V. Molinari

Mathematical Modelling of 3D Electron-Photon Transport in Microbeam Analysis

Abstract. In electron microbeam techniques, the particle beam is focused on the material to be analysed. When the electron beam enters the target, the electrons give rise to ionization processes producing secondary electrons and photons, the latter being used to characterize the material. As a consequence, a detailed description of the photon diffusion requires the solution of two coupled equations describing respectively electron and photon diffusion. The approach considering two transport equations, even if formally correct, is almost unaffordable because of the high mathematical complexity of the electron transport equation. In this article, an alternative approach is suggested which is based on the use of an approximate solution for the electron transport using the Fokker-Planck equation [5]. The resulting electron distribution, computed analytically as a solution of the above equation, is very similar to the ionization distribution and is used as the source term in the Boltzmann transport equation describing the photon diffusion in the material. The 3D photon transport equation for unpolarised photons with this source term is solved to obtain a detailed description of the photon fluorescence from a homogeneous slab.

Diffusion of polarized photons in the frame of the transport theory

Abstract In the frame of the multiple applications of synchrotron radiation X-ray spectrometry (SRXRS), a detailed description of the transport of polarized photons in condensed media is of utmost importance. The effect of polarization requires four parameters to describe an X-ray beam in place of the single intensity of the models without polarization. Further, the state of polarization changes every time the photon undergoes a scattering event. Accordingly, a proper description of photon transport including polarization effects, here represented with the Stokes parameters, involves a system of four coupled equations of transfer. In this paper, the system of transport equations, describing the diffusion of X-ray photons (including polarization effects) in a homogeneous target of infinite thickness, is solved. An iterative solution, universally valid for all the interactions in the X-ray regime, is obtained. The solution is applied, e.g. to study Rayleigh scattering of (initially) unpolarized X-rays. The first and second order Rayleigh intensities are compared with similar terms computed with a scalar model using a kernel with averaged polarization, in order to quantify the influence of including, rigorously, polarization in the prediction of multiple scattering intensities of the Rayleigh effect.

X-Ray Photon Spectroscopy Calculations

X-ray photons - as many other particles - interact with matter producing secondary radiation that carries useful information about the atoms comprising the target. The availability of intense sources of highly monochromatic X-rays and the great improvement in detector technology intensified research in X-ray spectrometry in the last twenty years. New techniques allowed the attenuation coefficients and the physics of the atom to be better known: Extended X-ray Absorption Fine Structure (EXAFS), X-ray Absorption Near Edge Structure (XANES), and Inelastic X-ray Scattering Spectroscopy (IXSS). Old techniques, like X-ray Fluorescence (XRF), gained in precision thus extending the horizon of applicability to new elements and energy ranges, and consequently Energy Dispersive X-ray Fluorescence (EDXRF) and Synchrotron Radiation X-ray Fluorescence (SRXRF) were evolved. Particle induced X-ray emission spectroscopy also benefited from this improvement. The field of application of X-ray pectrometry has grown from atomic, to nuclear, to plasma physics, to astrophysics.

Effect of the X-ray scattering anisotropy on the diffusion of photons in the frame of the transport theory

Abstract In the frame of the multiple applications of X-ray techniques a detailed description of the photon transport under several boundary conditions in condensed media is of utmost importance. In this work the photon transport equation for a homogeneous specimen of infinite thickness is considered and an exact iterative solution is reported, which is universally valid for all types of interactions because of its independence of the shape of the interaction kernel. As a test probe we use a specially simple elastic scattering expression that renders possible the exact calculation of the first two orders of the solution. It is shown that the second order does not produce any significant improvement over the first one. Due to its particular characteristics, the first-order solution for the simplified kernel can be extended to include the form factor, thus giving a more realistic description of the coherent scattering of monochromatic radiation by bound electrons. The relevant effects of the scattering anisotropy are also placed in evidence when they are contrasted with the isotropic solution calculated in the same way.

Diffusion of photons with arbitrary state of polarization: the Monte Carlo code MCSHAPE

Abstract When X-rays penetrate in the matter, they interact with the atoms, producing secondary radiation that carries important information about the composition of the target. The polarization state is one of the properties of the incoming photons which changes as a consequence of the number and the type of the undergone interaction. Therefore, to study properly the atomic properties of a material, it is necessary to consider the evolution of the polarization state of radiation. It is presented MCSHAPE, a Monte Carlo code developed to describe the evolution of the polarization state of X-ray photons as a consequence of the multiple scattering collisions undergone during the diffusion into the sample. In order to study properly the transport of photons with an arbitrary state of polarization, the model adopted in this code is derived from the so called ‘vector’ transport equation [Radiative Transfer, Chapter 1, Section 15, Clarendon, Oxford, 1950; Nucl. Instr. and Meth. B 73 (1993) 341]. Using the Stokes parameters I, Q, U and V, having the dimension of an intensity and containing all the physical information about the polarization state, MCSHAPE simulates the full state of polarization of the photons at any given position, wavelength and solid angle.

Detailed dose distribution prediction of Cf-252 brachytherapy source with boron loading dose enhancement

The purpose of this work is to evaluate the dose rate distribution and to determine the boron effect on dose rate distribution for (252)Cf brachytherapy source. This study was carried out using a Monte Carlo simulation. To validate the Monte Carlo computer code, the dosimetric parameters were determined following the updated TG-43 formalism and compared with current literature data. The validated computer code was then applied to evaluate the neutron and photon dose distribution and to illustrate the boron loading effect.

Dispersion relations in weakly degenerate plasmas

From a quantum mechanical point of view, electrons in laser produced plasmas can be regarded as weakly degenerate. For instance, for a plasma with electron density of 1022 cm−3 and electron temperature of 1 eV, Sommerfelds parameter is between 1 and 2. Under these conditions the usual dispersion relations for waves in plasmas need be corrected to account for degeneracy. In the present work, starting from the transport equation with a simplified version of the Boltzmann–Uehling–Uhlenbeck collision kernel the propagation of waves impinging on a plasma with weakly degenerate electrons is investigated and dispersion relations accounting for degeneracy are derived. These dispersion relations give the classical ones in the limit for Sommerfelds parameter approaching zero. A shift of the wavenumber value and a non-collisional damping due to degeneracy effects are predicted which render a weakly degenerate plasma more opaque to radiation than a non-degenerate one.

A Derivation of Quantum Kinetic Equation from Bohm Potential

In Bohms interpretation of Quantum Mechanics, quantum effects are governed by a “quantum potential” (known as Bohm potential), and particles follow definite trajectories. In the present work, Liouvilles theorem is invoked, an appropriate Liouville equation is derived, and following the BBGKY method a quantum kinetic equation (QKE) is derived. To demonstrate the working of the QKE, two examples of application are presented: the thermal equilibrium of a quantum gas and the propagation of disturbances in a force free gas of non-interacting bosons. In contrast to the classical collisionless Boltzmann equation, waves are found to be possible in the absence of interaction or external forces, due only to Bohm potential (zero sound propagation).

A transport theory approach to percolation of liquids through porous media

AbstractThe percolation of a liquid through a porous material is investigated with the help of equations of the Onsager type. An expression is derived for the molecular attraction, starting from Sutherland’s potential approximation to the van der Waals interaction. Then appropriate Onsager equations incorporating this molecular attraction are written from transport theory considerations, in terms of dimensionless variables. As an application, the system of self-similar equations so derived is applied to a simplified situation.

Wave propagation and “Landau-type” damping from Bohm potential

From Bohms interpretation of quantum mechanics, a quantum kinetic equation (QKE) can be derived. It is found that waves propagate in force-free gases of non interacting particles, only due to Bohm potential. In the present article the existence of Landau damping in such propagations is investigated. It is found that the Bohm potential alone gives indeed rise to a damping entirely analogous to the classical Landau damping, both for bosons and for weakly degenerate fermions.