C2 ,((PHR' PHL) = C2 PHLR,
(3) (4)
where C~ and C2 are constants independent of the light Lo or the position x. Figs. 5b and 5c give plots o f In(PHR/PHL) and PHLR as a function o f x, the position along the scintillator. A l ° 6 R u fi-source was used to obtain these results. Differences from the expected behavior result from the fact that the light attenuation curves are not purely exponential. The value of PHLR is essentially independent of x. For any particular counter, the standard deviation from a constant value is about 5%. With C~ and D in eq. (3) chosen to fit the ~°°Ru data for a particular counter, the error in the position given by eq. (3) is less than _+ I cm except at
150
I00
5O -4, 3He
~P
F I
I,
I
I
40 80 Kinetic energy (MeV)
I
I
120
Fig. 3. Energy response of the NE 102A scintillator (counter ,,,6) to various energy particles. The beam energy was varied by introducing degraders. The energy uncertainties result from differences between various energy loss tabulations and uncertainties in the thickness o f various material in the beam line. Corrections to the pulse height were introduced for a slight A D C nonlinearity at large pulse heights. The particles with a range equal to the scintillator thickness have energies of 25 MeV for protons, 90 MeV for SHe and 103 MeV for alphas.
/ Fig. 4. Diagram of one hodoscope counter with the coordinates used ill this article. Both the timing (TL, TR) and the pulse area (or pulse height PHI PHR) are measured.
SCINTILLATION
COUNTER HOI)OSCOPE
the ends of the scintillator. M o r e accurate values o f the position x and the light L o for each event can be obtained from the individual curves for each c o u n t e r such as those in figs. 5b and 5c. Finally, pulse heights for particles o f various energies were measured for each o f the ten h o d o s c o p e elements. These particles were l ° 6 R u fi-particles that passed completely t h r o u g h the h o d o s c o p e , 44 and 1 0 7 M e V SHe, 28 and 1 0 3 M e V alphas, and 4 7 M e V p r o t o n s (energies are given at the front surface of the scintillator). The values o f the quantity PHLR were c o m p a r e d to reduce the d e p e n d e n c e o f the results on the position along the counter, since the runs at the 88" cyclotron with the different beams were made over
1.2
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I
--'----°~-~°~o~o~
A second procedure for o b t a i n i n g the position in the scintillator is to use the difference in time o f arrival of the light at the two ends o f the counter. A s s u m i n g a constant velocity v o f light in the scintillator, then
o 0.6 + °o"-"2"--.-_..
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T e = 7~ + ( s + x ) / c , ,
(5)
IR = ~1~.+ (S-- X)/t~ ,
t6)
where T,, is the time o f arrival o f the particle in the counter. F o r simplicity, constants to take into account p h o t o t u b e transit times, cable lengths, and delays in the electronics have been omitted. Therefore, ( T e + TR) is independent o f the position x, and the time difference is linear in x with an a p p a r e n t velocity o f ½ c.
Cour,ter No. 6
a: I.Zl
a period o f several weeks, and there was no simple way to guarantee that the beam always entered the hodoscope at the same place. It was found that the pulse heights for a given particle type and energy were the same for all counters (within a gain factor for each counter) to _+ 5%. The observed differences could be caused by many factors, such as p h o t o m u l t i p l i e r gain changes with time, uncertainties in locating the peak in the pulse height distributions, changes in the location of the various beams as they entered the scintillators, etc. A n y additional effects caused by intrinsic differences in the response of the ten counters to the various energy particles are at most a few percent, even though there are large variations in other properties o f the counters, such as the light a t t e n u a t i o n curves. Therefore, for the elastic scattering experiment we assumed that all the h o d o s c o p e counters respond in the same way to a given type o f particle at a certain energy (experimentally verified to +_ 5%). 4. P o s i t i o n f r o m timing
No.5
c
=, % 0.4 5
267
7[+TR = 2(Z,+s/v),
(7)
L
x/(7[-
T~) = ½c.
(8)
Counter No,6
'
6
'
IOcm
vl
Position (x)
Fig. 5. (a) Variation of pulse height in one phototube as a function of position x along the scintillator for several hodoscope cotlnters. Note the departures from purely exponential light attenuation. (b) Plot of the logarithm of the pulse height ratio as a function of position x for counter ,6. (c) Change in PHLR = \.. (PHL" PHR) with position v. If the light attenuation were purely logarithmic, this quantity would be constant along the scintillator. Betaparticles from a ~°6Ru source were used for all the data shown.
t
Fig. 6. The assumed pulse shape from the photomultipliers for the simple model described in the text. Vo is the maximum amplitude of the pulse and Vt is the threshold for the leadingedge discriminators.
268
J.V.
GEAGA
When leading-edge discriminators are used, the above equations are modified. To illustrate the effect, phototube pulses will be assumed to have a linear rise for t - To < r (see fig. 6)
et al.
TABLE [ O b s e r v e d effective v e l o c i t i e s for different particles.
I'crf(cm/ns) Particle
V -
KLL~° ( t - T o )
exp[-(s+x)/D].
The value of Lo is the light emitted in the scintillator, KL is the gain constant for the left phototube (K L :t: Ge because K L corresponds to the pulse amplitude and GL corresponds to the pulse area), To is the time referred to before as TL, and the exponential term accounts for light attenuation. A similar equation applies for the right photomultiplier (To = TR in this case). Equating the voltage V with the threshold voltage Vt on the leading-edge discriminators ( V J K is taken to be the same for all phototubes and their discriminators) and solving for the time t = tL (tR) when the discriminator triggers, then in the limit x <~ D te + t R ~ 2Z, + const.,
(Io)
x / ( t e - - t R ) ~ I~ +
(ll)
2 E z'- e x p ( s / ) D 1 -I = v~fr. KLoD
The effective velocity Xeer is even slower than ½ t, and it is dependent on L0. In reality, the photomultiplier pulse does not have a perfectly linear rise, the phototube gains and the discriminator thresholds are different, and x can be comparable to D. However, the overall features of the model above are experimentally verified. Fig. 7 shows that the measured time difference (te--tR) is linear in i
i
i
i
i
1
/ o/°/
Counler NO5 -
///
/'0"
// /// I
,/ I
-I0
I
I
0
I
I
Counter 6
6.9=t=0.3 6,3 4,7
6.6=1=0.3 6.3 4.7
(9)
"C
i
Counter 5
I
IOcm
Position (x) Fig. 7. Variation o f the time differences tL--¢R for one h o d o s c o p e c o u n t e r as a function o f position x along the scintillator using l°6Ru fl-particles,
105 MeV "*He 32 MeV '~He ~°6Ru ,B-particles
position x using l°6Ru /3-particles [ V t / ( K L o ) ~ ] . The average effective velocity for the ten hodoscope scintillators was about 4.8 cm/ns with a standard deviation of 12% for the l°6Ru/3-particles. Also, it was found that l,~ increases with D, which qualitatively agrees with the simple model. A serious problem with the time-difference technique is that t:eff changes with pulse height (see table I). The effective velocity decreased by a few percent as the incident alpha energy changed from 105 to 32 MeV and decreased by a factor of 1.4 from I05 MeV alphas to the 106Ru/~-particles. The change in t'efr becomes largest for small pulses [ V t / ( K L o ) ~ I]. The results in table 1 are in fair agreement with eq. (1 I ). It should be observed that the two methods of determining position the time-difference and the ratio-of-pulse-height techniques-are not completely independent since both are influenced by the pulse height. As an example of the correlation between them, consider the case of a series of particles all entering the scintillator at the same position x0 and depositing the same energy. Statistical effects will cause variations in the observed pulse heights PHL and PHR. Both methods of measuring the position would reconstruct events with large PHL and small PHR to the left of the true x0, and events with small PHL and large PHR to the right of the true Xo.
5. Pulse height, timing, and spatial resolutions The resolution ~eH of the position corrected pulse height PHLR was investigated with the I°6Ru source and with the cyclotron beams. The value of apH/PHL~ observed for the l°6Ru fl-particles is consistent with that expected from the Landau-Symon distribution of energy losses in the scintillator2°). The observed pulse height resolutions for all the cyclotron data taken with the aluminum degraders are consistent with energy straggling (see refs. 21, 22) and thickness variations in the degraders. For the cyclotron data taken without the degraders, the beams passed completely through the hodoscope scintillators, Energy straggling in the
SCINTILLATION COUNTER HODOSCOPE scintillator was estimated to be a substantial part o f the observed aeH for these particles, with the exception of the 103 MeV alphas which had very little energy left after passing through the hodoscope. The resolution of the pulse height PHL~ for the 103 MeV alphas, corrected for A D C nonlinearities but not for energy straggling, was (3.3-1-0.5)% fwhm. Tests were made of the pulse height resolutions for PHLR as a function of position along the scintillator. The resolution ~pH/PHLR was larger by a factor o f about 1.15 at the ends than in the center o f the hodoscope counters or 105 MeV alphas. The observed resolution was independent of position to within +_6% for 106Ru/?-particles for 32 MeV alphas; however, apH was 3000
I
]
[
I
I
105 MeV c~-porticles 200{
8
:"
x:-15,2cm
x=-7.6
x=O'
x=7
x=15.2
IOOC
TOo
-
-120
•
-
ae~
--- 140
,
LL-
i~o
]6o-
tL-t R (chonnels)
° lI LL
1.0
Time-diff. ~ u e
I
4
E O.4 5
§ 0.2
o
F
5 0.5
o rO6Ru /~-porlicles × 4He (no correction I ; I() 20 40 I00 Pulse height ( ~ )
I 200
400
Fig. 8. (a) Variation of the time difference with position along the counter using 105 MeV alphas incident on the scintillator. One channel corresponds to about 0.075 ns. (b) Spatial and timing resolution for the time-difference technique as a function of pulse height. All points are corrected for the beam spot size with the exception of some 4He data which was taken with a small trigger scintillator. The line drawn (~7~,TOyoc PH-°'6) is a guide to the eye only. The t°6Ru fl-particle point corresponds to o-.. =5.2 cm but or = 1.10 ns as described in the text, T O Y
269
dominated by energy straggling effects for these particles. The improvement in the pulse height resolution obtained by the use of two phototubes can be illustrated with the 103 MeV alpha data from all ten hodoscope elements. For a small beam spot size, the average value of O'pH/PHLR was (,3.3-t-0.5)% fwhm. The average value o f ~pHL/PHL and ~e,R/PHR for a single photomultiplier was (4.5+__0.7)% fwhm, roughly ~/'2 times larger. As the size of the beam spot increases, the resolution from a single photomultiplier deteriorates rapidly compared to the resolution of P H L g = \ / ( P H L . P H ~ ) from the two photomultiplier case. If the scintillator were uniformly illuminated, the approximate pulse height resolutions would be 15% fwhm (PHLR) and 45% fwhm (PHL or PHR only). The resolution ~rT of the time difference (t L - Q) for the hodoscope counters was investigated as a function of location in the counters (see fig. 8a) and pulse height. From section 4 [see eq. (11), for example] the timing resolution with leading-edge discriminators depends on (a) the pulse height resolution in each phototube, (b) the beam spot size and the effective velocity r~ff, (c) the intrinsic timing resolution o f the electronics, and (d) the light attenuation curve. The exact relationship depends on details of the pulse shape from the photomultipliers. There was a spread in the position x o f the particles entering the counters caused by the source collimation or the beam spot size. The spread in x affected the observed timing resolution, but there was a way to correct for it approximately. As noted in sections 3 and 4, the position along the counter can be estimated by two methods - the time-difference and the ratio-ofpulse-height techniques. Assuming they are independent (this will be demonstrated later), then the corrected crT can be obtained directly from a scatter plot of (tL--tR) versus ln(PHR/PHL). Both quantities are roughly linear in x, and the observed band or correlation in the scatter plot is caused by the spread in position of the particles. The corrected timing resolutions obtained in this manner are plotted in fig. 8b. The error bars reflect the uncertainty in determining the resolutions from the scatter plots. Note that all the points fall on the same curve within the error bars. The pulse height was taken as PHLg to reduce effects caused by different average positions for the different energy particles. The value of ~T was found to vary by less than about 10% with position in the counters for 105 and 32 MeV alphas incident on the hodoscope (see fig. 8a), but was roughly 20% worse at the ends than in the center for the 1°6Ru tq-particles.
270
J.v.
G E A G A et al.
For comparison, some data were collected with the alpha beam and a 0.95 cm diameter trigger scintillator 5 cm upstream of the hodoscope. Resolutions from these data are also plotted in fig. 8 b without corrections for a spread in position x. For 105 MeV alphas, a T = 0 . 1 6 n s f w h m = 2 . 1 c h a n n e l s . Note that these uncorrected results lie close to the corrected data. This gives an indication that the correction was properly performed. Since ( / L - - / R ) is proportional to position, o-T is related to the spatial resolution Ox,TOF obtained by the time-difference technique by O'xITO F z
/)effGT.
Therefore, the vertical scales of fig. 8b are labeled in terms of both a T and O'x,vO F. Note that the variation of v~ff over this range of pulse heights is only a few percent (see table I), except for the ~°6Ru /~-particles. That point is plotted at the appropriate value for ~r~,VOv (5.2 cm fwhm). The corresponding time resolution is O"T = 1.1 ns fwhm. The results of fig. 8b indicate that the timing and spatial resolutions improve as the amount of light reaching the photomultipliers increases. This conclusion agrees with the observations of Bollini et al.~6). They obtained the best spatial resolution for scintillators with a small distance between the phototubes and with larger thickness along the beam. Good spatial and timing resolutions can be achieved by depositing a large amount of energy in the scintillator (large L0) and/or by making the light guide and scintillator short (small s) so that there is little attenuation of the light. If events with a small range in the energy deposited or the light L0 are to be studied, the spatial resolution for these events can be improved by using leading-edge discriminators with the threshold set near the minimum pulse amplitude. This causes a timing walk, which in turn gives rise to a small effective velocity V~fr (or a large effective index of refraction hen. = c / G f r - ref, 16) as described in section 4. For example, if t%~r were constant for all the data in fig. 8b, the spatial resolution would have been worse for the ~°6Ru ,B-particles than shown. The slower effective velocity for the data with small PHLR gave an improvement in ~r,.TOv. Another example is the comparison of tests 8 and 9 in ref. 16 using leading-edge and zero-crossing discriminators. The slower effective velocity v¢~ more than compensated for the poorer timing resolution with leadingedge discriminators. Therefore, the spatial resolution was better with leading-edge discriminators (with the
threshold set near the minimum pulse amplitude) than with zero-crossing discriminators. As mentioned before, the effects of noise or photostatistics in the two phototubes may influence both the timing and pulse height in such a way as to give an incorrect value of x. Thus they could give rise to a correlation in the ( t L - - t R ) versus In(PHR/PHL) scatter plot. However, noise or photostatistics probably do not significantly affect the data in fig. 8 b. First, the pulse heights are quite large, so the timing walk is negligible (ven'~½ v) and thus the timing should be nearly independent of photostatistics. Second, the noise pulses were very small, and noise in the phototube anode circuit or in the discriminator need not correspond to noise in the dynode circuit in our setup. Third, the beam spot size estimated from the scatter plot agrees with the size expected from multiple scattering in the degraders and the trigger scintillator23). Finally, the uncorrected timing resolutions for the protons increase monotonically with the degrader thickness, while the pulse height first increases and then decreases (see fig. 3). This behavior would not be expected, unless the beam spot size dominated the observed correlation in the scatter plot. The resolution ¢7~ of the time of flight or time of arrival T,, was not directly measured. In the case of the elastic scattering experiment for which the hodoscope was designed, the starting or reference time for T~, is
20
Rofio of pulse heiqhl lechniqu_e
LL
.2co
'~ 1°6Ru /~-parlicles I
I
I0
20
I
I
40 I00 Pulse heigN ( ~ )
I
200
400
Fig. 9. Spatial resolution from the ratio-of-pulse-height technique. All data are corrected for the beam spot size. For comparison, the line is the same as the one in fig. 8b. ax.pH iS roughly a factor of 1.8 larger than ¢7x.rot.
SCINTILLATION COUNTER HODOSCOPE taken from one o f the scintillators on the magnetic spectrometer. The value of aa is completely dominated by the timing resolution of this spectrometer scintillator except for very small pulse heights in the hodoscope. Information from the scatter plot of (t e - tR) versus In(PHR/PHL) also gives the spatial resolution ~,PH from the ratio-of-pulse-height technique. These values corrected for the beam spot size, are plotted in fig. 9. For comparison, a line representing the approximate values of ~x,VOV is also shown. It can be seen that the spatial resolution from the time-difference technique is about a factor of 1.8 better than a~,PH over the full range of pulse heights investigated.
6. Conclusions
The use of two photomultipliers on opposite ends of a scintillator gives improved pulse height and timing resolutions compared to the case of a scintillator with a single phototube. The timing and pulse height variations with position can be nearly eliminated with the information from the second phototube. The timing and pulse height resolutions are not constant, but are slightly poorer near the ends than near the center o f the hodoscope counters described. In addition to the improved pulse height and timing resolutions, the position of events can be measured by two nearly independent techniques. For the counters tested, the time-difference technique is roughly a factor of 1.8 better than the ratio-of-pulse-height method. On the other hand, (tL--tR) is pulse height dependent 400,
400
l
--
271
(timing walk) when leading-edge discriminators are used. This is not the case for the ratio PHR/PHL. Zero-crossing or constant-fraction discriminators can also be used for the time-difference technique. The variation of (tL--tR) with pulse amplitude is reduced, but the spatial resolution may be poorer. Significant differences in effective velocities and light attenuation curves were noted for the 10 hodoscope elements even though they were all "identical". In order to obtain the most complete information from these scintillators, the gain and relative timing of each phototube and the effective velocity and light attenuation curve of each counter must be measured. This poses a large job to calibrate the entire hodoscope. On the other hand, the relative pulse response of the counters to particles of different types and different energies seems to be the same within a few percent. Finally, the mass resolution can be estimated. It will be assumed that photostatistics dominates the pulse height resolution at all pulse heights of interest. The value of O'pH/PHLRwill be taken as 3.3% fwhm for a pulse height corresponding to 103 MeV alphas incident on the scintillators. The target to hodoscope distance for the elastic scattering experiment is 3 m. Assuming a resolution of 2 ns fwhm for the time of flight (T,) and assuming negligible matter between the target and hodoscope, then it should be possible to resolve 3He and ~He from 15 to 100 MeV. (The position resolution for these particles is roughly 0.7-4 cm fwhm and the mass resolution is less than 13% fwhm.) The scintillator hodoscope should also be able to resolve protons and deuterons from below 5 MeV up to 25 MeV. For
T-----
i
(bl
(o) (y) c
8
200
2oo
E Z
3He
~He
I o
I
Iooo
I
2000 3000 4000
Mass (MeV)
5000
iooo
2000
3o00
40O0
5000
Mass (MeV)
Fig. 10. Mass of the recoil particle calculated from the pulse height and time of flight measured by the hodoscope. These data were taken in a p+4He elastic scattering experiment at an incident proton momentum of 3.5 GeV/e. Arrows indicate the approximate positions of the 3He mass (see the text). Two different ranges of alpha energies are shown: (a) kinetic energy at the target = 20-40 MeV and at the surface of the hodoscope scintillators =6-34 MeV. (b) kinetic energy at the target = 50-80 MeV and at the surface of the hodoscope scintillators = 28-67 MeV.
272
J.v. GEAGA et al.
energies above the upper limits, the particles pass t h r o u g h the hodoscope counters and a range technique can be used to distinguish between the different types of particles. F o r energies below the lower limits, the pulse height resolution is too poor for good mass separation. Fig. 10 presents a plot of the recoil particle mass from the p + 4 H e elastic scattering experiment. Very weak cuts have been applied to the data. The energy calibration for alphas from fig. 3 was used to convert the observed pulse heights to a particle energy striking the hodoscope scintillator. These energies were then corrected, again a s s u m i n g that the particles were alphas, for energy losses in the material between the 4He target and the scintillators. The mass was calculated from the corrected energy and the time of flight. This procedure overestimates the masses of 3He's, tritons, deuterons, and protons because the wrong energy calibration (fig. 3) a n d incorrect energy losses are used for these particles. A n arrow in fig. 10 indicates the expected position of 3He. It can be seen that the mass resolution is sufficient to resolve aHe and 4He down to an energy of a b o u t 10 MeV at the surface of the scintillator. Note that the mass resolution improves at higher energies, primarily because of the improved pulse height resolution ap./PHLR. In addition, the spatial i n f o r m a t i o n from the hodoscope and angle i n f o r m a t i o n from the magnetic spectrometer permits the calculation of o p e n i n g angle and coplanarity for each event. These quantities are quite useful in separating the elastic and inelastic events. We would like to thank Drs. D. Hendrie, Y. Terrien, and J. M a h o n e y a n d the operating crew at the Lawrence Berkeley L a b o r a t o r y 88" cyclotron for their assistance with the accelerator, and P. Oillataguerre for his help with the design of the scintillator hodoscope. We also express our gratitude to Dr. A.L. Sagle for reading the manuscript.
References i) j. F. Arens, Nucl. instr, and Meth. 120 (1974) 275. 2) E. H. Rogers. J. F. Arens and H. Whiteside, Nuc[. Instr. and Meth. 121 (1974) 599. 3) N. Chirapatpimol, J.C. Fong, M.M. Gazzaly, G. lgo, A. D. Liberman, R. J. Ridge, S. L. Verbeck, C. A. Whitten, Jr., J. Arvieux and V. Perez-Mendez, Nucl. Instr. and Meth. 133 (1976) 475. 4) j. G. Asbury and F.J. Loeffler, Nucl. Instr. and Meth. 34 (1965) 284. 5) B. Gottschalk and S. L. Kannenberg, Nucl. Instr. and Meth. 81 (1970) 85. ~') P. K. F. Grieder, Nucl. Instr. and Meth. 55 (1967) 295. ~) I. Lehraus and P. Manhewson, Nucl. Instr. and Meth. 81 (1970) 85. s) T.W. Millar and J.V. Jovanovich, Nucl. Instr. and Meth. 104 (1972) 447. 9) G. Charpak, L. Dick and L. Feuvrais, Nucl. Instr. and Meth. 15 (1962) 323. ~o) D. Bollini, A. Buhler-Broglin, P. Dalpiaz, T. Massam, F, Navach, F. L. Navarria, M. A. Schneegans, F. Zetti and A. Zichichi, Nuovo Cimento 61A (1969) 125. ~) M. Elfield, E. L. Miller, N. W. Reay, N. R. Stanton, M.A. Abolins, M.T. Lin and K.W. Edwards, Nucl. Instr. and Meth. 100 (1972) 237. ~2) R. Sumner, Nucl. Instr. and Meth. 100 (1972) 371. ~3) A. N. Khrenov, S. V. Rikhvitsky and I. N. Semenyushkin, Nucl. Instr. and Meth. 123 (1975) 471. 14) L. Paoluzi and R. Visentin, Nucl. Instr. and Meth. 65 (1968) 345. 15) C. Ward, A. Berick, E. Tagliaferri and C. York, Nucl. Instr. and Meth. 30 (1964) 61. ~6) D. Bollini, P. Dalpiaz, P. L. Frabetti, T. Massam, F. Navach, F.L. Navarria, M.A. Schneegans and A. Zichichi, Nucl. Instr. and Meth. 81 (1970) 56. 17) j. F. Janni, U.S. Air Force Weapons Lab. Report AFWLTR-65-150 (1960). ~s) M. Rich and R. Madey, UCRL-2301 (1954). 19) C. F. Williamson, J.-P. Boujot and J. Picard, CEA-R 3042 (1966). 20) B. Rossi, High-energy particles (Prentice-Hall, New York, 1952) pp. 29-35. 2~) C. Tschalar, Nucl. Instr. and Meth. 61 (1968) 141. 22) C. Tschalar, Nucl. Instr. and Meth, 64 (1968) 237. 23) j. B. Marion and B. A. Zimmerman, Nucl. Instr. and Meth. 51 (1967) 93.
INSTRUMENTS
AND
METHODS
I41
(~977)
263-272;
CC~ N O R T H - H O L L A N D
PUBLISHING
CO.
A S C I N T I L L A T I O N COUNTER H O D O S C O P E FOR LOW ENERGY L I G H T IONS* J . V . G E A G A , G . J . IGO, J. B. M c C L E L L A N D , M . A . NASSER, S. SANDER**, H, S P I N K A t . D. A. T R E A D W A Y ti"
Physics Department, UniversiO, of CaliJbrnia, Los Angeles, Cal~[brnia 90024, U.S.A. J. B. CARROLL§, D. FREDR1CKSON§§, V. P E R E Z - M E N D E Z and E . T . B . W H I P P L E
Lawrence Berkeley Laboratory, Berkeley, CaliJbrnia 94720, U.S,A. Received 9 November 1976 A 10-counter plastic scintillator hodoscope to measure pulse height, timing and position is described. The spatial, timing and pulse height resolutions were measured in a number of tests, and the mass resolution is discussed. The spatial resolution using the time-difference technique (0.7 cm fwhm for 100 MeV ~-partic[es) is roughly a factor of 1.8 better than the resolution using the ratio-of-pulse-height method for these counters.
1. Introduction
Studies of proton-nucleus elastic scattering have recently been extended into the region above 2 GeV/c. Below this region, the differential cross sections are usually measured by observing the scattered proton in a conventional magnetic spectrometer or by observing the recoil nucleus in a solid state counter telescope. At higher momenta, a high resolution spectrometer or a solid state counter telescope with good angular resolution (and thus poor solid angle) are required in order to reject inelastic events. An alternate method is to use a "low resolution'" spectrometer to obtain the momentum and angle of the scattered proton and a detector for the recoil nucleus. This last approach was chosen for measurements of p + 4 H e elastic scattering up to 5.75 GeV/c at the Lawrence Berkeley Laboratory Bevatron. The magnetic spectrometer has an angular resolution of better than 2 mrad (standard deviation) and a momentum resolution of 0.7% fwhm (full width at half maximum). This is not small enough to resolve elastic events. The recoiling light nuclei are detected in a 10-element *
Work supported in part by the United States Energy Research and Development Administration. ** Present address: Department of Environmental Health Engineering, California Institute of Technology, Pasadena, California 91109, U,S.A. ? Present address: High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A. t ? Present address: Hughes Aircraft Company, El Segundo, California 90245, U.S.A. § Present address: Department of Physics, University of California, Los Angeles, California 90024, U.S.A. §§ Present address: Stanford Medical Center, Stanford, California, U.S.A.
scintillator hodoscope, which is the subject of this paper. The energy deposited in the hodoscope ranges from a few MeV to about 100 MeV. Using a reference time derived from a scintillator in the spectrometer, and assuming that the events originate at the target (a 6.3 mm thick copper collimator was used), the energy, scattering angle and mass of the recoil particles can be computed. A comparison of the recoil angles from the hodoscope and the forward angles from the magnetic spectrometer (tests of coplanarity and opening-angle) is very helpful in identifying elastic events. In order to be able to reject inelastic events during the data analysis, it is important to achieve the best possible timing, pulse height and spatial resolutions from the hodoscope scintillators. The performance of the hodoscope is described in this article. Section 2 gives details of the hodoscope construction. Next, two methods of measuring the position along the scintillators are discussed, the first using pulse heights (section 3) and the second using timing (section 4). Results for measurements of timing, pulse height and spatial resolutions are given in section 5. Section 6 contains a discussion of the mass resolution of the hodoscope and the conclusions. The construction of the hodoscope is shown in fig. 1. One coordinate of a particle's position in the hodoscope is given by which hodoscope element was struck by the particle. The orthogonal coordinate (position along the scintillator) can be obtained from the pulse heights measured in the photomultipliers at the two ends of the counter, as recently described by Arens et al.l'2). The ratio of pulse heights should depend only on position and not on the energy deposited in the scintillator, In addition, the pulse height
264
J.v. GEAGA et al.
resolution for such a detector is improved because independent measurements of the pulse heights can be made with the two phototubes. A position-dependent correction to these pulse heights improves the pulse height resolution even more, especially for large scintillators (for example, see refs. 3-8). An alternate method of obtaining the position along the scintillator is to measure the difference in the time of arrival of the light at the two ends of the counter. The time-difference technique was first discussed by Charpak et al.9), who achieved a spatial resolution of 5 cm fwhm for a collimated 9°St source. Charpak et al. also noted that the sum of the arrival times at the two phototubes on the ends of the detector is approximately independent of position along the scintillator. Thus the timing resolution for this type of detector is better than that of a scintillator with a single phototube, for which the timing depends on position. They also pointed out that summing the light output from the two phototubes (after properly adjusting the gains) gives a pulse height response more nearly independent of position than the output from either phototube alone. The time-difference technique of Charpak et al. was subsequently used by a number of groups (for example, see refs. 10-13). The scintillators were usually used to detect neutrons, and the quoted spatial resolution was the same as ref. 9 within about a factor of two. Improvements in the timing resolution with the use of two photomultipliers per scintillator were noted in refs. 3, 12, 14, 15. A significant improvement in the spatial resolution obtained from the time-difference technique was observed by Bollini et a1.16). They found that the spatial resolution was a function of the distance between phototubes. As the distance increases, the number of photons reaching the photomultiplier cathodes decreases, and the spatial resolution is poorer. A resolution of 0.35 cm fwhm was achieved with a 540 MeV proton beam incident on a counter of length 8 cm, height 2 era, and thickness 3 cm along the beam coupled directly to the phototubes. Bollini et al. also found better spatial resolution (but poorer timing resolution) with leading-edge discriminators than with zero-crossing discriminators. They explained this result in terms of light attenuation in the scintillator and timing walk in the leading-edge discriminators (see section 5). 2. Hodoscope construction and tests
The NE 102A scintillator used for the detectors was cut and polished by the manufacturer (Nuclear
Enterprises, Inc., San Carlos, California). The scintillator dimensions of 0.63 x 5.1 × 38 cm 3 were chosen for the elastic scattering experiments. Two pieces of ultraviolet transmitting lucite are epoxied together to form the light guide. One piece (0.63 x 5.1 x 10cm J) is epoxied directly to the scintillator and the other is a 5.1 cm diameter by 13 cm long lucite cylinder. An air gap of about 1-2 mm is present between the light guide and phototube, though a glue joint between them might improve the pulse height and timing resolutions. The scintillator and light guide are wrapped in a single layer of 25 pm of aluminum foil. The foil is covered with black masking tape except on the side of the detector that faces the experimental target. All tests were conducted with the particles entering the scintillator through the aluminum foil. RCA 8575 phototubes are used since they were found to give better spatial resolution using the time-difference method than other tubes tested (RCA 6810 and Amperex 56 DVP photomultipliers). The phototubes are wrapped in copper foil, which is maintained at the photocathode potential (about 2000-2400 V), then in mylar foil, and finally in magnetic shielding. The copper extends about 5 cm beyond the photocathode and it is insulated from both the lucite light guide and the aluminum foil wrapping. The hodoscope was designed to accept a wide range of pulse heights, from those produced by minimum ionizing protons up to those from alpha particles with an energy loss of about 100 MeV. Each phototube is operated with enough gain so that the anode pulses from the minimum ionizing particles trigger the
g.-----
!':
z
Fig. I. Diagram of the scintillator hodoscope,
SCINTILLATION
~']'~ ~
LTTOc H-.¢.~-~'~"~ ~r ANODE
COUNTER
HODOSCOPE
265
TO ANODE_ PMR,I~DYNODE r ~. . . . f "--'PLATCH PMR,2~ l ~ ~ _ _
PM''I PML,2[
"~ (TL)
TO LATCH
lU'~l -~ANODE |PML'IO[ f
---,!,.JDYNODE
PMRIIO ANODE "
r ' ~
~Ul::;uJ
TO LATCH
TRIGGERSCINT. TO
T-O TDC TDC STOP START Fig. 2. Schematic of the electronics used during tests of the hodoscope. Charge sensitive A D C s were employed. The T D C was actually an Ortec time-to-amplitude converter and an ADC. The latch (coincidence register), A D C and T D C information was collected by a C A M A C system and was stored on magnetic tape. Later it was analyzed as described in the text.
discriminators (the pulses are about 0.2 V). In order to avoid saturation effects in the last stages of the photomultiplier, the analog information is taken from the 11 th dynode. The response has been tested to be linear over the desired dynamic range in pulse height of about 100. The hodoscope electronics is shown in fig. 2. Chronetics 101 discriminators with leading-edge timing are used. This scheme requires substantially less equipment than if each hodoscope element has its own time-todigital converter (TDC) and two analog-to-digital converters (ADC) though the latter scheme would be necessary at high count rates. In addition to the leftright time difference, the left and right arrival times are measured relative to one of the magnetic spectrometer scintillators for the elastic scattering experiment. The hodoscope was tested with a I°6Ru source and with beams of 120MeV aHe, 120MeV 4He, and 50 MeV protons from the Lawrence Berkeley Laboratory 88" cyclotron. A I ° 6 R u fl-source (endpoint energy 3.5 MeV) was used to measure the pulse height and timing response as a function of position along the scintillator. A trigger scintillator was placed behind the hodoscope counters to insure that the fl-particles counted were nearly minimum ionizing when passing through the scintillators. With this coincidence requirement a peak could be observed in the pulse height distribution from the l°6Ru source. For one test with the 120 MeV alpha beam there was no trigger counter: only a left-right coincidence was
required. In all other tests with the cyclotron beams, a trigger scintillator was used to define the position of the beam particles entering the hodoscope. The main purpose of the cyclotron tests was to measure the light output as a function of energy for proton, 3He and alpha beams. A series of aluminum sheets were inserted into the beam upstream of the hodoscope to degrade the beam energy. The beam intensity was about 103-104 particles per second. The results for one counter are given in fig. 3. The energies have been corrected for losses in the beam pipe exit window, degraders, air, trigger scintillator, and aluminum foil on the hodoscope counters. A number of different energy loss tabulations were used to determine the degraded beam energy (refs. 17-19). A correction for the nonlinearity of the analog-todigital converters was applied; it affected only the largest pulse heights. The error bars in fig. 3 reflect uncertainties in the nonlinearity correction, the pulse height, the degrader thicknesses, and the energy loss calculations. A number of other tests were performed, mainly with the alpha beam. These include the variation of pulse height and timing with position, and the dependence of the spatial, timing, and pulse height resolutions upon the amount of light emitted in the scintillator. The use of degraders allowed the data to be collected rapidly and without changes to the cyclotron or beam line operating conditions. However, the degraders introduced multiple scattering and energy
266
J.v.
G E A G A el al.
straggling to the beam particles, which affected the resolution measurements. These are discussed further in section 5.
3. Position from pulse heights As a simple model o f a scintillation counter with a phototube at each end, assume that measurements are made o f the pulse height frorn each photomultiplier (PH u, PH R these are actually assumed to be pulse areas, because charge sensitive A D C ' s were used in the measurements described) and o f the time o f arrival of each pulse relative to some reference time (T u, Tr). Light attenuation in the light guide and scintillator will be assumed purely exponential. Let x be the distance along the scintillator from the center of the counter (see fig. 4). Then the pulse heights are
200
PHL = GILo e x p [ - (s+x)/D],
(I)
PH R = GRL o e x p [ - ( s - x ) / D ] ,
(2)
where L 0 is the light produced in the scintillator by the charged particle, GL and G R are the photomultiplier gains, 2s is the scintillator length, and D is the light attenuation distance. Fig. 5a gives light attenuation curves measured for four o f the hodoscope counters using a I°6Ru source. As can be seen, the light attenuation curves are not truly exponential. However, an exponential was fitted to the data from each o f the ten counters. The average value of D from the ten fits is about 8 0 c m with a standard deviation o f 31%. This variation is present even though the NE 102A scintillators were all purchased and polished at the same time, and the counter construction techniques were identical for all counters. Combining the two eqs. (1) and (2) above, one obtains x
= ~ D In(PHR/PHL) + C I ,
Lo = C2 ,((PHR' PHL) = C2 PHLR,
(3) (4)
where C~ and C2 are constants independent of the light Lo or the position x. Figs. 5b and 5c give plots o f In(PHR/PHL) and PHLR as a function o f x, the position along the scintillator. A l ° 6 R u fi-source was used to obtain these results. Differences from the expected behavior result from the fact that the light attenuation curves are not purely exponential. The value of PHLR is essentially independent of x. For any particular counter, the standard deviation from a constant value is about 5%. With C~ and D in eq. (3) chosen to fit the ~°°Ru data for a particular counter, the error in the position given by eq. (3) is less than _+ I cm except at
150
I00
5O -4, 3He
~P
F I
I,
I
I
40 80 Kinetic energy (MeV)
I
I
120
Fig. 3. Energy response of the NE 102A scintillator (counter ,,,6) to various energy particles. The beam energy was varied by introducing degraders. The energy uncertainties result from differences between various energy loss tabulations and uncertainties in the thickness o f various material in the beam line. Corrections to the pulse height were introduced for a slight A D C nonlinearity at large pulse heights. The particles with a range equal to the scintillator thickness have energies of 25 MeV for protons, 90 MeV for SHe and 103 MeV for alphas.
/ Fig. 4. Diagram of one hodoscope counter with the coordinates used ill this article. Both the timing (TL, TR) and the pulse area (or pulse height PHI PHR) are measured.
SCINTILLATION
COUNTER HOI)OSCOPE
the ends of the scintillator. M o r e accurate values o f the position x and the light L o for each event can be obtained from the individual curves for each c o u n t e r such as those in figs. 5b and 5c. Finally, pulse heights for particles o f various energies were measured for each o f the ten h o d o s c o p e elements. These particles were l ° 6 R u fi-particles that passed completely t h r o u g h the h o d o s c o p e , 44 and 1 0 7 M e V SHe, 28 and 1 0 3 M e V alphas, and 4 7 M e V p r o t o n s (energies are given at the front surface of the scintillator). The values o f the quantity PHLR were c o m p a r e d to reduce the d e p e n d e n c e o f the results on the position along the counter, since the runs at the 88" cyclotron with the different beams were made over
1.2
(28
I
--'----°~-~°~o~o~
A second procedure for o b t a i n i n g the position in the scintillator is to use the difference in time o f arrival of the light at the two ends o f the counter. A s s u m i n g a constant velocity v o f light in the scintillator, then
o 0.6 + °o"-"2"--.-_..
"to.6
0.2
°~
S C3_
°'%-..o....° ~o ~o
02 ][
i
IO
> 9
i
i
~
i
i
i
r
I
I
~
'
-,0
T e = 7~ + ( s + x ) / c , ,
(5)
IR = ~1~.+ (S-- X)/t~ ,
t6)
where T,, is the time o f arrival o f the particle in the counter. F o r simplicity, constants to take into account p h o t o t u b e transit times, cable lengths, and delays in the electronics have been omitted. Therefore, ( T e + TR) is independent o f the position x, and the time difference is linear in x with an a p p a r e n t velocity o f ½ c.
Cour,ter No. 6
a: I.Zl
a period o f several weeks, and there was no simple way to guarantee that the beam always entered the hodoscope at the same place. It was found that the pulse heights for a given particle type and energy were the same for all counters (within a gain factor for each counter) to _+ 5%. The observed differences could be caused by many factors, such as p h o t o m u l t i p l i e r gain changes with time, uncertainties in locating the peak in the pulse height distributions, changes in the location of the various beams as they entered the scintillators, etc. A n y additional effects caused by intrinsic differences in the response of the ten counters to the various energy particles are at most a few percent, even though there are large variations in other properties o f the counters, such as the light a t t e n u a t i o n curves. Therefore, for the elastic scattering experiment we assumed that all the h o d o s c o p e counters respond in the same way to a given type o f particle at a certain energy (experimentally verified to +_ 5%). 4. P o s i t i o n f r o m timing
No.5
c
=, % 0.4 5
267
7[+TR = 2(Z,+s/v),
(7)
L
x/(7[-
T~) = ½c.
(8)
Counter No,6
'
6
'
IOcm
vl
Position (x)
Fig. 5. (a) Variation of pulse height in one phototube as a function of position x along the scintillator for several hodoscope cotlnters. Note the departures from purely exponential light attenuation. (b) Plot of the logarithm of the pulse height ratio as a function of position x for counter ,6. (c) Change in PHLR = \.. (PHL" PHR) with position v. If the light attenuation were purely logarithmic, this quantity would be constant along the scintillator. Betaparticles from a ~°6Ru source were used for all the data shown.
t
Fig. 6. The assumed pulse shape from the photomultipliers for the simple model described in the text. Vo is the maximum amplitude of the pulse and Vt is the threshold for the leadingedge discriminators.
268
J.V.
GEAGA
When leading-edge discriminators are used, the above equations are modified. To illustrate the effect, phototube pulses will be assumed to have a linear rise for t - To < r (see fig. 6)
et al.
TABLE [ O b s e r v e d effective v e l o c i t i e s for different particles.
I'crf(cm/ns) Particle
V -
KLL~° ( t - T o )
exp[-(s+x)/D].
The value of Lo is the light emitted in the scintillator, KL is the gain constant for the left phototube (K L :t: Ge because K L corresponds to the pulse amplitude and GL corresponds to the pulse area), To is the time referred to before as TL, and the exponential term accounts for light attenuation. A similar equation applies for the right photomultiplier (To = TR in this case). Equating the voltage V with the threshold voltage Vt on the leading-edge discriminators ( V J K is taken to be the same for all phototubes and their discriminators) and solving for the time t = tL (tR) when the discriminator triggers, then in the limit x <~ D te + t R ~ 2Z, + const.,
(Io)
x / ( t e - - t R ) ~ I~ +
(ll)
2 E z'- e x p ( s / ) D 1 -I = v~fr. KLoD
The effective velocity Xeer is even slower than ½ t, and it is dependent on L0. In reality, the photomultiplier pulse does not have a perfectly linear rise, the phototube gains and the discriminator thresholds are different, and x can be comparable to D. However, the overall features of the model above are experimentally verified. Fig. 7 shows that the measured time difference (te--tR) is linear in i
i
i
i
i
1
/ o/°/
Counler NO5 -
///
/'0"
// /// I
,/ I
-I0
I
I
0
I
I
Counter 6
6.9=t=0.3 6,3 4,7
6.6=1=0.3 6.3 4.7
(9)
"C
i
Counter 5
I
IOcm
Position (x) Fig. 7. Variation o f the time differences tL--¢R for one h o d o s c o p e c o u n t e r as a function o f position x along the scintillator using l°6Ru fl-particles,
105 MeV "*He 32 MeV '~He ~°6Ru ,B-particles
position x using l°6Ru /3-particles [ V t / ( K L o ) ~ ] . The average effective velocity for the ten hodoscope scintillators was about 4.8 cm/ns with a standard deviation of 12% for the l°6Ru/3-particles. Also, it was found that l,~ increases with D, which qualitatively agrees with the simple model. A serious problem with the time-difference technique is that t:eff changes with pulse height (see table I). The effective velocity decreased by a few percent as the incident alpha energy changed from 105 to 32 MeV and decreased by a factor of 1.4 from I05 MeV alphas to the 106Ru/~-particles. The change in t'efr becomes largest for small pulses [ V t / ( K L o ) ~ I]. The results in table 1 are in fair agreement with eq. (1 I ). It should be observed that the two methods of determining position the time-difference and the ratio-of-pulse-height techniques-are not completely independent since both are influenced by the pulse height. As an example of the correlation between them, consider the case of a series of particles all entering the scintillator at the same position x0 and depositing the same energy. Statistical effects will cause variations in the observed pulse heights PHL and PHR. Both methods of measuring the position would reconstruct events with large PHL and small PHR to the left of the true x0, and events with small PHL and large PHR to the right of the true Xo.
5. Pulse height, timing, and spatial resolutions The resolution ~eH of the position corrected pulse height PHLR was investigated with the I°6Ru source and with the cyclotron beams. The value of apH/PHL~ observed for the l°6Ru fl-particles is consistent with that expected from the Landau-Symon distribution of energy losses in the scintillator2°). The observed pulse height resolutions for all the cyclotron data taken with the aluminum degraders are consistent with energy straggling (see refs. 21, 22) and thickness variations in the degraders. For the cyclotron data taken without the degraders, the beams passed completely through the hodoscope scintillators, Energy straggling in the
SCINTILLATION COUNTER HODOSCOPE scintillator was estimated to be a substantial part o f the observed aeH for these particles, with the exception of the 103 MeV alphas which had very little energy left after passing through the hodoscope. The resolution of the pulse height PHL~ for the 103 MeV alphas, corrected for A D C nonlinearities but not for energy straggling, was (3.3-1-0.5)% fwhm. Tests were made of the pulse height resolutions for PHLR as a function of position along the scintillator. The resolution ~pH/PHLR was larger by a factor o f about 1.15 at the ends than in the center o f the hodoscope counters or 105 MeV alphas. The observed resolution was independent of position to within +_6% for 106Ru/?-particles for 32 MeV alphas; however, apH was 3000
I
]
[
I
I
105 MeV c~-porticles 200{
8
:"
x:-15,2cm
x=-7.6
x=O'
x=7
x=15.2
IOOC
TOo
-
-120
•
-
ae~
--- 140
,
LL-
i~o
]6o-
tL-t R (chonnels)
° lI LL
1.0
Time-diff. ~ u e
I
4
E O.4 5
§ 0.2
o
F
5 0.5
o rO6Ru /~-porlicles × 4He (no correction I ; I() 20 40 I00 Pulse height ( ~ )
I 200
400
Fig. 8. (a) Variation of the time difference with position along the counter using 105 MeV alphas incident on the scintillator. One channel corresponds to about 0.075 ns. (b) Spatial and timing resolution for the time-difference technique as a function of pulse height. All points are corrected for the beam spot size with the exception of some 4He data which was taken with a small trigger scintillator. The line drawn (~7~,TOyoc PH-°'6) is a guide to the eye only. The t°6Ru fl-particle point corresponds to o-.. =5.2 cm but or = 1.10 ns as described in the text, T O Y
269
dominated by energy straggling effects for these particles. The improvement in the pulse height resolution obtained by the use of two phototubes can be illustrated with the 103 MeV alpha data from all ten hodoscope elements. For a small beam spot size, the average value of O'pH/PHLR was (,3.3-t-0.5)% fwhm. The average value o f ~pHL/PHL and ~e,R/PHR for a single photomultiplier was (4.5+__0.7)% fwhm, roughly ~/'2 times larger. As the size of the beam spot increases, the resolution from a single photomultiplier deteriorates rapidly compared to the resolution of P H L g = \ / ( P H L . P H ~ ) from the two photomultiplier case. If the scintillator were uniformly illuminated, the approximate pulse height resolutions would be 15% fwhm (PHLR) and 45% fwhm (PHL or PHR only). The resolution ~rT of the time difference (t L - Q) for the hodoscope counters was investigated as a function of location in the counters (see fig. 8a) and pulse height. From section 4 [see eq. (11), for example] the timing resolution with leading-edge discriminators depends on (a) the pulse height resolution in each phototube, (b) the beam spot size and the effective velocity r~ff, (c) the intrinsic timing resolution o f the electronics, and (d) the light attenuation curve. The exact relationship depends on details of the pulse shape from the photomultipliers. There was a spread in the position x o f the particles entering the counters caused by the source collimation or the beam spot size. The spread in x affected the observed timing resolution, but there was a way to correct for it approximately. As noted in sections 3 and 4, the position along the counter can be estimated by two methods - the time-difference and the ratio-ofpulse-height techniques. Assuming they are independent (this will be demonstrated later), then the corrected crT can be obtained directly from a scatter plot of (tL--tR) versus ln(PHR/PHL). Both quantities are roughly linear in x, and the observed band or correlation in the scatter plot is caused by the spread in position of the particles. The corrected timing resolutions obtained in this manner are plotted in fig. 8b. The error bars reflect the uncertainty in determining the resolutions from the scatter plots. Note that all the points fall on the same curve within the error bars. The pulse height was taken as PHLg to reduce effects caused by different average positions for the different energy particles. The value of ~T was found to vary by less than about 10% with position in the counters for 105 and 32 MeV alphas incident on the hodoscope (see fig. 8a), but was roughly 20% worse at the ends than in the center for the 1°6Ru tq-particles.
270
J.v.
G E A G A et al.
For comparison, some data were collected with the alpha beam and a 0.95 cm diameter trigger scintillator 5 cm upstream of the hodoscope. Resolutions from these data are also plotted in fig. 8 b without corrections for a spread in position x. For 105 MeV alphas, a T = 0 . 1 6 n s f w h m = 2 . 1 c h a n n e l s . Note that these uncorrected results lie close to the corrected data. This gives an indication that the correction was properly performed. Since ( / L - - / R ) is proportional to position, o-T is related to the spatial resolution Ox,TOF obtained by the time-difference technique by O'xITO F z
/)effGT.
Therefore, the vertical scales of fig. 8b are labeled in terms of both a T and O'x,vO F. Note that the variation of v~ff over this range of pulse heights is only a few percent (see table I), except for the ~°6Ru /~-particles. That point is plotted at the appropriate value for ~r~,VOv (5.2 cm fwhm). The corresponding time resolution is O"T = 1.1 ns fwhm. The results of fig. 8b indicate that the timing and spatial resolutions improve as the amount of light reaching the photomultipliers increases. This conclusion agrees with the observations of Bollini et al.~6). They obtained the best spatial resolution for scintillators with a small distance between the phototubes and with larger thickness along the beam. Good spatial and timing resolutions can be achieved by depositing a large amount of energy in the scintillator (large L0) and/or by making the light guide and scintillator short (small s) so that there is little attenuation of the light. If events with a small range in the energy deposited or the light L0 are to be studied, the spatial resolution for these events can be improved by using leading-edge discriminators with the threshold set near the minimum pulse amplitude. This causes a timing walk, which in turn gives rise to a small effective velocity V~fr (or a large effective index of refraction hen. = c / G f r - ref, 16) as described in section 4. For example, if t%~r were constant for all the data in fig. 8b, the spatial resolution would have been worse for the ~°6Ru ,B-particles than shown. The slower effective velocity for the data with small PHLR gave an improvement in ~r,.TOv. Another example is the comparison of tests 8 and 9 in ref. 16 using leading-edge and zero-crossing discriminators. The slower effective velocity v¢~ more than compensated for the poorer timing resolution with leadingedge discriminators. Therefore, the spatial resolution was better with leading-edge discriminators (with the
threshold set near the minimum pulse amplitude) than with zero-crossing discriminators. As mentioned before, the effects of noise or photostatistics in the two phototubes may influence both the timing and pulse height in such a way as to give an incorrect value of x. Thus they could give rise to a correlation in the ( t L - - t R ) versus In(PHR/PHL) scatter plot. However, noise or photostatistics probably do not significantly affect the data in fig. 8 b. First, the pulse heights are quite large, so the timing walk is negligible (ven'~½ v) and thus the timing should be nearly independent of photostatistics. Second, the noise pulses were very small, and noise in the phototube anode circuit or in the discriminator need not correspond to noise in the dynode circuit in our setup. Third, the beam spot size estimated from the scatter plot agrees with the size expected from multiple scattering in the degraders and the trigger scintillator23). Finally, the uncorrected timing resolutions for the protons increase monotonically with the degrader thickness, while the pulse height first increases and then decreases (see fig. 3). This behavior would not be expected, unless the beam spot size dominated the observed correlation in the scatter plot. The resolution ¢7~ of the time of flight or time of arrival T,, was not directly measured. In the case of the elastic scattering experiment for which the hodoscope was designed, the starting or reference time for T~, is
20
Rofio of pulse heiqhl lechniqu_e
LL
.2co
'~ 1°6Ru /~-parlicles I
I
I0
20
I
I
40 I00 Pulse heigN ( ~ )
I
200
400
Fig. 9. Spatial resolution from the ratio-of-pulse-height technique. All data are corrected for the beam spot size. For comparison, the line is the same as the one in fig. 8b. ax.pH iS roughly a factor of 1.8 larger than ¢7x.rot.
SCINTILLATION COUNTER HODOSCOPE taken from one o f the scintillators on the magnetic spectrometer. The value of aa is completely dominated by the timing resolution of this spectrometer scintillator except for very small pulse heights in the hodoscope. Information from the scatter plot of (t e - tR) versus In(PHR/PHL) also gives the spatial resolution ~,PH from the ratio-of-pulse-height technique. These values corrected for the beam spot size, are plotted in fig. 9. For comparison, a line representing the approximate values of ~x,VOV is also shown. It can be seen that the spatial resolution from the time-difference technique is about a factor of 1.8 better than a~,PH over the full range of pulse heights investigated.
6. Conclusions
The use of two photomultipliers on opposite ends of a scintillator gives improved pulse height and timing resolutions compared to the case of a scintillator with a single phototube. The timing and pulse height variations with position can be nearly eliminated with the information from the second phototube. The timing and pulse height resolutions are not constant, but are slightly poorer near the ends than near the center o f the hodoscope counters described. In addition to the improved pulse height and timing resolutions, the position of events can be measured by two nearly independent techniques. For the counters tested, the time-difference technique is roughly a factor of 1.8 better than the ratio-of-pulse-height method. On the other hand, (tL--tR) is pulse height dependent 400,
400
l
--
271
(timing walk) when leading-edge discriminators are used. This is not the case for the ratio PHR/PHL. Zero-crossing or constant-fraction discriminators can also be used for the time-difference technique. The variation of (tL--tR) with pulse amplitude is reduced, but the spatial resolution may be poorer. Significant differences in effective velocities and light attenuation curves were noted for the 10 hodoscope elements even though they were all "identical". In order to obtain the most complete information from these scintillators, the gain and relative timing of each phototube and the effective velocity and light attenuation curve of each counter must be measured. This poses a large job to calibrate the entire hodoscope. On the other hand, the relative pulse response of the counters to particles of different types and different energies seems to be the same within a few percent. Finally, the mass resolution can be estimated. It will be assumed that photostatistics dominates the pulse height resolution at all pulse heights of interest. The value of O'pH/PHLRwill be taken as 3.3% fwhm for a pulse height corresponding to 103 MeV alphas incident on the scintillators. The target to hodoscope distance for the elastic scattering experiment is 3 m. Assuming a resolution of 2 ns fwhm for the time of flight (T,) and assuming negligible matter between the target and hodoscope, then it should be possible to resolve 3He and ~He from 15 to 100 MeV. (The position resolution for these particles is roughly 0.7-4 cm fwhm and the mass resolution is less than 13% fwhm.) The scintillator hodoscope should also be able to resolve protons and deuterons from below 5 MeV up to 25 MeV. For
T-----
i
(bl
(o) (y) c
8
200
2oo
E Z
3He
~He
I o
I
Iooo
I
2000 3000 4000
Mass (MeV)
5000
iooo
2000
3o00
40O0
5000
Mass (MeV)
Fig. 10. Mass of the recoil particle calculated from the pulse height and time of flight measured by the hodoscope. These data were taken in a p+4He elastic scattering experiment at an incident proton momentum of 3.5 GeV/e. Arrows indicate the approximate positions of the 3He mass (see the text). Two different ranges of alpha energies are shown: (a) kinetic energy at the target = 20-40 MeV and at the surface of the hodoscope scintillators =6-34 MeV. (b) kinetic energy at the target = 50-80 MeV and at the surface of the hodoscope scintillators = 28-67 MeV.
272
J.v. GEAGA et al.
energies above the upper limits, the particles pass t h r o u g h the hodoscope counters and a range technique can be used to distinguish between the different types of particles. F o r energies below the lower limits, the pulse height resolution is too poor for good mass separation. Fig. 10 presents a plot of the recoil particle mass from the p + 4 H e elastic scattering experiment. Very weak cuts have been applied to the data. The energy calibration for alphas from fig. 3 was used to convert the observed pulse heights to a particle energy striking the hodoscope scintillator. These energies were then corrected, again a s s u m i n g that the particles were alphas, for energy losses in the material between the 4He target and the scintillators. The mass was calculated from the corrected energy and the time of flight. This procedure overestimates the masses of 3He's, tritons, deuterons, and protons because the wrong energy calibration (fig. 3) a n d incorrect energy losses are used for these particles. A n arrow in fig. 10 indicates the expected position of 3He. It can be seen that the mass resolution is sufficient to resolve aHe and 4He down to an energy of a b o u t 10 MeV at the surface of the scintillator. Note that the mass resolution improves at higher energies, primarily because of the improved pulse height resolution ap./PHLR. In addition, the spatial i n f o r m a t i o n from the hodoscope and angle i n f o r m a t i o n from the magnetic spectrometer permits the calculation of o p e n i n g angle and coplanarity for each event. These quantities are quite useful in separating the elastic and inelastic events. We would like to thank Drs. D. Hendrie, Y. Terrien, and J. M a h o n e y a n d the operating crew at the Lawrence Berkeley L a b o r a t o r y 88" cyclotron for their assistance with the accelerator, and P. Oillataguerre for his help with the design of the scintillator hodoscope. We also express our gratitude to Dr. A.L. Sagle for reading the manuscript.
References i) j. F. Arens, Nucl. instr, and Meth. 120 (1974) 275. 2) E. H. Rogers. J. F. Arens and H. Whiteside, Nuc[. Instr. and Meth. 121 (1974) 599. 3) N. Chirapatpimol, J.C. Fong, M.M. Gazzaly, G. lgo, A. D. Liberman, R. J. Ridge, S. L. Verbeck, C. A. Whitten, Jr., J. Arvieux and V. Perez-Mendez, Nucl. Instr. and Meth. 133 (1976) 475. 4) j. G. Asbury and F.J. Loeffler, Nucl. Instr. and Meth. 34 (1965) 284. 5) B. Gottschalk and S. L. Kannenberg, Nucl. Instr. and Meth. 81 (1970) 85. ~') P. K. F. Grieder, Nucl. Instr. and Meth. 55 (1967) 295. ~) I. Lehraus and P. Manhewson, Nucl. Instr. and Meth. 81 (1970) 85. s) T.W. Millar and J.V. Jovanovich, Nucl. Instr. and Meth. 104 (1972) 447. 9) G. Charpak, L. Dick and L. Feuvrais, Nucl. Instr. and Meth. 15 (1962) 323. ~o) D. Bollini, A. Buhler-Broglin, P. Dalpiaz, T. Massam, F, Navach, F. L. Navarria, M. A. Schneegans, F. Zetti and A. Zichichi, Nuovo Cimento 61A (1969) 125. ~) M. Elfield, E. L. Miller, N. W. Reay, N. R. Stanton, M.A. Abolins, M.T. Lin and K.W. Edwards, Nucl. Instr. and Meth. 100 (1972) 237. ~2) R. Sumner, Nucl. Instr. and Meth. 100 (1972) 371. ~3) A. N. Khrenov, S. V. Rikhvitsky and I. N. Semenyushkin, Nucl. Instr. and Meth. 123 (1975) 471. 14) L. Paoluzi and R. Visentin, Nucl. Instr. and Meth. 65 (1968) 345. 15) C. Ward, A. Berick, E. Tagliaferri and C. York, Nucl. Instr. and Meth. 30 (1964) 61. ~6) D. Bollini, P. Dalpiaz, P. L. Frabetti, T. Massam, F. Navach, F.L. Navarria, M.A. Schneegans and A. Zichichi, Nucl. Instr. and Meth. 81 (1970) 56. 17) j. F. Janni, U.S. Air Force Weapons Lab. Report AFWLTR-65-150 (1960). ~s) M. Rich and R. Madey, UCRL-2301 (1954). 19) C. F. Williamson, J.-P. Boujot and J. Picard, CEA-R 3042 (1966). 20) B. Rossi, High-energy particles (Prentice-Hall, New York, 1952) pp. 29-35. 2~) C. Tschalar, Nucl. Instr. and Meth. 61 (1968) 141. 22) C. Tschalar, Nucl. Instr. and Meth, 64 (1968) 237. 23) j. B. Marion and B. A. Zimmerman, Nucl. Instr. and Meth. 51 (1967) 93.