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Effective positron source based on coherent radiation of relativistic electrons in crystal
Nuclear Instruments and Methods in Physics Research B I 15(1996)393-395
Beam InteractIons with Materials A Atoms
ELSEVIER
Effective positron source based on coherent radiation of relativistic electrons in crystal
*,
V.P. Lapko aT I.N. Mom-b-us a, N.N. Nasonov
a, A. Jejcic b, J. Maillard b, J. Silva b
a NSC Kharkov Insriture of Physics & Technology, Kharkov 310108, Ukraine b College de France, Paris 75231, France
Abstract A two stage positron source with a crystalline radiator is considered. The dependence of the positron yield on the primary electron beam divergence and the radiator materials is studied. At the high energy, the radiator from light elements provides a higher position yield but needs beams with a less divergence.
1. Introduction Recently a great attention has been drawn to the study of nonconventional positron sources employing high intensity of channelling radiation [l]. Such source consists of the separate crystalline radiator and amorphous converter. Tbe gamma quanta emitted in the radiator are transformed into e+, e- pair in the converter. Until recently, radiators made from crystals with a high atomic number 2 seemed to be preferable. Encouraging results were obtained for the positron source with the tungsten single crystal radiator [2]. This concept was revised in Refs. [3,4] in which dependence of the positron yield on the atomic number of radiator material was studied. It was found that, at high primary electron energies, when radiation is essentially non-dipole, the source efficiency increases with the atomic number of the radiator material decreasing. The results of Refs. [3,4] were obtained at the primary electron beam divergence about y-l. Besides, the calculation method did not permit us to take into account a number of factors affecting the source characteristics. In this work, the calculation method has been generalised to include into consideration the channelled electron contribution to the radiation and the radiation suppression in the low frequency part of the spectrum. The effect of the primary electron beam divergence on the positron yield has been studied as well.
2. Calculation
method
The small thickness, compared to the radiation length, both of the radiator and of the converter are typical for the
* Corresponding author. Tel. +7 0572 356523; 351738; e-mail: [email protected]. 0168-583X/%/$15.00 Copyright PII SOl68-583X(96)00169-3
fax +7 0572
source version under consideration. It allows us in a first approximation to neglect the electromagnetic shower and simplify the calculation. It is essential for the radiator calculation that the crystal is oriented strictly along the primary beam axis. In this case, only incoherent multiple scattering, which is the same as in an amorphous medium, must be taken into account. We obtained the photon spectrum at the radiator exit by integrating the radiation intensity over the crystal thickness with the weight, which is a Gaussian distribution function and describes the electron flux evolution along the crystal. The photon absorption and electron energy losses were, of course, taken into account. The radiation intensity was calculated by means of the method developed in our previous work [5]. Following it, we usually considered electron interaction with a single crystal string and then averaged the radiation over the electron beam phase space. Two improvements have been introduced in this work. The first allows us to calculate more precisely the radiation intensity for the low energy photons. The point is that an electron interacts on the coherence length with several crystal strings in this case, a number of which grows with photon energy decreasing. The interference between the radiation emitted from different strings is of importance and has to be taken into account. To deal with this problem we calculated the radiation intensity considering the interaction with four strings. This specific number is a proper compromise between two contradictory demands: to extend taking account of interference to more lower energy photons and to decrease computer running time. The second allows us to check the assumption that, at the radiator thickness exceeding considerably the dechanneling length, one can neglect the contribution to the radiation made by the channelled electrons. We did not restrict ourselves to
0 1996 Elsevier Science B.V. All rights reserved
V. CRYSTAL ASSISTED PROCESSES
394
V.P. Lapko et al./Nucl.
Instr. and Meth. in Phys. Res. B I15 (1996) 393-395
considering only above barrier electrons as it was in our previous works [3,4]. The electron beam was separated into the channelled and above barrier fractions and the radiation intensity was calculated for both of them. To calculate the converter the physical model of the positron production process has been developed. It is based on the assumption that positron multiple scattering plays the main role in the positron beam formation at the source exit. In this case, one can neglect the photon beam angle dimensions and the angle spread of the positrons created in a certain converter transverse cross section. The photon absorption and the energy losses of produced positrons were taken into account.
E=l
0.60 -
OGeV
.c
.
0.40
f,,,_
0.00 0.0
~~
0.1
0.4
0.5
Of/LraOd3
Fig. 2. The same as Fig. 1 for the primary electron energy 10 GeV.
3. Results and discussion The positron yield dependence on the radiator thickness was studied at three values of the primary electron energy: E = 2, 10 and 20 GeV and the values of the beam divergence: 10e3 and 0.3 X 10e3. As radiator materials we took diamond, silicon, germanium and tungsten crystals oriented along the (111) axis. The diamond crystals with such thickness are not realisable. They were considered to demonstrate the tendency to the positron yield growth. The previous analysis proved that the positron yield depended weakly on the converter materials. So we considered only the tungsten converter with the thickness of half radiation length. The yield of the positron having the energies from 5 to 50 MeV and the angle divergence A6 < 10” has been calculated. The results are presented in Figs. l-3. The curves describe the positron yield per incident electron versus the radiator thickness expressed in the units of the radiation length. The parameters are an electron beam divergence and a radiator material atomic number.
The obtained results confirm the data of Refs. [3,4]. The character of the Z-dependence changes drastically if the electron energy increases from 2 to 20 GeV. The reasons of such behaviour were discussed in detail in Refs. [3,4]. We will only point out that the fall in the positron yield accompanying the growth in the radiator material atomic number is associated with the non-dipole nature of the radiation at the high electron energy. It this case, the radiation energy rises due to high energy photons. Their numbers fall proportionally to l/o and they make therefore a small contribution to the positron yield. It was found that the allowance for the channelled electrons enhanced the photon yield by 10% at the radiator thickness of half radiation length, which justifies our early approximation. The obtained results indicate also that the positron yield drops if the primary electron beam divergence rises. Its effect is almost negligible at the low electron energy and get stronger at the high energy, being more appreciable for the light elements. Nevertheless, the comparison with our previous results does not show the positron yield to be very sensitive to this parameter. For example, if the diver-
E=ZG~V
E=20GeV
0.80
0.60
.q
0.40
z? 0.20
0.00 0.0
Fig. 1. The positron yield versus radiator thickness. The primary electron energy is 2 GeV. The primary electron beam divergence is 10v3 (dots) and 0.3 X 10m3 (solid). The radiator material is C l,Si-¤,Ger,WT.
0.1
0.2 L/LraOd3
0.4
0.5
Fig. 3. The same as Fig. 1 for the primary electron energy 20 GeV.
V.P. Lapka et al. / Nucl. Instr. and Meth. in Phys. Res. B I IS
gence rises from y -’ to 0.3 X 10e3 which is 12 times as large at the electron energy 20 GeV, the positron yield gets only 1.5 times as small.
4. Conclusions The previous results concerning the positron yield dependence on the radiator material atomic number are confirmed with additional factors taken into account. There is a weak dependence at the low electron energy. At the high energy, the radiator from light elements provides a higher positron yield but needs beams with a less divergence.
f 1996) 393-395
395
References
[l] R. Chehab, Positron Sources,LAL/RT 9-02 and CERN 89-05, p. 105. [2] X. Artru, V.N. Baier, R. Chehab and A. Jejcic, Nucl. Instr. and Meth. A 344 (1994) 434. [3] V.P. Lapko, I.N. Mondrus and N.N. Nasonov, Pis’ma Zh. Tech. Fiz. 20 (14) (1994) p. 66. [4] V.P. Lapko, I.N. Mondrus and N.N. Nasonov, Proc. 4th European Particle Accelerator Conf. vol. 2. p. 1492. [5] B. Bartz, V. Lapko, N. Nasonov and N. Shlyakhov, Dok. Acad. Nauk Ukr. 12 (1992) p. 34.
V. CRYSTALASSISTEDPROCESSES
Beam InteractIons with Materials A Atoms
ELSEVIER
Effective positron source based on coherent radiation of relativistic electrons in crystal
*,
V.P. Lapko aT I.N. Mom-b-us a, N.N. Nasonov
a, A. Jejcic b, J. Maillard b, J. Silva b
a NSC Kharkov Insriture of Physics & Technology, Kharkov 310108, Ukraine b College de France, Paris 75231, France
Abstract A two stage positron source with a crystalline radiator is considered. The dependence of the positron yield on the primary electron beam divergence and the radiator materials is studied. At the high energy, the radiator from light elements provides a higher position yield but needs beams with a less divergence.
1. Introduction Recently a great attention has been drawn to the study of nonconventional positron sources employing high intensity of channelling radiation [l]. Such source consists of the separate crystalline radiator and amorphous converter. Tbe gamma quanta emitted in the radiator are transformed into e+, e- pair in the converter. Until recently, radiators made from crystals with a high atomic number 2 seemed to be preferable. Encouraging results were obtained for the positron source with the tungsten single crystal radiator [2]. This concept was revised in Refs. [3,4] in which dependence of the positron yield on the atomic number of radiator material was studied. It was found that, at high primary electron energies, when radiation is essentially non-dipole, the source efficiency increases with the atomic number of the radiator material decreasing. The results of Refs. [3,4] were obtained at the primary electron beam divergence about y-l. Besides, the calculation method did not permit us to take into account a number of factors affecting the source characteristics. In this work, the calculation method has been generalised to include into consideration the channelled electron contribution to the radiation and the radiation suppression in the low frequency part of the spectrum. The effect of the primary electron beam divergence on the positron yield has been studied as well.
2. Calculation
method
The small thickness, compared to the radiation length, both of the radiator and of the converter are typical for the
* Corresponding author. Tel. +7 0572 356523; 351738; e-mail: [email protected]. 0168-583X/%/$15.00 Copyright PII SOl68-583X(96)00169-3
fax +7 0572
source version under consideration. It allows us in a first approximation to neglect the electromagnetic shower and simplify the calculation. It is essential for the radiator calculation that the crystal is oriented strictly along the primary beam axis. In this case, only incoherent multiple scattering, which is the same as in an amorphous medium, must be taken into account. We obtained the photon spectrum at the radiator exit by integrating the radiation intensity over the crystal thickness with the weight, which is a Gaussian distribution function and describes the electron flux evolution along the crystal. The photon absorption and electron energy losses were, of course, taken into account. The radiation intensity was calculated by means of the method developed in our previous work [5]. Following it, we usually considered electron interaction with a single crystal string and then averaged the radiation over the electron beam phase space. Two improvements have been introduced in this work. The first allows us to calculate more precisely the radiation intensity for the low energy photons. The point is that an electron interacts on the coherence length with several crystal strings in this case, a number of which grows with photon energy decreasing. The interference between the radiation emitted from different strings is of importance and has to be taken into account. To deal with this problem we calculated the radiation intensity considering the interaction with four strings. This specific number is a proper compromise between two contradictory demands: to extend taking account of interference to more lower energy photons and to decrease computer running time. The second allows us to check the assumption that, at the radiator thickness exceeding considerably the dechanneling length, one can neglect the contribution to the radiation made by the channelled electrons. We did not restrict ourselves to
0 1996 Elsevier Science B.V. All rights reserved
V. CRYSTAL ASSISTED PROCESSES
394
V.P. Lapko et al./Nucl.
Instr. and Meth. in Phys. Res. B I15 (1996) 393-395
considering only above barrier electrons as it was in our previous works [3,4]. The electron beam was separated into the channelled and above barrier fractions and the radiation intensity was calculated for both of them. To calculate the converter the physical model of the positron production process has been developed. It is based on the assumption that positron multiple scattering plays the main role in the positron beam formation at the source exit. In this case, one can neglect the photon beam angle dimensions and the angle spread of the positrons created in a certain converter transverse cross section. The photon absorption and the energy losses of produced positrons were taken into account.
E=l
0.60 -
OGeV
.c
.
0.40
f,,,_
0.00 0.0
~~
0.1
0.4
0.5
Of/LraOd3
Fig. 2. The same as Fig. 1 for the primary electron energy 10 GeV.
3. Results and discussion The positron yield dependence on the radiator thickness was studied at three values of the primary electron energy: E = 2, 10 and 20 GeV and the values of the beam divergence: 10e3 and 0.3 X 10e3. As radiator materials we took diamond, silicon, germanium and tungsten crystals oriented along the (111) axis. The diamond crystals with such thickness are not realisable. They were considered to demonstrate the tendency to the positron yield growth. The previous analysis proved that the positron yield depended weakly on the converter materials. So we considered only the tungsten converter with the thickness of half radiation length. The yield of the positron having the energies from 5 to 50 MeV and the angle divergence A6 < 10” has been calculated. The results are presented in Figs. l-3. The curves describe the positron yield per incident electron versus the radiator thickness expressed in the units of the radiation length. The parameters are an electron beam divergence and a radiator material atomic number.
The obtained results confirm the data of Refs. [3,4]. The character of the Z-dependence changes drastically if the electron energy increases from 2 to 20 GeV. The reasons of such behaviour were discussed in detail in Refs. [3,4]. We will only point out that the fall in the positron yield accompanying the growth in the radiator material atomic number is associated with the non-dipole nature of the radiation at the high electron energy. It this case, the radiation energy rises due to high energy photons. Their numbers fall proportionally to l/o and they make therefore a small contribution to the positron yield. It was found that the allowance for the channelled electrons enhanced the photon yield by 10% at the radiator thickness of half radiation length, which justifies our early approximation. The obtained results indicate also that the positron yield drops if the primary electron beam divergence rises. Its effect is almost negligible at the low electron energy and get stronger at the high energy, being more appreciable for the light elements. Nevertheless, the comparison with our previous results does not show the positron yield to be very sensitive to this parameter. For example, if the diver-
E=ZG~V
E=20GeV
0.80
0.60
.q
0.40
z? 0.20
0.00 0.0
Fig. 1. The positron yield versus radiator thickness. The primary electron energy is 2 GeV. The primary electron beam divergence is 10v3 (dots) and 0.3 X 10m3 (solid). The radiator material is C l,Si-¤,Ger,WT.
0.1
0.2 L/LraOd3
0.4
0.5
Fig. 3. The same as Fig. 1 for the primary electron energy 20 GeV.
V.P. Lapka et al. / Nucl. Instr. and Meth. in Phys. Res. B I IS
gence rises from y -’ to 0.3 X 10e3 which is 12 times as large at the electron energy 20 GeV, the positron yield gets only 1.5 times as small.
4. Conclusions The previous results concerning the positron yield dependence on the radiator material atomic number are confirmed with additional factors taken into account. There is a weak dependence at the low electron energy. At the high energy, the radiator from light elements provides a higher positron yield but needs beams with a less divergence.
f 1996) 393-395
395
References
[l] R. Chehab, Positron Sources,LAL/RT 9-02 and CERN 89-05, p. 105. [2] X. Artru, V.N. Baier, R. Chehab and A. Jejcic, Nucl. Instr. and Meth. A 344 (1994) 434. [3] V.P. Lapko, I.N. Mondrus and N.N. Nasonov, Pis’ma Zh. Tech. Fiz. 20 (14) (1994) p. 66. [4] V.P. Lapko, I.N. Mondrus and N.N. Nasonov, Proc. 4th European Particle Accelerator Conf. vol. 2. p. 1492. [5] B. Bartz, V. Lapko, N. Nasonov and N. Shlyakhov, Dok. Acad. Nauk Ukr. 12 (1992) p. 34.
V. CRYSTALASSISTEDPROCESSES