Alexander Borisovich Kukushkin

Generalization of the Chapman-Enskog method to the case of large gradients of hydrodynamic velocity allowed us to obtain an integral (over spatial coordinates) representation of the viscous stress tensor in the Navier-Stokes equation. In the case of small path lengths of the medium disturbance, the tensor goes over to the standard form, which, as is known, is difficult to apply to the description of tangential discontinuities and separated flows. The obtained expression can allow numerical modeling of the nonlocality of turbulence, expressed by the empirical Richardson t^3 law for pair correlations in a turbulent medium.

A new ray tracing code, Fast_mp_ECH_startup, for calculating the multipass electron cyclotron (EC) absorption of injected radiation in plasma at the initial stage of discharge in tokamaks has been presented. For conditions close to the initial stage of discharge in tokamak reactors, the EC absorption efficiency calculated by the new code has been compared with calculations using the ray-tracing code GENRAY and with calculations based on the model of isotropic and homogeneous mixing of the injected radiation after one or more reflections from the vacuum chamber wall.

A method for calculating sputtering of the tokamak first wall by fast charge-exchange neutral atoms of hydrogen isotopes in the near-wall plasma has been proposed. The application of the method has been shown by the example of sputtering of the assumed first-wall materials under the near-wall plasma conditions in the ITER tokamak. Using the BM1D2V code based on the ballistic model of hydrogen recycling kinetics in the tokamak main vacuum chamber, the velocity distribution function (VDF) of neutral atoms and molecules of hydrogen isotopes in the near-wall plasma has been calculated. Using the calculated VDFs, the sputtering rate of beryllium, tungsten, and boron from the surface of the first wall of the tokamak vacuum chamber in a typical ITER divertor operating mode has been estimated. The reflection coefficients of atoms of hydrogen isotopes from the first wall used in the ballistic model and the sputtering coefficients have been calculated using the SDTrimSP code.

A simple qualitative model of the influence of grouping of atomic levels on the radiation losses of impurity ions in a near-wall low temperature plasma is proposed using the example of line radiation losses when excited states are populated by impact excitation by plasma electrons. A comparison of the relevant data simulated by the ADAS codes for low-charge ions of argon, neon, and nitrogen ions confirms the predicted effects of possible underestimation or overestimation of radiation losses when the number of atomic levels taken into account in the simulation in the collisional-radiative model decreases.

Electron cyclotron (EC) resonance heating in the T-15MD tokamak is calculated using the GENRAY code. The injection schemes without current generation for heating plasma using an extraordinary wave with a frequency of 140 GHz at the third harmonic of the fundamental EC frequency are considered. The cases of the wave injected through vertical, upper inclined, and equatorial port-plugs for three scenarios of the T-15MD operation—the baseline configuration and two configurations with different moderate values of plasma elongation and triangularity—are analyzed. A comparison of calculations performed using the GENRAY code with the published calculations based on the OGRAY code shows that the efficiency of EC heating in single-pass absorption and the spatial position of the absorbed power maximum are in good agreement, while the shape of the spatial profile of the absorbed power can differ significantly.

The success of the Special Issue (SI) “Symmetry in Physics of Plasma Technologies” https://www

A new method for estimating the global erosion of beryllium (Be) in ITER is proposed. The method uses ray tracing-aided tomography to reconstruct the three-dimensional (3D) profile of beryllium visible-light emissivity in boundary plasma from images captured with filtered cameras of VIS/IR wide angle viewing system, H-alpha (and Visible) Spectroscopy diagnostics and signals collected with divertor impurity monitor. The light reflected into the detectors from metallic plasma-facing components (PFCs) is filtered out in the process. The reconstructed Be emissivity is then used to assess the Be influx density distribution along all Be PFCs by integrating the product of the emissivity and the S/XB coefficient along the normal to the PFC surface. The accuracy of this method is evaluated by a comparison with synthetic emissivity data produced by recent simulation of global Be erosion and migration in ITER using the ERO2.0 code. The impact of the uncertainty of PFC light reflection properties on the error in reconstructing the 3D Be emissivity profile and Be influx density is analyzed. The method allows to recover with good accuracy the Be influx density in plasma-wetted areas under the conditions of H-mode fusion power operation with high plasma density in far scrape-off layer (SOL). Under the conditions of lower far-SOL plasma density and L-mode operation, only the total Be influx integrated over the area of the first wall panels with relatively high Be erosion can be reconstructed with a high accuracy. It is shown that neglecting the effects of light reflection may lead to a twofold overestimation of the total Be influx.

The effect of thermodynamic nonequilibrium of hydrogen isotope recycling, which consists in significant deviation of the velocity distribution function (VDF) of neutral hydrogen isotope atoms from the Maxwellian VDF, on the passive signal of the charge-exchange recombination spectroscopy (CXRS diagnostics) of edge plasma in tokamaks is analyzed using the ITER tokamak reactor as an example. The calculations of the VDF for atomic and molecular deuterium are carried out using the three-dimensional Monte Carlo code EIRENE as a part of the two-dimensional transport code SOLPS and the semi-analytical Ballistic Model BM1D2V, which is one-dimensional in coordinate and two-dimensional in projections of atomic velocity. The source of level population of the Be IV beryllium ion, the line radiation of which is used in the CXRS diagnostics, is calculated for the above two methods of calculating the VDF and the average atomic kinetic energy, as well as in the case of neglecting the thermodynamic nonequilibrium of recycling, when the temperature of atoms is equal to the temperature of the plasma ions. The calculations of the cross section for the charge-exchange reaction of beryllium ions Be V on deuterium atoms using the ARSENY code and other codes and the erosion kinetics of the beryllium first wall using the three-dimensional code ERO2.0 are used. The calculations of the level populations of the Be IV beryllium ion using the nl-KinRyd code, the luminosity of the ions, and the passive charge-exchange radiation intensity on the observation chord are carried out for the three indicated cases of the VDF of deuterium atoms. A significant dependence of the results of the conducted predictive modeling on the thermodynamic nonequilibrium of recycling is shown.

The development of synthetic diagnostics for passive plasma spectroscopy systems of the T-15MD tokamak is started using the Cherab software library for modeling fusion plasma spectroscopy. The calculation of signals in the visible wavelength range is performed with the Raysect code using the ray tracing technique, taking into account the reflection of light from the surfaces of the first wall specified as a full CAD model. The results of measuring the characteristics of light reflection by samples of the T-15MD graphite first wall before and after plasma exposure are used. The parameters of the model functions of graphite reflectivity are chosen by fitting the measurements. The results of edge plasma modeling by the SOLPS code are used to calculate the intensity of the spectral line H_α and the fraction of reflected light in the observed intensity depending on the geometry of the line of sight. It is shown that, during radial observation of the scrape-off layer plasma, the reflected light fraction in the observed intensity does not exceed 50%, and after a long-term exposure of the wall to the plasma, it should decrease to 10–20%. For lines of sight of diagnostics that measure the effective plasma charge profile, the bremsstrahlung and photorecombination radiation spectra are calculated on the basis of the combined data of modeling by the ASTRA and SOLPS codes. It is shown that only the lines of sight observing the peripheral plasma are subject to a significant influence of reflected light, where the intensity of bremsstrahlung is minimal. As in the case of H_α radiation, a long-term exposure of the wall to the plasma is expected to reduce the reflected light fraction in the observed intensity by a factor of 3–4.

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t³ scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in Shlesinger and colleagues’ about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman–Holstein approach to examine the transfer of excitation of a medium by photons, generalized in order to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson’s t³ scaling law to the combined regime of Lévy flights and Lévy walks in fluids and gases.