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X-ray transition radiation detector (XTRD) for hadron identification in high-energy beams
Nuclear Instruments and Methods in Physics Research A 398 (1997) 1899194
NUCUAR INSTUUMENTS &hamfmS IN PWSICS
X-ray transition radiation detector (XTRD) for hadron identification in high-energy beams1 K.K. Shikhliarov”, N.Z. Akopov, V.G. Gavalian Yerevan Physics Institute, Alikhanian Brothers St. 2. 375036 Yerevan, Armenia
Received 27 starch 1996; received in revised form 10 January 1997
Abstract A project of a hadron identifier for secondary beams of Eh 2 0.25Tev is proposed. The XTR quanta detection is carried out due to their Compton scattering in the radiator made of a light substance. So the charged particles do not pass through the quantum detector and do not produce a background due to ionization losses. The lateral XTR quanta are registered by gaseous-xenon detector made in the form of a cylinder with almost 4x geometry. The Monte-Carlo calculation of the beam identifier has been carried out for a LiH radiator with the number of 0.05 mm-thick layers of 3360 at h = 1 mm air gaps.
1. Introduction Recently at Fermilab, a 24-modular beam XTRD was built and successfully operated in order to separate pions from protons and kaons in a E, = 250GeV incident hadron beam [l]. The detector was capable with efficiencies exceeding of identifying pions 90% and with < 3% contamination due to the nearly equally copius protons and kaons in the beam. An XTRD was operated in combination with a differential isochronous self-focusing Cherenkov counter (DISC), which gave a positive tag for the incident kaons and had a resolution of Afi 2 4 x lo-?. It is difficult to use DISC at more higher energies. That is why it is very desirable to have the beam XTRD which could separate R, K, p simultaneously. In this case the XTRD could acquire properties of a differential detector of particles. A number of works are dedicated to the beam XTRD problem [2-41.
2. Ideology of the proposed XTRD The basic idea in the operating principle of the beam identifier is the dependence of XTR intensity on the
‘The work has been carried out under the financial support of the grant 211-5291 YPI of the German Bundesministerium fur Forschung und Technologie. * Corresponding author. Tel.: 8852 34500, fax: 8852 350030
particle mass at a given momentum. To improve the efficiency of this method, it is desirable to provide the particle separation from radiation without magnetic deflection, i.e. to digress from the traditional scheme of multimodular detectors in which the particle and the radiation are registered in the same volume. This is achieved by the Compton scattering of the XTR quanta produced and scattered in the same radiator. The aside scattered radiation is registered by a gaseous-xenon quantum detector that surrounds the radiator and has an effective geometry of almost 4x. The principle of such XTRD operation is illustrated in Fig. 1. The Comptonscattering method was first proposed by G.M. Garibian in his doctoral thesis and was considered later in Ref. C2,7,6].
3. XTR radiator The identification efficiency of particles directly depends on the overlap of quanta distributions registered from various particles. The smaller the sum of dispersions the larger is the difference between the average numbers and more effective is the result. The relation between the average number for quanta having a Poisson distribution is mainly determined by the properties of transition radiation. That is why the main problem is to increase the average number of quanta for a light particle, and this automatically brings about the fluctuation decrease of their number. The number of the quanta produced by the
OILS-9~2~97/Sl7.00 Copyright (c 1997 Published by Elsevier Science B.V. AH rights reserved PII
SO168-9002(97)00768-7
K.K. Shikhliarov et al. / Nuci. lnstr. arzd Meth. in Ph,vs. Res. A 398 (1997) 189- 194
190
/
LIHprotector
1.6
LiH plate
1.4
g,cm-1 ’ CJIOi
/
0.6 a.4 0.2 Fig. I. The Compton TRD schematic view.
D -0
20
40
60
80
100
720
Fig. 2. Different cross-sections for the y-LiI-I interaction.
particle is a function of the matter amount in the radiator. The principal restriction imposed on the matter amount (number of quanta) in the radiator is stipulated by electromagnetic and nuclear processes. A reasonable limit of the matter amount n? can be taken to be I 10% from radiation and nuclear-interaction length. So, with other conditions being equal, the longer the nuclear and radiation lengths of radiator material, the more quanta can be obtained. On the other hand, the scattering principle itself also requires sufficiently large amount of matter for quantum scattering effect. In this case, the scattering cross-section towards the total cross-section ratio must be maximal. All these requirements are best met by the radiator made of LiH, for which the radiation and nuclear lengths are about L, E 173cm and i. 5 169 cm. It is very important, that LiH has relatively large plasma frequency (wO = 18.6eV) owing to p = 0.825 g/cm” density, and the atom of H il~proves the scattering.
4. Frequency range The transition radiation is usually considered in the frequence range of - l-100 keV. Really, a frequency interval of - 3-30 keV with maximum at - 6-8 keV is detected in the multimodular TR system. But the situation is changed in quanta scattering regime. The crosssections for photoabsorbtion ((T,,J, non-coherent (gnncoh) and coherent (G~J scattering on coupled electrons, their sum a,, = (G,,,~ + o;,,.,) and also the total cross-section a,, = (Q, + gssc)for LiH [9,10] are illustrated in Fig. 2. It is seen that o,, begins to predominate over gph at E, 2 8 keV. At E,? = 10 keV, a,,/~,, = 0.53 and at E, = 20keV, (T~,,/G~~ = 0.05. So, TR quanta with energy E, > 20 keV will either mainly scatter or escape from the radiator in the direction of the particle motion. Consequently. LiH plate’s parameters must correspond to the interference maximum in the frequency region higher than 8 keV. If one chooses maximum at fre-
quency w,, then the plate’s thickness a is defined from expression [9]
where w, (keV) and o,, (eV). At w, = 15 keV and a)0 = 18.6eV n = 50pm. So, the plates must be rather thick. That will increase the number of useful quanta for light particles (x) In Fig. 3(a) the TR spectra for one LiH plate with u = 50 pm thickness at energy E, = 0.5 TeV are given. The spectra correspond to a plate located in a stack of other plates [lo]. It can be noted that the interference maximum for pion is in the E;. > 8 keV range. Also note that more massive particles do not have this kind of maximum yet, their spectra are significantly softer and have rapidly decreasing character. That is why in the quantum scattering process, i.e., effective at frequencies higher than 10 keV, high dynamism of spectrum dist~but~on naturally appears in this frequency region. From the above, two important consequences are expected (1) The hadron identification diapazone shift to higher values of the Lorentz factor y. (2) The TR quantum scattering efficiency in lateral directions has to vary for diKerent types of hadrons. Let us elucidate what has been said above. Let the yin be the relative quantity of quanta scattered aside for pion ‘I, = II,,,, Jn, where n, is the total number ofquanta produced by pion in radiator at the Frequency range l-100 keV. Let us define vk and yipin the same manner. As follows from spectra in Fig. 3(a) it is expected that in the region of effective identification qn > )I* and qn > qk. This difference has to shift to the left of the Poisson distributions of scattered quantum for heavy particles relative to the pion distribution, additionally.
K.K. Shikhiiarov
et al. / Nucl. Instr. and Meth. in Ph.vs. Rex A 39% (1997) 189-194
?.O()OE_()6 L 0
1 10
1 20
1 30
’ 40
1 1 50 60
Taking into account the value of z for the radiator’s material and the fact that only heavy particles are considered, the first two types of backgrounds can be neglected. At the same time when a particle flies through the radiator it creates a considerable amount of 6 electrons. For example in a LiH sample of 1Ocm thickness, the value of nd at E, z 1keV is about 600. But because of the specific kinematics of the process for heavy particles in the TeV energy region, all of the 6 electrons including those which have E, 2 1 MeV fly out at the angle of n/2 and are absorbed in the plate. Furthermore, the proposed type of construction for radiator (Fig. 1) naturally provides the protective cover made out of LiH. which can easily shut off all the S electrons with energies E, 5 0.3 MeV, already at the thickness of I mm and which does not affect the TRD efficiency.
a)
E,,=O.5Tev
:‘:‘*. 70 80
90 100
0.1 _
dn/dl+keV-’
-Liz--@
1
191
For T
6. Monte-Carlo calculation results i.OOOE-04
1
11
21
31
41
61
61
61
71
71
31
91
101
0:
Inldb,keV-’ 0.0.
For p 1.000E.“0~
LOOOE-04
l.OOOE-06
f.OOOE-06
l.OOOE-07 1
11
21
31
41
51
31
91
lo1
111
Monte-Carlo calculations were done for Compton TRD with m = 3360 LiH plates at the thickness of n = 50 pm, which is only about 10% of the nuclear interaction length. The distance between plates is b = 1 mm. The 7c,K. p hadron energy have been varying from E, = 0.25 to 4STeV corresponding to the variation of the ;jn from - 1.8 x lo3 to -3.2 x 10’. The diameter of the plates was chosen to be d = 5cm, because it was suggested that transverse sizes of the focused hadron beam have to be about 1 cm. It was assumed that scattered aside TR quanta get into the Xe chamber, where they can be absorbed in the solid angle defined by TRD sizes. In principle, the Xe thickness has not got any restrictions. In the Monte-Carlo calculations, the Xe thickness was split to the radial direction on thin detecting layers with I,, = 5mm thickness. The TR spectrum for one plate located in the stack of plates, when the particle with given type and energy E flies through the radiator, was calculated in the frequency region l-100 keV by the formula [lo]
Fig. 3. The XTR spectra: (a) generated by rc. K, p in one plate of LiH(a = 50 pm). at E, = 0.5 Tel’; (b) 1 - generated by TI in one plate, 2 - scattered (cob. + ncoh.), 3 - scattered noncoherent; (c) 1 - generated by p in one plate, 2 - scattered(coh. + ncoh), 3 - scattered non-coherent.
5. Back~ound Generally, the beam particles can create three types of backgrounds in the radiator (1) K ionization in LiH. (2) Bremsstraugling radiation in LiH. (3) fi electrons in LiH.
where (1 is the plate thickness, h the distance between plates, P = a + h, y = #a(1 - p2)/(2xu)2, w0 = aa/Zkv, o the square of the plasma’s frequency value for the plate’s material, B = v/c, nmin = l/Z[o,/w + ~w/o&J. The integral over the spectrum defines the mean value of the quanta number n1 radiated on a plate, n, < 1. Ifthere was some radiation on the plate, the quanta number is
192
K.K. Shikhliarov et al. JNucl. Instr. and Meth. in Ph.vs. Res. A 398 (1997) 189-194
simulated by the Poisson distribution and their energy - by quanta spectrum. The history for each quantum with the given energy is tracked up to one of the three possible cases _ the quantum is absorbed in the LiH; _ the quantum is absorbed in the Xe; _ the quantum flies out of the detector together with particle. The differential cross-section atom can be written as [ 111 d,c = Zd,c,&
f degromson [
for scattering
on the
tion form, because mean solid angle in which it is impossible to register the quanta is - 1O-4 rad (A0 N 1”). As for
the second term of the sum (2), the angular distribution contained in it is undefined, although, it is clear that transfering momenta are small and the process is directed forward, but the part of quanta, which gets into the interval A6 N 1’ is unknown. Taking into account the above-mentioned, two types of calculations were done. For the first type the simulation was done using relative cross-sections for non-coherent process (cnncah/cssc) as well as for the coherent one (cr&~) at the same angular distribution. The obtained spectrum of scattered quanta of rt and p at E, = 1 TeV is shown in Fig. 3(b) and (c) (second curve). For the second type, the simulation was done using only non-coherent part of the cross-section. The Q = 0 condition can be included in the Monte-Carlo program. However, the expected differential effect in some parts of the spectrum can be less than statistical fluctuations. That is why, the non-coherent (dn/dE,),,,, and coherent (dn/dE,),,, spectra were extracted in spectra 2 in Fig. 3(b) and (c) and some part of the coherent spectrum An(E,) was again added to the non-coherent spectrum
j’:1’=On,,,, +da~com (2)
where Z is the atom number, &~k_~ is the KlienNishina’s differential cross-section for non-coherent scattering on the free electron, S is the function of noncoherent scattering, decTamsonis the Thomson differential cross-section for elastic scattering on the free electron, f, is the electron scattering form factor, [I:= if,]” is the square of atomic form-factor value. The first term of the sum describes the non-coherent process. The relation between S and I/@,, e), where f3is the scattering angle, is shown in Fig. 4 [12], where
An(&) =
-$ i
Pn,&,)( y
1 -
P&y))-
l >
>cob
(3)
whet-e f,,,(EJ = kWdE,)nmhlkWdE,) and%h = (dnl~,),,/ (WdE,). Note that pncoh(Ey)+ Pooh(E,) + P,,(E,) +
where t( is a constant. For each fixed 0 and if E, --t 0, + 0, consequently enncoh + 0 too. It can S -+ 0 and dolc,,ncoh be observed in Fig. 2. On the other hand, for any fixed E, and at Q-+ 0 also dolt,_+, + 0, i.e. for non-coherent process the scattering under small angles is suppressed. Therefore, the angle distribution of quanta for noncoherent scattering is given by expression d,o, _ $ (I’). It should be noted, that the number of quanta registered in Xe does not practically depend on the angular distribu-
P,,,(E,) = 1, where Pph is the probability of the photoabsorbtion, P,,, is the probability of quantum flying out radiator together with particle. The spectra, obtained by the use of such analytical subtraction are shown in Fig. 3(b) and (c). As a result of this subtraction, the number of useful quanta has been decreased by 13% for pions and decreased by 40% for protons. Such results for mean values of (n,) and (n,) can be easily understood taking into account the shape of spectra and behaviour of a,,,(E,) in Fig. 2. Greater shift
V=ctE,sin
i 0
,
,“:‘-->
j
,“y’“C
1
Fig. 4. The non-coherent S function’s dependence versus V(E,, 0).
6
11
16
21
26
31
36
41
46
Fig. 5. The integrated spectra of the scattered XTR quanta versus the number of registered quanta with energy higher than the given (o,,,,. is disabled) one.
193
K.K. Shikhliarov et al. /Nucl. Instr. and Meth. in Phys. Rex A 398 (1997) 189-194 1 0.1 0.01 l.OOOE-03 l.OOOE-04 l.OOOE-06 l.OOOE-03 i.OOOE-07
4 P/K+0.7)
i.OOOE-03 1.0008-09 l.OOOE- 10
k
0 0 TeV ,,OOOf_ ,, .___._L..._._..~~_-__.* -_ -.-.E,, I.-...-.-.-. J
0 Fig. 6. The average number of registered XTR quanta in the Xe [for the Xe width -+ CCversus the hadron energy. The digits on the curve are the q(n, K. p) coefficients (see the text).
“0
10
20
30
46
50
60
70
1
2
3
4
5
Fig. 8. The rejection factor’s dependence versus the hadron energy. The curves (14) are our results. The value of acceptance was chosen taking into account the probability for the particle to pass the radiator without nuclear interaction. The curve 5 is from Ref. [13].
Fig. 7 illustrates the disposition of distribution by number of quanta for rt, K, p at E, = 1.5 TeV. Practically, the full separation for x/p and n/k is seen. The relation between the rejection factor and the hadron energy E, is given in Fig. 8. For comparison, in Fig. 8, the curve for Rk,,, given in Ref. [ 131 for the fully optimized usual TRD with lithium radiator is given. The device consists of 12 modules, containing 8 g/cm’ of material or - 11% of nuclear interaction length.
Fig. 7. The number of quanta distributions for ?E,K, p with Eh = 1.5TeV.
7. Conclusions of (n,) could lead to the improvement of rejection; however, the decrease of absolute value of mean number of quanta gives the disunion increase. This compensated the positive effect and the rejection has not changed. In Fig. S the spectra 3 (Fig. 3(b) and (c)) in integral form are given. They show the relative number of useful quanta with energy greater than the given energy E,. It can be noted that for rt the number of quanta with E, > 11 keV is 80% and for p - 20%, i.e. for x the spectrum of useful quanta is significantly harder. The mean energy of quanta for E is equal to 19.7 keV and for p -7.6 keV at E = 1 TeV, i.e., to say the quanta spectrum for rc is about 2-3 times harder than in usual TRD, which has to provide a wider working interval in terms of y factor. In Fig. 6 the relation between the mean number of quanta registered m Xe(&,-+ co) and hadron energy is given. The numbers on the curves are r~~,k,~coefficient values, showing the quantum scattering efficiency for different hadrons. For rejection calculations the Xe thickness was restricted by 10 layers (k = 10, Ix, = 50mm).
The Monte-Carlo calculation of Compton TRD for hadron identifications in high-energy beams shows that this detector should work adequately to the principles on which it is based. These principles provide four important advantages (1) The separation of quanta registration region from initial particles that allows to exclude the ionization background as well as the registration of beam with high density of particles in a small part of the space. (2) Using the differences in the frequency spectra for 71,K, p. It allows to provide more effective scattering of quanta for pion. (3) The usage of a harder part of spectra for H, which appears in higher dynamics with respect to the Lorentsfactor and increases the dynamical range of TDR. (4) Use of quantum scattering principle in the radiator, provides the linear dependence on the radiator length and leads to a higher factor of rejection. Such a high value of the rejection R,,, and R,,, gives good opportunities for the TRD optimization in the sense of
K.K. Shikhliarov et al. /Nucl. Instr. and Meth. in Phvs. Rex A 398 (1997) 189-194
194
radiator length.
length
from 0.1 to 0.05 of nuclear
interaction
References Cl] D. Errede et al., Nucl. Instr. and Meth. A 309 (1991) 386. 123 J.E. Mack et al.. Phys. Rev. Lett. 33(26) (1974) 1582. [3] A.T. Avundjian, S.A. Kankanian. A.G. Oganessian, L.M. Petrossian, Nucl. Instr. and Meth. A 283 (1989) 612. [4] K.A. Ispirian, R.K. Ispirian, A.T. Margarian, Nucl. Instr. and Meth. A 336 (1993) 533. [S] M.P. Lorikian, Pribori i Tekhnika Exsperimenta 3 (1971) 73. [6] M.P. Lorikian, K.K. Shikhliarov, V.Y. Yaralov, Sci. Rep. YerPhI 31 (1973). p. 9.
[7] E. Storm, H. Israel, Photon
cross-section from 0.001 to 100MeV for Elements 1 through 100, Los Alamos Scient. Lab.. New Mexico, 1967. [S] O.F. Nemets. V.V. Gofman, A Handbook in Nuclear Physics, Kiev, 1975. [9] M.L. Cherry, G. Hartmann, D. Muller. Th.A. Prince, Phys. Rev. D lO(11) (1974) 3594. [lo] G.M. Garibian et al.. Nucl. Instr. and Meth. 125(1975) 133. [l l] Kai Siegbahn (Ed.), Alpha-Beta and Gamma-Ray Spectroscopy, vol. 1, North-Holland, Amsterdam, 1965, p. 73. [12] Kai Siegbahn (Ed.), Alpha-Beta and Gamma-Ray Spectroscopy, vol. 1. North-Holland, Amsterdam, 1965. p. 77. [13] C.W. Fabjan et al., Preprint CERN EP/83-45.
NUCUAR INSTUUMENTS &hamfmS IN PWSICS
X-ray transition radiation detector (XTRD) for hadron identification in high-energy beams1 K.K. Shikhliarov”, N.Z. Akopov, V.G. Gavalian Yerevan Physics Institute, Alikhanian Brothers St. 2. 375036 Yerevan, Armenia
Received 27 starch 1996; received in revised form 10 January 1997
Abstract A project of a hadron identifier for secondary beams of Eh 2 0.25Tev is proposed. The XTR quanta detection is carried out due to their Compton scattering in the radiator made of a light substance. So the charged particles do not pass through the quantum detector and do not produce a background due to ionization losses. The lateral XTR quanta are registered by gaseous-xenon detector made in the form of a cylinder with almost 4x geometry. The Monte-Carlo calculation of the beam identifier has been carried out for a LiH radiator with the number of 0.05 mm-thick layers of 3360 at h = 1 mm air gaps.
1. Introduction Recently at Fermilab, a 24-modular beam XTRD was built and successfully operated in order to separate pions from protons and kaons in a E, = 250GeV incident hadron beam [l]. The detector was capable with efficiencies exceeding of identifying pions 90% and with < 3% contamination due to the nearly equally copius protons and kaons in the beam. An XTRD was operated in combination with a differential isochronous self-focusing Cherenkov counter (DISC), which gave a positive tag for the incident kaons and had a resolution of Afi 2 4 x lo-?. It is difficult to use DISC at more higher energies. That is why it is very desirable to have the beam XTRD which could separate R, K, p simultaneously. In this case the XTRD could acquire properties of a differential detector of particles. A number of works are dedicated to the beam XTRD problem [2-41.
2. Ideology of the proposed XTRD The basic idea in the operating principle of the beam identifier is the dependence of XTR intensity on the
‘The work has been carried out under the financial support of the grant 211-5291 YPI of the German Bundesministerium fur Forschung und Technologie. * Corresponding author. Tel.: 8852 34500, fax: 8852 350030
particle mass at a given momentum. To improve the efficiency of this method, it is desirable to provide the particle separation from radiation without magnetic deflection, i.e. to digress from the traditional scheme of multimodular detectors in which the particle and the radiation are registered in the same volume. This is achieved by the Compton scattering of the XTR quanta produced and scattered in the same radiator. The aside scattered radiation is registered by a gaseous-xenon quantum detector that surrounds the radiator and has an effective geometry of almost 4x. The principle of such XTRD operation is illustrated in Fig. 1. The Comptonscattering method was first proposed by G.M. Garibian in his doctoral thesis and was considered later in Ref. C2,7,6].
3. XTR radiator The identification efficiency of particles directly depends on the overlap of quanta distributions registered from various particles. The smaller the sum of dispersions the larger is the difference between the average numbers and more effective is the result. The relation between the average number for quanta having a Poisson distribution is mainly determined by the properties of transition radiation. That is why the main problem is to increase the average number of quanta for a light particle, and this automatically brings about the fluctuation decrease of their number. The number of the quanta produced by the
OILS-9~2~97/Sl7.00 Copyright (c 1997 Published by Elsevier Science B.V. AH rights reserved PII
SO168-9002(97)00768-7
K.K. Shikhliarov et al. / Nuci. lnstr. arzd Meth. in Ph,vs. Res. A 398 (1997) 189- 194
190
/
LIHprotector
1.6
LiH plate
1.4
g,cm-1 ’ CJIOi
/
0.6 a.4 0.2 Fig. I. The Compton TRD schematic view.
D -0
20
40
60
80
100
720
Fig. 2. Different cross-sections for the y-LiI-I interaction.
particle is a function of the matter amount in the radiator. The principal restriction imposed on the matter amount (number of quanta) in the radiator is stipulated by electromagnetic and nuclear processes. A reasonable limit of the matter amount n? can be taken to be I 10% from radiation and nuclear-interaction length. So, with other conditions being equal, the longer the nuclear and radiation lengths of radiator material, the more quanta can be obtained. On the other hand, the scattering principle itself also requires sufficiently large amount of matter for quantum scattering effect. In this case, the scattering cross-section towards the total cross-section ratio must be maximal. All these requirements are best met by the radiator made of LiH, for which the radiation and nuclear lengths are about L, E 173cm and i. 5 169 cm. It is very important, that LiH has relatively large plasma frequency (wO = 18.6eV) owing to p = 0.825 g/cm” density, and the atom of H il~proves the scattering.
4. Frequency range The transition radiation is usually considered in the frequence range of - l-100 keV. Really, a frequency interval of - 3-30 keV with maximum at - 6-8 keV is detected in the multimodular TR system. But the situation is changed in quanta scattering regime. The crosssections for photoabsorbtion ((T,,J, non-coherent (gnncoh) and coherent (G~J scattering on coupled electrons, their sum a,, = (G,,,~ + o;,,.,) and also the total cross-section a,, = (Q, + gssc)for LiH [9,10] are illustrated in Fig. 2. It is seen that o,, begins to predominate over gph at E, 2 8 keV. At E,? = 10 keV, a,,/~,, = 0.53 and at E, = 20keV, (T~,,/G~~ = 0.05. So, TR quanta with energy E, > 20 keV will either mainly scatter or escape from the radiator in the direction of the particle motion. Consequently. LiH plate’s parameters must correspond to the interference maximum in the frequency region higher than 8 keV. If one chooses maximum at fre-
quency w,, then the plate’s thickness a is defined from expression [9]
where w, (keV) and o,, (eV). At w, = 15 keV and a)0 = 18.6eV n = 50pm. So, the plates must be rather thick. That will increase the number of useful quanta for light particles (x) In Fig. 3(a) the TR spectra for one LiH plate with u = 50 pm thickness at energy E, = 0.5 TeV are given. The spectra correspond to a plate located in a stack of other plates [lo]. It can be noted that the interference maximum for pion is in the E;. > 8 keV range. Also note that more massive particles do not have this kind of maximum yet, their spectra are significantly softer and have rapidly decreasing character. That is why in the quantum scattering process, i.e., effective at frequencies higher than 10 keV, high dynamism of spectrum dist~but~on naturally appears in this frequency region. From the above, two important consequences are expected (1) The hadron identification diapazone shift to higher values of the Lorentz factor y. (2) The TR quantum scattering efficiency in lateral directions has to vary for diKerent types of hadrons. Let us elucidate what has been said above. Let the yin be the relative quantity of quanta scattered aside for pion ‘I, = II,,,, Jn, where n, is the total number ofquanta produced by pion in radiator at the Frequency range l-100 keV. Let us define vk and yipin the same manner. As follows from spectra in Fig. 3(a) it is expected that in the region of effective identification qn > )I* and qn > qk. This difference has to shift to the left of the Poisson distributions of scattered quantum for heavy particles relative to the pion distribution, additionally.
K.K. Shikhiiarov
et al. / Nucl. Instr. and Meth. in Ph.vs. Rex A 39% (1997) 189-194
?.O()OE_()6 L 0
1 10
1 20
1 30
’ 40
1 1 50 60
Taking into account the value of z for the radiator’s material and the fact that only heavy particles are considered, the first two types of backgrounds can be neglected. At the same time when a particle flies through the radiator it creates a considerable amount of 6 electrons. For example in a LiH sample of 1Ocm thickness, the value of nd at E, z 1keV is about 600. But because of the specific kinematics of the process for heavy particles in the TeV energy region, all of the 6 electrons including those which have E, 2 1 MeV fly out at the angle of n/2 and are absorbed in the plate. Furthermore, the proposed type of construction for radiator (Fig. 1) naturally provides the protective cover made out of LiH. which can easily shut off all the S electrons with energies E, 5 0.3 MeV, already at the thickness of I mm and which does not affect the TRD efficiency.
a)
E,,=O.5Tev
:‘:‘*. 70 80
90 100
0.1 _
dn/dl+keV-’
-Liz--@
1
191
For T
6. Monte-Carlo calculation results i.OOOE-04
1
11
21
31
41
61
61
61
71
71
31
91
101
0:
Inldb,keV-’ 0.0.
For p 1.000E.“0~
LOOOE-04
l.OOOE-06
f.OOOE-06
l.OOOE-07 1
11
21
31
41
51
31
91
lo1
111
Monte-Carlo calculations were done for Compton TRD with m = 3360 LiH plates at the thickness of n = 50 pm, which is only about 10% of the nuclear interaction length. The distance between plates is b = 1 mm. The 7c,K. p hadron energy have been varying from E, = 0.25 to 4STeV corresponding to the variation of the ;jn from - 1.8 x lo3 to -3.2 x 10’. The diameter of the plates was chosen to be d = 5cm, because it was suggested that transverse sizes of the focused hadron beam have to be about 1 cm. It was assumed that scattered aside TR quanta get into the Xe chamber, where they can be absorbed in the solid angle defined by TRD sizes. In principle, the Xe thickness has not got any restrictions. In the Monte-Carlo calculations, the Xe thickness was split to the radial direction on thin detecting layers with I,, = 5mm thickness. The TR spectrum for one plate located in the stack of plates, when the particle with given type and energy E flies through the radiator, was calculated in the frequency region l-100 keV by the formula [lo]
Fig. 3. The XTR spectra: (a) generated by rc. K, p in one plate of LiH(a = 50 pm). at E, = 0.5 Tel’; (b) 1 - generated by TI in one plate, 2 - scattered (cob. + ncoh.), 3 - scattered noncoherent; (c) 1 - generated by p in one plate, 2 - scattered(coh. + ncoh), 3 - scattered non-coherent.
5. Back~ound Generally, the beam particles can create three types of backgrounds in the radiator (1) K ionization in LiH. (2) Bremsstraugling radiation in LiH. (3) fi electrons in LiH.
where (1 is the plate thickness, h the distance between plates, P = a + h, y = #a(1 - p2)/(2xu)2, w0 = aa/Zkv, o the square of the plasma’s frequency value for the plate’s material, B = v/c, nmin = l/Z[o,/w + ~w/o&J. The integral over the spectrum defines the mean value of the quanta number n1 radiated on a plate, n, < 1. Ifthere was some radiation on the plate, the quanta number is
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simulated by the Poisson distribution and their energy - by quanta spectrum. The history for each quantum with the given energy is tracked up to one of the three possible cases _ the quantum is absorbed in the LiH; _ the quantum is absorbed in the Xe; _ the quantum flies out of the detector together with particle. The differential cross-section atom can be written as [ 111 d,c = Zd,c,&
f degromson [
for scattering
on the
tion form, because mean solid angle in which it is impossible to register the quanta is - 1O-4 rad (A0 N 1”). As for
the second term of the sum (2), the angular distribution contained in it is undefined, although, it is clear that transfering momenta are small and the process is directed forward, but the part of quanta, which gets into the interval A6 N 1’ is unknown. Taking into account the above-mentioned, two types of calculations were done. For the first type the simulation was done using relative cross-sections for non-coherent process (cnncah/cssc) as well as for the coherent one (cr&~) at the same angular distribution. The obtained spectrum of scattered quanta of rt and p at E, = 1 TeV is shown in Fig. 3(b) and (c) (second curve). For the second type, the simulation was done using only non-coherent part of the cross-section. The Q = 0 condition can be included in the Monte-Carlo program. However, the expected differential effect in some parts of the spectrum can be less than statistical fluctuations. That is why, the non-coherent (dn/dE,),,,, and coherent (dn/dE,),,, spectra were extracted in spectra 2 in Fig. 3(b) and (c) and some part of the coherent spectrum An(E,) was again added to the non-coherent spectrum
j’:1’=On,,,, +da~com (2)
where Z is the atom number, &~k_~ is the KlienNishina’s differential cross-section for non-coherent scattering on the free electron, S is the function of noncoherent scattering, decTamsonis the Thomson differential cross-section for elastic scattering on the free electron, f, is the electron scattering form factor, [I:= if,]” is the square of atomic form-factor value. The first term of the sum describes the non-coherent process. The relation between S and I/@,, e), where f3is the scattering angle, is shown in Fig. 4 [12], where
An(&) =
-$ i
Pn,&,)( y
1 -
P&y))-
l >
>cob
(3)
whet-e f,,,(EJ = kWdE,)nmhlkWdE,) and%h = (dnl~,),,/ (WdE,). Note that pncoh(Ey)+ Pooh(E,) + P,,(E,) +
where t( is a constant. For each fixed 0 and if E, --t 0, + 0, consequently enncoh + 0 too. It can S -+ 0 and dolc,,ncoh be observed in Fig. 2. On the other hand, for any fixed E, and at Q-+ 0 also dolt,_+, + 0, i.e. for non-coherent process the scattering under small angles is suppressed. Therefore, the angle distribution of quanta for noncoherent scattering is given by expression d,o, _ $ (I’). It should be noted, that the number of quanta registered in Xe does not practically depend on the angular distribu-
P,,,(E,) = 1, where Pph is the probability of the photoabsorbtion, P,,, is the probability of quantum flying out radiator together with particle. The spectra, obtained by the use of such analytical subtraction are shown in Fig. 3(b) and (c). As a result of this subtraction, the number of useful quanta has been decreased by 13% for pions and decreased by 40% for protons. Such results for mean values of (n,) and (n,) can be easily understood taking into account the shape of spectra and behaviour of a,,,(E,) in Fig. 2. Greater shift
V=ctE,sin
i 0
,
,“:‘-->
j
,“y’“C
1
Fig. 4. The non-coherent S function’s dependence versus V(E,, 0).
6
11
16
21
26
31
36
41
46
Fig. 5. The integrated spectra of the scattered XTR quanta versus the number of registered quanta with energy higher than the given (o,,,,. is disabled) one.
193
K.K. Shikhliarov et al. /Nucl. Instr. and Meth. in Phys. Rex A 398 (1997) 189-194 1 0.1 0.01 l.OOOE-03 l.OOOE-04 l.OOOE-06 l.OOOE-03 i.OOOE-07
4 P/K+0.7)
i.OOOE-03 1.0008-09 l.OOOE- 10
k
0 0 TeV ,,OOOf_ ,, .___._L..._._..~~_-__.* -_ -.-.E,, I.-...-.-.-. J
0 Fig. 6. The average number of registered XTR quanta in the Xe [for the Xe width -+ CCversus the hadron energy. The digits on the curve are the q(n, K. p) coefficients (see the text).
“0
10
20
30
46
50
60
70
1
2
3
4
5
Fig. 8. The rejection factor’s dependence versus the hadron energy. The curves (14) are our results. The value of acceptance was chosen taking into account the probability for the particle to pass the radiator without nuclear interaction. The curve 5 is from Ref. [13].
Fig. 7 illustrates the disposition of distribution by number of quanta for rt, K, p at E, = 1.5 TeV. Practically, the full separation for x/p and n/k is seen. The relation between the rejection factor and the hadron energy E, is given in Fig. 8. For comparison, in Fig. 8, the curve for Rk,,, given in Ref. [ 131 for the fully optimized usual TRD with lithium radiator is given. The device consists of 12 modules, containing 8 g/cm’ of material or - 11% of nuclear interaction length.
Fig. 7. The number of quanta distributions for ?E,K, p with Eh = 1.5TeV.
7. Conclusions of (n,) could lead to the improvement of rejection; however, the decrease of absolute value of mean number of quanta gives the disunion increase. This compensated the positive effect and the rejection has not changed. In Fig. S the spectra 3 (Fig. 3(b) and (c)) in integral form are given. They show the relative number of useful quanta with energy greater than the given energy E,. It can be noted that for rt the number of quanta with E, > 11 keV is 80% and for p - 20%, i.e. for x the spectrum of useful quanta is significantly harder. The mean energy of quanta for E is equal to 19.7 keV and for p -7.6 keV at E = 1 TeV, i.e., to say the quanta spectrum for rc is about 2-3 times harder than in usual TRD, which has to provide a wider working interval in terms of y factor. In Fig. 6 the relation between the mean number of quanta registered m Xe(&,-+ co) and hadron energy is given. The numbers on the curves are r~~,k,~coefficient values, showing the quantum scattering efficiency for different hadrons. For rejection calculations the Xe thickness was restricted by 10 layers (k = 10, Ix, = 50mm).
The Monte-Carlo calculation of Compton TRD for hadron identifications in high-energy beams shows that this detector should work adequately to the principles on which it is based. These principles provide four important advantages (1) The separation of quanta registration region from initial particles that allows to exclude the ionization background as well as the registration of beam with high density of particles in a small part of the space. (2) Using the differences in the frequency spectra for 71,K, p. It allows to provide more effective scattering of quanta for pion. (3) The usage of a harder part of spectra for H, which appears in higher dynamics with respect to the Lorentsfactor and increases the dynamical range of TDR. (4) Use of quantum scattering principle in the radiator, provides the linear dependence on the radiator length and leads to a higher factor of rejection. Such a high value of the rejection R,,, and R,,, gives good opportunities for the TRD optimization in the sense of
K.K. Shikhliarov et al. /Nucl. Instr. and Meth. in Phvs. Rex A 398 (1997) 189-194
194
radiator length.
length
from 0.1 to 0.05 of nuclear
interaction
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[7] E. Storm, H. Israel, Photon
cross-section from 0.001 to 100MeV for Elements 1 through 100, Los Alamos Scient. Lab.. New Mexico, 1967. [S] O.F. Nemets. V.V. Gofman, A Handbook in Nuclear Physics, Kiev, 1975. [9] M.L. Cherry, G. Hartmann, D. Muller. Th.A. Prince, Phys. Rev. D lO(11) (1974) 3594. [lo] G.M. Garibian et al.. Nucl. Instr. and Meth. 125(1975) 133. [l l] Kai Siegbahn (Ed.), Alpha-Beta and Gamma-Ray Spectroscopy, vol. 1, North-Holland, Amsterdam, 1965, p. 73. [12] Kai Siegbahn (Ed.), Alpha-Beta and Gamma-Ray Spectroscopy, vol. 1. North-Holland, Amsterdam, 1965. p. 77. [13] C.W. Fabjan et al., Preprint CERN EP/83-45.