The mechanism of Vavilov-Cherenkov radiation

The mechanism of generation of Vavilov-Cherenkov radiation is discussed in this article. The developers of the theory of the Vavilov-Cherenkov effect, I.E. Tamm and I.M. Frank, attributed this effect to their discovery of a new mechanism of radiation when a charged particle moves uniformly and rectilinearly in the medium. As such a mechanism presupposes the violation of the laws of conservation of energy and momentum, they proposed the abolition of these laws to account for the Vavilov-Cherenkov radiation mechanism. This idea has received a considerably wide acceptance in the creation of other theories, for example, transition radiation theory. In this paper, the radiation mechanism for the charge constant motion is demonstrated to be incorrect, because it contradicts not only the laws of conservation of energy and momentum, but also the very definitions of uniform and rectilinear motion (Newton's First Law). A consistent explanation of the Vavilov-Cherenkov radiation microscopic mechanism that does not contradict the basic laws is proposed. It is shown that the radiation arises from the interaction of the moving charge with bound charges that are spaced fairly far away from its trajectory. The Vavilov-Cherenkov radiation mechanism bears a slowing down character, but it differs fundamentally from bremsstrahlung, primarily because the Vavilov-Cherenkov radiation onset results from a two-stage process. First, the moving particle polarizes the medium; then, the already polarized atoms radiate coherently, provided that the particle velocity exceeds the phase speed of light in the medium. If the particle velocity is less than the phase speed of light in the medium, the polarized atoms return energy to the outgoing particle. In this case, radiation is not observed. Special attention is given to the relatively constant particle velocity as the condition of the coherent composition of waves. However, its motion cannot be designated as a uniform and rectilinear one in the sense of its definition by Newton's First Law, and it also contradicts the laws of conservation of energy and momentum.     

Radiation from uniformly moving sources (Vavilov-Cherenkov effect,transition radiation,and some other phenomena)

The radiation produced by uniformly moving sources (the Vavilov-Cherenkov effect, the transition radiation, and some other phenomena) is discussed. This area of physical research originated in the Lebedev Physical Institute of the Russian Academy of Sciences and now represents an integral part of modern physics.     

Radiation of charged particles interacting with interface of two different transparent media

It is shown that the Vavilov-Cherenkov radiation has an essential contribution in experiments on optical transition radiation. The properties of the Vavilov-Cherenkov radiation, such as direction, threshold condition, and polarization, are considered. Peculiarities appearing at sliding incidence of electrons at the target in experiments on optical transition radiation are discussed.     

Features of transition and Cherenkov radiations and the correlation between them

It is shown that transition radiation arising at the boundary of two media is being emitted as a Cherenkov one, if the phase velocity of transition radiation waves in the medium of transition radiation propagation becomes equal to the velocity of the moving radiating particle (the necessary condition for the Cherenkov radiation). The proof of this statement is based on the analysis of the transition radiation formation zone, which may become large enough and provide interference between the field of transition radiation and the own Coulomb field of the moving particle, in case when the Cherenkov radiation condition is fulfilled. As a result, the transition radiation field transforms into the Cherenkov field. The problem is considered for cases of both a waveguide and free space.     

Transition radiation measurements at distances from the transition point comparable to the formation length

The spatial distribution of the electromagnetic field excited by a relativistic particle crossing the surface of a metal is studied. It is shown that the field of the uniformly moving charge must also be taken into account during measurements at distances comparable to the path length for formation of the radiation. Expressions describing the effect of the self-field of the charge on the transition radiation field are derived. Zh. Tekh. Fiz. 67, 89–93 (September 1997)     

Vavilov-Cherenkov effect in a chiral waveguide

The Vavilov-Cherenkov radiation appearing in a circular regular ideal waveguide with a chiral medium is considered. The features of the emission spectrum excited by a charge moving along the waveguide axis are investigated. Expressions for the energy loss of a moving charge are obtained. Zh. Tekh. Fiz. 69, 69–71 (March 1999)     

Analysis of Tamm's problem on charge radiation at its uniform motion over a finite trajectory

The main results of Tamm's problem on radiation produced by an electron moving uniformly along a finite rectilinear section of its trajectory in a transparent medium are analysed. The radiation is compared with the bremsstrahlung occurring at an instant charge acceleration with allowance for dielectric properties of the medium. The Tamm formula is shown to describe the resulting radiation from interference of two bremsstrahlungs caused by double change in the particle velocity in the same and opposite way. This mechanism can be another approach to explanation of the Vavilov-Cerenkov effect.Finally, the authors express their deep gratitude to Professor B. M. Bolotovskii for valuable discussions and coments, and to A. P. Kobzev for discussions that initiated this paper.     

Transition radiation from an extended bunch of charged particles

The spatial distribution of the transition radiation generated by an extended system of charges is studied. The charges sequentially cross the interface at equispaced points. Also, the transition from a spherical bunch with the uniform charge distribution is considered. The radiation patterns produced by the point charge and by the bunch of the charges are shown to differ significantly at certain sizes of the bunch expressed in terms of the wavelength. Charge distributions such that the transition radiation exhibits the properties typical of the Doppler effect or of Vavilov-Cherenkov radiation are found to be possible.     

On transition radiation

Summary A treatment of transition radiation between two dielectric media is presented which is based on the exact expressions for the fields of the particle in the two media. Expressions for the spectral distribution of the energy emitted forward and for that emitted backward are derived. The results are in accord with experimental findings for ultra-relativistic particles. In the asymptotic region the energy spectrum becomes discrete. It is indicated how the treatment can be extended to the case of a plate and to that of a wave guide, as well as to emission by a monopole. The case of the simultaneous emission of transition radiation and Čerenkov radiation is considered and the relationship between them is clarified. In particular, it is shown that, when the particle can emit Čerenkov radiation in the forward medium, it will also emit an interference signal. This is several orders of magnitude smaller than the usual transition radiation and is concentrated in the forward direction. It is also found that the Čerenkov wave emitted by the particle in the backward medium will be partially reflected and partially refracted into the forward medium, after the particle crosses the boundary between the two media. The linear energy density for the refracted wave is calculated and it is shown that under certain feasible conditions this is amenable to experimental verification. This work was done while the author was a summer visitor at Stanford Linear Accelerator Center, Stanford University. It was supported by the U.S. Department of Energy, contract DE-AC03-76SF00515.     

Cherenkov-like mechanism of surface waves excitation

The theory of the excitation of surface waves by a fast charged particle moving though a thin homogeneous metal film surrounded by a dielectric medium is proposed. The Vavilov-Cherenkov effect is shown to occur for surface waves at the particle velocity one or two orders of magnitude lower than the corresponding velocities in a homogeneous medium.     

Field Structure of the Cherenkov Radiation in a Waveguide

We study the field structure of the Vavilov-Cherenkov radiation in planar and cylindrical waveguides filled with a continuous dielectric medium or a uniaxial crystal. It is shown that the Vavilov-Cherenkov radiation has the form of wave packets propagating with the same phase and group velocities. Radiation from a system of charged-particle bunches is considered.     

Angular distribution of Cherenkov radiation from relativistic heavy ions taking into account deceleration in the radiator

Numerical methods are used to study the dependence of the structure and the width of the angular distribution of Vavilov-Cherenkov radiation with a fixed wavelength in the vicinity of the Cherenkov cone on the radiator parameters (thickness and refractive index), as well as on the parameters of the relativistic heavy ion beam (charge and initial energy). The deceleration of relativistic heavy ions in the radiator, which decreases the velocity of ions, modifies the condition of structural interference of the waves emitted from various segments of the trajectory; as a result, a complex distribution of Vavilov-Cherenkov radiation appears. The main quantity is the stopping power of a thin layer of the radiator (average loss of the ion energy), which is calculated by the Bethe-Bloch formula and using the SRIM code package. A simple formula is obtained to estimate the angular distribution width of Cherenkov radiation (with a fixed wavelength) from relativistic heavy ions taking into account the deceleration in the radiator. The measurement of this width can provide direct information on the charge of the ion that passes through the radiator, which extends the potentialities of Cherenkov detectors. The isotopic effect (dependence of the angular distribution of Vavilov-Cherenkov radiation on the ion mass) is also considered.     

The parametric doppler effect upon oblique radiation incidence in quartz glass

Frequency and reflection angle of probe radiation from a refractive-index inhomogeneity induced by an intense pumping pulse in quartz glass and moving with a relativistic velocity are calculated. Conditions under which the normal component of the wave vector of the reflected wave is directed to the opposite or to the same direction as the same component for the incident wave are determined. Comparison with the case of radiation reflection from a relativistic mirror in vacuum is performed. Conditions of the appearance of the Vavilov-Cherenkov radiation from a relativistic refractive-index inhomogeneity induced in the medium by an intense laser pulse are discussed.     

X-ray radiation toward relativistic electrons incident on a flat target

Features of X-ray radiation emitted toward the velocity vector of relativistic electrons incident on a flat target are discussed. The contribution of polarization bremsstrahlung (PB) considered as scattering of the intrinsic field of a fast charge by electrons of the medium is estimated taking into account its dispersion properties. Spectral-angular characteristics of coherent and incoherent PB are analyzed for unstructured and structured targets. Such PB feature not only different intensities, but also different angular dependences reaching a maximum near the velocity direction of a fast charge. It is shown that coherent PB emitted from the target surface layer is characterized by an extraordinary, i.e., inversely proportional to the squared frequency, intensity dependence.     

Peculiarities of the generation of Vavilov-Cherenkov radiation induced by a charged particle moving past a dielectric target

We consider Vavilov-Cherenkov radiation occurring as a result of uniform motion of a point charge in vacuum near a finite-size prismatic target with an arbitrary permittivity. The expression derived for the spectral-angular density of radiation contains a center of emission of Vavilov-Cherenkov radiation, which depends on the angle of flight of the point charge relative to the target. The results indicate that the main contribution to the formation of Vavilov-Cherenkov radiation comes from the polarization current occurring at the interface between the media.     

Intensity of radiation of charged particles passing through crystals

We have calculated the intensity of radiation of a relativistic charged particle moving in a crystalline medium, taking into account the interaction of the charge with the crystal as well as with the radiation. Various modifications to the usual Cerenkov radiation are discussed and under certain conditions enhancement occurs.     

Transition radiation emitted by a particle moving along the axis of a perfectly conducting conical surface

The spatial field distribution is determined for the transition radiation emitted by a relativistic particle moving along the axis of a perfectly conducting circular conical surface with a fixed apex. Emission from particles moving away from and towards the apex is examined. Expressions are obtained that can be used to calculate the angular distribution of radiation intensity for various apex angles between 0 and π. Significant differences are demonstrated between the spatial distributions of radiation generated by outgoing and incoming particles.     

Cherenkov radiation in biaxial crystals—I

The radiation emitted by a uniformly moving point charge in a biaxial crystal is studied by a new method. Fourier integrals for the field are set up for the general case without imposing any restriction on the dielectric and magnetic properties of the crystal or on the direction of motion of the charge. In the case of motion along a principal dielectric axis the integrals are evaluated exactly and closed expressions for the radiated energy are obtained. For radiation of either kind these expressions involve Heuman's Lambda function and the complete elliptic integral of the first kind.     

Influence of an ambipolar field and target boundary blurring on transition radiation from fast electrons of laser plasma

It is shown that the blurring of the rear side of a thin laser target leads to a decrease in the intensity of higher harmonics in the spectrum of coherent transition radiation and that the scale of the boundary inhomogeneity can be estimated from the amplitude ratio of harmonics. Deceleration of the electron flow in an ambipolar electric field at the rear boundary of a target leads to a decrease in the intensity of lower harmonics in the spectrum of coherent transition radiation, and the strength of the ambipolar field can be estimated from the amplitude ratio of harmonics. A change in the permittivity of a dielectric laser target with frequency can lead to an increase in the intensity of some harmonics in the spectrum due to the Vavilov-Cherenkov mechanism.     

On the theory of polarization radiation in media with sharp boundaries

Polarization radiation generated when a point charge moves uniformly along a straight line in vacuum in the vicinity of media with a finite permittivity ɛ(ω) = ɛ′ + iɛ″ and sharp boundaries is considered. A method is developed in which polarization radiation is represented as the field of the current induced in the substance by the field of the moving charge. The solution to the problem of radiation induced when a charge moves along the axis of a cylindrical vacuum channel in a thin screen with a finite radius and a finite permittivity is obtained. Depending on the parameters of the problem, this solution describes various types of radiation (Cherenkov, transition, and diffraction radiation). In particular, when the channel radius tends to zero and the outer radius of the screen tends to infinity, the expression derived for the emitted energy coincides with the known solution for transition radiation in a plate. In another particular case of ideal conductivity (ɛ″ → ∞), the relevant formula coincides with the known results for diffraction radiation from a circular aperture in an infinitely thin screen. The solution is obtained to the problem of radiation generated when the charge flies near a thin rectangular screen with a finite permittivity. This solution describes the diffraction and Cherenkov mechanisms of radiation and takes into account possible multiple re-reflections of radiation in the screen. The solution to the problem of radiation generated when a particles flies near a thin grating consisting of a finite number of strips having a rectangular cross section and a finite permittivity and separated by vacuum gaps (Smith-Purcell radiation) is also obtained. In the special case of ideal conductivity, the expression derived for the emitted energy coincides with the known result in the model of surface currents.