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The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.

The results of experimental investigations devoted to initiating the promising nuclear fusion reaction $${}^{11}$$ B $$(p,3\alpha)$$ in picosecond laser plasmas at a laser-radiation intensity of $$5\times 10^{18}$$ W/cm $${}^{2}$$ are presented. A new tool for determining the absolute yield of alpha particles in the reaction $${}^{11}$$ B $$(p,3\alpha)$$ on the basis of simultaneously measuring the number of neutrons in the reference nuclear reaction $${}^{11}$$ B $$(p,n)^{11}$$ C is proposed. At the above values of the laser-pulse parameters, the application of this new procedure to estimating the total number of alpha particles per pulse from the reaction $${}^{11}$$ B $$(p,3\alpha)$$ leads to a value of 10 $${}^{8}$$ particles within a solid angle of 4 $$\pi$$ sr. The results presented here differ substantially from the data obtained in measuring the single-channel yield of alpha particles.

The results of studying the propagation of plasma flows in the surrounding medium performed on the PF-3 plasma focus facility in the laboratory simulation of astrophysical jets from young stellar objects are presented. The modes with the plasma formations which retain their compactness when propagated over significant distances are obtained. The decrement of the flow’s deceleration as a result of its interaction with the background gas is determined. A technique is developed for estimating the plasma temperature by the ratio of radiation intensities from various parts of the spectrum. It is shown that the background gas is heated by the flow radiation, which leads to a change in its ionization state. Thus, the plasma flow propagates not in a neutral gas but in a weakly ionized plasma.

A statistical description is proposed for the shape of heavy impurity spectra observed in tokamaks and stellarators, corresponding to the quasicontinuous radiation distribution, and called the quasicontinuum. For the tungsten ions, in particular, it is located in the spectral range of ∼2 to 7 nm. The method is based on the statistical plasma model of atom, which allows expressing the quasicontinuum structure through the electron density distribution of multielectron ions. The Slater distribution is used as a model density distribution. The quasicontinuum is formed by the great number of closely spaced lines of heavy ions with different degrees of ionization, and its calculation is very complicated. A comparison of the results obtained within the statistical approach with the results of the level-by-level quantum mechanical calculations shows that such a model plausibly describes the envelopes of the individual line arrays in the ion spectra. In contrast to the level-by-level calculation codes, the statistical atom model is rather simple and it can be used by a large number of users. The quasicontinuum was simulated for the tungsten, gold, lead, and gadolinium ions, which are observed in plasmas of fusion facilities. The simulation results are in fairly good agreement with the experimental data. The studies of the tungsten quasicontinuum are of interest from the point of view of plasma diagnostics, as well as determination of the tungsten impurity density and its transport in fusion facilities.

Data on the cross section and kinetic rate of charge exchange (CX) between the bare beryllium nucleus, the ion Be(+4) and the neutral hydrogen atom are of great interest for visible-range high-resolution spectroscopy in the ITER tokamak because beryllium is intended as the material for the first wall in the main chamber. Here an analysis of available data is presented, and the data needs are formulated. Besides the active probe signal produced by the CX of the diagnostic hydrogen neutral beam with impurity ions in plasma, a passive signal produced by the CX of impurity ions with cold edge plasma is also important, as it shows in observation data from the JET (Joint European Torus) tokamak with an ITER-like beryllium wall. Data in the range of a few eV/amu to ~100 eV/amu (amu stands for the atomic mass unit) needed for simulations of level populations for principal and orbital quantum numbers in the emitting beryllium ions Be(+3) can be obtained with the help of two-dimensional kinetic codes. The lack of literature data, especially for data resolved in orbital quantum numbers, has instigated us to make numerical calculations with the ARSENY code. A comparison of the results obtained for the one-centre Coulomb problem using an analytic approach and for the two-centre problem using numerical simulations is presented.

Laser-induced fluorescence (LIF) on ITER will be used for local measurement of helium density nHe and ion temperature Ti in divertor. The LIF diagnostic is combined with the divertor Thomson scattering (DTS) via common laser injection and signal collection optics. Collisional-radiative model developed for helium ions is used to estimate laser parameters required for robust measurement of laser-induced signals against plasma background radiation. The estimations demonstrate feasibility of measuring nHeII with laser parameters provided by available optical parametric oscillator pumped by Nd:YAG. New approach for measuring Ti is proposed and the expected errors are estimated using numerical simulations.

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. The analytical solution of the problem is unachievable with famous Chandrasekhar–Von-Neumann results up to the present time. The alternative methods are connected with modeling of a real ion Coulomb field dynamics by approximate models. One of the most accurate theories of ions dynamics effect on line shapes in plasmas is the Frequency Fluctuation Model (FFM) tested by the comparison with plasma microfield numerical simulations. The goal of the present paper is to make a detailed comparison of the FFM results with analytical ones for the linear and quadratic Stark effects in different limiting cases. The main problem is connected with perturbation additions laws known to be vector for small particle velocities (static line shapes) and scalar for large velocities (the impact limit). The general solutions for line shapes known in the frame of scalar perturbation additions are used to test the FFM procedure. The difference between “scalar” and “vector” models is demonstrated both for linear and quadratic Stark effects. It is shown that correct transition from static to impact limits for linear Stark-effect needs in account of the dependence of electric field jumping frequency in FFM on the field strengths. However, the constant jumping frequency is quite satisfactory for description of the quadratic Stark-effect. The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented.

In this chapter the statistical description of atomic radiative-collisional processes for complex heavy ions in electron atomic collisions is developed. The local plasma frequency model and the Thomas-Fermi electron density distribution are applied for the description of collisional processes making it possible to express the atomic characteristics (energy structure and oscillator strengths) as well as transition probabilities in terms of a functional of the electron density distribution inside atoms and ions. The Fermi method of equivalent photons allows to express the collisional rates in terms of photo-excitation or ionization cross sections. The statistical description is applied for efficient calculations of ionization cross sections and rates for different highly charged ions demonstrating a very good correspondence with detailed quantum mechanical calculations. Likewise, the dielectronic recombination rates obtained from statistical models are compared with quantum results for different ionization states of many chemical elements. The statistical method is in very good agreement with sophisticated detailed level-by-level quantum calculations and is of much higher precision than the usually applied Burgess formula. Finally, the statistical approach is applied for calculations of radiative energy losses of tungsten ions in hot thermonuclear plasmas. The results for the low-density case (coronal condition) of magnetically confined plasmas demonstrate a rather good correspondence with more detailed numerical calculations and measurements. In addition, the transition from the low-density corona condition to the high-density Boltzmann limit can be described via a simple application of detailed balance in the two-state approximation. In general, quite reasonable precision of the statistical model for different kinds of radiative-collisional processes is demonstrated. Moreover, general formulae and scaling relations can be obtained from the statistical approach that would otherwise difficult to obtain.

In a low-density environment, where atoms and ions are essentially free, atomic population kinetics of gases and plasmas has been very successful in many different scientific and technical disciplines. As density increases, the free atom model breaks down resulting in a perturbation of the atomic energy levels and a corresponding ionization potential depression IPD. The IPD is of great fundamental interest, for thermodynamic applications and also for the understanding of the various radiative properties (emission, absorption, scattering). Different IPD models are discussed including the finite temperature ion sphere FTIS model and the Atomic-Solid-Plasma ASP model. The ASP model accounts for the difference between real atomic ionization potentials in solids and free atoms taking into account the structure of the valence band and the Fermi energy. The FTIS model accounts for self-consistent screening effects of both bound and free electrons inside the ion sphere with effective radius depending on plasma density. Different regimes of ionization potential depression are considered as well as plasma polarization shifts of X-ray spectral lines. Finally, Fermi surface rising in much above solid density compressed matter is discussed leading to increased K-edge energies rather than decreased ones.

The atomic populations are the fundamental quantities for various different disciplines in science and applications. Although the rate equation model has widely been employed, it has principal deficiencies as it considers only populations related to the squared of the wave functions, while all mixed populations (coherences) are missing. In plasmas, however, large effects of strong plasma electric microfields on atomic (usually highly charged ions) energy levels are encountered that require more advanced descriptions, e.g., energy level evolution under the action of a quasi-static electric ion field including coherence effects. For real systems, these phenomena cannot be described consistently in the framework of the Schrodinger picture but request the density matrix description in contrast to the standard population balance rate equations. The general system of density matrix equations, however, is extremely challenging. It is demonstrated that the system can be transformed to a standard form of population kinetic rate equations with additional terms describing the effect of the ion electric field, the so-called quantum F-matrix theory (QFMT) allowing to construct real (large) closed model systems. The density matrix approach results in a new understanding of the fundamental physical problem connected with the transition of atomic populations to the Boltzmann equilibrium in dense plasmas. The standard transition is provided by electron collisions only satisfying the principle of detailed balance related to a statistical population of energy levels over magnetic quantum numbers. However, the effect of static electric fields on the atomic population is selective in magnetic quantum numbers resulting in a destruction of statistical Boltzmann populations. The interplay between the statistical effect of electrons and non-statistical effect of quasi-static ions is illustrated in detail for autoionizing atomic states of highly charged ions in dense laser-produced plasmas.

The chapter is devoted to an introduction of the main radiative characteristics of atoms and ions to describe the light-matter interaction. The presentation is based on the correspondence principle between classical and quantum physics in order to derive the basic radiative properties, including the Einstein coefficients and the dynamic polarizability of the atom. Attention is also paid to the description of the dynamic polarizability of atoms and ions including the static, high-frequency and resonance case. The innovative concept of local plasma frequency is introduced for the atom that allows describing the polarizability of many-electron systems at a semi-quantitative level. Finally, the prospective interesting polarizability of metal nanoparticles placed in a solid-state matrix is considered within the framework of the Mie theory and the dipole approximation.

Applications to plasma spectroscopy are presented for different types of plasmas that are currently of great interest for science and applications: low-density tokamak plasmas, dense optical laser-produced plasmas, high-current Z-pinch plasmas, and X-ray Free Electron Lasers interacting with solids. The general principles of plasma electron temperature and density measurements as well as the characterization of suprathermal (hot electrons) and non-equilibrium phenomena are presented. Particular attention is based on the innovative concepts of dielectronic satellite and hollow ion X-ray emission. The effect of a neutral background that is coupled to plasma ions via charge exchange is considered in the framework of nonlinear atomic kinetics. Transient phenomena in the start-up phase, impurity diffusion, sawtooth oscillations, and superthermal electrons are discussed for magnetic fusion plasmas. For dense laser-produced plasmas and charge exchange coupling of colliding plasmas, the dynamics of fast ions in space and energy distribution functions are presented. The interaction of XFEL with solids is considered in the framework of a new kinetic plasma theory, where generalized atomic processes provide a link from the cold solid until the hot diluted plasma. Three-body recombination and Auger electrons constitute a generalized three-body recombination that is identified to play also a new role as a direct heating mechanism. General principles and new theories are illustrated along with detailed comparisons with experimental data.

The theory of electron–atom collisions including excitation, ionization, and recombination is presented in the framework of Fermi’s equivalent photon method, the similarity function approach, and semi-empirical analytical formulas. Collisional excitation is described via a quasi-classical consideration. Dipole-allowed, dipole-forbidden, and intercombination electron transitions are considered including intermediate coupling effects. Comparisons between different theoretical approaches and experimental data for excitation cross-sections are provided for various atoms and type of electronic transitions. Semi-empirical analytical formulas for excitation, de-exciation, ionization, and three-body recombination are given. Complex dielectronic recombination rates in dense plasmas are presented with account for density and electric field effects. Extensive numerical data for dielectronic recombination into H-, He-, and Li-like ions taking into account multi-channel Auger and radiative decay are given for all elements with nuclear charge Zn = 2–42 together with easy to use scaled semi-empirical formulas. The theory of excited states coupling and collisional redistribution for dielectronic recombination is developed.

In this chapter, we consider the probability of photoprocesses including bound–bound, bound–free, and free–free electronic transitions. This concerns atomic radiation transitions in the discrete energy spectrum, radiative recombination, Bremsstrahlung including polarization channel, photoionization, photodetachment of negative ions, and phase control of photoprocesses by ultrashort laser pulses. Considerable attention has been paid to various types of broadening of the spectral lines of atomic radiative transitions, including plasma broadening mechanisms. The rotational approximation of the Kramers electrodynamics is presented which is suitable for describing both free–free and free–bound electronic transitions in the high frequency limit. The photoionization of atoms is described both within the framework of a rigorous quantum mechanical approach and with the help of a number of approximate methods. Analytical generalized photoionization cross section formulas from K-, L-, M-, N-, and O-shell that include also possible inner-shell photoionization are presented. Finally, generalized scaled formulas for radiation recombination rates into all states with principal quantum numbers n = 1–9 and orbital quantum numbers l = 0–8 are given that can be applied for a large variety of practical cases.

This chapter introduces to the theory of atomic population kinetics and radiative properties of atomic and ionic bound–bound transitions. Particular attention is devoted to the general problems related to an extremely large number of kinetic equations describing populations of Rydberg and autoionization atomic states in plasmas. A new method of reduced kinetics for autoionizing states, the virtual contour shape kinetic theory (VCSKT), is described in details. The method is based on a probability method for LTE- and non-LTE-level populations that allows effective level reduction while preserving all detailed atomic transitions. The representation employs effective relaxation constants that have analytical solutions. The comparison with detailed level-by-level calculations demonstrates high accuracy and large efficiency of the VCSKT. In order to solve many states’ kinetic problems for Rydberg atomic states, the quasi-classical representation of the system of kinetic equations is proposed. In particular, the two-dimensional radiative cascades between Rydberg atomic states are described by a purely classical motion of atomic electrons in a Coulomb field that lose energy and orbital momentum. The general collisional-radiative model for large principal quantum numbers is reduced to an effective diffusion in two-dimensional energy and orbital momentum space. The results of these new kinetic models are compared with standard collisional-radiative kinetics demonstrating an important reduction of computer times, the possibility to obtain scaling relations and to independently study the precision of complex quantum calculations for these many level kinetic problems.

International audience; Novel phenomena and methods related to dielectronic capture and dielectronic recombination are studied for non-local thermodynamic equilibrium (LTE) plasmas and for applications to non-LTE ionization balance. It is demonstrated that multichannel autoionization and radiative decay strongly suppress higher-order contributions to the total dielectronic recombination rates, which are overestimated by standard approaches by orders of magnitude. Excited-state coupling of dielectronic capture is shown to be much more important than ground-state contributions, and electron collisional excitation is also identified as a mechanism driving effective dielectronic recombination. A theoretical description of the effect of angular-momentum-changing collisions on dielectronic recombination is developed from an atomic kinetic point of view and is visualized with a simple analytical model. The perturbation of the autoionizing states due to electric fields is discussed with respect to ionization potential depression and perturbation of symmetry properties of autoionization matrix elements. The first steps in the development of statistical methods are presented and are realized in the framework of a local plasma frequency approach. Finally, the impact of collisional–radiative processes and atomic population kinetics on dielectronic recombination is critically discussed, and simple analytical formulas are presented.

The absorption of ultrashort laser pulses by diatomic CO and HF molecules is studied theoretically. The probability of absorption in the total pulse action time and its dependence on the pulse duration and carrier frequency are calculated. In contrast to atomic systems, where the finite pulse duration effects are noticeable on time scales of the order of femtoseconds, these effects in molecular structures manifest themselves on time scales of the order of picoseconds. In this case, the vibrational–rotational structure of molecular transitions plays a significant role. The results of our calculations of the vibrational–rotational spectra for the absorption of ultrashort laser pulses by diatomic CO and HF molecules are presented. The transition from the nonlinear dependence of the absorption probability for short pulse durations to the standard dependence at long pulse durations corresponding to the transition probabilities per unit time is investigated.

It is shown that for sufficiently short pulses the resonance scattering probability becomes a nonlinear function of the pulse duration. For fs X-ray pulses scattered on atoms in plasmas maxima and minima develop in the nonlinear regime whereas in the limit of long pulses the probability becomes linear and turns over into the standard description of the electromagnetic pulse scattering. Numerical calculations are carried out in terms of a generalized scattering probability for the total time of pulse duration including fine structure splitting and ion Doppler broadening in hot plasmas. For projected X-ray monocycles, the generalized nonlinear approach differs by 1–2 orders of magnitude from the standard theory.

Laser-induced fluorescence diagnostics on ITER will be used for local measurements of helium density (nHeI) and ion temperature (Ti) in the divertor area. The diagnostics is combined with divertor Thomson scattering via common laser injection and signal collection optics. Multichannel filter polychromators with design similar to those developed for Thomson scattering will be used to perform spectral analysis of the fluorescent signals. Both the fluorescent signals and the background radiation are estimated using the collisional-radiative models developed for He I and He II. The estimations demonstrate the feasibility of measuring nHeI with the temporal resolution 20 ms and accuracy ΔnHeI

We describe the general analytic derivation of the dielectronic recombination (DR) rate coefficient for multielectron ions in a plasma based on the statistical theory of an atom in terms of the spatial distribution of the atomic electron density. The dielectronic recombination rates for complex multielectron tungsten ions are calculated numerically in a wide range of variation of the plasma temperature, which is important for modern nuclear fusion studies. The results of statistical theory are compared with the data obtained using level-by-level codes ADPAK, FAC, HULLAC, and experimental results. We consider different statistical DR models based on the Thomas–Fermi distribution, viz., integral and differential with respect to the orbital angular momenta of the ion core and the trapped electron, as well as the Rost model, which is an analog of the Frank–Condon model as applied to atomic structures. In view of its universality and relative simplicity, the statistical approach can be used for obtaining express estimates of the dielectronic recombination rate coefficients in complex calculations of the parameters of the thermonuclear plasmas. The application of statistical methods also provides information for the dielectronic recombination rates with much smaller computer time expenditures as compared to available level-by-level codes.

A new channel of radiative losses in fusion plasma with impurities of multielectron ions associated with their excitation by fast alpha particles has been studied. It has been shown that this loss channel for tungsten impurity is comparable with standard radiative losses of plasma electrons.

The investigations of tungsten transport in T-10 plasma are presented in the current paper. The process of tungsten accumulation in OH discharges and its dependence on parameters ne, Ip, and Zeff are discussed. Peaked tungsten density profiles nW(r) are observed in plasmas with Zeff ≈ 1–1.5. In plasmas with Zeff ≈ 3–4, W accumulation is mainly integral with no profile peaking with regard to electron density ne(r). Lower densities of W are observed in discharges with a lithized T-10 vacuum vessel in comparison with plasma contaminated with light impurities. The disposal of W accumulation is produced by auxiliary ECRH input. During the central ECRH, the tungsten density profile flattens with the central density drop off by ~10 times together with W source increase up to 4 times.

International audience; The general properties of ultra-short electromagnetic pulse (USP) interactions with highly charge ions in dense and high temperature plasmas are considered. The application of USP in X-ray spectral range provided by modern technology including free-electron laser machines opens up new opportunities for investigations of dense plasmas. They are based on the possibility of USP penetration into optically dense media due to their broad spectral distribution. In the framework of the use of USP for active spectroscopy in high energy density plasmas, new expressions of the transition probabilities are proposed. An aluminum plasma at local thermodynamic equilibrium is considered. The interaction of USP with hydrogen-like ions at N e =2⋅10 22 cm-3 and T=1 keV is analyzed in details by taking into account both the specificity of the USP and the plasma effects, such as Stark and Doppler effects on the line profile of the excited radiative transitions. The results are applied for demonstration of optical depth and pulse duration effects on excitation probabilities of the n=1 to n=3 radiative transition, which is the simplest atomic scheme to observe fluorescence signal.

The radial dependence of the free electron density within the ion sphere radius in finite temperature dense plasmas shows characteristic scaling laws that permit us to derive analytical plasma screening potentials. A generalized analytical approach is developed which shows good agreement with self-consistent quantum mechanical calculations. It is empirically discovered that anomalous strong scaling in the analytical model provides agreement with data obtained in a regime where the lattice structure still prevails.

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Excitation of highly charged ions in plasmas under the action of ultrashort electromagnetic pulses is investigated theoretically in the frame of perturbation theory. The study is based on analytical expression for probability of bound-bound transition which is derived for Gaussian pulse and Doppler broadening of spectral line shape of the transition. Electronic transitions from the ground state of hydrogen-like ions are considered with account for fine splitting of upper energy levels. The main attention is paid to the dependence of the excitation probability on pulse duration for various ion charges and carrier frequencies of the pulse. The results obtained are of interest for plasma diagnostics based on ion excitation from ground state by ultrashort pulses. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Calculation of the total dielectronic recombination (DR) rates was done in the frame of a statistical model of atoms. The model is based on the idea of collective excitations of atomic electrons with the local plasma frequency, which depends on atomic electrons density distribution. The electron density is described in a frame of the Thomas-Fermi model of atoms. Simple scaling laws for temperature Te and nuclear charge Z dependences follow from the statistical model of DR. Results of the statistical model were compared with other numerical data following detailed level-by-level computations for different multielectron ions. The specific attention is paid to Ni-like ion sequences of different chemical elements in order to check the Z -dependence of DR rates. A comparison with numerical data of Flexible Atomic Code (FAC) is presented for tungsten ions. The reasonable correspondence between the statistical model and the detailed numerical data is demonstrated. The application of the statistical model provides very simple and fast calculations of the DR rates useful in modern plasma modelling. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Statistical models combined with the local plasma frequency approach applied to the atomic electron density are employed to study the photoionization cross-section for complex atoms. It is demonstrated that the Thomas–Fermi atom provides surprisingly good overall agreement even for complex outer-shell configurations, where quantum mechanical approaches that include electron correlations are exceedingly difficult. Quantum mechanical photoionization calculations are studied with respect to energy and nl quantum number for hydrogen-like and non-hydrogen-like atoms and ions. A generalized scaled photoionization model (GSPM) based on the simultaneous introduction of effective charges for non-H-like energies and scaling charges for the reduced energy scale allows the development of analytical formulas for all states nl. Explicit expressions for nl = 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and 5s are obtained. Application to H-like and non-H-like atoms and ions and to neutral atoms demonstrates the universality of the scaled analytical approach including inner-shell photoionization. Likewise, GSPM describes the near-threshold behavior and high-energy asymptotes well. Finally, we discuss the various models and the correspondence principle along with experimental data and with respect to a good compromise between generality and precision. The results are also relevant to large-scale integrated light–matter interaction simulations, e.g., X-ray free-electron laser interactions with matter or photoionization driven by a broadband radiation field such as Planckian radiation.

The standard approach to calculate the Thomson scattering probability is reconsidered for the case of ultrashort incident laser pulses (USLPs). We established a new model for the interaction of USLP with plasmas that is based on Fermi's equivalent photon conception to calculate the spectral-angular differential Thomson scattering probability. The simulations demonstrate that the scattering probability for USLP is a non-monotonic function of pulse duration in contrast to the standard long-pulse model showing linear dependence. An analytical approach is developed to study the nonlinear behavior of the scattering probability as a function of pulse duration and other parameters.

An investigation of the probability of hydrogen atom ionization by ultra-short electromagnetic pulses is carried out in the frame of perturbation theory We consider the case when the electric field strength amplitude E0 in a pulse by two orders lower than characteristic atomic field strength Ea (Ea ≅ 5.1 · 109 V/cm). A detailed investigation of the dependence of the probabilities on the pulse duration was performed for Gaussian pulse shapes. In the case where the carrier frequency of the Gaussian pulse is larger than the atomic ionization potential, the probability goes to the standard limit of perturbation per unit time. At the same pulse durations, the probabilities for carrier frequencies less than the ionization potential go to zero. The frequency dependence of the ionization probability becomes equal to the standard threshold dependence with increasing pulse duration time. A comparison between the ionization effects caused by wavelet pulses without carrier frequency and Gaussian pulses with carrier frequency shows that the same ionization probability values are achieved when the pulse carrier frequency is detuned by about 20% from the ionization threshold. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The universal statistical approach for calculation of radiative and collisional processes with multielectron ions in plasmas is developed. It is based on the atomic structure representation similar to that used in a condensed medium. The distribution of local atomic electron density determines the set of elementary excitations with classical plasma frequency. The statistical method is tested by the calculations of the total electron impact single ionization cross-sections, ionization rates and radiative losses of various ions. In the coronal limit the radiative losses of heavy plasma impurities with any type of multielectron ions are determined by the excitation of collective atomic oscillations due to collisions with plasma electrons. It is shown that for low plasma densities the tungsten ions total radiative loss scatter within universal statistical approach does not exceed similar results of current complex numerical codes in the wide range of plasma temperatures. The general expression for the radiative losses in the case of the intermediate state between limiting cases of coronal and Boltzmann population distributions is derived as well. The total electron impact ionization cross-sections and ionization rates for ions of various charge stages for a wide range of elements from Ar to U are compared with experimental and conventional complex code data showing satisfactory agreement. As the universal statistical method operates in terms of collective excitations, it implicitly includes direct and indirect ionization processes.

The statistical model for calculations of the collisional-radiative processes in plasmas with tungsten impurity was developed. The electron structure of tungsten multielectron ions is considered in terms of both the Thomas-Fermi model and the Brandt-Lundquist model of collective oscillations of atomic electron density. The excitation or ionization of atomic electrons by plasma electron impacts are represented as photo-processes under the action of flux of equivalent photons introduced by E. Fermi. The total electron impact single ionization cross-sections of ions Wk+ with respective rates have been calculated and compared with the available experimental and modeling data (e.g., CADW). Plasma radiative losses on tungsten impurity were also calculated in a wide range of electron temperatures 1 eV–20 keV. The numerical code TFATOM was developed for calculations of radiative-collisional processes involving tungsten ions. The needed computational resources for TFATOM code are orders of magnitudes less than for the other conventional numerical codes. The transition from corona to Boltzmann limit was investigated in detail. The results of statistical approach have been tested by comparison with the vast experimental and conventional code data for a set of ions Wk+. It is shown that the universal statistical model accuracy for the ionization cross-sections and radiation losses is within the data scattering of significantly more complex quantum numerical codes, using different approximations for the calculation of atomic structure and the electronic cross-sections.

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.

The dielectronic recombination rate of multielectron ions was calculated by means of the statistical approach. It is based on an idea of collective excitations of atomic electrons with the local plasma frequencies. These frequencies are expressed via the Thomas-Fermi model electron density distribution. The statistical approach provides fast computation of DR rates that are compared with the modern quantum mechanical calculations. The results are important for current studies of thermonuclear plasmas with the tungsten impurities.

International audience; Elastic scattering of electromagnetic pulses on atoms in XUV and soft X-ray ranges is considered for ultra-short pulses. The inclusion of the retardation term, non-dipole interaction and an efficient scattering tensor approximation allowed studying the scattering probability in dependence of the pulse duration for different carrier frequencies. Numerical calculations carried out for Mg, Al and Fe atoms demonstrate that the scattering probability is a highly non-linear function of the pulse duration and has extrema for pulse carrier frequencies in the vicinity of the resonance-like features of the polarization charge spectrum. Closed expressions for the non-dipole correction and the angular dependence of the scattered radiation are obtained.

The problems related to the spectral line-shape formation in the scrape of layer (SOL) in fusion reactor plasma for typical observation chords are considered. The SOL plasma is characterized by the relatively low electron density (1012–1013 cm−3) and high temperature (from 10 eV up to 1 keV). The main effects responsible for the line-shape formation in the SOL are Doppler and Zeeman effects. The main problem is a correct modeling of the neutral atom velocity distribution function (VDF). The VDF is determined by a number of atomic processes, namely: molecular dissociation, ionization and charge exchange of neutral atoms on plasma ions, electron excitation accompanied by the charge exchange from atomic excited states, and atom reflection from the wall. All the processes take place step by step during atom motion from the wall to the plasma core. In practice, the largest contribution to the neutral atom radiation emission comes from a thin layer near the wall with typical size 10–20 cm, which is small as compared with the minor radius of modern devices including international test experimental reactor ITER (radius 2 m). The important problem is a strongly non-uniform distribution of plasma parameters (electron and ion densities and temperatures). The distributions vary for different observation chords and ITER operation regimes. In the present report, most attention is paid to the problem of the VDF calculations. The most correct method for solving the problem is an application of the Monte Carlo method for atom motion near the wall. However, the method is sometimes too complicated to be combined with other numerical codes for plasma modeling for various regimes of fusion reactor operation. Thus, it is important to develop simpler methods for neutral atom VDF in space coordinates and velocities. The efficiency of such methods has to be tested via a comparison with the Monte Carlo codes for particular plasma conditions. Here a new simplified method for description of neutral atoms penetration into plasma is suggested. The method is based on the ballistic motion of neutrals along the line-of-sight (LoS) in the forward–back approximation. As a result, two-dimensional distribution functions, dependent on the LoS coordinate and the velocity projection on the LoS, and responsible for the Doppler broadening of the line shape, are calculated. A comparison of the method with Monte Carlo calculations allows the evaluation of the accuracy of the ballistic model. The Balmer spectral line shapes are calculated for specific LoS typical for ITER diagnostics.

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.