Mikhail B. Kadomtsev

Statistical model of electron impact ionization of multielectron ions

The statistical method for ab initio calculations of the electron impact ionization cross sections of multielectron ions and related ionization rates is developed. It is created based on an idea of collective excitations of atomic electrons alike in condensed medium. The Thomas–Fermi model density distribution of atomic electrons is assumed and their collective oscillations are described by the local plasma frequency model. Using a proposed statistical approach the calculations of the total single electron impact ionization cross sections of multielectron ions for several chosen chemical elements from argon up to uranium, taken in the various charge states, are performed and compared with available experimental and theoretical data, demonstrating a satisfactory agreement.

Statistical model of radiation losses for heavy ions in plasmas

The new statistical approach for calculation of radiation processes with heavy multielectron ions in plasma is developed. The method consists in consideration of atomic structure as a condensed medium, characterized by the spectrum of elementary excitations with plasma frequency, determined by local atomic electron density. The radiation losses in this model are due to excitation of plasma type oscillations in atom under its collisions with plasma electrons and could be expressed in a universal statistical form for all sorts of multielectron ions. The calculations of radiation losses on tungsten ions are performed in the wide range of plasma temperature variation, typical for physics of high temperature plasma with magnetic confinement. It is shown that the universal statistical approach results are within the data scattering of current numerical codes. The proposed statistical method for description of collective excitations in complex atoms for calculations of plasma radiation losses is of general physical interest. It allows obtaining the necessary data faster with the lesser computational resources.

Electron impact ionization of tungsten ions in a statistical model

The statistical model for calculations of the electron impact ionization cross sections of multielectron ions is developed for the first time. The model is based on the idea of collective excitations of atomic electrons with the local plasma frequency, while the Thomas-Fermi model is used for atomic electrons density distribution. The electron impact ionization cross sections and related ionization rates of tungsten ions from W+ up to W63+ are calculated and then compared with the vast collection of modern experimental and modeling results. The reasonable correspondence between experimental and theoretical data demonstrates the universal nature of statistical approach to the description of atomic processes in multielectron systems.

Equivalence of the method of the kinetic equation and the fluctuating-frequency method in the theory of the broadening of spectral lines

A new expression for the Stark profiles of spectral lines in plasma has been obtained by the method of the kinetic equation taking into account the dynamics of the plasma microfield. The result represents a dynamic line profile in the form of simple functionals of a static profile. The relation of the new solution with the known fluctuating-frequency method has been analyzed. It has been shown that this method is a discrete analog of the method of the kinetic equation and passes to the latter method in the limit of the continuous fluctuations. Simple formulas (4), (5), and (21) for dynamic line profiles provide ultrafast calculations of the profiles of spectral lines taking into account the dynamics of the plasma microfield.

Parameterization of Balmer-alpha asymmetric line shape in tokamak SOL plasmas

A parameterization of the Balmer-alpha spectral line shape asymmetry in the tokamak scrape-off layer (SOL) plasmas is suggested, which describes the contribution of nonMaxwellian components of the neutral atom velocity distribution function. Parameterization is needed for a fast-routine interpretation of high-resolution spectroscopy data and should be incorporated into the algorithms for the recovery of hydrogen neutral atom parameters in the SOL. We illustrate the efficiency of the parameterization on the example of spectral data calculated using the predictive modeling of the International Thermonuclear Experimental Reactor (ITER) tokamak operation.

Universal two-dimensional kinetics of the populations of Rydberg atoms in plasmas

Universal kinetics has been developed for calculating the two-dimensional populations (in the space of principal n and orbital l quantum numbers) of Rydberg atomic states in plasmas. It has been shown that the direct population of the atomic states by three-body and radiative recombination sources should be taken into account, because the radiative cascade is of quantum character. The subsequent two-dimensional radiation-collision cascade is constructed in the framework of the classical approach. The developed model makes it possible to obtain the populations in the form of universal functions of temperature and density. The numerical calculations of the populations of highly excited hydrogen states (n ∝ 100) in low-density plasmas (103–1013 cm−3) at moderate temperatures (1 eV) indicate a significantly nonequilibrium population both in n and in l, which is important for the diagnostics of astrophysical and laboratory plasmas.

Nonequilibrium Kinetics of Rydberg Atomic States

Two‐dimensional quasi‐classical model of the radiative‐collisional cascade for hydrogen‐like systems is developed. The model establishes the correspondence between the quantum and classical approaches. Our calculations of the two‐dimensional populations of highly excited atomic hydrogen states for three‐body and photorecombination sources of population allow the data of one‐dimensional kinetic models to be refined. The calculated intensities of recombination lines demonstrate the degree of nonequilibrium of the Rydberg state populations under typical astrophysical plasma conditions.

Semiclassical theory of the radiative-collisional cascade in a Rydberg atom

We have developed a two-dimensional semiclassical model of the radiative-collisional cascade for hydrogen-like systems. We describe the collisions with electrons and ions by classical diffusion in the space of principal and orbital quantum numbers and use an iterative procedure that consistently takes into account the quantum nature of the radiative cascade for radiative transitions. The model establishes the correspondence between the quantum and classical approaches and indicates that the latter cannot be directly used to calculate the population kinetics of highly excited atomic states. Our calculations of the two-dimensional populations of highly excited atomic hydrogen states for selective, three-body, and photorecombination sources of population allow the data of one-dimensional kinetic models to be refined. The calculated intensities of recombination lines demonstrate the degree of nonequilibrium of the Rydberg state populations under typical astrophysical plasma conditions.