Emission Of Cerenkov Radiation Research Articles

Analysis of VEEL spectra of diamond using a dedicated STEM: isolation of Čerenkov loss contributions

The analysis of multiple EEL (electron energy-loss) spectra often requires normalisation of data to eliminate, for example, relative variations in thickness. In this case, data would only be reliable if it were normalised to a region in the spectrum, where the intensity varied with thickness alone. This raises the question of where an appropriate region is located, from which to extract the normalisation constants. The introduction of structure into the spectrum at certain thicknesses, such as energy lost via Cerenkov radiation emission, are clear regions to avoid. Identifying energy-loss contributions in the valence band region will provide further clarification for this process.

Generation of Čerenkov radiation at the cyclotron frequency of a conducting medium

The excitation of coherent cyclotron radiation by a relativistic charged particle moving through a conducting medium has been studied. The medium consists of free electrons embedded in a host medium which has the shape of a slab of finite widthL and dielectric constant ɛh (for example, the medium could be either a semiconductor or a plasma). It is well known that, in the presence of a uniform magnetic field, which, for simplicity, is taken normal to the sides of the slab, such a medium behaves like an anisotropic uniaxial crystal. From Maxwell’s equations and boundary conditions, exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. It is shown that there are two components associated with the electromagnetic field inside the slab, namely the ordinary and the extraordinary component, as is expected from the anisotropy of the medium. It is also shown from the corresponding dispersion relations for the ordinary and extraordinary components that the index of refraction of the extraordinary component can satisfy the Cerenkov condition for frequency components close to the electron cyclotron frequency, while this condition may not be satified by the ordinary component. Therefore, the emission of Cerenkov radiation, due to the extraordinary component, is possible. By means of the method of stationary phase, approximate expressions are derived for the fields, the radiation pattern and the radiated-energy spectrum in the forward and backward directions, far away from the slab.

Many-body optics II. Dielectric constant formulation of the binding energy of a molecular fluid

For Pt I see abstr. 37680 of a1968. Indicates how the microscopic optical scattering theory already reported elsewhere can be developed into a theory of the binding energy of a molecular fluid. The author first reports (k, omega ) dependent dielectric constants for the molecular fluid: these determine the linear response in all processes which depend on virtual optical processes alone. He then briefly describes bulk contributions to the stopping power, to the emission of Cerenkov radiation and to the collective molecular binding in terms of these dielectric constants. Full account is taken of the radiation field at every order in the ensemble averaged polarization diagram approximation and we extend the theory of the non-relativistic Lamb shift. It is shown that, in the continuum approximation which neglects thermal fluctuations, the molecular binding energy is completely determined by the frequency spectrum of the transverse complex refractive index. A numerical estimate is made of the importance of strictly transverse contributions to the binding energy in this approximation.

On the energy lost by a relativistic ionizing particle in a material medium and on the Cerenkov radiation

The problem of the energy lost by a relativistic ionizing particle in a polarizable material medium is studied by considering separately the energy dissipated in proximity of the track of the ionizing particle, and that which is sent at a larger distance as radiation (Cerenkov radiation). A general formula is stated (Eq. (30)), which allows the calculation of the energy locally dissipated (valid for impact parameters larger than atomic dimensions) whatever may be the mechanism of the dissipation process. On the lines of the Fermi theory the problem of the energy locally dissipated in excitation of the atoms of the medium is studied, taking into account only the excitation directly produced by the ionizing particle and neglecting the one due to the reabsorption of the Cerenkov radiation (Eq. (41)). It is shown that for the calculation of this energy it is necessary to take into account the damping constants (gi) of the bound electrons of the medium, while the ideal, but physically impossible assumption of a perfectly transparent medium leads to results in contradiction with experience. Actually it is found that in the separation of the energy loss into energy absorbed in the excitation of the atoms of the medium and energy dispersed as Cerenkov radiation, an essential role is played by the ratio (form. (45)): breadth of the spectroscopic lines/density of the medium (multiplied by constant quantities which make it adimensional). It is seen that the larger this ratio is the more favoured is the local dissipation causing the excitation of the atoms of the medium, and the more disfavored is the emission of Cerenkov radiation. In this way one may easily explain, on the lines of the Fermi theory, the particular attitude of dense media to the emission of Cerenkov radiation. The problem of the energy by loss ionization is classically discussed by supposing the absorption bands for ionization as pertinent to very broad absorption lines. It is thus found that the energy loss by ionization, with energy transfers smaller than η, should be represented by formula (57). This formula gives a good agreement with experiments (Fig. 1, 2). In the case of emulsions in particular, (Fig. 1), it is possible to explain the rapid increase beyond the minimum experimentally observed. A formula allowing the calculation of the intensity and the spectral distribution of the Cerenkov radiation (formula (66)) is also given. It is pointed out that in particular there should exist some relation between the broadness of the spectroscopic lines and the structure of the Cerenkov bands, suitable for experimental verification. In the case of solids, only the natural width of the lines required by the uncertainty principle should prevent the emission of part of the Cerenkov bands in the X-ray region. This theory leads to the expectation that in the case of dense media a simultaneous increase of ionization and Cerenkov radiation ought to be observed in favorable conditions.

Ionization at relativistic energies and polarization effects

A theory of the polarization effects in the energy loss of a charged particle is given, in which the mechanism of the loss is different from that of the Fermi theory. This theory leads to a distribution of the loss between ionization-excitation and emission of Cerenkov radiation which differs considerably from that of the theories on Fermi’s lines, although the stopping power is not essentially changed, being somewhat less than in those theories. This treatment leads to an increase of the direct ionization at impact parameters larger than atomic dimensions after the relativistic minimum, the increase being large in the case of gases. The Fermi saturation effect of the loss at distances larger than atomic dimensions does also exist in the present theory, although due to a different mechanism. The relativistic increase of the loss in distant interactions is due largely to an increase of the radii of action for ionization and excitation (Bohr-Williams mechanism), but there is also a contribution of the Cerenkov radiation (Fermi mechanism). The saturation arises from a limitation of the increase of the radii of action due to the polarization of the medium and to the saturation of the emission of Cerenkov radiation. This theory leads to a modification of the formula of Frank and Tamm for the rate of emission of Cerenkov radiation, the emission of high energy Cerenkov radiation being considerably reduced.

The theory of ionization and the emission of Cerenkov radiation

The theory of ionization and the emission of Cerenkov radiation

Mechanism of the loss of energy by collisions in a material medium (I)

The theory of the loss of energy of a non accelerated charged particle in a material medium is investigated, using classical electrodynamics. Special attention is given to the mechanism of the loss. The results of Fermi, Halpern and Hall, Wick and A. Bohr are generalized and further extended. The points of view of action at a distance (Bohr) and field theory (Fermi) are discussed and compared. The mechanism of the emission of Cerenkov radiation is examined and the relations with the emission of acceleration radiation analysed.