HIGH-ENERGY COHERENT BREMSSTRAHLUNG EFFECT IN A SINGLE-CRYSTAL SYNCHROTRON TARGET

B. N. KALININ, V. N. KUZMIN, A. P. PRIVEZENTSEV, Yu. I. SERTAKOV,
V. D. KHORUNZHY

(Presented by the scientific seminar of NIIYaF&A)

For experiments in high-energy physics, the production and use of monoenergetic and polarized beams of \(\gamma\)-quanta is of considerable interest. The use of such \(\gamma\)-quanta for reactions of photoproduction of \(\pi\)-mesons will make it possible to obtain additional information on the interactions of elementary particles. One of the experiments being prepared at the 1.5-GeV synchrotron of the Nuclear Physics Research Institute of TPI, with the aim of obtaining quasi-monoenergetic polarized \(\gamma\)-quanta, is the study of bremsstrahlung radiation from electrons on crystalline targets.

The quasi-monoenergetic character of bremsstrahlung on a single crystal can be predicted from a classical consideration of the process. The bremsstrahlung pulse may be represented as the result of interference of waves of different frequency [1]. The shape of the pulse is determined by the phase relations between its component waves. For an electron moving at a distance \(b\) above a periodic row of Fourier atoms, the image of the acceleration, which determines the spectral composition of the pulse, has the multiplier

\[ F(\omega)= \frac{\sin \frac{1}{2}N\omega\frac{a}{v}} {\sin \frac{1}{2}\omega\frac{a}{v}}, \tag{1} \]

where \(a\) is the distance between atoms,
\(v\) is the electron velocity.

At the points \(\omega_n = 2\pi \frac{v}{a} n\), function (1) has sharp maxima; consequently, peaks will be observed in the bremsstrahlung spectrum at these points. An exact quantum-mechanical calculation of the bremsstrahlung cross section on single crystals and of its polarization was carried out by Überall [2, 3]. Let an electron beam be incident at a small angle \(\Theta\) to the crystal axis \(b\). The recoil momenta of the nuclei on which the electron is decelerated have discrete values, multiples of reciprocal-lattice vectors. The endpoints of the vectors of these momenta are located in a narrow disco-

shaded region (Fig. 1). This disk is perpendicular to the momentum of the incident electron, its radius is \(mc\), and its thickness is

\[ \delta=\frac{mc^{2}}{2E_{0}}\frac{x}{1-x}, \tag{2} \]

where

\[ x=\frac{K}{E_{0}}; \]

\(K\) is the energy of the bremsstrahlung \(\gamma\)-quantum,
\(E_{0}\) is the energy of the initial electron.

Fig. 1. Kinematic diagram of bremsstrahlung in the reciprocal lattice. \(\vec P_{0}\) is the momentum of the incident electron, \(a\) is the lattice constant of the direct lattice; the hatched part of the \(\vec b_{2}\vec b_{3}\) plane indicates the region of its intersection with the momentum disk. Points that fall into this region contribute to the bremsstrahlung cross section.

The disk is very thin, and at small angles \(\Theta\) the contribution to the cross section is made by points of the reciprocal lattice of the crystal plane \(\vec b_{2}\vec b_{3}\). When \(x\) changes, the number of points contributing to the bremsstrahlung cross section changes. The same effect can be achieved by changing the angle \(\Theta\). Thus

Thus, the bremsstrahlung spectrum has a number of quasi-monoenergetic peaks. From formula (2) it is not difficult to find the values of \(x\) at which maxima will be observed:

\[ x_m=\frac{1}{1+\left(\frac{a m c^2}{4\pi n_2 \Theta E_0}\right)^2}. \tag{3} \]

The meaning of the letter designations in formula (3) is clear from Fig. 1. The sharpest peaks will be observed in the low-energy part of the spectrum, \(n_2=1,2\). The use of a crystal makes it possible to obtain intense bremsstrahlung beams with a high degree of polarization. As is known, polarized \(\gamma\)-quanta can be obtained by angular selection of part of the spectrum of ordinary bremsstrahlung; however, multiple scattering of electrons in polycrystalline targets permits the use only of thin targets, which reduces the radiation intensity. Bremsstrahlung from a single crystal makes it possible to use the full bremsstrahlung cone. The effect of multiple scattering in a single crystal is small; therefore thicker targets can be used and no large collimation of the \(\gamma\)-beam is required. To obtain a quasi-monoenergetic spectrum, single crystals are chosen from materials with a high Debye temperature and low \(Z\). For such crystals the root-mean-square displacement of atoms as a result of thermal vibrations is small, and the broadening of the interference pattern caused by them is insignificant. From this point of view the most suitable material is diamond. In Fig. 2 are given the results of calculations of the values of \(x_m\) as a function of \(\Theta E_0\) and of the magnitude of the jump in intensity in the spectrum \(\Delta I\) as a function of \(x_m\), for diamond and silicon crystals. The calculation was carried out according to the method proposed by Lutz et al. [4]. The computations were made on an M-20 electronic computer. The nuclear screening function in the calculations was chosen in the form

\[ F(q)=\frac{1}{1+q^2(111Z^{-1/3})^2}, \tag{4} \]

where \(q\) is the momentum transferred to the nucleus,
\(Z\) is the nuclear charge.

From the curves (Fig. 2) for the magnitude of the intensity peak it is seen that it is easiest to isolate the quasi-monoenergetic part of the spectrum for small \(x\). At constant initial electron energy this corresponds to small angles \(\Theta\). The Debye temperature of diamond is higher than that of silicon; therefore, as is not difficult to see from the curves of Fig. 2, the magnitude of the intensity peaks is higher for diamond. The layout of the experimental setup for obtaining monoenergetic and polarized \(\gamma\)-quanta at the TPI “Sirius” synchrotron is shown in Fig. 3. A diamond or silicon crystal is placed on the inner side of the vacuum chamber of the synchrotron. The electrons are dumped onto the target crystal by switching off the high-frequency accelerating voltage of the accelerator. In the first experiments it is proposed to use a silicon single crystal with optically polished surfaces, rectangular in shape, \(15\times15\times0.25\ \mathrm{mm}^3\), cut along the (110) plane. The (110) plane coincides with the large face of the crystal to an accuracy of \(\pm 5\) minutes. Subsequently, diamond of dimensions \(5\times10\times2\ \mathrm{mm}^3\), also with the (110) plane along the large face, will be used.

Rotation of the crystal about two mutually perpendicular axes is carried out with the aid of a goniometer. In Fig. 4 is shown the kinematic scheme of the goniometer, designed and manufactured at

Curve designations:

• \(x\) — diamond, \(n=1\)
• \(xx\) — diamond, \(n=2\)
• \(\square\) — silicon, \(n=1\)
• \(\square\square\) — silicon, \(n=2\)

Fig. 2. Dependence of \(x_m\) on the value of \(E_0\) and the height of the intensity peak \(\Delta I\) above the continuous part of the spectrum as a function of \(x_m\).

Fig. 3. Experimental setup diagram: 1—goniometer with crystal; 2, 3, 4—collimators; 5—cleaning magnet of the SP-58-B type; 6—vacuum tube; 7—pair magnetic gamma spectrometer; 8—quantum meter.

NIIYaF. The goniometer makes it possible to rotate the crystal about the horizontal axis \(\Theta_v\) within \(\pm 2.5^\circ\), and about the vertical axis \(\Theta_h\) within \(\pm 45^\circ\). The resolution is no worse than 10 sec. In this goniometer design, to ensure high accuracy in rotating the crystal, high-precision measuring instruments are used: micrometer 15 and theodolite limb 9.

Fig. 4. Kinematic diagram of the goniometer: 1—crystal, 2—crystal holder, 3—hinge, 4—rod, 5—tube, 6—spring, 7—bellows transition, 8—vacuum seal, 9—limb, 10—worm wheel, 11–12—worm pairs, 13—selsyn, 14—vacuum seal, 15—micrometer, 16—worm reducer, 17—selsyn, 18—bracket.

Crystal 1 is mounted in crystal holder 2, which is rigidly connected to rod 4. In turn, rod 4 is connected by hinge to bracket 18, rigidly fixed on tube 5. Tube 5 has a rigid connection with the theodolite limb 9, to which worm wheel 10 is attached. Theodolite limb 9 can rotate on a thrust sliding bearing. Rotation of the limb is transmitted through a two-stage worm reducer with gear ratio \(i = 2015\). Together with the limb, tube 5, rod 4, and the crystal holder with crystal 1, which are rigidly connected to it, rotate. The angle of rotation \(\Theta_h\) is read from the limb scale with the aid of an eyepiece fixed on the base of the goniometer. Rotation of the crystal about the horizontal

the axis is accomplished by the micrometer screw of micrometer 15. The micrometer screw pushes the lower end of rod 4 and thereby rotates it about hinge 3. The angle of rotation \(\Theta_z\) is read from the micrometer scale. Reliable contact of the rod with the micrometer screw is ensured by spring 6. The micrometer screw is rotated through a single-stage worm reducer 16 with gear ratio \(i=60\). The worm wheel of reducer 16 is connected to micrometer 15 by means of a guiding sliding key. The goniometer is connected to the vacuum chamber of the synchrotron through bellows transition piece 7.

The necessary operating pressure in the chamber is maintained by vacuum seals 8 and 14. The entire goniometer is mounted on a table (not shown in the figure), which is designed so as to make it possible to move the goniometer vertically (up and down) in order to set the crystal into the working position. The goniometer is controlled remotely by means of selsyn pairs. For investigations of the polarization of bremsstrahlung, a goniometer will be used that makes it possible to rotate the crystal also in its own plane by \(90^\circ\).

To clean the \(\gamma\)-beam of charged particles, an SP-58 B type magnet with an air gap of \(50\ \mathrm{mm}\) and a field in the gap of \(30\ \mathrm{kG}\) is used. The distance from the cleaning magnet to the spectrometer, \(8300\ \mathrm{mm}\), was chosen so that electrons with energy \(1.5\ \mathrm{GeV}\) would not enter the spectrometer window. From the cleaning magnet to the spectrometer the \(\gamma\)-beam passes through a vacuum tube. The collimators are lead blocks \(50\ \mathrm{cm}\) long with apertures of \(5\), \(10\), and \(50\ \mathrm{mm}\).

The spectrum of coherent bremsstrahlung is measured by a 5-channel pair magnetic \(\gamma\)-spectrometer with the following characteristics: 1) energy resolution at an energy of \(0.1\ \mathrm{GeV}\), \(4\)—\(5\%\), and at the maximum energy—\(1.5\ \mathrm{GeV}\), \(1\)—\(2\%\); 2) the efficiency of one energy channel is \((1\)—\(2)\cdot 10^{-6}\) for an aluminum converter thickness of \(5\cdot 10^{-3}\) radiation length. As the analyzing magnet of the spectrometer, an SP-57-A-1 type magnet with specially fabricated triangular poles is used. With an air gap of \(80\ \mathrm{mm}\), the maximum value of the magnetic field is \(16\ \mathrm{kOe}\). Triangular poles are used to ensure focusing of the electrons and to obtain maximum efficiency. As detectors of electron–positron pairs, 3 pairs of scintillation counters are used. The resolving time of the double-coincidence circuit is \((5\)—\(7\cdot 10^{-9}\ \mathrm{s}\). The registering apparatus is built using tunnel diodes, transistors in avalanche mode, OG-3 and OG-4 decatrons, and IN-1 type indicating instruments. The spectrometer has an air chamber with a pressure of \(0.1\)—\(0.2\ \mathrm{torr}\).

Fig. 5. Block diagram of registration of the ionization current of the quantometer: \(E_a\)—power supply of the quantometer, 1—quantometer, 2—integrator, 3—integrator calibrator, 4—cathode follower, 5—information-processing unit, 6—dose counter.

The beam energy is measured by a Wilson-type quantometer [5]. It consists of 12 copper plates \(1\ \mathrm{cm}\) thick with gaps of 1 and \(2\ \mathrm{mm}\), filled with air. The constant of the quantometer when filled with air is \(7.79\cdot 10^{18}\ \mathrm{MeV/coulomb}\).

The block diagram of the recording of the ionization current of the quantometer is shown in Fig. 5. A current–frequency converter with a pulse duration of 2 μsec was used as the integrator. The error of the recording circuit is 0.5%.

A detailed presentation of the experimental results will be published subsequently.

In conclusion, the authors thank TTU engineer N. E. Yakovlev for assistance in carrying out the numerical calculations.

References

1. Ya. B. Zel’dovich. JETP Letters 4, 426 (1966).
2. H. Überall. Phys. Rev. 103, 1055 (1956).
3. H. Überall. Phys. Rev. 107, 223 (1957).
4. G. Bologna, G. Lutz, H. Schulz, U. Timm, W. Zimmerman. Nuovo Cimento, X4, NA 42168 (1966).
5. R. Wilson. Nucl. Instruments 1, 101 (1957).