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Low energy protons as a tool for high energy vertex detector calibration
Nuclear Instruments and Methods in Physics Research A254 (1987) 327-332 North-Holland, Amsterdam
327
LOW ENERGY PROTONS AS A TOOL FOR HIGH ENERGY VERTEX DETECTOR CALIBRATION M. C A C C I A 1), L. C A S O L I 2)., p. G U A Z Z O N I 1,2), D. M A R I O L I 1,3), C. M E R O N I 1), N. R E D A E L L I 1,4), D. T O R R E T T A t) a n d G. V E G N I 1,2) *) lstituto Nazionale di Fisica Nucleate, Sezione di Milano, Italy 2) Dipartimento di Fisica dell'UniversittJ di Milano, Italy 3) Dipartimento A utomazione lndustriale, Universitd di Brescia, Italy 4) CERN, Geneva, Switzerland
Received 4 February 1986 and in revised form 25 June 1986 This paper describes a method developed for the calibration of silicon detectors used to measure high multiplicity of charged particles in high energy experiments; its peculiarity is the use of low energy protons from a cyclotron. This method guarantees an useful improvement in calibration accuracy. 1. Introduction In the following we will describe a calibration method that we have developed for the silicon vertex detector of the CERN WA71 experiment using low energy protons from a cyclotron. This method could be of general interest for application of silicon detectors in the high energy field. We remind that, in a high energy experiment, it is possible to deduce the number of fast charged particles (produced in interactions a n d / o r decays) that have crossed a silicon detector by measuring the ionization energy deposited in it. On the other hand, a low energy proton crossing a thin layer of silicon has an ionization energy deposition equivalent to that of many fast charged particles. Therefore using a setup which is much simpler than that normally required in high energy experiments (see sect. 3), information on the behaviour of detectors can be obtained, even if they have complex geometrical characteristics. The WA71 experiment at CERN has been designed to search for beauty particles and to measure their mean lifetime. The signature of the events to be selected is mainly given by a charge multiplicity difference (DT) measured between two sets of silicon detectors (" telescope" arrangement) called T1 and T2. These detectors consist respectively of three and ten 200 g m thick sheets, which are perpendicular to the beam direction. The charge multiplicity of interesting events lies in the range 10-25 minimum ionizing particles (m.i.p.) and the expected DT is about 2-5 m.i.p. The selected events have to be searched in a nuclear emulsion target [1]. The detector system and the signal processing electronics are described in refs. [2,3]. * Permanent adress: LABEN, Vimodrone, Milano, Italy. 0168-9002/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Optimization of the signal-to-noise ratio is a crucial point for a hybrid experiment with nuclear emulsion in which the search for the selected events is difficult and time-consuming. The background to the beauty-charm decay signal, i.e. an accidental charge multiplicity jump between T1 and T2, is mainly due to energy loss fluctuations in the silicon detectors. Another important contribution to the "false jump" background, however, comes from systematic errors in the overall silicon detector calibration. Energy loss fluctuations are theoretically predicted and experimentally well verified. Particular care has been taken, therefore, in studying ways of minimizing the other source of background, namely calibration errors. In the following we describe the results on this subject.
2. Experimental method The pulse-height/charge-multiplicity calibration of each silicon detector chain has been obtained a) directly by utilizing events of well known multiplicity (in m.i.p., minimum ionizing particles); b) in two steps: firstly by converting the measured pulse height into deposited energy and secondly this energy into m~i.p. It is in the first of these steps that we have established the advantage of using low energy protons. 2.1. Direct calibration
We have used the peak values (most probable energy loss) of the pulse height distributions for one particle (beam) and for 3 and 5 track events as selected by T R I D E N T (the program developed to reconstruct geometry and kinematics of events; see ref. [4]) among
328
M. Caccia et a L / Low energy protons for vertex detector calibration
calibration data taken at CERN during the experiment. Because of Trident's inefficiency the value of charge multiplicity has been assigned with a level of uncertainty that increases rapidly as a function of the real multiplicity. In fact, when we consider the experimental distribution of energy losses for a collection of events of multiplicity M (given by Trident) we have indeed a "contamination" from events in which the number of charged particles is not M. This inefficiency affects more seriously the high multiplicity (_> 10) distributions, making them not useful for calibrations. Instead, if we consider events with a low number of charged particles, the uncertainty on the assignment of multiplicity could affect the tail of the distribution (and thus the mean value) but not the peak region. On the other hand, the assignment of muliplicity for each event using silicon detector signals has to be made referring to the mean value of energy loss, which grows linearly with the number of particles unlike the most probable value (see sect. 2.2). For these reasons calibration using this method has become rather complex. After having collected events according to the assigned multiplicity (1 _< M < 5), we have determined the ADC channel corresponding to the peak of the distribution for each multiplicity. Then, according to the theoretical link between the most probable and the mean value of the distribution (see sect. 2.2), we have calculated the channel corresponding to the mean energy loss. This is the value to which we shall refer to attribute the multiplicity using signals from the silicon detector. After this it has been necessary to extrapolate the pulse height-m.i.p, relation obtained from the low multiplicity events up to the region of interest for our experiment (10-25 m.i.p.). Finally the difference between the mean energy loss and the mean deposited energy has to be taken into account. It is this last quantity that should be used for the assignement of a single event multiplicity. In this way each electronic chain has been calibrated in m.i.p, and from the mean values of T2 and T1 we obtain the multiplicity jump T2-T1. Using this method the overall estimated error which we attribute to the charge multiplicity of each telescope is about 5%. Since the calibrations of the two telescopes are independent, the relative error on T2-T1 is about ¢r~ × 5% = 7%. The expected mean multiplicity of "beauty events" is 15-20 charged particles, so the error on T2-T1 would be about 2 m.i.p, while the expected T2-T1 signal is in the range 2-5 m.i.p., i.e. a relative error about 100-40%.
error on the energy-m.i.p, conversion affects all the detectors in the same way. Consequently its error propagation on the T2-T1 signal is less important. For the pulse height-keV relation the injection of a known charge through a test capacity is generally used. These capacities should be quite small, of the order of a fraction of a picofarad. Consequently a precise measurement, which takes into account also parasitic effects and the different shapes of artificial and real detector signals, is difficult to perform. Generally the resulting accuracy is about 10% in the usual operating conditions of high-energy experiments. The need of finding a more precise calibration method brought us to exploit the possibility of using the proton beam of the Milan AVF cyclotron. For our measurements we chose energies ranging from 25 to 40 MeV which is near to the maximum value attainable by the accelerator. In this region the d E / d x curve changes rapidly and we can simulate a wide range of m.i.p, multiplicity. Since our detector is made of 13 totally depleted silicon diodes 200 ~m thick, we have, for example, a 40 MeV proton with a mean energy loss of 569 keV in the first detector and 700 keV in the last one (after a path of 2.6 mm of silicon) leaving the telescopes with a residual energy of 32 MeV, while a 25 MeV proton loses 834 keV in the first detector and 1585 keV in the 13th one, the residual energy being 10.6 MeV. This energy loss range (569-1585 keV) is equivalent to a multiplicity range of 7-20 m.i.p. The energy losses have been calculated using a range-energy loss table for silicon. After comparison of different tables used in low energy nuclear research, we have chosen the most accurate in number of points and decimal digits [5] that is also well compatible with available data within experimental errors. This table also shows the best result in the multiple regression fit we used to interpolate between the quoted points. One of the advantages of using low energy protons for silicon detector calibration is that the energy loss distribution is relatively narrower and more symmetric than that for a corresponding equivalent number of minimum ionizing particles. As far as the distribution of energy loss is concerned we recall that, according to Vavilov [6], the probability f ( x , A) d A that an ionizing particle loses an amount of energy between A and A + d A passing through a thin layer x is given by:
f(x,
A) d A
1
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+ a In this kind of method the pulse-height-to-energy conversion is independent for each detector while the
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M. Caccia et al. / Low energy protons for vertex detector cafibration
329
ax = ( a ) ,
In our case k equals 0.5, 1.3, 8.0 respectively protons of 40, 25 and 10 MeV, so the Gaussian haviour is dominant in our data. One can remark example that, using the formulas shown, we have protons with kinetic energy 25 MeV:
k=--
(A)=835keV,
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Cm a x is the maximum energy transferred during a single collision, x is given g / c m 2, Z = atomic number of the mean, A = atomic weight, m = electron mass, tic = velocity of the incident particle, M = its mass, C = 0.577--. (Euler's constant), Ei(x) is the exponential integral function. Vavilov shows that if: (a) k < 0.01 the distribution reduces to the wellknown Landau distribution [7] and we have for the most probable energy loss [8] Amp= ~ log (1__/32)12 where I is the mean ionization energy of the medium and for the full width at half-maximum [8] fwhm = 4.02 ~; the link between most probable value and mean value is: Amp = (A)
-[-
~[ --0.223 -[- (1 + f12 -- C) + log k ] ;
(b) k >> 1 (k -- 10; see ref. [9]) f ( x , A) becomes a Gaussian curve and its variance is [9] o=~
1 _fl2k
If we have n relativistic ionizing particles passing at the same time through a thin layer, the distribution f,,(x, A) of their energy loss is given by the convolution of n Vavilov curves; anyway f . ( x , A ) is well fitted by the Vavilov curve characterized by
for befor for
fwhm = 143 keV
versus a fwhm = 326 keV which characterizes 22 m.i.p. distribution. Experimentally our lower energy distributions in the last detectors are slightly larger than the theoretically expected ones. We have verified using a Monte Carlo calculation that a Gaussian spreading (with o = 200 keV) in the energy of incoming protons and straggling effects reproduce the trend we observed. In any case, this fact does not affect the most probable value. The determination of the peak value (most probable value) of each pulse height distribution is generally more precise than the evaluation of the mean value because of background contamination, more evident in the distribution tails. On the other hand, the already quoted range/energy relation allowed us to calculate the mean energy losses. We used the data of ref. [11] to transform it into most probable energy losses. Since we are in the Gaussian or quasi-Gaussian regions, the applied corrections are quite small (between 0.2% and 3%). As far as the second step of this indirect method is concerned, i.e. the relation energy-m.i.p., it is necessary to measure the energy deposited in the detector by a single particle; in order to do this we used data taken at CERN. In fact, for highly relativistic particles, the deposited energy also depends on the experimental setup (in particular on the detector thickness and on the upstream material) but it is independent of their velocity (the so-called relativistic rise, characteristic of the mean energy loss, does not appear in this case [12]). As a result the deposited energy is a linear function of the number of charged particles crossing the detector.
3. Setup
~°=n~, (A ( n ) ) = n (A (1)),
Amp(n ) = n(Zmp(1 ) + ~ log(n)), i.e. a curve rcfcrrcd to a single relativisticparticle crossing a layer n x [10].
The experimental setup we have used at the cyclotron is sketched in fig. 1, where C1 and C2 are collimators, T1 and T2 the silicon telescopes and SC a plastic scintillator. The proton beam is extracted from the vacuum pipe
330
M. Caccia et al.
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detectors, 200/~m thick, 26 mm diameter. Between the two telescopes there is a 10 mm long "decay space". These detectors have been manufactured with the planar process and their performance is described elsewhere
through a thin AI window, 50 /~m thick, and then collimated through a 9 mm diameter collimator. Telescope T1 is made of 3 n-type silicon detectors, 200/~m thick and 10 mm diameter, while T2 is made of 10
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331
M. Caccia et al. / Low energy protons for oertex detector calibration
[13,3]. T1 + T2 is followed by a 1 in. plastic scintillator which has the task of limiting to +_8° the acceptance cone and to trigger the acquisition system. The direct beam intensity ranges between a few/~A and a few nA (the lowest value allowed by the machine stability), i.e., 1013-109 p / s , while the rate required by us lies in the range 103-107 p/s. The usual method of employing protons elastically scattered from a thin target gave a rate too low, so it has been necessary to proceed in an unusual way in order to use the direct beam, with drastically reduced intensity. This decrease was obtained by defocusing the beam before the last switching magnet and closing the defining slits of the analyzing magnet. Keeping the last quadrupole lenses on, we also obtained a well sized beam spot. The analog electronics employed for T1 and T2 is reliable up to counting rates of 3 x 106 pulses/s. The analog channel consigts of a preamplifier and a linear amplifier which, besides the gain function, implements also a time-invariant Gaussian prefiltering. The gated integrator at the input of the charge-sensing ADC adds a time-variant filtering function. The resulting weighting function is a trapezoid with erfc-type leading and trailing edge. When the analog channel is employed with a pulsed accelerator, periodical baseline stabilization is performed during the interburst times, thus enabling very high counting rates with no sacrifice in signal-to-noise ratio. The Milan cyclotron supplies a proton flux which can be considered practically steady for our purpose, while we needed a pulsed beam to have a correct baseline stabilization. This goal has been achieved by building a new power supply for the internal ion source. This power supply, designed and built by our group (fig. 2) is able to switch rapidly the source anode working point from 220 V and up to 50 # A to - 13 V, 0 A at a repetition rate less than 1 Hz. A negative voltage is needed to sweep out from the accelerating system the ions thermally produced during the interburst time.
4. Data taking and analysis At the cyclotron, data have been collected at four differents energies: 24.9, 27.6, 35.5, 40 MeV and at each energy a statistics of 105 events has been accumulated. Our data taking acquisition rate was about 30K events/h *, so we have divided our sample in subsam-
* The data acquisition has been done using standard LRS ADCs read by an APPLE II personal computer• In order to speed up the on-line data analysis we have written a compiled basic code, and we have substituted the standard APPLE II microprocessor at 1 MHz frequency with a 6502 microprocessor at 3.5 MHz cycle.
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ples in order to check the peak position stability. This resulted to be of the order of 0.4%. For each energy and detector we have then calculated the peak position and the corresponding most probable energy loss and performed a linear regression fit through them obtaining the relation energy/count for every channel. In figs. 3a, b the pulse height distributions in the first and in the last detector are shown. The estimated resolution on the channel-energy loss conversion is about 1%. A systematic error coming from the precision of the range-energy tables of about 1% has to be taken into account, but since it is the same for each detector it has a very limited effect on T2-T1 (see below). Measurement of the energy deposited by a single relativistic particle was obtained, as already mentioned
332
M. Caccia et al. / Low energy protons for vertex detector calibration
(see sect. 2.2) from C E R N data; this measurement leads to another systematic error. As previously said, energy deposition depends also on the apparatus geometry; for an isolated 200 # m thick silicon detector, the deposited energy is typically 70 keV/m.i.p. [14]. Our specific setup has a complex geometry and it works in the 18 k G magnetic field of the f2' spectrometer at CERN. For this particular arrangement, using the one and three particle pulse height distributions, we obtained ( A ( t = 200 # m ) ) = (82 _+ 5) keV/m.i.p., i.e. c = 0.06. We have then used this value to calculate the m . i . p / c o u n t relation for each value, that is: energy, energy = m.i.p. count " m.i.p, count In conclusion, the relative systematic error coming from the range-energy and the energy-m.i.p, relation is Csyst(T) = I/0.06 2 + 0.012 = 0.06, and the relative measurement error coming from the cyclotron direct energy calibration is trois(T)= 0.01. The global error that affects our measurement of the charged multiplicity difference is then e ( D T ) = ~¢mis(T12 + T22) "k Csyst(T2 - T1) 2 . For a typical multiplicity of about 15 m.i.p, and a difference D T = 3 m.i.p, the error is about e(DT) = 0.3 m.i.p. As a term of comparison, if in the same situation we had used only the direct calibration method with low multiplicity data obtained at CERN, the measurement error would have been 5 times bigger and the resulting error e ( D T ) = 1 m.i.p, would have been incompatible with the precision required in our experiment.
5. Conclusion We have shown that in order to calibrate semiconductor detectors for multiparticle high energy experiments it can be quite useful to use cyclotron proton beams instead of test beams produced in huge accelerators. Furthermore we would like to underline that besides the economic savings and a reduced complexity of instrumentation, this method requires the use of a
cyclotron, which is an accelerator in widespread use, and therefore problems related to accessibility for tests to large accelerators are reduced.
Acknowledgements This article is dedicated to the memory of Prof. Francesco Resmini. He had encouraged us in the use of the cyclotron for this activity and has suggested the way to pulse the source in order to adapt the pre-existing beam to the special needs of high energy physics instrumentation. He always wanted to be up to date with our work (or "on-line", as he used to say jokingly), even until a few hours before his death. Other persons who contributed to the sucess of our activity: Prof P.F. Manfredi who gave us constant and precious advice about the development and adjustment of the readout electronics. The necessary assistance for a correct operation of the accelerator has been provided by Mr. G. Varisco and Mr. G. Baccaglioni, as well as by the cyclotron operator Mr. M. Fusetti. Mr. E. Macavero gave an essential contribution in assembling the source pulsing circuit, whereas Dr. P.G. Veneziani and Mr. R. Diaferia positively took part in many stages of our activity while working on their graduation theses. To all the abovementioned persons we would like to express our deepest gratitude.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
WA71 proposal, CERN/SPSC/81-18, SPSC P159. S. Benso et al., Nucl. Instr. and Meth. 201 (1982) 329. A Igiuni et al., Nucl. Instr. and Meth. 226 (1984) 85. J. Lassalle et al., CERN DD/80/8. C. Williamson and J.P. Boujout, Rapport CEA n. 2189. P.V. Vavilov, Sov. Phys. JETP 5 (1957) 749. L. Landau, J. Phys. USSR 8 (1944) 201. G. Hall, Nucl. Instr. and Meth. 220 (1984) 356. S.M. Seltzer and M.J. Berger, NAS-NRC publ. no. 1133 (1964) 187. S. Hancock et al., Nucl. Instr. and Meth. B1 (1984) 16. D.J. Skyrme, Nucl. Instr. and Meth. 57 (1967) 61. E.H.M. Heijne, Yellow Report CERN 83-06 EF. J. Kernmer, Nucl. Instr. and Meth. 169 (1980) 499. H. Esbensen et al., Phys. Rev. B18 (1978) 1039.
327
LOW ENERGY PROTONS AS A TOOL FOR HIGH ENERGY VERTEX DETECTOR CALIBRATION M. C A C C I A 1), L. C A S O L I 2)., p. G U A Z Z O N I 1,2), D. M A R I O L I 1,3), C. M E R O N I 1), N. R E D A E L L I 1,4), D. T O R R E T T A t) a n d G. V E G N I 1,2) *) lstituto Nazionale di Fisica Nucleate, Sezione di Milano, Italy 2) Dipartimento di Fisica dell'UniversittJ di Milano, Italy 3) Dipartimento A utomazione lndustriale, Universitd di Brescia, Italy 4) CERN, Geneva, Switzerland
Received 4 February 1986 and in revised form 25 June 1986 This paper describes a method developed for the calibration of silicon detectors used to measure high multiplicity of charged particles in high energy experiments; its peculiarity is the use of low energy protons from a cyclotron. This method guarantees an useful improvement in calibration accuracy. 1. Introduction In the following we will describe a calibration method that we have developed for the silicon vertex detector of the CERN WA71 experiment using low energy protons from a cyclotron. This method could be of general interest for application of silicon detectors in the high energy field. We remind that, in a high energy experiment, it is possible to deduce the number of fast charged particles (produced in interactions a n d / o r decays) that have crossed a silicon detector by measuring the ionization energy deposited in it. On the other hand, a low energy proton crossing a thin layer of silicon has an ionization energy deposition equivalent to that of many fast charged particles. Therefore using a setup which is much simpler than that normally required in high energy experiments (see sect. 3), information on the behaviour of detectors can be obtained, even if they have complex geometrical characteristics. The WA71 experiment at CERN has been designed to search for beauty particles and to measure their mean lifetime. The signature of the events to be selected is mainly given by a charge multiplicity difference (DT) measured between two sets of silicon detectors (" telescope" arrangement) called T1 and T2. These detectors consist respectively of three and ten 200 g m thick sheets, which are perpendicular to the beam direction. The charge multiplicity of interesting events lies in the range 10-25 minimum ionizing particles (m.i.p.) and the expected DT is about 2-5 m.i.p. The selected events have to be searched in a nuclear emulsion target [1]. The detector system and the signal processing electronics are described in refs. [2,3]. * Permanent adress: LABEN, Vimodrone, Milano, Italy. 0168-9002/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Optimization of the signal-to-noise ratio is a crucial point for a hybrid experiment with nuclear emulsion in which the search for the selected events is difficult and time-consuming. The background to the beauty-charm decay signal, i.e. an accidental charge multiplicity jump between T1 and T2, is mainly due to energy loss fluctuations in the silicon detectors. Another important contribution to the "false jump" background, however, comes from systematic errors in the overall silicon detector calibration. Energy loss fluctuations are theoretically predicted and experimentally well verified. Particular care has been taken, therefore, in studying ways of minimizing the other source of background, namely calibration errors. In the following we describe the results on this subject.
2. Experimental method The pulse-height/charge-multiplicity calibration of each silicon detector chain has been obtained a) directly by utilizing events of well known multiplicity (in m.i.p., minimum ionizing particles); b) in two steps: firstly by converting the measured pulse height into deposited energy and secondly this energy into m~i.p. It is in the first of these steps that we have established the advantage of using low energy protons. 2.1. Direct calibration
We have used the peak values (most probable energy loss) of the pulse height distributions for one particle (beam) and for 3 and 5 track events as selected by T R I D E N T (the program developed to reconstruct geometry and kinematics of events; see ref. [4]) among
328
M. Caccia et a L / Low energy protons for vertex detector calibration
calibration data taken at CERN during the experiment. Because of Trident's inefficiency the value of charge multiplicity has been assigned with a level of uncertainty that increases rapidly as a function of the real multiplicity. In fact, when we consider the experimental distribution of energy losses for a collection of events of multiplicity M (given by Trident) we have indeed a "contamination" from events in which the number of charged particles is not M. This inefficiency affects more seriously the high multiplicity (_> 10) distributions, making them not useful for calibrations. Instead, if we consider events with a low number of charged particles, the uncertainty on the assignment of multiplicity could affect the tail of the distribution (and thus the mean value) but not the peak region. On the other hand, the assignment of muliplicity for each event using silicon detector signals has to be made referring to the mean value of energy loss, which grows linearly with the number of particles unlike the most probable value (see sect. 2.2). For these reasons calibration using this method has become rather complex. After having collected events according to the assigned multiplicity (1 _< M < 5), we have determined the ADC channel corresponding to the peak of the distribution for each multiplicity. Then, according to the theoretical link between the most probable and the mean value of the distribution (see sect. 2.2), we have calculated the channel corresponding to the mean energy loss. This is the value to which we shall refer to attribute the multiplicity using signals from the silicon detector. After this it has been necessary to extrapolate the pulse height-m.i.p, relation obtained from the low multiplicity events up to the region of interest for our experiment (10-25 m.i.p.). Finally the difference between the mean energy loss and the mean deposited energy has to be taken into account. It is this last quantity that should be used for the assignement of a single event multiplicity. In this way each electronic chain has been calibrated in m.i.p, and from the mean values of T2 and T1 we obtain the multiplicity jump T2-T1. Using this method the overall estimated error which we attribute to the charge multiplicity of each telescope is about 5%. Since the calibrations of the two telescopes are independent, the relative error on T2-T1 is about ¢r~ × 5% = 7%. The expected mean multiplicity of "beauty events" is 15-20 charged particles, so the error on T2-T1 would be about 2 m.i.p, while the expected T2-T1 signal is in the range 2-5 m.i.p., i.e. a relative error about 100-40%.
error on the energy-m.i.p, conversion affects all the detectors in the same way. Consequently its error propagation on the T2-T1 signal is less important. For the pulse height-keV relation the injection of a known charge through a test capacity is generally used. These capacities should be quite small, of the order of a fraction of a picofarad. Consequently a precise measurement, which takes into account also parasitic effects and the different shapes of artificial and real detector signals, is difficult to perform. Generally the resulting accuracy is about 10% in the usual operating conditions of high-energy experiments. The need of finding a more precise calibration method brought us to exploit the possibility of using the proton beam of the Milan AVF cyclotron. For our measurements we chose energies ranging from 25 to 40 MeV which is near to the maximum value attainable by the accelerator. In this region the d E / d x curve changes rapidly and we can simulate a wide range of m.i.p, multiplicity. Since our detector is made of 13 totally depleted silicon diodes 200 ~m thick, we have, for example, a 40 MeV proton with a mean energy loss of 569 keV in the first detector and 700 keV in the last one (after a path of 2.6 mm of silicon) leaving the telescopes with a residual energy of 32 MeV, while a 25 MeV proton loses 834 keV in the first detector and 1585 keV in the 13th one, the residual energy being 10.6 MeV. This energy loss range (569-1585 keV) is equivalent to a multiplicity range of 7-20 m.i.p. The energy losses have been calculated using a range-energy loss table for silicon. After comparison of different tables used in low energy nuclear research, we have chosen the most accurate in number of points and decimal digits [5] that is also well compatible with available data within experimental errors. This table also shows the best result in the multiple regression fit we used to interpolate between the quoted points. One of the advantages of using low energy protons for silicon detector calibration is that the energy loss distribution is relatively narrower and more symmetric than that for a corresponding equivalent number of minimum ionizing particles. As far as the distribution of energy loss is concerned we recall that, according to Vavilov [6], the probability f ( x , A) d A that an ionizing particle loses an amount of energy between A and A + d A passing through a thin layer x is given by:
f(x,
A) d A
1
e *(1
~2¢ri'm
+o2c'f~+i~°exp ( zXl a-ioo
2.2. Indirect calibration method using low energy protons
+ a In this kind of method the pulse-height-to-energy conversion is independent for each detector while the
×dz d~,
)(log
- FJ(-
- e-q }
M. Caccia et al. / Low energy protons for vertex detector cafibration
329
ax = ( a ) ,
In our case k equals 0.5, 1.3, 8.0 respectively protons of 40, 25 and 10 MeV, so the Gaussian haviour is dominant in our data. One can remark example that, using the formulas shown, we have protons with kinetic energy 25 MeV:
k=--
(A)=835keV,
where: A --~X
- -
-
k(1
+ ,8 "~ -
C),
C max
£max
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= 0.300 mc2 Z
#2 A'
cmax
1 - B2
1
+
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1
_+i 12] -'
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k=1.38,
fwhm=144keV
in the first detector. ( A ) = 835 keV corresponds approximately to the mean energy lost by 12 m.i.p. (assurning ( A ( 1 ) ) = 70 keV for 1 m.i.p.), whose distribution has fwhm = 171 keV. The same proton has a residual energy - 12 MeV before crossing the last detector and therefore ( A ) ----1580 keV (22 m.i.p.), k = 5.44,
Cm a x is the maximum energy transferred during a single collision, x is given g / c m 2, Z = atomic number of the mean, A = atomic weight, m = electron mass, tic = velocity of the incident particle, M = its mass, C = 0.577--. (Euler's constant), Ei(x) is the exponential integral function. Vavilov shows that if: (a) k < 0.01 the distribution reduces to the wellknown Landau distribution [7] and we have for the most probable energy loss [8] Amp= ~ log (1__/32)12 where I is the mean ionization energy of the medium and for the full width at half-maximum [8] fwhm = 4.02 ~; the link between most probable value and mean value is: Amp = (A)
-[-
~[ --0.223 -[- (1 + f12 -- C) + log k ] ;
(b) k >> 1 (k -- 10; see ref. [9]) f ( x , A) becomes a Gaussian curve and its variance is [9] o=~
1 _fl2k
If we have n relativistic ionizing particles passing at the same time through a thin layer, the distribution f,,(x, A) of their energy loss is given by the convolution of n Vavilov curves; anyway f . ( x , A ) is well fitted by the Vavilov curve characterized by
for befor for
fwhm = 143 keV
versus a fwhm = 326 keV which characterizes 22 m.i.p. distribution. Experimentally our lower energy distributions in the last detectors are slightly larger than the theoretically expected ones. We have verified using a Monte Carlo calculation that a Gaussian spreading (with o = 200 keV) in the energy of incoming protons and straggling effects reproduce the trend we observed. In any case, this fact does not affect the most probable value. The determination of the peak value (most probable value) of each pulse height distribution is generally more precise than the evaluation of the mean value because of background contamination, more evident in the distribution tails. On the other hand, the already quoted range/energy relation allowed us to calculate the mean energy losses. We used the data of ref. [11] to transform it into most probable energy losses. Since we are in the Gaussian or quasi-Gaussian regions, the applied corrections are quite small (between 0.2% and 3%). As far as the second step of this indirect method is concerned, i.e. the relation energy-m.i.p., it is necessary to measure the energy deposited in the detector by a single particle; in order to do this we used data taken at CERN. In fact, for highly relativistic particles, the deposited energy also depends on the experimental setup (in particular on the detector thickness and on the upstream material) but it is independent of their velocity (the so-called relativistic rise, characteristic of the mean energy loss, does not appear in this case [12]). As a result the deposited energy is a linear function of the number of charged particles crossing the detector.
3. Setup
~°=n~, (A ( n ) ) = n (A (1)),
Amp(n ) = n(Zmp(1 ) + ~ log(n)), i.e. a curve rcfcrrcd to a single relativisticparticle crossing a layer n x [10].
The experimental setup we have used at the cyclotron is sketched in fig. 1, where C1 and C2 are collimators, T1 and T2 the silicon telescopes and SC a plastic scintillator. The proton beam is extracted from the vacuum pipe
330
M. Caccia et al.
I
10 mm
/
Low energy protons for vertex detector calibration C2
sc
I
T2 ___~
1
Ct
T± _1 .
.
.
.
.
.
:
.
-
-
i
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i I
59
12.8
Fig. 1. Experimental setup during the data acquisition at the Milan cyclotron.
detectors, 200/~m thick, 26 mm diameter. Between the two telescopes there is a 10 mm long "decay space". These detectors have been manufactured with the planar process and their performance is described elsewhere
through a thin AI window, 50 /~m thick, and then collimated through a 9 mm diameter collimator. Telescope T1 is made of 3 n-type silicon detectors, 200/~m thick and 10 mm diameter, while T2 is made of 10
2N 5416
1 KLJ r--]
I~
1/
39,(1 B g ~
i I
220 V
-
±
2 lO~'l
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-
®
G : Q M TN
Fig. 2. Block schemeof the internal proton sourcepowersupp|y.
:Voul
331
M. Caccia et al. / Low energy protons for oertex detector calibration
[13,3]. T1 + T2 is followed by a 1 in. plastic scintillator which has the task of limiting to +_8° the acceptance cone and to trigger the acquisition system. The direct beam intensity ranges between a few/~A and a few nA (the lowest value allowed by the machine stability), i.e., 1013-109 p / s , while the rate required by us lies in the range 103-107 p/s. The usual method of employing protons elastically scattered from a thin target gave a rate too low, so it has been necessary to proceed in an unusual way in order to use the direct beam, with drastically reduced intensity. This decrease was obtained by defocusing the beam before the last switching magnet and closing the defining slits of the analyzing magnet. Keeping the last quadrupole lenses on, we also obtained a well sized beam spot. The analog electronics employed for T1 and T2 is reliable up to counting rates of 3 x 106 pulses/s. The analog channel consigts of a preamplifier and a linear amplifier which, besides the gain function, implements also a time-invariant Gaussian prefiltering. The gated integrator at the input of the charge-sensing ADC adds a time-variant filtering function. The resulting weighting function is a trapezoid with erfc-type leading and trailing edge. When the analog channel is employed with a pulsed accelerator, periodical baseline stabilization is performed during the interburst times, thus enabling very high counting rates with no sacrifice in signal-to-noise ratio. The Milan cyclotron supplies a proton flux which can be considered practically steady for our purpose, while we needed a pulsed beam to have a correct baseline stabilization. This goal has been achieved by building a new power supply for the internal ion source. This power supply, designed and built by our group (fig. 2) is able to switch rapidly the source anode working point from 220 V and up to 50 # A to - 13 V, 0 A at a repetition rate less than 1 Hz. A negative voltage is needed to sweep out from the accelerating system the ions thermally produced during the interburst time.
4. Data taking and analysis At the cyclotron, data have been collected at four differents energies: 24.9, 27.6, 35.5, 40 MeV and at each energy a statistics of 105 events has been accumulated. Our data taking acquisition rate was about 30K events/h *, so we have divided our sample in subsam-
* The data acquisition has been done using standard LRS ADCs read by an APPLE II personal computer• In order to speed up the on-line data analysis we have written a compiled basic code, and we have substituted the standard APPLE II microprocessor at 1 MHz frequency with a 6502 microprocessor at 3.5 MHz cycle.
la I
15C]0.
I
I
i
I
l
I
Atllt
1
I
,
I
i l l i l i
,
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40.0 MeV 35.5 MeV 27.6 MeV 24.9 MliV
---
', ~
2
~
;I
iI ~ ;, '~ ;
'~.'
,
--
;I !'i i
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i
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i
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I
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1200.
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,
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1500.
,
I
t
----
b /"lj
I
i
I
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---
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MeV
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i
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i¢
51~0.
0.0
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)
II
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'~.'
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Fig. 3. Pulse height distributions in the first (a) and in the last detector (b) for the various beam energies used. At the entrance of the last detector the actual beam energies were respectively 31.7, 25.4, 15.7, 12 MeV.
ples in order to check the peak position stability. This resulted to be of the order of 0.4%. For each energy and detector we have then calculated the peak position and the corresponding most probable energy loss and performed a linear regression fit through them obtaining the relation energy/count for every channel. In figs. 3a, b the pulse height distributions in the first and in the last detector are shown. The estimated resolution on the channel-energy loss conversion is about 1%. A systematic error coming from the precision of the range-energy tables of about 1% has to be taken into account, but since it is the same for each detector it has a very limited effect on T2-T1 (see below). Measurement of the energy deposited by a single relativistic particle was obtained, as already mentioned
332
M. Caccia et al. / Low energy protons for vertex detector calibration
(see sect. 2.2) from C E R N data; this measurement leads to another systematic error. As previously said, energy deposition depends also on the apparatus geometry; for an isolated 200 # m thick silicon detector, the deposited energy is typically 70 keV/m.i.p. [14]. Our specific setup has a complex geometry and it works in the 18 k G magnetic field of the f2' spectrometer at CERN. For this particular arrangement, using the one and three particle pulse height distributions, we obtained ( A ( t = 200 # m ) ) = (82 _+ 5) keV/m.i.p., i.e. c = 0.06. We have then used this value to calculate the m . i . p / c o u n t relation for each value, that is: energy, energy = m.i.p. count " m.i.p, count In conclusion, the relative systematic error coming from the range-energy and the energy-m.i.p, relation is Csyst(T) = I/0.06 2 + 0.012 = 0.06, and the relative measurement error coming from the cyclotron direct energy calibration is trois(T)= 0.01. The global error that affects our measurement of the charged multiplicity difference is then e ( D T ) = ~¢mis(T12 + T22) "k Csyst(T2 - T1) 2 . For a typical multiplicity of about 15 m.i.p, and a difference D T = 3 m.i.p, the error is about e(DT) = 0.3 m.i.p. As a term of comparison, if in the same situation we had used only the direct calibration method with low multiplicity data obtained at CERN, the measurement error would have been 5 times bigger and the resulting error e ( D T ) = 1 m.i.p, would have been incompatible with the precision required in our experiment.
5. Conclusion We have shown that in order to calibrate semiconductor detectors for multiparticle high energy experiments it can be quite useful to use cyclotron proton beams instead of test beams produced in huge accelerators. Furthermore we would like to underline that besides the economic savings and a reduced complexity of instrumentation, this method requires the use of a
cyclotron, which is an accelerator in widespread use, and therefore problems related to accessibility for tests to large accelerators are reduced.
Acknowledgements This article is dedicated to the memory of Prof. Francesco Resmini. He had encouraged us in the use of the cyclotron for this activity and has suggested the way to pulse the source in order to adapt the pre-existing beam to the special needs of high energy physics instrumentation. He always wanted to be up to date with our work (or "on-line", as he used to say jokingly), even until a few hours before his death. Other persons who contributed to the sucess of our activity: Prof P.F. Manfredi who gave us constant and precious advice about the development and adjustment of the readout electronics. The necessary assistance for a correct operation of the accelerator has been provided by Mr. G. Varisco and Mr. G. Baccaglioni, as well as by the cyclotron operator Mr. M. Fusetti. Mr. E. Macavero gave an essential contribution in assembling the source pulsing circuit, whereas Dr. P.G. Veneziani and Mr. R. Diaferia positively took part in many stages of our activity while working on their graduation theses. To all the abovementioned persons we would like to express our deepest gratitude.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
WA71 proposal, CERN/SPSC/81-18, SPSC P159. S. Benso et al., Nucl. Instr. and Meth. 201 (1982) 329. A Igiuni et al., Nucl. Instr. and Meth. 226 (1984) 85. J. Lassalle et al., CERN DD/80/8. C. Williamson and J.P. Boujout, Rapport CEA n. 2189. P.V. Vavilov, Sov. Phys. JETP 5 (1957) 749. L. Landau, J. Phys. USSR 8 (1944) 201. G. Hall, Nucl. Instr. and Meth. 220 (1984) 356. S.M. Seltzer and M.J. Berger, NAS-NRC publ. no. 1133 (1964) 187. S. Hancock et al., Nucl. Instr. and Meth. B1 (1984) 16. D.J. Skyrme, Nucl. Instr. and Meth. 57 (1967) 61. E.H.M. Heijne, Yellow Report CERN 83-06 EF. J. Kernmer, Nucl. Instr. and Meth. 169 (1980) 499. H. Esbensen et al., Phys. Rev. B18 (1978) 1039.