FEASIBILITY OF LASER DIAGNOSTICS OF A BEAM OF ACCELERATED ELECTRONS

A. V. Peshkov, V. A. Avgustinovich, B. A. Nechaev

(Presented by the Scientific and Technical Seminar of the High-Energy Laboratory of the Research Institute of Nuclear Physics)

At present, probably the most important method of plasma diagnostics has become the method of determining plasma parameters from the scattering of laser radiation by plasma electrons [1]. The scattering of light by electrons can also be used to determine the parameters of beams of relativistic electrons. Previously, the process of Compton scattering of laser radiation was investigated for the purpose of obtaining polarized quasi-monoenergetic gamma quanta [2, 3, 4].

The kinematic features of Compton scattering of laser radiation by relativistic electrons make it possible to use this phenomenon for diagnostics of bunches of high-energy electrons in those cases where traditional methods of beam investigation prove to be of low effectiveness.

Since the scattering of light photons occurs on relativistic electrons, the differential cross section of Compton scattering has a sharp maximum in the direction of the electron momentum. And all the radiation is concentrated in a cone with an angular aperture of order \(\dfrac{mc^2}{E}\), where \(mc^2\) is the electron rest energy and \(E\) is the electron energy.

The energy of the scattered photon is related to the emission angle of the scattered photon and reaches its maximum value in the head-on interaction of the laser beam and the electron beam, when the direction of the scattered photon coincides with the direction of motion of the electron and is given by the expression

\[ \omega_2 = 4\omega_1 \left( \frac{E}{mc^2} \right)^2, \]

where \(\omega_1\) is the energy of the laser photon,

\(\omega_2\) is the energy of the scattered photon.

Thus, the frequency of the scattered photon changes by the amount \(4(E/mc^2)^2\). Owing to the change in frequency of the scattered radiation, the problem of background caused by scattering of the laser radiation on various parts of the experimental setup is completely eliminated. And the main source of background will be only bremsstrahlung on the residual gas in the vacuum chamber of the setup.

When probing an electron beam it is very important to reduce the interaction region in order to obtain good spatial resolution.

The smallest attainable diameter of the focal spot \(\Delta y\) is determined, on the one hand, by the diameter \(d\) of the laser rod and the divergence \(\Theta\) of the laser beam, and, on the other hand, by the possible aperture ratio \(D:f\) for the laser beam at the entrance to the vacuum chamber (\(D\) is the aperture of the focusing lens, \(f\) is the focal length of the lens)

\[ \Delta y=\frac{d\theta}{D:f}. \]

Usually, for lasers \(\Theta = 5\cdot 10^{-3}\) rad. According to calculations carried out in Ref. [5], the interaction intensity of two counterpropagating particle beams decreases to \(16\%\) when the diameter of one of the interacting beams, as a result of divergence, exceeds the diameter of the other by a factor of 3. When a short-focus optical system is used, the interaction region can be limited to a few millimeters.

We have investigated the possibility of using a laser beam to probe an electron beam in the vacuum chamber of a synchrotron. The experiment was carried out on the “Sirius” electron synchrotron. For this purpose, an improvement was introduced into the installation—created for producing polarized and monoenergetic gamma quanta by the method of Compton scattering of laser radiation by relativistic electrons (Fig. 1)—which made it possible to move the laser in the transverse direction relative to the aiming line. A neodymium laser was used in the experiment; its beam was focused into a spot 1.5 mm in diameter, and therefore, according to our estimates, the length of the interaction region was 30 cm.

Fig. 1. Diagram of the experimental setup. S — scintillation spectrometer, K — collimator, CM — cleaning magnet, M\(_2\) — monitor of the number of accelerated electrons, AKT — autocollimator, FEU-3 — photomultiplier recording the laser radiation, OKG — laser, PP — turning prism, D\(_1\) and D\(_2\) — alignment diaphragms, FEU-1 — photomultiplier used for alignment, L\(_1\) — focusing lens, FEU-2 — synchrotron-radiation intensity monitor, Sh — shutter, VK — synchrotron vacuum chamber, YS — alignment grid.

Figure 2 shows a typical angular distribution of Compton-scattered gamma quanta. The angular aperture of the cone in which the scattered gamma quanta were recorded is \(1.4\cdot 10^{-3}\) rad. This value is approximately 10% smaller than the angular distribution calculated with allowance for betatron oscillations of the electrons in the “Sirius” chamber. The decrease in the angular distribution in comparison with the theoretical value is explained by the fact that the recording apparatus detected gamma quanta with energies of the order of \(0.5\,\omega_2\) and higher.

Fig. 2. Angular distribution of Compton gamma quanta.

Fig. 3. Position of the maxima of Compton gamma quanta as a function of the position of the laser focus on the beam cross section.

The distribution of electron density in the transverse direction was measured by moving the laser focal spot. For each position of the focal spot, the angular distribution was recorded. From the magnitude of the maximum of the angular distribution one could judge the electron density in the interaction region; in addition, from the position of the maximum relative to the beam axis one can determine the preferred direction of the electron momentum in the interaction region.

Figure 3 shows the angular distributions of Compton-scattered gamma quanta for different positions of the laser focal spot in the cross section of the electron beam.

The maxima of these distributions in the central part of the beam lie within the angular alignment error of \(5\cdot 10^{-5}\) rad, and only at the edges of the electron beam does the direction of electron motion relative to the equilibrium orbit amount to \(2\cdot 10^{-4}\) rad. The theoretical estimate of the angular spread of the electrons caused by betatron oscillations is of the order of \(1.4\cdot 10^{-4}\) rad for the “Sirius” synchrotron.

Fig. 4. Electron distribution density over the beam cross section.

In Fig. 4 the distribution of electron density in the transverse direction over the beam cross section is shown.

This work and work [6] have shown that a laser beam can be used as a nonperturbing probe for diagnosing an electron beam.

REFERENCES

1. Methods of Plasma Research. Edited by V. Lochte-Holtgreven. Moscow, “Mir,” 1971.

2. O. F. Kulikov, Yu. Ya. Tel’nov, E. I. Filippov, M. I. Yakimenko. ZhETF, 47, 1519 (1964).

3. C. Bemporad, R. H. Milburn, N. Tanaka, M. Fotino. Phys. Rev. 133, 1546 (1965).

4. A. V. Peshkov, E. I. Aleksandrov, A. V. Karakuts. Proceedings of the VII Interuniversity Conference on Electron Accelerators (Tomsk, 1968), issue 4. Atomizdat, 1970.

5. R. H. Milburn. SLAC Report, No. 41 (1965).

6. J. R. Saur, R. H. Milburn, C. K. Sinclair, M. Fotino. IEEE, Transactions on Nuclear Science 16, 1077 (1968).