Mikhail Ivanovich Ryazanov

Diffraction radiation from relativistic particles

Foreword Preface 1. Radiation from Relativistic Particles 2. General Properties of Diffraction Radiation 3. Diffraction Radiation at Optical and Lower Frequencies 4. Diffraction Radiation in the Ultraviolet and Soft X-Ray Regions 5. Diffraction Radiation at the Resonant Frequency 6. Diffraction Radiation from Media with Periodic Surfaces 7. Coherent Radiation Generated by Bunches of Charged Particles 8. Diffraction Radiation in the Pre-Wave (FRESNEL) Zone 9. Experimental Investigations of Diffraction Radiation Generated by Relativistic Electrons References

Experimental Investigations of Diffraction Radiation Generated by Relativistic Electrons

The theory of diffraction radiation was founded in the 1950s, but the first experimental investigation of the characteristics of diffraction radiation generated by relativistic electrons was carried out only in 1995 [1]. The scheme of the experiment is shown in Fig. 9.1. The measurements were performed with a 150-MeV electron beam consisting of bunches with a length of about 1 mm and a diameter of about 2.5 mm. The population of a bunch was 1.5·108e−. In the experiment, the spectrum of coherent diffraction radiation in a wavelength range of λ = 0.1−5 mm, as well as the angular distribution of forward and backward diffraction radiations, is measured. Discs with the hole diameters d=10,15,20 mm, as well as a transition radiation target (disc without hole), were used to generate coherent radiation.

Diffraction Radiation in the Pre-wave (Fresnel) Zone

The notion of the formation (coherence) length introduced in the early 1950s (see detailed references in [1,2]) was described in the framework of classical electrodynamics in Sects. 1.2 and 2.2 for bremsstrahlung and polarization radiation mechanisms, respectively. The quantum-mechanical consideration of this problem provides the identical result [2]. The notion of the formation length appeared to be useful for describing not only electromagnetic, but also strong interactions [3,4]. The main physical idea underlying the notion of the formation length for polarization emission mechanisms (including transition radiation and diffraction radiation) is the interference of the radiation fields emitted from different points of the emitting substance along particle trajectory (see Sect. 2.2). This concept is very close to the Fresnel zone widely known in optics.

Diffraction Radiation in the Ultraviolet and Soft X-Ray Regions

The majority of the problems on diffraction radiation that have been already studied theoretically were solved for ideally conducting targets. The perfect-conductivity model is applicable at large values of the imaginary part of the relative permittivity, i.e., for most metals at optical, infrared, and radio frequencies

Radiation from Relativistic Particles

It is well known that emission is the process of the formation of transverse electromagnetic waves by moving charged particles. Let us consider the emission process occurring when a relativistic charged particle moves according to the law

Coherent Radiation Generated by Bunches of Charged Particles

In one of the first works [1], where synchrotron radiation generated by an electron bunch containing N e electrons was considered, it was mentioned that, in the range of wavelengths comparable with the length of the electron bunch l B, radiation becomes coherent, i.e., the intensity of radiation generated by the bunch depends quadratically on the number of electrons in the bunch (on the “population” of the bunch).

Diffraction Radiation at the Resonant Frequency

Diffraction radiation is microscopically a result of the scattering of the self field of a uniformly moving charge from the atoms of a medium. The cross section for the scattering of an electromagnetic wave from an atom is maximal near resonance, so that the diffraction radiation intensity should increase at resonant frequencies. As known, the transverse field of a source at small distances is much lower than the longitudinal field. Therefore, the energy transfer from an exited atom to an unexcited atom in dense media occurs primarily through the transverse field by the dipole—dipole interaction rather than through the emission and absorption of resonant transverse waves. As a result, the interaction of a resonant photon with an atom most likely leads to disappearance of the photon and appearance of an electron excitation further migrating in the medium as an exciton. For this reason, the resonant photon, i.e., the photon whose energy is close to the exciton energy does not penetrate inside the medium. For the same reason, the emission of resonant transverse waves by an atom from the depth of a dense medium is impossible. Thus, the probability of the formation of diffraction radiation at the resonant frequency in the process of scattering from an atom in a dense medium is much lower than the probability of the formation of an exciton. Therefore, diffraction radiation is generated due to the scattering of the self field of the particle from the atoms of the surface layer. The thickness of this layer is determined by the absorption coefficient of transverse resonant waves. Since this layer is thin, we can use the approximation of the single scattering of the resonant component of the self field of the fast particle from the atoms of the medium. This approximation in the problem of the reflection of resonant electromagnetic waves from the surface of a medium was proposed by Fermi [1]. This makes it possible to solve the reflection problem without the usual macroscopic boundary conditions and provides a good agreement with experimental data.

Diffraction Radiation at Optical and Lower Frequencies

Calculation of the characteristics of radiation generated when a charged particle moves through a circular hole in an infinitely thin perfectly conducting screen is one of the most investigated problems in the theory of diffraction radiation. Such a screen can be a thin metal plate; in this case, radiation should be considered at frequencies below plasmon frequencies, i.e., at optical, infrared, millimeter, etc. frequencies.

General Properties of Diffraction Radiation

As mentioned above, diffraction radiation can be considered as radiation generated by polarization currents induced in a medium by the field of a moving charge. The distance between the charge trajectory and medium surface is usually much larger than the mean intermolecular distance in the medium.

Diffraction Radiation from Media with Periodic Surfaces

A charge moving in vacuum with a constant velocity near a perfectly conducting periodically deformed target (grating, see Fig. 6.1) induces on its surface a time-varying charge and current, which is a cause of the appearance of diffraction radiation.