Linearly polarized photon beam at MAX-lab

Nuclear Instruments and Methods in Physics Research A 763 (2014) 137–149

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Linearly polarized photon beam at MAX-lab V. Ganenko a,n, J. Brudvik b, D. Burdeinyi a, K. Fissum c, K. Hansen b, L. Isaksson c, K. Livingston d, M. Lundin b, V. Morokhovskii a, B. Nilsson b, D. Pugachov b, B. Schroder b,c, G. Vashchenko a,1 a

National Science Center, Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine MAX IV Laboratory, Lund University, SE-221 00 Lund, Sweden c Department of Physics, Lund University, SE-221 00 Lund, Sweden d Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, Scotland, UK b

art ic l e i nf o

a b s t r a c t

Article history: Received 21 February 2013 Received in revised form 21 May 2014 Accepted 25 May 2014 Available online 11 June 2014

A linearly polarized photon beam has been produced at MAX-lab using the coherent bremsstrahlung of electrons with an energy of 192.6 MeV in a 0.1 mm thick diamond crystal. The intensity and shape of the coherent maxima and their dependence on the crystal orientation are similar to the features observed at higher electron energies (
1 GeV) and are well described by coherent bremsstrahlung theory. The linear polarization of the uncollimated beam at the coherent peak energy E 50–60 MeV is about 20% and can be increased to 40–45% if collimation of half the characteristic angle is used. At present the degree of polarization is high enough to allow the study of polarization observables in photo-nuclear reactions at MAX-lab in the energy range from Giant Dipole Resonance up to E80 MeV. & 2014 Published by Elsevier B.V.

Keywords: Electrons Diamond crystal Crystal orientations Coherent bremsstrahlung Photon spectra Polarization

1. Introduction Experimental investigations of photonuclear processes using linearly polarized photon beam allow one to obtain information about polarization observables. Photon beam asymmetry is one of the most extensively studied polarization observables, resulting from the dependence of a reaction cross-section on direction of the photon polarization. There are also other polarization observables which can be obtained when the polarized photon beam is used in combination with a polarized target, or the polarization of the reaction products is measured. Because the polarization observables are described through interference of the reaction amplitudes, contributions from small amplitudes, which, practically, do not affect the reaction cross-section, can be strengthened in these observables. Thus, experiments with linearly polarized photons are sensitive to the reaction mechanisms and allow one to extract detailed information on the process. The methods which are used for generation of the linearly polarized photons in intermediate energy range (up to some GeV) are based on the well-known physical effects: the coherent bremsstrahlung (CB) of electrons in crystals, the backscattering

n

Corresponding author. E-mail address: [email protected] (V. Ganenko). 1 DESY, 15738 Zeuthen, Germany.

http://dx.doi.org/10.1016/j.nima.2014.05.110 0168-9002/& 2014 Published by Elsevier B.V.

of a laser radiation on ultrarelativistic electrons and the bremsstrahlung angular selection under specific angle θs
θγ to the beam axis (θγ ¼ me c2 =E0 is the characteristic angle of bremsstrahlung, E0 and me are the electron energy and mass). The maximum electron energy available at the photon tagging facility of Swedish national laboratory MAX-lab is E0 ≲200 MeV [1], which is too low for laser backscattering. The technique of bremsstrahlung angular selection has not been widely adopted due to low beam intensity and strong degradation of the beam polarization due to influence of experimental factors such as electron beam size, divergence, and multiple scattering in the radiator [2–4]. Thus, the coherent bremsstrahlung is the technique best suited for production of a polarized photon beam at MAX-lab. The CB spectrum has an intensive peak whose position can be easily changed. The radiation in the maximum is linearly polarized and the polarization degree can be considerable increased by collimation of the gamma radiation [5]. The first coherent bremsstrahlung beam was produced by Diambrini et al. at Frascati in 1960 [6] at interaction of E0
1 GeV electrons with a diamond crystal. Then the CB beams have been produced practically at all electron accelerators with beam energies
1 GeV and larger, see e.g., [7]: Tokyo (1965), Hamburg (1966), Kharkov (1968), Cambridge (1968), Tomsk (1969), Erevan (1970), Cornell (1970), Stanford (1970), Daresbury (1973), and Bonn (1979). At present the CB beams are successfully operated in Mainz [8], JLAB [9] and ELSA [10,11].

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The possibility of producing a CB beam at MAX-lab opened up due to the modernization of the facility which began at the end of 90s. For the electron beam used for photonuclear research this resulted in an increase in maximum energy up to E0
200 MeV. Although this was lower than which had been used at other facilities where CB had been produced, calculations [12] showed that the expected electron beam parameters would be suitable for obtaining the CB beam with reasonable characteristics if the photon beam was collimated to one half of a characteristic angle. The coherent bremsstrahlung beam at MAX-lab was first produced in September 2007 [13,14], then a more detailed study of the characteristics was made during a second beam period in April 2008 [15]. The results from this run are discussed in the paper. The kinematics and main properties of coherent bremsstrahlung are well documented [16–28]. It has been shown that ! the CB was produced when the momentum q , transferred to the ! ! ! crystal coincided with some reciprocal lattice vector g , q ¼ g , (the, so-called, Laue condition). The kinematical region allowed for ! the recoil momentum q , contributing to the coherent bremsstrahlung at fixed photon energy, looks like a thin disk “pancake” with thickness d and radius
1. δ is the minimal longitudinal momentum transfer. Its value is related to the fractional photon energy x ¼ Eγ =E0 according to the following equation: δ¼

1 x 2E0 1  x

ð1Þ

(ℏ ¼ c ¼ me ¼ 1 system of units is used). Due to the Laue condition only a discrete group of the vectors ! ! q ¼ g contribute to the CB. The photon spectrum resulting from any reciprocal lattice vector has a specific maximum above the smooth incoherent spectrum, with sharp upper edge and smooth decreasing left side. Its shape results from the dynamic of the “pancake” with increasing fractional photon energy. The lower edge of the “pancake” increases with the x and when it exceeds ! the longitudinal component of the reciprocal lattice vector g L , the discontinuity occurs in the radiation cross-section at the fractional energy xd: xd ¼

2E0 δ ð1 þ2E0 δÞ

2.1. Experimental set-up The electron beam was extracted from the MAX-I storage ring, which worked in a stretcher mode. Injection of electrons into the ring was performed by a double-section linear accelerator with a frequency of 10 Hz and duration of the injected electron pulse
200 ns. The electron energy was E0 ¼192.7 MeV. The electrons were extracted from the MAX-I ring during the 100 ms pulse and delivered into the experimental hall. The first part of the extracted beam produced a “flash” pulse, thus the electronics was gated out by the acquisition system for
1 ms, starting from the beginning of the injection. A schematic picture of the experimental hall, the beam line and experimental set up are shown in Fig. 1. A dipole magnet (1) directed the electron beam towards photon radiators, fixed in a target holder of the goniometer (5). The goniometer was placed in a vacuum chamber between the magnets of the end-point tagger (ET) (4) and the main tagger (MT) (6). The electron current on photon radiators was
5–10 nA, and it was strongly reduced (
104 times) when the CB spectra were measured with a NaI detector. The beam size on the radiators was no more than 2 mm. The non-interacting part of the electron beam was deflected to the beam dump (8) by the MT magnet, where it was absorbed by a Faraday cup. At the MT magnet operating mode, used in the experiment, the electrons passed a section of air (
135 cm) and two steel 25 μm foils on their way to the beam dump [1]. Thus, there were additional sources of background for the focal plane detectors, especially noticeable at reduced electron beam current. At high electron intensity the background was no more than 1–2%.

ð2Þ

The linear polarization of the CB photons is found in the plane ƒ! ! ð p0 ; g Þ. The detail analysis has shown (e.g. [24]) that its maximum value can be obtained if to use a diamond crystal and to provide the conditions when only one of the reciprocal lattice vectors g ¼ ½0 7 2 7 2 mainly contributes to the CB production. A calculation which takes account of the main experimental factors, has been introduced by Rambo et al. [29] and further developed by the Tuebingen Group [30], whose version has been used widely. The results of this calculation are in good agreement with CB spectra produced in Mainz [8], JLAB [9], ELSA [11], and have also been used more recently in Mainz to understand the angular distribution of CB [31]. This code will be used in this paper to calculate the CB spectra and polarization.

2. Experimental apparatus and technique The recently upgraded MAX-lab facility has the infrastructure for precision photonuclear experiments in the energy range up to some tens of MeV above pion threshold: (i) An electron beam with maximum energy E0
225 MeV, duty cycle
50%, and current up to 20 nA; (ii) Two tagging systems with energy resolution 0.5–1 MeV and tagged photon interval from 10 to 180 MeV; (iii) Systems of beam diagnostic and control. The nuclear physics facility was described in detail in Ref. [1].

Fig. 1. Scheme of the MAX-lab beam line for photonuclear researches. 1 – Bending magnet (501); 2 – vertical and horizontal steering magnets; 3 – photon radiator for end-point tagger; 4 – end-point tagger (ET); 5 – goniometer; 6 – main tagger (MT); 7 – additional dump magnet (601); 8 – Faraday cup; 9 – shielding; 10 – photon collimator; 11 – gamma monitor; 12 – NaI detector; 13 – photon camera; 14 – photon beam-dump.

V. Ganenko et al. / Nuclear Instruments and Methods in Physics Research A 763 (2014) 137–149

A photon collimator was placed at a distance of 2140 mm from the photon radiators, before the shielding wall. The collimator design was described in detail in the Ref. [1]. It consisted of heavy metal main collimator 108.5 mm long with the variable entrance openings 19, 12 and 5.4 mm in diameter, followed by a scrubber magnet 100 mm long, and a scrubber collimator 200 mm long. The above stated holes provided the collimation angle values θc
1:9θγ ,
1:2θγ ,
0:5θγ , respectively, for a point-like electron beam. The intensity of the photon beam was controlled by a scintillation gamma beam monitor (IBM) (11). It consisted of three scintillation counters with sizes 70 mm (horizontal)  100 mm (vertical)  0.5 mm (thick). The monitor worked in counting rate “:1&2&3” mode with the first counter acting as a charged-particle veto. An Al converter 0.5 mm thick was placed between scintillators 1 and 2 to increase the monitoring efficiency by producing charged particles for downstream counters 2 and 3. The focal plane (FP) hodoscope, used in the experiment, consisted of two rows of scintillators 26 mm wide and 3.2 mm thick [1]. The overlap between scintillators of the rows was 50%. The coincidence requirement of overlapping scintillators resulted in 62 channels for detecting post-bremsstrahlung electrons. The hodoscope was placed along the MT magnet focal plane, which was different from the standard location due to the upstream shift of the position of the photon radiators, fixed in the goniometer target holder. Exact position of the new focal plane was calculated by tracing electrons in the known magnetic field of MT. Its position is shown in [1,32]. The angle between the direction of the scattered electron trajectories and the new MT focal plane is about

Fig. 2. Photo of the goniometer. The diamond crystal is in the center of the rotating goniometer target holder. There are five step-motor drives (rotation stages) to rotate ! ! crystal around (top-down) an azimuthal axis ð A Þ, a horizontal axis ð H Þ, a vertical axis ! ð V Þ and to shift in a vertical and horizontal direction. See text for details.

139

52.61 that results in a difference between the momentum acceptance of odd and even channels if overlap between scintillators is 50%. In order to extend the tagging interval to lower photon energies, the hodoscope was shifted from the standard position, corresponding to usual operation range of the MT spectrometer þ40% to  20% of PC (PC is the central momentum of the MT spectrometer), where the focal plane is “flat”. As a result, the energy interval above the þ40% mark, corresponding to the energies Eγ ¼ 21:9–33:8 MeV (the tagger channels 50–62) was included, and the total tagged energy range was Eγ ¼ 21:9– 78:8 MeV. The calculated energy resolution of the tagger was smoothly varied from 0.8 MeV, for the high end of the tagged range Eγ  78:8 MeV, to 1 MeV at Eγ  34 MeV, and then it was almost constant till low end of the tagged range.

2.2. Goniometer In order to perform orientation of the crystal a 3-axes goniometer was built [32], using as a prototype the goniometer described in Ref. [33]. The goniometer was assembled from five commercial moving stages produced by NEWPORT, Fig. 2. Three ! stages performed rotation of the target holder around vertical ð V Þ, ! ! horizontal ð H Þ and azimuthal ð A Þ axes, two translation stages performed its vertical and horizontal shift. The rotating goniometer target holder has five positions for radiators. The diamond crystal 0.1 mm thick was fixed at the center of the holder (the ! ! ! common center of three goniometer axes V , H , A ). In the other locations a 300 μm Si crystal, a 50 μm Al radiator, a viewing screen and an empty slot were positioned. The kinematical scheme of the ! goniometer is shown in Fig. 3. The horizontal axis H is perpendi! cular to the V axis and can be rotated within the horizontal plane by changing the angle ΦV , the azimuthal axis can be rotated within a vertical plane by varying ΦH and its horizontal projection can be rotated within a horizontal plane by changing the angle ΦV . The azimuthal rotation of the crystal holder does not influence the axis

Fig. 3. The kinematical scheme of the goniometer with the crystal in the center. ! The angles ΦV , ΦH , ΦA are the rotation angles around the vertical ð V Þ, horizontal ! ! ð H Þ and azimuthal ð A Þ axes of the goniometer. θ and α are the polar and azimuthal ƒ! ƒ! ƒ! ƒ! angles of the p0 in the crystal reference frame ( b1 , b2 , b3 ). bi ¼ 2πlc =a are the basic reciprocal lattice vectors, a is the lattice constant of the crystal, lc is the Compton wavelength of electron. ϕ is the azimuthal angle of the reciprocal lattice ! ! vector g ¼ ∑bi ni (i ¼ 1,2,3), responsible for the CB production ðni ¼ 0; 7 1; 7 2; …Þ. ! β is the angle between the plane of maximum polarization and the vertical axis V .

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Table 1 Characteristics of the moving stages [32]. Movement

Travel range

Unidirectional repeatability

Hysteresis

Resolution

Azimuthal (1) Vertical/horizontal (1) Vertical shift Horizontal shift (μm)

360 7 45

0.003 0.004

0.006 0.02

0.001 0.001

4 mm 50

0:2 μm 1:5

3 μm 3

0:1 μm 1

! ! V and H . The smallest step of the angular motion is 0.0011 for all axes. Optical test measurements showed that the angular uncertainties related to unidirectional repeatability were 0.0031 for azimuthal and 0.0041 for vertical and horizontal rotations. The main characteristics of the goniometer are presented in Table 1. Control of the goniometer was provided by MM4006 controller connected to RS-232 port of a PC. The angles ΦV , ΦH , ΦA determine rotation of the crystal relatively the electron beam in the goniometer reference frame. The relationships between these angles and the angles θ; α; ϕ (see, Fig. 3) are given in Ref. [8] and presented below: ΦV ¼ arcsinð sin θ sin ðα þ ΦA ÞÞ ΦH ¼  arctanð tan θ cos ðα þ ΦA ÞÞ:

Both methods are based on the same principle – determination of the crystal planes positions, using effect of the radiation intensity increasing when the electron beam direction approaches to the crystal planes and axes. 2.3.1. The Stonehenge technique The Stonehenge alignment procedure relies on measurement of the orientation dependence of the coherent bremsstrahlung spectrum. This is determined by a so-called quasi-azimuthal scan, where the crystal is rotated about the horizontal and vertical goniometer axes simultaneously according to Eqs. (5) and (6), where the angle ω varies from 01 to 3601 in small steps: ΦV ¼ θsc cos ω

ð5Þ

ΦH ¼ θsc sin ω:

ð6Þ

In this case the normal to the crystal plate (and the axis ƒ! b1 ¼ ½100, as well) describes a cone of an angular radius θSC . For each step in the scan the photon spectrum is measured by the focal plane hodoscope. The spectra are normalized to the amorphous spectrum (from 50 μm Al radiator in our case) in order

ð3Þ

The inverse relations are θ ¼ arccosð cos ΦH cos ΦV Þ α ¼ arccosð½  cos ΦA sin ΦH cos ΦV þ sin ΦA sin ΦV = sin θÞ; ϕ ¼ ΦA þ β:

ð4Þ

In these formulas the angles ΦV ; ΦH ; ΦA are counted from the, socalled, “zero angles” ΦV 0 , ΦH0 , ΦA0 , corresponding to “zero posiƒ! tion” of the crystal. At this position the b1 ¼ ½100 axis direction ƒ! coincides with the initial electrons momentum p0 , the axes ƒ! ƒ! ! b2 ¼ ½010 and b3 ¼ ½001 are directed along the axes V and ! H , respectively, and the crystal planes (0 7 2 72) locate under 7 451 to the horizontal plane, therefore, the angles θ, α, ΦA are zero in the “zero position”. The crystal plate was cut in such a way that axis [100] was perpendicular to the plate. The plate was fixed in the center of the target holder parallel to the holder's plane, and in the course of preliminary optical alignment the normal to the plate was directed along the electron beam axis. As a result, the axis [100] direction was close to the direction of electron beam. The possible small misalignment, resulted from inaccuracy of optical device and the ƒ! crystal cutting, is described by the angles ΦV 0 , ΦH0 . The axes b2 ƒ! and b3 may also deviate from the vertical and horizontal directions, and this misalignment results in deviation of the crystal planes (0 7 27 2) from the directions 7451 to the horizontal plane by the azimuthal angle ΦA0 . In many cases it is enough to determine these three “zero angles” (ΦV0 , ΦH0 , ΦA0 ) which determine the relative directions of the electron beam and the axis ƒ! b1 ¼ ½100, and position of the main crystal planes (0 72 72). 2.3. Crystal alignment Two methods were applied for determination of the “zero angles”. The first method was the Stonehenge technique proposed by Livingston [34]. It is adapted to photon tagging facilities, and it was successfully used at MAMI, JLAB, and ELSA [9–11]. The second method was proposed by Luckey and Schwitters [35] and was successfully applied at some laboratories [36], as well. In contrast to the Stonehenge technique it does not require a photon tagger.

Fig. 4. Stonehenge plots for nonaligned crystal scan with radius θsc ¼ 150 mrad (top), and for aligned crystal scan with radius θsc ¼ 80 mrad, (bottom), from [1]. The grey-scale color-code represents the radiation intensity. See text for details.

V. Ganenko et al. / Nuclear Instruments and Methods in Physics Research A 763 (2014) 137–149

to get a more distinct coherent maxima, and are plotted in a 2D histogram with axes ΦV and ΦH . The photon energy increases from inner to outer radius of the plot. The intensity variations are shown by the color scheme. The Stonehenge plot, obtained by a scan for a non aligned crystal, is shown in Fig. 4 (top). The azimuthal angle value is ΦA ¼ 451. The plot has a 4-fold symmetrical pattern. The lighter radial ridges on the plot (the regions of the strongest intensity) trace of the position of the energy of the coherent peaks, resulting from the vectors [0 72 72], as a function of the crystal rotation angles. At zero photon energy the neighboring ridges should converge and determine four points, indicating the angles ΦV , ΦH at which the planes (0 72 72) are parallel to the incoming electron beam. However, these points are not observed due to limitation of the tagged energy interval. Thus, the four points were determined on the inner radius of the histogram, A1  4 , symmetrically located relative to the neighbouring ridges of stronger intensity, which approximately pointed out position of the planes. A fit was made by fitting these four points to two orthogonal lines (thick lines in Fig. 4), representing the orientation of the (022) and ð02  2Þ planes. The planes (040) and (004) also revealed themselves as the ridges of less intensity. An analogous procedure was made, and additional points C 1  4 were determined, which were fitted to two orthogonal (dashed) lines with 451 to the first pair of lines. The point B ðΦV ; ΦH Þ off all these lines intersection corresponds to the crystal position, where the ƒ! b1 ¼ ½100 axis coincides with the electron beam direction, and its coordinates are the “zero angles” for the given azimuthal angle ΦA ¼ 451. The observed “zero angles” values are ΦV 0  5:24 mrad and ΦH0  65:76 mrad. The planes (022) and ð02  2Þ were found to be almost parallel to the horizontal and vertical planes, respectively, that is, the “zero” azimuthal angle is ΦA0  0, so the preliminary optical orientation provided enough accuracy. A control scan was performed at scan radius θsc ¼ 80 mrad, at which the angles ΦV and ΦH were counted from the observed “zero angles” ΦV0 and ΦH0 , Fig. 4 (bottom). The obtained 2D histogram has good symmetry and the fitting procedure described above gives intersection point in the plot center, so the crystal is well aligned. In more detail the method is described in Ref. [34]. 2.3.2. The Luckey method This method was proposed by Luckey and Schwitters [35]. They proceeded from the specific relation which exists between the goniometer rotation angles ΦV and ΦH , when the coherent peak is ! produced from some reciprocal lattice vector g at very low energy, xd -0. The radiation intensity is strongly increased in this case, and there is a linear relation between the angles ΦV and ΦH [35]:

(finite) motion in the transverse direction within this plane (axis). The total energy of transverse particles motion (kinetic plus potential) is ε ? o 0, and angle of the electron movement relatively plane χ (or the axis θ) should be less than the critical angle of the planar ψpl (axial ψax) channeling, χ o ψ pl ðθ oψ ax Þ. In the case of above barrier motion the particles can pass from one plane (axis) to another, but as a whole the movement has regular, periodic character. Such motion is possible if transverse energy ε ? 4 0, and the angles χ(or θ) are more than the corresponding critical angles χ 4ψ pl ðθ 4 ψ ax Þ. The electrons being in such regimes of the movement radiate very intensively in low energy range. Thus, the photon detector should be sensitive to the low energy photons. The positions of the lines are determined from measurements of the photon beam intensity as a function of the angle of crystal ! ! rotation around one goniometer axis, H or V (linear scans). When the electron beam crosses the crystal planes the radiation intensity increases and maxima appear in the scan. More intensive maxima are produced by the main crystal planes, so, height and position of the peaks allow one to identify the crystal planes and their locations. Because the maxima are caused by mechanisms that are very sensitive to the orientation of the electron beam relative to the crystal planes, their positions are determined with high accuracy. Three scans were performed as a function of the angle ΦH of the crystal rotation around horizontal axis, at fixed rotation angle around vertical axis at values ΦV ¼  1:21,  0.71, 1.81, and azimuthal angle ΦA ¼ 451. The photon flux was measured with the IBM gamma monitor which worked in a counting rate mode. The photon yield was normalized to the Faraday cup counting rate. The Faraday cup integrates the total charge of the electron beam, thus the electron beam “flash” contribution was also measured during the time, when the data collection was shut down by acquisition system (
1 ms). Thus, this normalization was not very precise, however, at high electron beam intensity the “flash” contribution was probably not so large, and normalization of the photon yield to the Faraday cup rate gave more stable orientation dependencies, in comparison with normalization to time. The orientation dependence measured for the fixed angle ΦV ¼ 1:81 is presented in Fig. 5. It demonstrates distinct symmetrical picture, a pronounced large central peak, corresponding to the strong plane ð02  2Þ, two smaller peaks on both sides from the central one, corresponding to the planes (040) and ð00  4Þ, and four weak maxima which correspond to the weak planes (062), ð06  2Þ, ð02 6Þ, ð0  2  6Þ. The analogous picture was obtained for scans at angles ΦV ¼  1:21 and  0.71. The symmetrical positions of the maxima relatively to the central peak are ƒ! evidence of good ƒ! 0 0 parallelism of the crystal axes b2 ¼ ½011 and b3 ¼ ½0–11 to the ! ! goniometer axes V and H , thus, the azimuthal “zero angle” is

ð7Þ

that is, the locus of the goniometer angles, which produce the ! coherent peak at xd
0 for any vector g , is a straight line on the ðΦV ; ΦH Þ plane. The “zero angles” values ΦV 0 , ΦH0 and ΦA0 are ! parameters of the relation (7), the same for various vectors g . The lines corresponding to different reciprocal lattice vectors intersect in the point ðΦV 0 ; ΦH0 Þ, and have a slope which is a function of the ! vector g Miller indexes and the “zero angle” ΦA0 . So, the “zero angles” can be obtained if the positions at least two such lines on the ðΦV ; ΦH Þ plane are known. Actually, these lines correspond to the positions of the crystallographic planes, thus when the angles ΦV and ΦH satisfy the Eq. (7), the electron beam impinges on the crystal along the crystal plane, and electrons can move in the crystal in regimes of a planar channeling and an above barrier movement [23,38]. In the case of planar (or axial) channeling the particles move near one isolated plane (axis) of the crystal and perform bound

02-2

140 120

040

00-4

100

Counts

ðΦV  ΦV0 Þðg 3 cos ΦA0  g 2 sin ΦA0 Þ ¼ ðΦH  ΦH0 Þðg 2 cos ΦA0 þg 3 sin ΦA0 Þ

141

80

062

06-2

02-6

0-2-6

60 40 20 0

-1

0

1

2

3

4

5

6

7

ΦH, deg. Fig. 5. Dependence of the photon yield as a function of the crystal rotation around horizontal axis at fixed rotation angle around vertical axis ΦV ¼ 1:81. The azimuthal angle is ΦA ¼ 451. The collimator hole diameter is 19 mm.

142

V. Ganenko et al. / Nuclear Instruments and Methods in Physics Research A 763 (2014) 137–149 180

8

160

7

062

140

5

06-2

4

02-2 02-6

3

1 -0.5

0

0.5

1

1.5

2

20 0

2.5

ΦV, deg.

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

ΦV, deg.

Fig. 6. Positions of the maxima on the ðΦV ; ΦH Þ plane for scans at fixed rotation angles ΦV ¼  1:21,  0.71, 1.81. Lines are the linear fit of the points, corresponding to the same crystal planes. The lines intersections determined a small domain, including the “zero angles” ΦV0 and ΦH0 .

ΦA0  01 with good accuracy. The coordinates of the maxima, corresponding to the above mentioned crystal planes, were determined for all scans and are plotted in Fig. 6. The points corresponding to the same crystal plane were fitted by lines. The points of the lines intersections determined a small domain, including the “zero angles” ΦV 0 and ΦH0 . The maxima corresponding to the different crystal planes, shown in Fig. 5, approach each other when the values of the rotation angles ΦV and ΦH approach to the region of the domain. And they merge into one large peak when these angles coincide with the “zero angles”, that is, when the electron beam moves along the crystal axis ([100] in our case). So, the “zero angles” can be directly measured. The results obtained by this method for ΦA ¼ 451 are: ΦV 0 ¼ 0:3361 (5.864 mrad), ΦH0 ¼ 3:541 (61.785 mrad) and agree to within
10% with the values obtained by the Stonehenge technique. The analogous orientation procedure, performed for azimuthal angle ΦA ¼ 01, gave the values of the “zero angles”: ΦV0 ¼  2:681 (  46.86 mrad) and ΦH0 ¼ 3:601 (62.83 mrad). The difference between the “zero angles” values obtained for azimuthal angles ΦA ¼ 451 and 01 may be due to the non-perpendicular direction of the axis ½100 to the crystal plate, and non-parallel the crystal plate to the plane of the target holder. The observed orientation dependences of the radiation intensity provide a means of estimating the electron beam divergence θb, because it contributes to the width of the peaks. When the electrons move along the plane ð02  2Þ, Fig. 5, the enhancement of the radiation yield is a factor of
2, and the width of the peak (FWHM) is Δθpl
0:181. For the case of axial orientation, shown in Fig. 7, the radiation enhancement is about a factor of 5, and the width of the peak is Δθax
0:251. Actually, the real radiation enhancement in the low energy range is more in both cases, because the gamma monitor detects charge particles, produced by photons with energies from the threshold to maximal energy E0. So, the channeling and above barrier mechanisms gave large contribution to the total flux of the radiation. The width of the peaks could be estimated by the formula: ΔθaxðplÞ
2ðψ 2axðplÞ þθ2msc þ θ2b Þ1=2

80

40

0-2-6 -1

100

60

00-4

2

0 -1.5

120

040

Counts

ΦH, deg.

6

ð8Þ

where θmsc is the angle of beam multiple scattering in the crystal, ψ axðplÞ is the critical angle of the axial (planar) channeling. For a diamond and electron energy E0
200 MeV they are ψ pl  0:0141 and ψ ax  0:0411. The angle of multiple scattering of electrons in disorientated diamond crystal (analogue of amorphous matter) in our case is θmsc  0:0811, i.e.,
1.5 and
1.1 times less than the widths of the axial and planar peaks, respectively. However, the multiple scattering

Fig. 7. Orientation dependence of the photon yield as a function of angle ΦV of crystal rotation around vertical axis at fixed angle of crystal rotation around horizontal axis corresponding to “zero angle”, ΦH0 ¼ 3:601. Position of the maximum corresponds to vertical “zero angle” ΦV0 ¼  2:681. ΦA ¼ 01. The collimator hole diameter is 19 mm.

for the axial or planar crystal orientations is more than for amorphous matter, (e.g.,
2  3 times for electrons with energy E0
1 GeV in silicon crystal at axial orientation [39]). So, the widths of the peaks are practically determined by the multiple scattering of the electrons in the crystal, and the initial beam divergence brings negligible contribution to the width, θ2b 5 θ2msc , that could be satisfied if the divergence is θb ≲0:031 (
0.5 mrad). This value agrees with the results of beam optic calculations [12], and it was used in the calculations with the ANB code. 2.4. Methods of photon spectra measurements Three methods were used for photon spectra measurements. The uncollimated photon spectra were measured by the focal plane hodoscope at high electron beam intensity. The FP hodoscope had 62 channels and covered energy interval Eγ ¼ 21:9– 78:8 MeV with energy resolution ΔEγ  0:8–1 MeV. The NaI detector ð25  25  25 cm3 Þ was used for measurements of the collimated photon spectra at strongly (
4 orders of magnitude) reduced electron beam intensity. It provided measurements in a wider energy interval Eγ  10–90 MeV, but with energy resolution E7–8%. Also, the measurements were produced using the FP hodoscope in coincidence with the NaI detector. A photon collimator with a variable circular aperture 5.4, 12 and 19 mm in diameter was used, which provided the angles of the photon beam collimation θc  0:5θγ ,  1:2θγ ,  1:9θγ , respectively, in the case of the pointlike electron beam approximation. To test the FP detectors efficiency, bremsstrahlung spectra were measured from the 50 μm Al radiator. The measurements have shown that there was a reductions in the detection efficiency of the post-bremsstrahlung electrons by the FP counters in the energy interval corresponding to the photon energies Eγ o 38 MeV. That could be the result of non-optimum performance of the FP detectors or a change of the MT magnet focusing properties along the focal plane above the point of þ40%, corresponding to this energy range. Thus, the energy interval of the photon spectra measurements with the FP hodoscope was restricted by Eγ ¼ 38–78:8 MeV. However, in the case of the relative measurements, and normalization of the coherent bremsstrahlung spectra to the bremsstrahlung spectrum from amorphous Al radiator, the energy interval can be increased to the full range Eγ ¼ 21:9–78:8 MeV due to cancellation of the FP detector's efficiency. The typical measured bremsstrahlung spectrum, produced in the 50 μm Al radiator, normalized to the calculated one is shown in Fig. 8. In order to exclude the odd–even effect, the number of counts of neighboring even and odd FP channels were averaged.

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Eγ , MeV Fig. 8. Bremsstrahlung spectrum from Al 50 μm radiator, measured by the FP array at normal electron beam intensity without collimation (circles); by the NaI (vertical lines) and by the FP hodoscope in coincidence with the NaI (squares) at reduced intensity and the photon collimator diameter 12 mm. The spectra are normalized to the calculated one for the collimator diameter 12 mm (solid line) and without collimation (dashed line). η ¼ σ 0 ZðZ þ 1:3Þ, σ 0 ¼ αr 20 ¼ 0:57947  1027 cm2 , Z-atomic number.

The count rate of the focal plane array was also corrected to take into account the different energy widths of the tagging channels. The calculated and measured spectra are in a good agreement. The statistical accuracy of the measurements was high ð  0:1%Þ, thus observed variations of the data points are due to difference of electron detection regimes of the FP counters, however as a whole, they were approximately similar. The NaI detector was placed on the beam line in the experimental hall. Signals produced by photons in the NaI detector were analyzed by an Analogue Digital Converter (ADC) with 2000 channels. The operating mode of the electronics was chosen to cover the energy interval up to Eγ  90 MeV, compatible with the interval covered by the FP hodoscope. In order to test a correlation between the energy of incoming photon and the NaI impulse amplitude (measured by the ADC), the energy calibration was produced using monochromatic ðΔEγ  1 MeVÞ tagged photons of the MAX-lab facility. The calibration measurements have shown, firstly, a linear dependence between the NaI signal and energy of the incoming photon in the interval Eγ ¼ 33–75 MeV, and, secondly, deviation from linearity for energies Eγ ≲33 MeV corresponding to channels 50–62 of the FP hodoscope. Such behavior could be due to changing the MT magnet focusing properties in this energy range, as it was stated above. Thus, the energy interval Eγ ¼ 33:8–78:8 MeV was taken where the experimental dependence between the NaI impulse amplitude and incoming photon energy was fitted by a line. The fit was extrapolated in the low energy range, and it was used for determination the energy of the detected photons in whole energy interval. For test of the NaI detector efficiency and energy calibration, the bremsstrahlung spectra, produced in Al radiator, were measured. It was found that the hardware threshold of the gamma-quanta registration was Eγ  7 MeV. The radiator-off measurements have also shown that there was a noticeable background in the low photon energy range, Eγ o9 MeV, due to induced activity in the experimental hall, while the background was low for energies Eγ Z9 MeV. Its sum yield in the interval, corresponding to the focal plane array Eγ ¼ 21:9–78:8 MeV, was E1.4% and E 1.8% of the Al radiator-on yields for the collimator holes 19 and 12 mm in diameter, respectively (under assumption of stable electron beam current during the measurements). Thus, interval of the spectra measurements with the NaI detector was restricted by the energies Eγ Z 9 MeV. For control of the low intensity beam stability during the spectra measurements, counting rates of the NaI detector, gamma

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monitor and the FP detectors were recorded after every 10 s intervals (one “step”). The total duration of the measurements was usually 50–100 “steps”. The measured spectra have energy dependence similar to ordinary bremsstrahlung, and they well agree with the calculated ones, as it is shown in Fig. 8. The radiator-off measurements have also shown that there was a large background contribution (E 30–50%) to the counting rate of the FP detectors at reduced beam intensity, most probably due to interaction of the electron beam with two steel foils and air on its way from MT chamber to the Faraday cup. The large level of the background and its unstable character did not allow to measure spectra by the FP array at reduced intensity without special background measurements, which required a control of the initial electron beam current. The background was eliminated when a coincidence requirement of the FP counters, and the NaI detector was applied. The bremsstrahlung spectrum measured in the coincidence mode, normalized to the calculated one, is shown in Fig. 8. The measured spectrum agrees well with the NaI data and with the calculated spectrum for energies Eγ Z 38 MeV. On the whole, results of the test bremsstrahlung measurements have shown that both the NaI detector and the FP hodoscope provided reliable gamma-radiation spectra measurements in the energy range Eγ  10–90 MeV. The periodical test measurements during the beam run of the bremsstrahlung produced in Al radiator have shown that the normalized to one “step” spectra differed no more than E15–20%. Thus, one may expect the electron beam current was approximately stable within these limits.

3. Coherent bremsstrahlung spectra at MAX-lab energy 3.1. Types of crystal orientations After the crystal alignment one can select, by special rotations, certain reciprocal lattice vectors for production a coherent bremsstrahlung with the needed coherent peak energy and direction of the linear polarization. As outlined above [8,24], maximal polarization is reached when only one of the reciprocal lattice vectors ! g ¼ ½0 7 2 7 2 of the crystal gives main contribution to the CB. At that, it has to lie in the allowed kinematical region on low edge of the “pancake”. Because there is practically no information on properties of coherent bremsstrahlung at such low electron energy, E0  200 MeV, available at MAX-lab, some other crystal orientations have been also tested. Appropriate positions of the “pancakes” are shown in Fig. 9. The orientation (A), shown in Fig. 9a, corresponds to the crystal position which has been obtained after the crystal rotation by azimuthal angle ΦA ¼ 451 from the “zero position”, Φ ¼ Φ ¼ Φ ¼ 01. As a result of such azimuth rotation, the axis V H A ƒ! ! 0 directed parallel to the vertical goniometer axis V , b2 ¼ ½011 is ƒ! 0 and the axis b3 ¼ ½01  1 is directed parallel to the horizontal ! goniometer axis H . The “pancake” region is perpendicular to the ƒ! initial electron momentum p0 and lies on small distance δ 5b1 from an interaction point (for photon energies x r0:5), very close to the plane of the reciprocal lattice vectors with g 1 ¼ 0. The lattice ! vectors [022] and ½0  2  2 are parallel to the vertical axis V , the ! vectors ½0  22 and ½02  2 are parallel to the axis H , and the ƒ! electron beam is directed along the axis [100] (axis b1 ). The vectors with g 1 a0 give small contribution to the CB cross-section, so, one may take into account only this plane for the coherent bremsstrahlung production, placing by special rotations the vectors being in this plane into the “pancake” region. One of the simple orientations is the orientation (B), shown in Fig. 9a, which can be obtained by the crystal rotation around horizontal axis of the goniometer. The primary electron

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Fig. 9. (a) Positions of the “pancake” (grey bands, not to scale). View on the diamond crystal from a direction opposite to the axis ½0  11. The primary electron momentum ƒ! ƒ! ƒ! 0 0 p0 is directed along the axis [100] (A) and under small angle θ to it (B). The large points are the projections of the main reciprocal lattice vectors being in the plane ð b2 ; b3 Þ ƒ! ƒ! 0 0 on the drawing plane. (b) Reciprocal lattice vectors in the plane ð b2 ; b3 Þ and intersections of the plane by the “pancake” for two orientations of the “row” types (B) and (C). Many vectors lie in the allowed kinematical regions. (c) The same as in Fig. 9b but for the “point” type orientations. The “para” and “perp” orientation were used for production linearly polarized beam for experiment on nuclear disintegration. See text for details.

ƒ! momentum p0 is directed under a small angle to the axis [100] ƒ! ƒ! 0 and lies in the plane ð b1 ; b2 Þ. The “pancake” crosses the plane in such a way that many reciprocal lattice vectors are in the allowed kinematical region, as shown in Fig. 9b. This is orientation of the, so-called, “row” type. There can be also other orientation of this ƒ! type, e.g., (C), when electron momentum p0 is directed under a ƒ! ƒ! small angle θ to the axis [100] and lies in the plane ð b1 ; b2 Þ. In order to get high degree of linear polarization, one has to provide the isolated contribution of one of the reciprocal lattice vectors ½0 7 2 7 2 to coherent bremsstrahlung. This is orientation of the, so-called, “point” type. Compared to orientation of the ƒ! “row” type, the angle θ is larger and p0 is tilted out of the plane, ƒ! ƒ! ƒ! ƒ! 0 ð b1 ; b2 Þ or ð b1 ; b2 Þ. Such orientations can be produced by two rotations, starting from the initial crystal position (A), shown in Fig. 9a. The first rotation is produced by a large angle ð  60–100 mradÞ around one goniometer axis, e.g., horizontal. As a result, the lattice vectors ½0 22 and ½02  2 are kept on the ! horizontal axis H and close to the “pancake”, whereas the vectors ½022 and ½0  2  2 are shifted far outside the region of the ! “pancake”. Then the second rotation around the axis V by a small angle ΦV , determined, e.g., in Ref. [8], sin ΦV ¼ δ=ðð2πλc =aÞðn22 þ n23 Þ1=2 Þ n2 ¼ n3 ¼ 2

ð9Þ

fixes one vector ½0  22 (or the ½02  2) on the lower kinematical border of the “pancake”. Polarization with good accuracy is in the horizontal plane (the “para” orientation). An analogous procedure has to be produced for obtaining linear polarization in the vertical direction. Keeping the azimuthal angle unmodified, the large and small angular rotations have to be changed – the rotation around ! ! V axis by large angle and a small rotation around H axis by angle [8]: sin ΦH ¼ δ=ðð2πλc =aÞ cos ΦV ðn22 þ n23 Þ1=2 Þ n2 ¼ n3 ¼ 2:

ð10Þ

One of the vectors, [022] or ½0 2  2, is used in this case (the “perp” orientation). The lines of intersection of the “pancake” with ƒ! ƒ! the plane ð b2 ; b3 Þ for “para” and “perp” orientations are shown in Fig. 9c. 3.2. Spectra and polarization of coherent bremsstrahlung for “point” type orientations Fig. 10 shows the uncollimated coherent bremsstrahlung spectra, measured by the FP hodoscope. The spectra were produced at the “point” type orientations (“para” and “perp”), shown in Fig. 9c, at which main contribution to the coherent bremsstrahlung results from the vectors ½0  22 and ½0 2  2, respectively. The CB peak energy is Eγ;d  50 MeV. The spectra are normalized to a

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Eγ , MeV Fig. 11. Relative coherent bremsstrahlung spectra for “point” type orientation presented in Fig. 9c (D). The main contribution results from the vector ½0  2  2 (see text for details). Squares – measurement with the NaI detector, empty circles – measurement by the FP array in coincidence with the NaI detector. The spectra normalized to a corresponding bremsstrahlung spectrum produced in Al radiator 50 μm thick. The diameter of the collimator is 12 mm. Curve is a result of calculation with ANB code.

bremsstrahlung spectrum produced in a 50 μm Al radiator: D=Al ¼ ðI coh þ I in Þ=I Al :

ð11Þ

Icoh, Iin, IAl are intensities of the coherent and incoherent parts of the CB, and bremsstrahlung from Al radiator. The spectra are practically identical and demonstrate a typical coherent maximum with low enhancement (or the so-called, coherent effect – the ratio (11) at the maximum) βmax  1:37. The calculation produced with the ANB code [31] is in a good agreement with the experimental data, except a small disagreement (E3%) at the end of energy range, which perhaps is due to the background contribution. Polarization,

calculated with the same values of experimental factors as for the spectrum calculation, reaches P γ  0:17 at the coherent peak energy. The influence of the moderate collimation on the CB spectrum can be seen in Fig. 11, where the collimated spectra of the coherent bremsstrahlung are presented. The spectra were measured by the NaI detector, and FP hodoscope in coincidence with the NaI at the photon collimator opening 12 mm in diameter (the collimation angle is θc  1:2θγ ). The orientation provided the same CB peak energy Eγ;d  50 MeV and vertical direction of the polarization, resulted from the vector ½0  2  2, as in the case of previous uncollimated spectrum in Fig. 10 for “perp” orientation, but the positions of the “pancake” was a little different, as it is shown in Fig. 9c (D) (the electron beam was ƒ! ƒ! slightly more (
2.31) tilted out of the plane ð b1 ; b2 Þ). As a whole, the spectra measured by both methods agree with each other, but the spectrum obtained by FP hodoscope in coincidence with the NaI is somewhat sharper and demonstrates a slightly larger enhancement. Such a difference is observed for other measurements too, and it can be due to better energy resolution provided by the FP detectors. Owing to the collimation, the coherent effect is increased to βmax  1:55. But the shape of the spectrum is similar to the previous uncollimated spectrum, there is no noticeable influence due to such changing in the “pancake” position. Theoretical calculations agree with the experimental spectra within the data accuracy. The calculated polarization reaches P γ  0:25 at the coherent peak energy, Fig. 12, that is about 1.5 times larger than for the uncollimated spectrum. In the next step the “pancake” was orientated in such a way that two vectors of the reciprocal lattice ½0  22 and [040] were near the low bound of the “pancake” region, as shown in Fig. 9c, and gave contribution to the coherent bremsstrahlung, practically, at the same coherent peak energy, Eγ;d  60 MeV. The spectrum corresponding to this orientation is shown in Fig. 13. The coherent effect is βmax  1:5 at this orientation, as for previous spectra with lower peak energy, however, polarization in the coherent maximum is P γ  0:2, Fig. 12. The low polarization at the relatively large enhancement is possibly due to a destructive contribution from the ½040 vector which increases the enhancements but decreases the polarization. The contribution from the other strong vector ½022, which produces polarization of opposite direction at this orientation, cannot be seen in the spectrum because it is at higher energy, Eγ;d
96 MeV, outside the interval of measurements. But it can be seen if the coherent peaks will be shifted to lower energies. Such orientation was realized for the spectrum presented in Fig. 14 where the first coherent peak energy resulted from the vector ½0  22 was at Eγ;d  50 MeV and the vector [040] contributed at a bit lower energy. The “pancake” ƒ! ƒ! intersection of the plane ð b1 ; b2 Þ for this orientation is shown in 0.3 0.2

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Fig. 12. Polarization of the coherent bremsstrahlung calculated with ANB code [30], for the spectra presented in Fig. 11 (dash line), in Fig. 13 (dash-dotted line) and Fig. 14 (solid line). The collimator diameter is 12 mm, corresponding to the angle of beam collimation angle θc
1:2θγ .

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Eγ , MeV Fig. 14. Coherent bremsstrahlung spectra for “point” type orientation presented in Fig. 9c (G). The contribution to the coherent peak at energy Eγ;d
50 MeV results from the vectors ½0 22 and [040], the second peak results from contribution the vector [022] (see text for details). Squares – measurement with the NaI detector, empty circles – measurement by the FP array in coincidence with the NaI detector. Empty squares are the bremsstrahlung spectrum from the Al radiator 50 μm thick, measured with the NaI detector. The experimental spectra are normalized to the corresponding calculated spectra. The collimator diameter is 12 mm. ν ¼ σ 0 ZðZ þ 1:3Þ, Z-atomic number, σ 0 ¼ αr 20 ¼ 0:57947  1027 cm2 .

Fig. 9c (line G). One can see that the coherent maximum became broader due to contributions from two vectors ½0  22 and [040] with close coherent peak energies. The enhancement in the first maximum is larger, βmax  1:7, however, the beam polarization is only P γ  0:25 due to destructive contribution from the vector ½040. There is a rather strong second maximum in the spectrum at energy Eγ;d  78 MeV from the vector [022]. It produces polarization of opposite direction which reaches P γ  0:13, Fig. 12. One may get higher polarization degree (P γ  0:25) if to use the tight photon beam collimation, θc  0:5θγ . Thus, such orientation gives a chance to perform measurements at two photon energies simultaneously. The calculations describe the energy behavior of the experimental data for these orientations. The effect of tight collimation of the beam to one half of a characteristic angle is shown in Fig. 15 (from [1]). The collimated coherent spectrum was measured for the “para” orientation when only vector ½0  22 contributed to the coherent bremsstrahlung. The coherent peak energy was Eγ;d  63 MeV. The spectrum was obtained by dividing the tagging efficiency, measured from the diamond radiator, by the tagging efficiency from the amorphous Al radiator, normalized to 100. The tagging efficiency is the ratio of the number of photons to the number of electrons for a specific tagger channel, εtag;i ¼ nγ;i =n0e;i where nγ;i is the rate of photons corresponding to hodoscope channel i and n0e;i is the rate of electrons in hodoscope channel i. The tagging efficiency thus

Fig. 15. Top: Relative spectrum of the collimated coherent bremsstrahlung for “para” orientation (from [1]), only vector ½0  22 contributes to the coherent bremsstrahlung. The collimation angle is θc
0:5θγ . The spectrum was obtained by dividing the tagging efficiency for the diamond by the tagging efficiency from the 50 μm thick Al radiator, normalized to 100 (see text). The curve is an analyticbremsstrahlung calculation. Bottom: The calculated polarization corresponding to the spectrum.

measures the probability that the bremsstrahlung photon corresponding to channel i passes through the photon-beam collimator and is incident upon the experimental target. In accordance with the theory, at stronger collimation the CB spectrum became narrower and the coherent effect increased, to βmax  1:7 in our case, due to suppression of the incoherent part of the radiation. The coherent peak was fitted using a program developed by Livingston [1,37]. In general the calculations agree with experiment within 3–5% except for the energy range 70–80 MeV, where there is some disagreement, perhaps, due to the background contribution to the FP detectors. The polarization in the coherent peak was estimated by calculation using an analytical code ANB taking into account the parameters of the electron beam (divergence, multiple scattering in the radiator, etc.) and the photon beam collimation. The expected polarization for this collimation angle and coherent peak energy is P γ  0:38, and the tagging efficiency is εtag  0:12. Comparison of the tagging efficiencies and expected polarization for the collimators, having apertures 5.4 and 12 mm diameter, presented in [1], shows that the collimator with aperture 12 mm may be preferable in photonuclear experiments with polarized photons, because the decrease in the tagging efficiency at the collimator, having aperture 5.4 mm in diameter is not compensated by the increase in photon polarization. 3.3. The spectra for “row” orientations For completeness, some measurements were made of the coherent bremsstrahlung spectra for the orientations of “row” type when many vectors of the crystal reciprocal lattice contributed to the coherent bremsstrahlung. The vectors have to satisfy

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Fig. 16. Relative coherent bremsstrahlung spectra for “row C” orientation (Fig. 9b) for peak energy Eγ;d  32 MeV measured with the NaI detector (squares) and by the FP array in coincidence with the NaI detector (empty circles). The spectra are normalized to a bremsstrahlung spectrum produced in Al radiator 50 μm thick. The collimator diameter is θc
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1:9θγ . η ¼ σ 0 ZðZ þ 1:3Þ, Z-atomic number, σ 0 ¼ αr 20 ¼ 0:57947  1027 cm2 .

the Laue condition and to be on the low kinematical border of the “pancake”. Such orientations can be obtained as a result of rotation ! ! by a small angle around H (or V ) axis, starting from the “zero” position, when ΦA ¼ 01, or from the initial position, shown in Fig. 9a, when azimuthal angle ΦA ¼ 451. Figs. 16–18 demonstrate the coherent bremsstrahlung spectra, produced at orientations corresponding the “pancake” position C, shown in Fig. 9b, for the coherent peak energies Eγ;d  32, 50 and 65 MeV. The measurements were performed with the NaI detector and with the FP hodoscope in coincidence with the NaI. The photon beam collimation angle was θc  1:9θγ . The results obtained by both methods are in agreement with each other, although there is a small difference between the spectra in the range of the CB maximum which, as in the previous cases, resulted from the different energy resolution of the FP and NaI detectors. On the whole, the measured coherent bremsstrahlung spectra are in good agreement with the calculated ones. The spectra demonstrate large coherent maxima of typical shape with large enhancement, βmax  2:4, for energy Eγ;d  32 MeV, and βmax  1:7 for Eγ;d  65 MeV, which are essentially more than for the “point” orientation, although the photon beam collimation is almost absent. However, the beam polarization is very low, P γ  6–8% in the coherent maxima, that is 2–3 times lower than the beam polarization for the “point” orientations. The low polarization in this case is the result of destructive contributions of the different reciprocal lattice vectors.

Fig. 18. Relative coherent bremsstrahlung spectra for “row” C orientation (Fig. 9b) for coherent peak energy Eγ;d
65 MeV (notations are the same as in Fig. 16). The collimation angle is θc
1:9θγ . The curve is the result of a calculation with the ANB code.

One of the features of the “row” type orientations is that the electron beam impinges on the crystal along the crystal planes, thus the conditions appear for the plane channeling and above barrier regimes of the movement of the particles at which the particles produce intensive radiation in the low energy range. The presence of these effects has been observed at the crystal orientation procedure by Luckey's method. For an electron energy E0  200 MeV and a diamond crystal, the radiation spectrum from the above mechanisms has a maximum at Eγ  1–2 MeV and extends to energies Eγ  15–20 MeV. The corresponding increase of the radiation intensity is observed in Fig. 18, where the coherent maximum lies at higher energy, and partly in Fig. 17. So, at the “row” type orientations one can observe three radiation mechanisms of the electrons in a crystal simultaneously – traditional coherent bremsstrahlung, the planar channeling and planar above barrier radiation.

4. Energy interval available for photo nuclear investigation with polarized photons at the MAX IV Laboratory As it was stated above, one can see that theoretical calculations based on the ANB code [31] describe rather well the experimental spectra of the coherent bremsstrahlung, measured for various crystal orientations and photon beam collimations. That allows one to use the ANB code for calculations the photon beam spectra and polarization, which can be produced at the MAX-lab. Fig. 19 demonstrates dependence of the beam polarization versus the collimation angle for the peak energy Eγ;d  50 MeV when one vector [022] mainly contributes to the coherent bremsstrahlung. The dependence is typical for various coherent peak energies. Calculations show that the photon polarization can reach P γ  0:2, practically, without collimation of the photon beam. The polarization can be considerably enhanced by tightly collimating the photon beam, at that, a noticeable increasing of the polarization degree begins with the collimation angle θc  0:9θγ (corresponds to the collimator diameter 8–9 mm for MAX-lab facility). The polarization can be increased to P γ  0:45 at the collimation angle θc  0:4θγ (the diameter of the collimator is E4 mm) for this peak energy. Thus, the collimators with moderate apertures (6–9 mm diameter) can be effective for photonuclear experiments at MAX-lab. The energy interval available to photonuclear researches with polarized photon beam at MAX-lab was estimated on the base of calculations of the beam polarization. The calculations have been produced for electron beam energy E0 ¼ 200 MeV, available at present, a diamond crystal 0.1 mm thick, oriented in such a way

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0:5θγ (from [12]).

that the reciprocal lattice vector [022] gave main contribution to the coherent bremsstrahlung, and collimation angles θc  0:4θγ ,  0:6θγ ,  1:2θγ . The results of the calculations are presented in Fig. 20, where it is also shown the results of the calculation for electron energy E0 ¼ 250 MeV and collimation angle θc
0:5θγ from Ref. [12]. If the polarization should be no less P γ  0:2 in order to be used in photonuclear experiments, the calculations show that at present time, owing to the limitation of the maximal electron energy by the value E0 ¼ 200 MeV, the energy interval of the investigations can be extend from Giant Dipole Resonance region up to Eγ  90, 80 and 60 MeV for the above collimation angles, respectively. But the restriction of the energy interval can be due to decreasing of the tagging efficiency of the photon beam with decreasing the collimation angle. An improvement of the coherent beam characteristics would be possible if the electron energy was increased to E0  250 MeV. This will allow us to extend the interval of photonuclear experiments up to point threshold, and to increase the merit function of the beam in the Giant Dipole Resonance energy range.

5. Summary A linearly polarized tagged photon beam has been produced at the MAX-lab photon facility using the coherent bremsstrahlung of electron with energy E0 ¼ 192:6 MeV in a diamond crystal with

thickness 0.1 mm. The CB beam characteristics have been studied for various crystal orientations, different coherent peak energies and collimations of the photon beam. The photon spectra were measured by the FP hodoscope of the MAX-lab tagging facility at high electron beam intensity, by the NaI detector and by the FP array in coincidence with the NaI detector at strongly reduced electron beam intensity. The measured spectra demonstrate similar features of the coherent bremsstrahlung that were observed at higher electron energies,
1 GeV – the shape of the coherent maxima, intensity and polarization dependence on the beam collimation and crystal orientation. Calculations on the base of ANB code [31] taking into account the electron beam divergence, multiple scattering in the crystal, beam spot size, and energy resolution describe rather well the observed experimental characteristics of the coherent bremsstrahlung spectra at this low electron energy. Calculations show that the photon polarization in the CB maximum can reach P γ  0:5 at the Giant Resonance region if only one crystal reciprocal lattice vector ½0 7 2 7 2 is involved and the tight beam collimation, θc  0:5θγ , is used. Because the coherent maximum width is usually 8–10 MeV, where the polarization degree is enough for photonuclear experiments ðP γ 4 0:2Þ, the Giant Dipole Resonance energy range can be covered by 2–3 setting of the coherent peak with energy resolution of
1 MeV provided by the MAX-lab tagging facility. At present, even with the initial energy of the electron beam at MAX-lab limited to
200 MeV, the uncollimated CB photon beam can provide good enough polarization for photonuclear research in the Giant Dipole Resonance region. This interval can, in principle, be extended to Eγ  90 MeV by collimating the photon beam to half the characteristic angle, θc  0:5θγ . A further, substantial improvement of the coherent bremsstrahlung beam parameters and extension the energy range could be obtained by increasing the maximum electron energy to 250 MeV.

Acknowledgments This work is supported by Swedish Research Council, the Craaford Foundation, the Wennergren Foundation, the Royal Physiographic Society in Lund and the Knut and Alice Wallenberg Foundation, by the European Community – Research Infrastructure Action under the FP6 “Structuring the European Research Area” Programme (through the Integrated Infrastructure Initiative “Hadron Physics”) and partly supported by STCU project 3239. The authors acknowledge the large support of the MAX IV Laboratory staff which made this experiment successful. References [1] J.-O. Adler, et al., Nuclear Instruments and Methods in Physics Research Section A 715 (2013) 1. [2] R.E. Taylor, R.F. Mozley, Physical Review 117 (1960) 835. [3] A.P. Potylitsyn, Polarized Photon Beams of High Energy, Moscow, Energoatomizdat, 1987, 120 p. (in Russian). [4] J. Yokokawa, et al., Journal of the Physical Society of Japan 57 (1988) 695. [5] R.F. Mozley, J. De Wire, Nuovo Cimento 27 (1963) 1281. [6] G. Bolonga, G. Diambrini, G.P. Murtas, Physical Review Letters 4 (1960) 134. [7] G.D. Kovalenko, L.Ya. Kolesnikov, A.L. Rubashkin, Topics in current physics, in: Coherent Radiation Sources. Coherent Bremsstrahlung – Experiment, vol. 38, Springer, Berlin, 1985, p. 33. [8] D. Lohmann, et al., Nuclear Instruments and Methods in Physics Research Section A 343 (1994) 494. [9] F.J. Klein, et al., The Coherent-Bremsstrahlung Facility in Hall B at Jefferson LAB, Preprint JLAB, 2005. [10] W. Hillert, The European Physical Journal A 28 (2006) 139. [11] D. Elsner, et al., arXiv:0810.1849v1 [nucl-ex], 10 Oct 2008. [12] J.-O. Adler, V. Ganenko, L-J. Lindgren, Report 01/01 LUNFD6/(NFFR-3086)1-31/ 2001, Lund 2001. [13] K. Fissum, et al., MAX-lab Activity Report 2007, p. 416.

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