Продолжаю публикацию информации на английском языке для специалистов об основных научных статьях, положенных в основу НАУЧНОЙ АКСИОМАТИКИ ФИЗИКИ И МИРОЗДАНИЯ. Они рассчитаны на профессионалов, и если покажутся вам сложными, то не обязательно читать их полностью. Для начала можно ограничиться АННОТАЦИЕЙ, основными идеями и выводами. Это уже позволит существенно поднять понимание сути физики и мироздания.
Важная статья на английском языке посвящена неравновесному транспорту пучков частиц – бурно развивающемуся разделу молекулярной физики (Nikerov V.A. Analytical Qualitative and Quantitative Model of the Transport of Photons and Accelerated Particles through Layers of Materials in the Generalized Diffusion Approximation. Mean Range, Backscattering and Transmission Coefficients, Energy of Backscattered Particles, Particle and Energy Distributions along the Coordinate, Angular Dependencies. International Journal of Advanced Research in Physical Science. 2021. V. 8. № 4. PP 1-15.):
Текст статьи в приложении https://t.me/NikerovV/1910.
Nikerov V.A. Analytical Qualitative and Quantitative Model of the Transport of Photons and Accelerated Particles through Layers of Materials in the Generalized Diffusion Approximation. Mean Range, Backscattering and Transmission Coefficients, Energy of Backscattered Particles, Particle and Energy Distributions along the Coordinate, Angular Dependencies. International Journal of Advanced Research in Physical Science. 2021. V. 8. № 4. PP 1-15.
Abctract
An analytical qualitative and quantitative model of the transport of photons and accelerated particles through the layers of materials in the generalized diffusion approximation is formulated consistently. It is based on the limiting cases of straightforward and diffusion transport, and also their stitching together. Mean ranges of the particles along the coordinate are calculated and analyzed. Analytical formulas are derived for the particles backscattering coefficient in straightforward and diffusion approximations, and their dependence on the angle of incidence of the particles on the surface. Analytical formulas are derived for the particles mean energy loss in layers and mean energy of the particles backscattered from the layer of material, as well as their dependence on the particles angle of incidence on the surface. An analytical formula is derived for the reflection coefficient of the beam energy from the surface of the layer in the diffusion approximation for a wide range of materials, as well as its dependence on the particles angle of incidence on the surface. Analytical formulas are derived for the transmission coefficient of particles through a layer of material in the straightforward and diffusion approximations, and their dependence on the particles angle of incidence on the surface. The distributions of particles and energy deposition over the depth of the layer are obtained. The possibility of a spatial maximum of energy input of a particle beam is analytically justified, the depth of this maximum location is calculated, as well as its dependence on the particles angle of incidence on the surface. The applicability and error origin the of the analytical model of the transport of photons and accelerated particles through the layers of materials in the approximation of generalized diffusion are estimated.
Keywords: accelerated particles, photons, generalized diffusion, straightforward transport, diffusion transport, mean range of the particles along the coordinate, the particles backscattering coefficient, the mean energy of the particles backscattered from the layer of material, the reflection coefficient of the beam energy from the surface of layer, the transmission coefficient of particles through the layer of material, particle and energy deposition distributions over the depth of the layer.
1. Introduction
The general problem of photons and accelerated particles transport through layers of materials has been considered for a long time (and is still considered by many researchers) to be difficult for analytical solutions, and was solved mainly by the Monte Carlo method [1]. However, in many cases analytical models and solutions, even approximate ones, are required. Firstly, they give a general visual picture of what is happening. Secondly, they are ideal for optimization problems. Thirdly, they work more reliably as an element of a more general and complex problems. And already G. Bethe and J. Jacob [2] in their age theory considered the semi-analytical spatial problem of accelerated electrons transport in the diffusion approximation. Moreover, the created approach proposed an analytical solution to the problem for materials with atomic charge Z> 7. Essential in the approach was the selection of the initial stage of transport and the creation of the concept of isotropization length. This stage provides the transformation of monodirectional beam electrons transport to diffusion transport and gives the possibility to describe the further problem by diffusion theory. Nevertheless, it was not possible to get the analytical solution of the problem and to estimate the electron ranges along the coordinate and reflection coefficients in this work. One of the reasons for this was the limitations of diffusion approximation, since in many important problems the transport is not completely diffusive, and in some cases, it is almost straightforward.
However, in the works performed at the Kurchatov Institute [3,4], it was possible to formulate the spatial-energy theory of the degradation-diffusion cascade and the model of generalized diffusion, which provide analytical solutions for a wide range of problems. In general, it gave the possibility to obtain solutions for the generalized diffusion of charged particles, atoms, and molecules in a wide range of initial energies. The transport problems of relativistic and nonrelativistic electron beams [3–8], physics of the upper atmosphere [4.8], and kinetics of the gamma laser [8,9] were considered. Later [10], it was possible to generalize the approach and to describe the transport of photons in transparent and nontransparent materials, typical for the problems of medical physics and optics, and also to calculate the volume reflection coefficient of particles from the materials in a straightforward approximation. Subsequently [11], a unified model of generalized diffusion for electrons and photons was formulated, including the concept of an imaginary particle source, which is located inside the layer and generates an isotropic particle flow in all directions.
In this paper, a substantial qualitative and quantitative development of the generalized diffusion model is carried out in relation to the more general problem of the photons and accelerated particles transport through layers of materials. For the first time, more than a dozen formulas were derived to describe the backscattering and transmission of particles through layers of materials, as well as the reflection coefficient of the beam energy from a layer, and the distribution of particles and energy deposition over the depth of a layer. The dependences of the main transport parameters on the particles angle of incidence on the surface of the layer are obtained.