O.V. Bogdanov

Basic channeling with Mathematica©: A new computer code

The Mathematica© software is a powerful tool to solve numerous problems in physics, essentially when the analytical solution is not possible. The channeling and related phenomena is just that case. Here we suggest to introduce a standard in calculations of channeling and related phenomena using Mathematica© software. The new computer code Basic Channeling with Mathematica© BCM-1.0, at the first stage, will include a set of packages to make symbolic calculation of the planar channeling phenomena.

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.

Relativistic electron radiation spectra at axial channeling in crystals

Typical trajectories of relativistic electrons and the corresponding radiation spectra at axial channeling in silicon and diamond crystals are revealed and constructed using the ©Mathematica 6.01 computer code. The radiation spectrum of 300 MeV electrons averaged over the trajectories in the 〈100〉 direction in a diamond crystal well coincides with the experimental spectra measured in work [6].

Effect of the band structure of energy levels on the angular distribution of diffracted X-ray radiation for positron plane channeling in silicon

It is shown that the inclusion of the band structure of energy levels of channeled positrons (as in the case of electrons) leads to a qualitative change in the angular distribution of X-ray radiation.

Peculiarities of channelling radiation spectra from 100 to 800 MeV electrons and positrons in (1 1 1) Si crystal

By means of numerical calculations, the channelling radiation spectra from relativistic electrons and positrons have been studied in detail for channelling along (1 1 1) double planes in a Si crystal. The evolution of the shape of radiation spectrum is studied under an increase of particles energies from 100 to 800 MeV and a change of the angle of incidence with respect to (1 1 1) double planes. It is shown that the (1 1 1) channelling radiation spectra have much more complicated structure and radiation yield is several times greater compared to the channelling along (1 0 0) or (1 1 0) planes.

Simulation of radiation energy losses by channeled relativistic electrons in a crystal

A computer code is developed to calculate the radiation energy losses (RELs) of electrons during both 〈100〉 axis and (100) plane channeling in a thin Si crystal. A computer simulation of these losses is carried out by taking the initial angular divergence of the beam into account, and the REL dependences on the angle of electron entry into the crystal are obtained for both axial and planar channeling (orientational dependences). The calculations are carried out in connection with experiments on the interaction of 20–255 MeV electrons with crystals conducted at the SAGA Light Source linear accelerator (Tosu, Saga, Japan). The simulation results show the possibility of using the orientational dependence of the RELs of channeled electrons in thin crystals to diagnose the initial angular divergence of the electron beam and to orient crystals.

New peculiarities in angular distribution of Cherenkov radiation from relativistic heavy ions caused by their stopping in radiator: numerical and theoretical research

A new method and theoretical base for calculation of the Cherenkov Radiation (ChR) angular distribution from relativistic heavy ions (RHI) taking into account stopping in radiator is suggested. Our method is based on the thin radiator approximation and the Bethe-Bloch formula for ionization energy loss (stopping) and provides fast calculations without using any special software. The simple formula for estimation of the ChR angular distribution width in vicinity of the Cherenkov angle taking into account RHI stopping in radiator is obtained. New peculiarities of ChR - dependence on the RHI charge and mass (isotopic effect), emission wavelength (index of refraction) and radiator length - are studied. These new features of ChR from RHI allow for their possible applications to simultaneously reconstruction of both velocity and charge of RHI penetrating through radiator and even to measure the masses of isotopes or radiator stopping power.

Features of the Formation of Radiation Spectra at (111) Planar Channeling of Relativistic Electrons in a Si Crystal

The spectral intensity of (111) channeling radiation from electrons is numerically calculated at the energy varying from 100 to 900 MeV and different electron incidence angles relative to the (111) planes in thin Si crystals. The calculation results show that the channeling radiation’s spectra have a more complicated structure, and the total channeling radiation’s yield is several times larger than that at (100) or (110) channeling.

Mass dependence of spectral and angular distributions of Cherenkov radiation from relativistic isotopes in solid radiators and its possible application as mass selector

The first proof of principle experiment with a prototype of a Time-of-Flight (TOF) - Cherenkov detector of relativistic heavy ions (RHI) exploiting a liquid Iodine Naphthalene radiator has been performed at Cave C at GSI (Darmstadt, Germany). A conceptual design for a liquid Cherenkov detector was proposed as a prototype for the future TOF measurements at the Super-FRS by detection of total number of Cherenkov photons. The ionization energy loss of RHI in a liquid radiator decreases only slightly this number, while in a solid radiator changes sufficiently not the total number of ChR photons, but ChR angular and spectral distributions. By means of computer simulations, we showed that these distributions are very sensitive to the isotope mass, due to different stopping powers of isotopes with initial equal relativistic factors. The results of simulations for light (Li, Be) and heavy (Xe) isotopes at 500–1000 MeV/u are presented indicating the possibility to use the isotopic effect in ChR of RHI as the mass selector.

Hybrid positron-source scheme intended for the SPARC accelerator facility at the LNF

A hybrid positron-source scheme based on an electron beam of the Sorgente Pulsata e Amplificata di Radiazione Coerente test facility installed at the Laboratori Nazionali di Frascati (Frascati, Italy) is proposed. In the case of a thin (0.1-mm-thick) amorphous converter, the positron yields per primary electron are compared at positron energies of 1–3 MeV under bremsstrahlung generation and (110)-plane channeling conditions. The radiation of 200-MeV electrons (200 MeV is the parameter of the SPARC accelerator at the LNF) channeled in a 10-µm-thick tungsten radiator is demonstrated to create positron yields of 104–105 s–1 in a 0.1-mm-thick W converter.