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Investigation of positron generation by relativistic electrons in aligned crystals
Nuclear Instruments and Methods in Physics Research B 145 (1998) 209±220
Investigation of positron generation by relativistic electrons in aligned crystals B.N. Kalinin a, G.A. Naumenko a, A.P. Potylitsin a, V.A. Verzilov a, I.E. Vnukov K. Yoshida b, K. Goto b, I. Endo c, T. Isshiki c, T. Kondo c, K. Matsukado c, T. Takashima c, T. Takahashi c, H. Okuno d, K. Nakayama e a
a,*
,
Nuclear Physics Institute, Tomsk Polytechnic University, P.O. Box 25, Lenin Ave. 2-a, 634050 Tomsk, Russian Federation b Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739, Japan c Faculty of Science, Hiroshima University, Higashi-Hiroshima 739, Japan d Institute for Nuclear Study, University of Tokyo, Tanashi 188, Japan e Energy and Mechanical Research Laboratory, Toshiba Corporation, Kawasaki 210, Japan Received 13 December 1997; received in revised form 24 April 1998
Abstract An experiment to investigate the positron production eciency by electrons moving in axially oriented tungsten and silicon single crystals has been conducted. The electron energy was 1.2 GeV. The positron yield from the aligned crystal 0.35 r.l. in thickness was 2.8 times that from the randomly oriented crystals for tungsten and 1.8 times higher for silicon. A simple model has been designed to simulate positron production by coherent bremsstrahlung (CB) photons. Comparison of the calculation with the experiment has shown that most contribution to the positron production in thick crystals comes from CB. Ó 1998 Elsevier Science B.V. All rights reserved. PACS: 29.25.-t; 78.70.-g; 61.85.+p
1. Introduction A few authors [1,2] suggested a novel approach to designing high-intensity positron sources for storage rings and colliders of a new generation. Their underlying idea is the use of aligned crystals
* Corresponding author. Tel.: +7 3822 42 3994; fax: +7 3822 42 3934; e-mail: [email protected].
as converters to generate positrons by electron beams. Positron sources used earlier employed amorphous converters whose thickness was chosen according to the maximum of the cascade curve (2±6 r.l. with respect to the initial electron energy) [3,4]. Evidently, the electron beam energy in such a thick crystal is virtually completely lost as heat, which imparts serious limitations on increasing positron yield from the converter [5]. The merits of using aligned crystals are, on the one hand, a decrease in
0168-583X/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 3 6 5 - 6
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the radiation length, and on the other, an increase in the yield of photons (channeling radiation and coherent bremsstrahlung (CB)). Performance of the source based on a converter made of an aligned tungsten crystal is analyzed at length in Ref. [6] using the results of numerical simulations. The authors of the work cited showed an evident advantage of the tungsten crystal over the amorphous converter in the region of initial electron energies 2±20 GeV. Nonetheless, the aforementioned work did not evaluate the eects of the perfection of crystals on radiation characteristics and, hence, on the positron yield. Modern technological processes for making tungsten crystals are known to produce crystals with mosaicity 0.5 mrad [7], which exceeds the critical channeling angle for electrons with the energy E > 5 GeV. On the other hand, some authors [8] point to a potential advantage of crystals with small Z (e.g. Si) in the energy range E 20 GeV, although it is still questionable for E 1 GeV. One of the objectives of the present work is to study the yield of positrons from an aligned single crystal silicon (mosaicity less than 0.05 mrad) and tungsten (mosaicity 1 mrad) and compare this yield with that from randomly oriented crystals.
2. Experimental method and facilities The experiment ES-164 was realized on the extracted electron beam of the INS synchrotron, Tokyo University. Schematics of the experiment is plotted in Fig. 1. The electron energy was E 1.2 GeV and the beam divergence was DH 0:12 mrad [9]. The following technique was used to monitor the electron beam. A multifoil target of 10 thin silicon crystals, each 16 lm thick, (Si) was placed in front of the main crystal converter (T) and was aligned by a goniometer at the Bragg angle HB 13°. The distance between the multifoil and the main targets was 200 mm. Photons of parametric X-rays and diracted transition radiation (PXR + DTR) were detected at the angle HD 2HB 26 by a NaI (Tl) spectrometer with the aperture DHx DHy 6:72 10ÿ5 sr [10]. The ratio of the X-ray counting rate to the electron beam intensity was calibrated with a low-intensity electron beam. This intensity measurement system was highly reliable, since it was free from the spurious signals due to soft components accompanying the electron beam. The experiment was carried out with an intensity of around 106 electrons per second. The additional target used here virtually did not aect the positron generation
Fig. 1. Experimental set-up. Si ± multifoil silicon target; T ± a crystal on the goniometer; M ± sweep magnet; MS ± magnetic spectrometer; S1 , S2 ± scintillation counters; Sc ± Compton scatterer. C1 ± a vertical 1 mm slit collimator; C2 and C3 ± positron collimators.
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process, since its thickness (1.71 ´ 10ÿ3 r.l.) was by far less than that of the main converter, and also because the additional electron beam divergence due to the multiple scattering of electrons in the multifoil target (Hms 0:72 mrad) was less than the tungsten crystal mosaicity (see below). Fig. 2(a) shows a typical PXR + DTR spectrum. For monitoring purpose we measured the yield of PXR + DTR which is given in the ``window'' of the ®gure. Contribution of the background did not exceed two percent. Employment of a multifoil crystal target results in a consider-
Fig. 2. (a) Spectrum of PXR + DTR from multifoil silicon target. (b) Horizontal pro®le of extracted electron beam.
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able increase in the yield of monochromatic photons per one electron. Fig. 2(b) shows the horizontal pro®le of the extracted beam which was measured while moving horizontally a vertical 1 mm ± slit collimator (C1 ) located immediately after the multifoil target. The tantalum collimator thickness was selected such that the PXR + DTR photons were totally absorbed in the collimator. The PXR + DTR yield thus detected is then proportional to the electron beam intensity in the location of the slit. As follows from the ®gure the width (in the base) of the electron beam was DX 6.5 mm. The main single crystal converter was aligned with respect to the electron beam by means of a goniometer. Use was made of silicon (B 70 ´ 35 mm, t 0.37 r.l.) and tungsten (B 9 ´ 1.18 mm, t 0.34 r.l.) converters. The c-ray diraction measurements of the tungsten crystal by means of c-quanta with an energy of 0.412 MeV (198 Au) revealed structural homogeneity (absence of single blocks turned by an angle greater than 1.5 mrad) on the surface and in the depth of the crystal. The silicon crystal surface mosaicity was estimated by means of Laue patterns. Its value was about 0.05 mrad. During electron transmission along the crystallographic plane or axis, at the same time as the bremsstrahlung component is generated, there forms a high-intensity ``soft'' component (with photon energy x < 100 MeV), called forth by channeling radiation and CB. A NaI(Tl) spectrometer positioned in Compton geometry at the angle HD 30 was used to detect the soft photons scattered in an aluminium plate (Sc) in the energy range xscat > 1 MeV. The scatterer was positioned 10 m behind the main target. A sweep magnet (M) placed between the scatterer and a magnetic spectrometer (MS) was used for cleaning the c-beam from charged particles. Fig. 3(a,b) shows typical orientation dependences of the scattered radiation yield (solid circles) for axis á1 0 0ñ in the tungsten and silicon crystals. For both crystals one observes a distinct maximum for the axial orientation while FWHMs of the curves are dierent (FWHMSi 0.6° 0.05° and FWHMW 1.1° 0.1°). This might be due to the dierence in the critical angle for the á1 0 0ñ axial
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Fig. 3. Orientation dependences of soft photons yield (dark circles) and positron yield (open circles) for tungsten (upper) and silicon (lower). Positron emission angle is equal to 0 , momentum of positrons is equal to 20 MeV/c.
p channeling, wc 2U0 =E, where U0 is the depth of the crystal axis potential, E is the electron energy, (wc 0:372 mrad for the silicon and wc 1.165 mrad for the tungsten crystal) as well as to a high-mosaic factor of the tungsten target. Another reason for the dierence may be the angle between the (1 1 0) crystallographic and horizontal planes. It is 0° for the silicon and 6° 1° for the tungsten crystal. It should be noted that the excess in the photon and positron yields on the crystallographic planes far from the axis are rather small (approximately 10±15% of the levels in disoriented targets). Positrons were detected in the momentum range Dp 5±40 MeV/c by a magnetic spectrom-
eter which was placed at linp 465 mm behind the crystal target. The spectrometer consisted of a 50° sector magnet, two lead collimators, 8 mm (C2 ) and 20 mm (C3 ) in diameter, two scintillation counters (S1 and S2 ), 30 ´ 40 ´ 3 mm each, and a NaI(Tl) spectrometer, B 63 ´ 63 mm, located at the focal point of the magnet. Measurements of the amplitude spectrum by the NaI(Tl) device provided an additional means to ``suppress'' the background. The path of the positron from the main crystal target to the collimator the C2 was enveloped in a helium bag to diminish multiple scattering, and the counters were shielded against background radiation. The magnet bearing the detecting system was capable of revolving around the crystal target, with the departure angles H 0±40 with respect to the electron beam. According to our estimates, the spectrometer momentum resolution was (Dp/ p) 5.5% for the positron momentum 20 MeV/c. The angular acceptances were 12 and 6 mrad in the horizontal and vertical directions, respectively. The spectrometer characteristics were calculated by the Monte Carlo method in the ®rst-order approximation. Within this approximation the real distribution of the magnetic ®eld was replaced by the constant distribution with eective boundaries. The in¯uence of the distorted magnetic ®eld on the movement of positrons in the vertical plane was taken into account. The acceptance was DXDp 1:68 10ÿ4 sr Mev/c for the positron momentum 20 MeV/c. Detailed description of the calculations of the spectrometer performance and the absolute eciency of positron detection will be presented in the paper to follow. Empty circles in Fig. 3(a,b) show the orientation dependence of the e yield (in relative units) from both crystals. The positron momentum p 20 MeV/c, the emission angle being null. One might note a coincidence of the e yield maximum with that of the channeling radiation within the accuracy of the goniometer error. Fig. 4 gives the yield of positrons measured (in relative units) with respect to their momenta for the axial alignment á1 0 0ñ of silicon, and for a misaligned crystal. The outgoing angle of positrons was H 5 . Shown in Fig. 5 are the same characteristics for W. It is apparent that in the case
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Fig. 4. Positron yield from oriented and disoriented silicon VS positron momentum for outgoing angle H 5 .
of axial alignment we observe a virtually uniform growth of the positron yield within H 0±20 over the whole energy range in question. Moreover, there is also a signi®cant increase in the positron yield from the tungsten crystal as comN . pared to silicon RW 2:6; RSi 1:7 R Nh100i rand
Fig. 5. The same for tungsten.
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Fig. 6. Angular distribution of positrons with p 20 MeV/c for the aligned (open circles) tungsten crystal and disoriented crystal (solid circles). Lines ± exponential ®t.
The angular spread of the output positrons from the aligned and randomly oriented tungsten crystal is plotted in Fig. 6. It was measured for the positron momentum p 20 MeV/c. Similar distributions for the silicon target are presented in Fig. 7. These ®gures also show the results of ®tting through exp ÿH=H0 . It follows from the plots that the ®ttings match the experiment satisfactorily.
Fig. 7. The same for the silicon crystal.
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The ®tting angles are H0 5:7 0:5 for the tungsten and H0 5:4 0:4 for the silicon crystals. One may (fairly roughly) estimate the average positron outgoing angle with respect to the eÿ momentum in the following manner. It is readily demonstrated that in fairly thin targets (of thickness t), where cascades can be neglected, during the e generation by electrons these electrons cover a path t=3 before emission of a photon, which, in its turn, travels t=3 before producing a pair, and, ®nally, each particle of this pair, on the average, covers t=3 before leaving the target. Therefore, the average angle of multiple scattering of the initial electronp before it gives a photon is Heÿ 21 MeV=E t=6 4 mrad, which in our case by far exceeds other characteristic angles, such as the photon emission angle Hc mc2 =E 0.4 mrad, the critical channeling angle and the mosaicity angle. The characteristic positron angle (with respect to photon momentum) may be evaluated as He mc=p 25 mrad (for p 20 MeV/c). Since the above value is signi®cantly higher than the multiple scattering angle of the initial electron, we may consider this particular angle to describe the intrinsic angular distribution of positrons with respect to the initial electron momentum direction in the target. Multiple scattering of positrons inside the target brings about a considerable broadening of the intrinsic angular distribution and typical angle may be dep scribed as He 21 MeV=cp t=3:2 220 mrad 12:5 (for t 0.34). The resulting quantity is only an estimate of the characteristic angle. As follows from the ®t the phenomenological values of this angle (H0 6 ) in their order of magnitude, although close to, still are considerably lower than the estimate obtained. Fig. 8 shows the positron emission into a small solid angle through the zero angle versus the thickness of the target. Measurements were taken for the momentum p 20 MeV/c from amorphous lead and tantalum targets and disoriented tungsten crystals of three thicknesses. One may note a practically linear growth of the yield up to as much as 2:5 r.l. This might be interpreted in the following way. For a comparatively thin target the probability of photon emission is in proportion to t=3 and, hence, the probability for each photon to
Fig. 8. Thickness dependence of positron yield with p 20 MeV/c for H 0 from amorphous lead and tantalum targets (open circles) and disoriented tungsten targets (solid circles). Triangle ± yield from the aligned tungsten crystal.
produce a pair is proportional to (2/3)t. Thus, the output of the pair into an open cone would be proportional to t2 . On the other hand, the angular spread of the cone is characterized by H2 21 MeV=cp 2 (t/6) (see above), therefore, the angular positron density would depend linearly on the thickness. Surprisingly, the dependence retains its linear behaviour to the thickness of 2±3 r.l., where the two-step approximation used is deliberately insucient. For comparison, Fig. 8 shows a point corresponding to the e yield from the aligned tungsten crystal. 3. Simulations As mentioned above, the main processes of soft c-radiation generation in aligned crystals by relativistic electrons are the channeling radiation and CB. Here and later we will discuss mainly the results of the tungsten crystal experiment because it is in this case that we observed the maximum enhancement in the positron production. The peak of the positron yield shown in Fig. 3(a) has a large angular width, ®ve times wider than the axial
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channeling critical angle wc . This suggests that the appreciable part of the peak comes from other radiation processes than the sub-barrier channeling radiation, such as the above-barrier channeling radiation and the CB at very small angles to the crystal axis [11,12]. Generally speaking, spectral characteristics of radiation in the above-barrier channeling are close to those of CB [12]. An estimation of the axial channeling radiation contribution to positron production for this experiment was made in [13,14] by combining the well-known computer code EGS-4 for the electromagnetic cascade-shower [15] with the formulae for channeling radiation calculation in a dipole approximation [16]. In the papers cited it was shown that for a perfect tungsten crystal with the same thickness (0.34 r.l.) the positron yield connected with the contribution from the axial channeling radiation was about 60% 10% of bremsstrahlung in an equivalent amorphous target. This value is about one third of the experimental dierence between the positron yields from the aligned and disoriented tungsten crystal (the contribution from the crystal structure into the positron production is approximately twice the bremsstrahlung, see Fig. 3). In Ref. [14] it was shown that the probability for the electrons to be captured into the axial channeling regime on the crystal surface is about a few percent. Inside the crystal the probability sharply decreases. The total 2 probability is proportional to wc =Hms , where Hms is the average angle of electron multiple scattering in the crystal (about 8 mrad). Usage of the dipole approximation instead of nondipole formulae (the critical angle of the axial channeling wc 1.165 mrad is much larger than the characteristic angle cÿ1 0.426 mrad) leads to an increase in the calculated positron yield in comparison with a more precise approach (see, e.g. [12,18]). Crystal mosaicity also reduces the probability of electrons being captured into axial channeling regime on the crystal surface. In the ®rst approximation the in¯uence of mosaicity is equivalent to the additional electron beam diver2 gence. The suppression factor is about wc =reff , 2 2 2 where reff rmos re . rmos and re are the mosaicity characteristic angle and the electron beam divergence, respectively. It means that the actual
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contribution of sub-barrier channeling radiation into the experimental positron enhancement is about 15±20%. Another approach to treat of fast electron radiation in single crystals is the so-called constant ®eld approximation [18]. For the á1 0 0ñ axis of a tungsten crystal the so-called Baier angle wcfa V0 =m, where V0 is the scale of the axis potential and m is the electron mass [17,18], is lower than the critical channeling angle. Therefore, the contribution of this mechanism into positron generation should be rather small too. Proceeding from the above mentioned, we calculated the radiation spectra taking into account the CB process only including the multiple scattering of the initial electron beam into the crystal and the crystal mosaicity. The calculation method is described in [19]. Fig. 9 shows the yield of CB photons outgoing from the tungsten crystal with the energy higher than 21 MeV versus the orientation angle. One may compare the width of the curve obtained with the theta-scan for the positron yield with p 20 MeV/c (see Fig. 3(a)). The dierence between two FWHMs is less than 10%. Using this method we calculated the orientation dependences of the positron yield (``theta-scans'') for dierent emission angles and positrons momenta. A similar calculation of positron yields was
Fig. 9. Calculated orientation dependence of photon yield with the energy greater than 21 MeV.
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made for an equivalent amorphous target. As the lower boundary of quantum energy we took 5 MeV. In accordance with this method the target is partitioned into a great number of layers. The angular distribution of electrons is calculated again after each layer by convolution of the distribution of multiply scattered particles in this layer with that of the incoming electrons. This distribution, in turn, is used to calculate the CB spectrum in the next layer, and so forth. The photon spectrum after every layer equals the sum of the incident spectrum taking into account the absorption of photons in the layer, and the spectrum of photons produced in this layer. The positrons yield from the layer is determined by the spectrum of incident photons. We used here the following assumptions: 1. The energy of an electron upon passing every layer is its energy before the layer minus the losses in the relevant layer. It was shown in [18] that a similar approach gives but a minor error (a few percent) in calculating the cascade curve in amorphous targets and about 10±15% in aligned crystals. 2. Multiple scattering of electrons is described by the Molier theory for amorphous material of the same atomic parameters and density. 3. The crystal mosaic factor is equivalent to the additional electron beam divergence. The eective angular distribution of electrons is obtained for each layer through convolution of the mosaicity distribution in the layer with that of the incoming electrons. 4. No account is made of c-radiation angular distribution since characteristic angles of multiple scattering of low-energy positrons by far exceed such angles of electrons. We compared the angular distributions of positrons from an equivalent amorphous target calculated with and without the angular distribution of radiation and found them to dier only by as low as 3± 5% for the detection angles smaller than 2°. For large angles the distributions completely match. 5. The pair creation probability in a crystal coincides with that in an amorphous target with the same atomic parameters.
6. The energy of a positron after it leaves the target is the dierence between its initial energy and the radiation and ionization losses, with the latter losses calculated for the average positron energy on the path from the nucleation site to the end of the target. 7. To calculate the radiation losses of the positron energy we used the complete-screening approximation. We did not include the dierence between the positron energy lost to produce radiation in the crystal and the losses for bremsstrahlung because this dierence decreases sharply with the particle energy. 8. We assumed that multiple scattering of positrons on their way from the point of production to the edge of the target is described by the Molier theory for mean-energy positrons. Straightforward veri®cation of this assumption showed that the dierence in the angular distributions, obtained following this approximation and the above approach, which includes gradual broadening in the angular distributions when a particle passes through the target and the losses therein, is as low 3±5% for the angles smaller than 3rm , where rm is the rms angle of multiple scattering for the given thickness and mean particle energy. 9. Positron production by radiation from the secondary particles was disregarded (our targets are considerably thin, see comments to Fig. 8). The calculation includes the density eect in ionization losses and the screening in¯uence on the energy spread of the positrons produced. Exact values for the pair production probability and photoabsorption were taken from [20]. In the calculation of the positron angular distribution we disregard the blocking eect in pair creation [21], because for our experiment wcfa is much smaller than the characteristic angular beam size of c-radiation. The doughnut scattering eect which consists in turning of the particle with respect to its azimuth angle around its crystallographic axis (e.g. [22]) can also aect the resulting angular spread and spectrum of positrons. It is known (see e.g. [12]), that the CB intensity is mainly determined by an angle between the particle direction and the axis. As pointed out in p. 4, multiple scattering of positrons predominates in
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forming their angular distribution. Therefore, the in¯uence of the doughnut scattering eect of electrons on the spectra and angular distributions of positrons is suciently small. It is known (see e.g. [12,22]), that coherent eects in particle scattering in crystals decrease markedly with particle energy. Therefore, for the positron energy lower than 50±80 MeV, and it is these particles that mainly form the angular distributions measured, non-coherent (conventional) multiple scattering prevails. Proceeding from the above, we did not take into account the doughnut scattering eect of electrons and positrons in crystals in our calculation. A more detailed description of the calculation technique, discussion of applicability of the approximations assumed and comparison of the experiment with the calculations made for the silicon crystal will be given in our next paper. Here and later in the text we cite the experimental and calculated positron yields per single electron for various observation angles and positron momenta divided by the magnetic spectrom-
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eter acceptance. While calculating the acceptance we included the transverse beam size on the main crystal target, the spectrometer geometry and the positron multiple scattering on the crystal-tocounter path. Fig. 10 shows the experimental and calculated ``theta-scan'' of the positron yield for the detection angle 5° and the positron momentum 20 MeV/c. The calculation was done for the misalignment angle 6 between the crystallographic (0 1 1) and horizontal planes. It is evident from the ®gure that the model used describes the ``theta-scan'' width quite well. The dierence in widths is lower than 15%. The dierence between the experimental and calculated data (about 20% in absolute value for close-to-axis orientation) might be due to the radiation contribution in axial and planar channeling and the assumptions made in the calculations. Fig. 11 plots the experimental dependences of the positron yield from positron momentum for axial crystal alignment and at large misalignment (5°) angles for 4 angles of observation. The curves show the calculations for an equivalent
Fig. 10. Orientation dependences of positron yield for tungsten (p 20 MeV/c, H 5 ). Points-experiment, line-calculation.
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Fig. 12. Angular distribution of the positrons with a momentum of 20 MeV/c from the tungsten crystal under the channeling condition (open circles) and o the channeling condition (solid circles). The curve is the calculation for an equivalent amorphous target.
Fig. 11. Yield of the positrons from the tungsten crystal at the channeling condition (open circles) and o the channeling condition (solid circles) for the positron emission angles 0 (a), 5 (b), 10 (c) and, 20 (d) degrees versus positron momentum. The curve is the calculation for an equivalent amorphous target.
amorphous target. Fig. 12 depicts the positron angular distribution at two crystal orientations. The particles momentum is 20 MeV/c. The curve is the angular distribution of positrons calculated for an equivalent amorphous target. It is clear that the shape of angular distribution is virtually independent of crystal orientation. For the orientation á1 0 0ñ one observes the same growth in the positron yield as for the misaligned crystal within 0± 20°. Particles with a dierent momentum do not exhibit any dependence on angular distributions
Fig. 13. The average enhancement factors of the positron emission from the tungsten crystal versus positron momentum. Open circles are the experimental and solid circles are the calculated results. The curve is the interpolation.
either. Fig. 13 shows the mean positron yield enhancement for the aligned and misaligned crystals versus the positron momentum. Also plotted in this ®gure are the calculation results. The dierence between the calculation and experiment seems
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to be due to the contribution from the the channeling radiation. 4. Discussion and conclusions As shown by Figs. 11 and 12, the experimental data on positron yield from a disoriented crystal and the calculations for an equivalent amorphous target match within the accuracy of the experimental error. We may, therefore, use the calculation results to derive the positron yield for the particle momenta 10±40 MeV/c and the angular range 0°±20°. Angular distributions of positrons with a ®xed momentum for the aligned crystal dier from those for the disoriented crystal only in the multiplier controlled by the particle momentum. The total positron yield for the aligned crystal is, therefore, derived through multiplying the calculated angular distributions of positrons with ®xed momenta by the relevant scale factor, followed by integration with respect to the angle and momentum. As the scale multiplier use was made of the interpolated curve which is obtained from the experimental enhancement and plotted in Fig. 13. Positron yield per one electron in the above range for the tungsten crystal with axial orientation and for the disoriented target were 1.02 ´ 10ÿ1 e /eÿ and 3.64 ´ 10ÿ2 e /eÿ , respectively. For the silicon crystal they were 5.34 ´ 10ÿ2 e /eÿ per one electron from the axially aligned crystal and 3.31 ´ 10ÿ2 e /eÿ from the misaligned crystal. The errors the yield values was about 7± 10% for tungsten and 10±15% for silicon. The reported experiment on generating positrons in thick tungsten and silicon crystals irradiated by electrons with the energy 1.2 GeV brings about the following conclusions: (a) Advantages of single crystal converters to generate positrons by electrons with the energy 1 GeV have been now experimentally proven for the crystal thicknesses below 0.5 r.l. The e yield increases almost twofold from the silicon crystal and by about three times from tungsten. (b) In the energy range used the yield of positrons from an aligned crystal having a large Z (tungsten) exceeds that from a crystal with
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small Z (silicon), despite the fact that the structure of tungsten is inferior to that of silicon. This may be connected with a larger value of the critical channeling angle in tungsten, a higher mean emission energy for channeling radiation in tungsten, the contribution from multiplicity of radiation emitted by one electron [23] and dierent energy losses of positrons when they move in silicon and tungsten. (c) The angular positron spread is described fairly well by the function exp ÿH=H0 (but not gaussian), with a characteristic parameter of distribution by far lower (about twice) than the rms angle of multiple scattering of positrons with a ®nite energy. (d) The angular distribution of positrons from aligned and randomly oriented crystals coincide within the accuracy of the experimental error. It is the positron multiple scattering and the energy losses that contribute mainly to the formation of this distribution. (e) The positron yield into a small solid angle depends linearly on the thickness of the target up to its values of 2.5±3.0 r.l. where it reaches saturation. The saturation thickness may be further decreased if use is made of single crystal targets. (f) Comparison of the calculations with the experiments shows that the greater part of positrons is produced by CB photons for the electron energy region near 1 GeV and thick crystals. CB theory may be used to estimate the positron yield produced by relativistic electrons with the energy in the order 1±2 GeV in thick crystals. (g) One may expect the positron yield from aligned crystals to be higher than that from disoriented target in case of perfect crystals and a higher electron energy. In the latter case the contribution from sub-barrier channeling radiation may exceed that from CB at the electron energy E P 5 GeV (for the ®xed tungsten thickness, t 0.34 r.l.). (h) The results obtained in this work seem to be very promising. Further investigation in this ®eld will promote application of crystal targets on already existing accelerators as well as on the facilities in plan.
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Acknowledgements This work is supported in part by Grant-in-aid for Basic Researches by Monbusho. References [1] R. Chehab, F. Couchot, A.R. Nyaiech et al., Study of a positron source generated by photons from ultrarelativistic channeled particles, Preprint LAL ± RT 89±01, 1989. [2] F.J. Decker, Channeling crystals for positron production, Preprint SLAC ± PUB ± 5482, 1991. [3] J.E. Clendenin, High±yield positron systems for linear colliders, Proceedings of the 1989 IEEE Particle Accelerator Conference, Chicago, 1989, pp. 1107±1111. [4] K. Flottmann, J. Rossbach, A high intensity positron source for linear colliders, Preprint DESY M±91±11, 1991. [5] E.M. Reuter, J.A. Hodgson, 3D numerical thermal stress analysis of the high powr target for the SLC positron source, Preprint SLAC-PUB-5370, 1991. [6] X. Artru, V.N. Baier, R. Chehab et al., Nucl. Instr. and Math. A 344 (1994) 443. [7] R. Moor, M.A. Parker, A. Baurichter et al., Measurement of pair-production by high energy photons in an aligned tungsten crystal, Preprint CERN-SL/95-79, 1995.
[8] V.N. Baier, V.A. Baskov, V.B. Ganenko et al., JETP Lett. 49 (10) (1989) 615. [9] Y. Hashimoto, et al., Institute for Nuclear Study, University of Tokyo, Annual Report, 75, 1995. [10] K. Aramitsu et al., Preprint HUPD±9513, 1995. [11] M. Tobiyama et al., Phys. Lett. A 166 (1992) 140. [12] A.I. Akhiezer, N.F. Shul'ga, High Energy Electrodynamics in Matter, Gordon and Breach, Luxemburg, 1996. [13] K. Yoshida et al., Preprint HURD-9706, 1997. [14] T. Isshiki, Master Thesis, Hiroshima University, 1997. [15] W.R. Nelson, H. Hirayama, D.W.O. Rogers, SLAC Report 265 (1985). [16] M.A. Kumakhov, Ch.G. Trikalinos, Phys. Stat. Solidi B 99 (1980) 449. [17] V.N. Baier, V.M. Katkov, V.M. Strakhovenko, Sov. Phys. JETP 65 (1987) 686. [18] V.N. Baier, V.M. Katkov, V.M. Strakhovenko, High Energy Electromagnetic Processes in Aligned Single Crystals, Nauka, Novosibirsk, 1989, in Russian. [19] I.E. Vnukov, B.N. Kalinin, A.P. Potylitsin, Sov. Phys. J. 34 (1991) 481. [20] J.H. Hubbel, H.A. Gimm, I. Overbo, J. Phys. Chem. Ref. Data 9 (4) (1980) 1023. [21] X. Artru et al., Phys. Lett. B 313 (1993) 483. [22] S.P. Fomin, N.F. Shul'ga, Phys. Lett. A 73 (1979) 131. [23] S.I. Blazhevich, G.L. Bochek, V.I. Kulibaba et al., Technical Physics 38 (5) (1993) 374.
Investigation of positron generation by relativistic electrons in aligned crystals B.N. Kalinin a, G.A. Naumenko a, A.P. Potylitsin a, V.A. Verzilov a, I.E. Vnukov K. Yoshida b, K. Goto b, I. Endo c, T. Isshiki c, T. Kondo c, K. Matsukado c, T. Takashima c, T. Takahashi c, H. Okuno d, K. Nakayama e a
a,*
,
Nuclear Physics Institute, Tomsk Polytechnic University, P.O. Box 25, Lenin Ave. 2-a, 634050 Tomsk, Russian Federation b Hiroshima Synchrotron Radiation Center, Hiroshima University, Higashi-Hiroshima 739, Japan c Faculty of Science, Hiroshima University, Higashi-Hiroshima 739, Japan d Institute for Nuclear Study, University of Tokyo, Tanashi 188, Japan e Energy and Mechanical Research Laboratory, Toshiba Corporation, Kawasaki 210, Japan Received 13 December 1997; received in revised form 24 April 1998
Abstract An experiment to investigate the positron production eciency by electrons moving in axially oriented tungsten and silicon single crystals has been conducted. The electron energy was 1.2 GeV. The positron yield from the aligned crystal 0.35 r.l. in thickness was 2.8 times that from the randomly oriented crystals for tungsten and 1.8 times higher for silicon. A simple model has been designed to simulate positron production by coherent bremsstrahlung (CB) photons. Comparison of the calculation with the experiment has shown that most contribution to the positron production in thick crystals comes from CB. Ó 1998 Elsevier Science B.V. All rights reserved. PACS: 29.25.-t; 78.70.-g; 61.85.+p
1. Introduction A few authors [1,2] suggested a novel approach to designing high-intensity positron sources for storage rings and colliders of a new generation. Their underlying idea is the use of aligned crystals
* Corresponding author. Tel.: +7 3822 42 3994; fax: +7 3822 42 3934; e-mail: [email protected].
as converters to generate positrons by electron beams. Positron sources used earlier employed amorphous converters whose thickness was chosen according to the maximum of the cascade curve (2±6 r.l. with respect to the initial electron energy) [3,4]. Evidently, the electron beam energy in such a thick crystal is virtually completely lost as heat, which imparts serious limitations on increasing positron yield from the converter [5]. The merits of using aligned crystals are, on the one hand, a decrease in
0168-583X/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 3 6 5 - 6
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the radiation length, and on the other, an increase in the yield of photons (channeling radiation and coherent bremsstrahlung (CB)). Performance of the source based on a converter made of an aligned tungsten crystal is analyzed at length in Ref. [6] using the results of numerical simulations. The authors of the work cited showed an evident advantage of the tungsten crystal over the amorphous converter in the region of initial electron energies 2±20 GeV. Nonetheless, the aforementioned work did not evaluate the eects of the perfection of crystals on radiation characteristics and, hence, on the positron yield. Modern technological processes for making tungsten crystals are known to produce crystals with mosaicity 0.5 mrad [7], which exceeds the critical channeling angle for electrons with the energy E > 5 GeV. On the other hand, some authors [8] point to a potential advantage of crystals with small Z (e.g. Si) in the energy range E 20 GeV, although it is still questionable for E 1 GeV. One of the objectives of the present work is to study the yield of positrons from an aligned single crystal silicon (mosaicity less than 0.05 mrad) and tungsten (mosaicity 1 mrad) and compare this yield with that from randomly oriented crystals.
2. Experimental method and facilities The experiment ES-164 was realized on the extracted electron beam of the INS synchrotron, Tokyo University. Schematics of the experiment is plotted in Fig. 1. The electron energy was E 1.2 GeV and the beam divergence was DH 0:12 mrad [9]. The following technique was used to monitor the electron beam. A multifoil target of 10 thin silicon crystals, each 16 lm thick, (Si) was placed in front of the main crystal converter (T) and was aligned by a goniometer at the Bragg angle HB 13°. The distance between the multifoil and the main targets was 200 mm. Photons of parametric X-rays and diracted transition radiation (PXR + DTR) were detected at the angle HD 2HB 26 by a NaI (Tl) spectrometer with the aperture DHx DHy 6:72 10ÿ5 sr [10]. The ratio of the X-ray counting rate to the electron beam intensity was calibrated with a low-intensity electron beam. This intensity measurement system was highly reliable, since it was free from the spurious signals due to soft components accompanying the electron beam. The experiment was carried out with an intensity of around 106 electrons per second. The additional target used here virtually did not aect the positron generation
Fig. 1. Experimental set-up. Si ± multifoil silicon target; T ± a crystal on the goniometer; M ± sweep magnet; MS ± magnetic spectrometer; S1 , S2 ± scintillation counters; Sc ± Compton scatterer. C1 ± a vertical 1 mm slit collimator; C2 and C3 ± positron collimators.
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process, since its thickness (1.71 ´ 10ÿ3 r.l.) was by far less than that of the main converter, and also because the additional electron beam divergence due to the multiple scattering of electrons in the multifoil target (Hms 0:72 mrad) was less than the tungsten crystal mosaicity (see below). Fig. 2(a) shows a typical PXR + DTR spectrum. For monitoring purpose we measured the yield of PXR + DTR which is given in the ``window'' of the ®gure. Contribution of the background did not exceed two percent. Employment of a multifoil crystal target results in a consider-
Fig. 2. (a) Spectrum of PXR + DTR from multifoil silicon target. (b) Horizontal pro®le of extracted electron beam.
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able increase in the yield of monochromatic photons per one electron. Fig. 2(b) shows the horizontal pro®le of the extracted beam which was measured while moving horizontally a vertical 1 mm ± slit collimator (C1 ) located immediately after the multifoil target. The tantalum collimator thickness was selected such that the PXR + DTR photons were totally absorbed in the collimator. The PXR + DTR yield thus detected is then proportional to the electron beam intensity in the location of the slit. As follows from the ®gure the width (in the base) of the electron beam was DX 6.5 mm. The main single crystal converter was aligned with respect to the electron beam by means of a goniometer. Use was made of silicon (B 70 ´ 35 mm, t 0.37 r.l.) and tungsten (B 9 ´ 1.18 mm, t 0.34 r.l.) converters. The c-ray diraction measurements of the tungsten crystal by means of c-quanta with an energy of 0.412 MeV (198 Au) revealed structural homogeneity (absence of single blocks turned by an angle greater than 1.5 mrad) on the surface and in the depth of the crystal. The silicon crystal surface mosaicity was estimated by means of Laue patterns. Its value was about 0.05 mrad. During electron transmission along the crystallographic plane or axis, at the same time as the bremsstrahlung component is generated, there forms a high-intensity ``soft'' component (with photon energy x < 100 MeV), called forth by channeling radiation and CB. A NaI(Tl) spectrometer positioned in Compton geometry at the angle HD 30 was used to detect the soft photons scattered in an aluminium plate (Sc) in the energy range xscat > 1 MeV. The scatterer was positioned 10 m behind the main target. A sweep magnet (M) placed between the scatterer and a magnetic spectrometer (MS) was used for cleaning the c-beam from charged particles. Fig. 3(a,b) shows typical orientation dependences of the scattered radiation yield (solid circles) for axis á1 0 0ñ in the tungsten and silicon crystals. For both crystals one observes a distinct maximum for the axial orientation while FWHMs of the curves are dierent (FWHMSi 0.6° 0.05° and FWHMW 1.1° 0.1°). This might be due to the dierence in the critical angle for the á1 0 0ñ axial
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Fig. 3. Orientation dependences of soft photons yield (dark circles) and positron yield (open circles) for tungsten (upper) and silicon (lower). Positron emission angle is equal to 0 , momentum of positrons is equal to 20 MeV/c.
p channeling, wc 2U0 =E, where U0 is the depth of the crystal axis potential, E is the electron energy, (wc 0:372 mrad for the silicon and wc 1.165 mrad for the tungsten crystal) as well as to a high-mosaic factor of the tungsten target. Another reason for the dierence may be the angle between the (1 1 0) crystallographic and horizontal planes. It is 0° for the silicon and 6° 1° for the tungsten crystal. It should be noted that the excess in the photon and positron yields on the crystallographic planes far from the axis are rather small (approximately 10±15% of the levels in disoriented targets). Positrons were detected in the momentum range Dp 5±40 MeV/c by a magnetic spectrom-
eter which was placed at linp 465 mm behind the crystal target. The spectrometer consisted of a 50° sector magnet, two lead collimators, 8 mm (C2 ) and 20 mm (C3 ) in diameter, two scintillation counters (S1 and S2 ), 30 ´ 40 ´ 3 mm each, and a NaI(Tl) spectrometer, B 63 ´ 63 mm, located at the focal point of the magnet. Measurements of the amplitude spectrum by the NaI(Tl) device provided an additional means to ``suppress'' the background. The path of the positron from the main crystal target to the collimator the C2 was enveloped in a helium bag to diminish multiple scattering, and the counters were shielded against background radiation. The magnet bearing the detecting system was capable of revolving around the crystal target, with the departure angles H 0±40 with respect to the electron beam. According to our estimates, the spectrometer momentum resolution was (Dp/ p) 5.5% for the positron momentum 20 MeV/c. The angular acceptances were 12 and 6 mrad in the horizontal and vertical directions, respectively. The spectrometer characteristics were calculated by the Monte Carlo method in the ®rst-order approximation. Within this approximation the real distribution of the magnetic ®eld was replaced by the constant distribution with eective boundaries. The in¯uence of the distorted magnetic ®eld on the movement of positrons in the vertical plane was taken into account. The acceptance was DXDp 1:68 10ÿ4 sr Mev/c for the positron momentum 20 MeV/c. Detailed description of the calculations of the spectrometer performance and the absolute eciency of positron detection will be presented in the paper to follow. Empty circles in Fig. 3(a,b) show the orientation dependence of the e yield (in relative units) from both crystals. The positron momentum p 20 MeV/c, the emission angle being null. One might note a coincidence of the e yield maximum with that of the channeling radiation within the accuracy of the goniometer error. Fig. 4 gives the yield of positrons measured (in relative units) with respect to their momenta for the axial alignment á1 0 0ñ of silicon, and for a misaligned crystal. The outgoing angle of positrons was H 5 . Shown in Fig. 5 are the same characteristics for W. It is apparent that in the case
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Fig. 4. Positron yield from oriented and disoriented silicon VS positron momentum for outgoing angle H 5 .
of axial alignment we observe a virtually uniform growth of the positron yield within H 0±20 over the whole energy range in question. Moreover, there is also a signi®cant increase in the positron yield from the tungsten crystal as comN . pared to silicon RW 2:6; RSi 1:7 R Nh100i rand
Fig. 5. The same for tungsten.
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Fig. 6. Angular distribution of positrons with p 20 MeV/c for the aligned (open circles) tungsten crystal and disoriented crystal (solid circles). Lines ± exponential ®t.
The angular spread of the output positrons from the aligned and randomly oriented tungsten crystal is plotted in Fig. 6. It was measured for the positron momentum p 20 MeV/c. Similar distributions for the silicon target are presented in Fig. 7. These ®gures also show the results of ®tting through exp ÿH=H0 . It follows from the plots that the ®ttings match the experiment satisfactorily.
Fig. 7. The same for the silicon crystal.
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The ®tting angles are H0 5:7 0:5 for the tungsten and H0 5:4 0:4 for the silicon crystals. One may (fairly roughly) estimate the average positron outgoing angle with respect to the eÿ momentum in the following manner. It is readily demonstrated that in fairly thin targets (of thickness t), where cascades can be neglected, during the e generation by electrons these electrons cover a path t=3 before emission of a photon, which, in its turn, travels t=3 before producing a pair, and, ®nally, each particle of this pair, on the average, covers t=3 before leaving the target. Therefore, the average angle of multiple scattering of the initial electronp before it gives a photon is Heÿ 21 MeV=E t=6 4 mrad, which in our case by far exceeds other characteristic angles, such as the photon emission angle Hc mc2 =E 0.4 mrad, the critical channeling angle and the mosaicity angle. The characteristic positron angle (with respect to photon momentum) may be evaluated as He mc=p 25 mrad (for p 20 MeV/c). Since the above value is signi®cantly higher than the multiple scattering angle of the initial electron, we may consider this particular angle to describe the intrinsic angular distribution of positrons with respect to the initial electron momentum direction in the target. Multiple scattering of positrons inside the target brings about a considerable broadening of the intrinsic angular distribution and typical angle may be dep scribed as He 21 MeV=cp t=3:2 220 mrad 12:5 (for t 0.34). The resulting quantity is only an estimate of the characteristic angle. As follows from the ®t the phenomenological values of this angle (H0 6 ) in their order of magnitude, although close to, still are considerably lower than the estimate obtained. Fig. 8 shows the positron emission into a small solid angle through the zero angle versus the thickness of the target. Measurements were taken for the momentum p 20 MeV/c from amorphous lead and tantalum targets and disoriented tungsten crystals of three thicknesses. One may note a practically linear growth of the yield up to as much as 2:5 r.l. This might be interpreted in the following way. For a comparatively thin target the probability of photon emission is in proportion to t=3 and, hence, the probability for each photon to
Fig. 8. Thickness dependence of positron yield with p 20 MeV/c for H 0 from amorphous lead and tantalum targets (open circles) and disoriented tungsten targets (solid circles). Triangle ± yield from the aligned tungsten crystal.
produce a pair is proportional to (2/3)t. Thus, the output of the pair into an open cone would be proportional to t2 . On the other hand, the angular spread of the cone is characterized by H2 21 MeV=cp 2 (t/6) (see above), therefore, the angular positron density would depend linearly on the thickness. Surprisingly, the dependence retains its linear behaviour to the thickness of 2±3 r.l., where the two-step approximation used is deliberately insucient. For comparison, Fig. 8 shows a point corresponding to the e yield from the aligned tungsten crystal. 3. Simulations As mentioned above, the main processes of soft c-radiation generation in aligned crystals by relativistic electrons are the channeling radiation and CB. Here and later we will discuss mainly the results of the tungsten crystal experiment because it is in this case that we observed the maximum enhancement in the positron production. The peak of the positron yield shown in Fig. 3(a) has a large angular width, ®ve times wider than the axial
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channeling critical angle wc . This suggests that the appreciable part of the peak comes from other radiation processes than the sub-barrier channeling radiation, such as the above-barrier channeling radiation and the CB at very small angles to the crystal axis [11,12]. Generally speaking, spectral characteristics of radiation in the above-barrier channeling are close to those of CB [12]. An estimation of the axial channeling radiation contribution to positron production for this experiment was made in [13,14] by combining the well-known computer code EGS-4 for the electromagnetic cascade-shower [15] with the formulae for channeling radiation calculation in a dipole approximation [16]. In the papers cited it was shown that for a perfect tungsten crystal with the same thickness (0.34 r.l.) the positron yield connected with the contribution from the axial channeling radiation was about 60% 10% of bremsstrahlung in an equivalent amorphous target. This value is about one third of the experimental dierence between the positron yields from the aligned and disoriented tungsten crystal (the contribution from the crystal structure into the positron production is approximately twice the bremsstrahlung, see Fig. 3). In Ref. [14] it was shown that the probability for the electrons to be captured into the axial channeling regime on the crystal surface is about a few percent. Inside the crystal the probability sharply decreases. The total 2 probability is proportional to wc =Hms , where Hms is the average angle of electron multiple scattering in the crystal (about 8 mrad). Usage of the dipole approximation instead of nondipole formulae (the critical angle of the axial channeling wc 1.165 mrad is much larger than the characteristic angle cÿ1 0.426 mrad) leads to an increase in the calculated positron yield in comparison with a more precise approach (see, e.g. [12,18]). Crystal mosaicity also reduces the probability of electrons being captured into axial channeling regime on the crystal surface. In the ®rst approximation the in¯uence of mosaicity is equivalent to the additional electron beam diver2 gence. The suppression factor is about wc =reff , 2 2 2 where reff rmos re . rmos and re are the mosaicity characteristic angle and the electron beam divergence, respectively. It means that the actual
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contribution of sub-barrier channeling radiation into the experimental positron enhancement is about 15±20%. Another approach to treat of fast electron radiation in single crystals is the so-called constant ®eld approximation [18]. For the á1 0 0ñ axis of a tungsten crystal the so-called Baier angle wcfa V0 =m, where V0 is the scale of the axis potential and m is the electron mass [17,18], is lower than the critical channeling angle. Therefore, the contribution of this mechanism into positron generation should be rather small too. Proceeding from the above mentioned, we calculated the radiation spectra taking into account the CB process only including the multiple scattering of the initial electron beam into the crystal and the crystal mosaicity. The calculation method is described in [19]. Fig. 9 shows the yield of CB photons outgoing from the tungsten crystal with the energy higher than 21 MeV versus the orientation angle. One may compare the width of the curve obtained with the theta-scan for the positron yield with p 20 MeV/c (see Fig. 3(a)). The dierence between two FWHMs is less than 10%. Using this method we calculated the orientation dependences of the positron yield (``theta-scans'') for dierent emission angles and positrons momenta. A similar calculation of positron yields was
Fig. 9. Calculated orientation dependence of photon yield with the energy greater than 21 MeV.
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made for an equivalent amorphous target. As the lower boundary of quantum energy we took 5 MeV. In accordance with this method the target is partitioned into a great number of layers. The angular distribution of electrons is calculated again after each layer by convolution of the distribution of multiply scattered particles in this layer with that of the incoming electrons. This distribution, in turn, is used to calculate the CB spectrum in the next layer, and so forth. The photon spectrum after every layer equals the sum of the incident spectrum taking into account the absorption of photons in the layer, and the spectrum of photons produced in this layer. The positrons yield from the layer is determined by the spectrum of incident photons. We used here the following assumptions: 1. The energy of an electron upon passing every layer is its energy before the layer minus the losses in the relevant layer. It was shown in [18] that a similar approach gives but a minor error (a few percent) in calculating the cascade curve in amorphous targets and about 10±15% in aligned crystals. 2. Multiple scattering of electrons is described by the Molier theory for amorphous material of the same atomic parameters and density. 3. The crystal mosaic factor is equivalent to the additional electron beam divergence. The eective angular distribution of electrons is obtained for each layer through convolution of the mosaicity distribution in the layer with that of the incoming electrons. 4. No account is made of c-radiation angular distribution since characteristic angles of multiple scattering of low-energy positrons by far exceed such angles of electrons. We compared the angular distributions of positrons from an equivalent amorphous target calculated with and without the angular distribution of radiation and found them to dier only by as low as 3± 5% for the detection angles smaller than 2°. For large angles the distributions completely match. 5. The pair creation probability in a crystal coincides with that in an amorphous target with the same atomic parameters.
6. The energy of a positron after it leaves the target is the dierence between its initial energy and the radiation and ionization losses, with the latter losses calculated for the average positron energy on the path from the nucleation site to the end of the target. 7. To calculate the radiation losses of the positron energy we used the complete-screening approximation. We did not include the dierence between the positron energy lost to produce radiation in the crystal and the losses for bremsstrahlung because this dierence decreases sharply with the particle energy. 8. We assumed that multiple scattering of positrons on their way from the point of production to the edge of the target is described by the Molier theory for mean-energy positrons. Straightforward veri®cation of this assumption showed that the dierence in the angular distributions, obtained following this approximation and the above approach, which includes gradual broadening in the angular distributions when a particle passes through the target and the losses therein, is as low 3±5% for the angles smaller than 3rm , where rm is the rms angle of multiple scattering for the given thickness and mean particle energy. 9. Positron production by radiation from the secondary particles was disregarded (our targets are considerably thin, see comments to Fig. 8). The calculation includes the density eect in ionization losses and the screening in¯uence on the energy spread of the positrons produced. Exact values for the pair production probability and photoabsorption were taken from [20]. In the calculation of the positron angular distribution we disregard the blocking eect in pair creation [21], because for our experiment wcfa is much smaller than the characteristic angular beam size of c-radiation. The doughnut scattering eect which consists in turning of the particle with respect to its azimuth angle around its crystallographic axis (e.g. [22]) can also aect the resulting angular spread and spectrum of positrons. It is known (see e.g. [12]), that the CB intensity is mainly determined by an angle between the particle direction and the axis. As pointed out in p. 4, multiple scattering of positrons predominates in
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forming their angular distribution. Therefore, the in¯uence of the doughnut scattering eect of electrons on the spectra and angular distributions of positrons is suciently small. It is known (see e.g. [12,22]), that coherent eects in particle scattering in crystals decrease markedly with particle energy. Therefore, for the positron energy lower than 50±80 MeV, and it is these particles that mainly form the angular distributions measured, non-coherent (conventional) multiple scattering prevails. Proceeding from the above, we did not take into account the doughnut scattering eect of electrons and positrons in crystals in our calculation. A more detailed description of the calculation technique, discussion of applicability of the approximations assumed and comparison of the experiment with the calculations made for the silicon crystal will be given in our next paper. Here and later in the text we cite the experimental and calculated positron yields per single electron for various observation angles and positron momenta divided by the magnetic spectrom-
217
eter acceptance. While calculating the acceptance we included the transverse beam size on the main crystal target, the spectrometer geometry and the positron multiple scattering on the crystal-tocounter path. Fig. 10 shows the experimental and calculated ``theta-scan'' of the positron yield for the detection angle 5° and the positron momentum 20 MeV/c. The calculation was done for the misalignment angle 6 between the crystallographic (0 1 1) and horizontal planes. It is evident from the ®gure that the model used describes the ``theta-scan'' width quite well. The dierence in widths is lower than 15%. The dierence between the experimental and calculated data (about 20% in absolute value for close-to-axis orientation) might be due to the radiation contribution in axial and planar channeling and the assumptions made in the calculations. Fig. 11 plots the experimental dependences of the positron yield from positron momentum for axial crystal alignment and at large misalignment (5°) angles for 4 angles of observation. The curves show the calculations for an equivalent
Fig. 10. Orientation dependences of positron yield for tungsten (p 20 MeV/c, H 5 ). Points-experiment, line-calculation.
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Fig. 12. Angular distribution of the positrons with a momentum of 20 MeV/c from the tungsten crystal under the channeling condition (open circles) and o the channeling condition (solid circles). The curve is the calculation for an equivalent amorphous target.
Fig. 11. Yield of the positrons from the tungsten crystal at the channeling condition (open circles) and o the channeling condition (solid circles) for the positron emission angles 0 (a), 5 (b), 10 (c) and, 20 (d) degrees versus positron momentum. The curve is the calculation for an equivalent amorphous target.
amorphous target. Fig. 12 depicts the positron angular distribution at two crystal orientations. The particles momentum is 20 MeV/c. The curve is the angular distribution of positrons calculated for an equivalent amorphous target. It is clear that the shape of angular distribution is virtually independent of crystal orientation. For the orientation á1 0 0ñ one observes the same growth in the positron yield as for the misaligned crystal within 0± 20°. Particles with a dierent momentum do not exhibit any dependence on angular distributions
Fig. 13. The average enhancement factors of the positron emission from the tungsten crystal versus positron momentum. Open circles are the experimental and solid circles are the calculated results. The curve is the interpolation.
either. Fig. 13 shows the mean positron yield enhancement for the aligned and misaligned crystals versus the positron momentum. Also plotted in this ®gure are the calculation results. The dierence between the calculation and experiment seems
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to be due to the contribution from the the channeling radiation. 4. Discussion and conclusions As shown by Figs. 11 and 12, the experimental data on positron yield from a disoriented crystal and the calculations for an equivalent amorphous target match within the accuracy of the experimental error. We may, therefore, use the calculation results to derive the positron yield for the particle momenta 10±40 MeV/c and the angular range 0°±20°. Angular distributions of positrons with a ®xed momentum for the aligned crystal dier from those for the disoriented crystal only in the multiplier controlled by the particle momentum. The total positron yield for the aligned crystal is, therefore, derived through multiplying the calculated angular distributions of positrons with ®xed momenta by the relevant scale factor, followed by integration with respect to the angle and momentum. As the scale multiplier use was made of the interpolated curve which is obtained from the experimental enhancement and plotted in Fig. 13. Positron yield per one electron in the above range for the tungsten crystal with axial orientation and for the disoriented target were 1.02 ´ 10ÿ1 e /eÿ and 3.64 ´ 10ÿ2 e /eÿ , respectively. For the silicon crystal they were 5.34 ´ 10ÿ2 e /eÿ per one electron from the axially aligned crystal and 3.31 ´ 10ÿ2 e /eÿ from the misaligned crystal. The errors the yield values was about 7± 10% for tungsten and 10±15% for silicon. The reported experiment on generating positrons in thick tungsten and silicon crystals irradiated by electrons with the energy 1.2 GeV brings about the following conclusions: (a) Advantages of single crystal converters to generate positrons by electrons with the energy 1 GeV have been now experimentally proven for the crystal thicknesses below 0.5 r.l. The e yield increases almost twofold from the silicon crystal and by about three times from tungsten. (b) In the energy range used the yield of positrons from an aligned crystal having a large Z (tungsten) exceeds that from a crystal with
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small Z (silicon), despite the fact that the structure of tungsten is inferior to that of silicon. This may be connected with a larger value of the critical channeling angle in tungsten, a higher mean emission energy for channeling radiation in tungsten, the contribution from multiplicity of radiation emitted by one electron [23] and dierent energy losses of positrons when they move in silicon and tungsten. (c) The angular positron spread is described fairly well by the function exp ÿH=H0 (but not gaussian), with a characteristic parameter of distribution by far lower (about twice) than the rms angle of multiple scattering of positrons with a ®nite energy. (d) The angular distribution of positrons from aligned and randomly oriented crystals coincide within the accuracy of the experimental error. It is the positron multiple scattering and the energy losses that contribute mainly to the formation of this distribution. (e) The positron yield into a small solid angle depends linearly on the thickness of the target up to its values of 2.5±3.0 r.l. where it reaches saturation. The saturation thickness may be further decreased if use is made of single crystal targets. (f) Comparison of the calculations with the experiments shows that the greater part of positrons is produced by CB photons for the electron energy region near 1 GeV and thick crystals. CB theory may be used to estimate the positron yield produced by relativistic electrons with the energy in the order 1±2 GeV in thick crystals. (g) One may expect the positron yield from aligned crystals to be higher than that from disoriented target in case of perfect crystals and a higher electron energy. In the latter case the contribution from sub-barrier channeling radiation may exceed that from CB at the electron energy E P 5 GeV (for the ®xed tungsten thickness, t 0.34 r.l.). (h) The results obtained in this work seem to be very promising. Further investigation in this ®eld will promote application of crystal targets on already existing accelerators as well as on the facilities in plan.
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Acknowledgements This work is supported in part by Grant-in-aid for Basic Researches by Monbusho. References [1] R. Chehab, F. Couchot, A.R. Nyaiech et al., Study of a positron source generated by photons from ultrarelativistic channeled particles, Preprint LAL ± RT 89±01, 1989. [2] F.J. Decker, Channeling crystals for positron production, Preprint SLAC ± PUB ± 5482, 1991. [3] J.E. Clendenin, High±yield positron systems for linear colliders, Proceedings of the 1989 IEEE Particle Accelerator Conference, Chicago, 1989, pp. 1107±1111. [4] K. Flottmann, J. Rossbach, A high intensity positron source for linear colliders, Preprint DESY M±91±11, 1991. [5] E.M. Reuter, J.A. Hodgson, 3D numerical thermal stress analysis of the high powr target for the SLC positron source, Preprint SLAC-PUB-5370, 1991. [6] X. Artru, V.N. Baier, R. Chehab et al., Nucl. Instr. and Math. A 344 (1994) 443. [7] R. Moor, M.A. Parker, A. Baurichter et al., Measurement of pair-production by high energy photons in an aligned tungsten crystal, Preprint CERN-SL/95-79, 1995.
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