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The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena in various fields of science and engineering. In addition, it should be noted that studies of the characteristics of turbulent flows, for example, have still not been completed. This is inspiring a great deal of interest in this topic, both in the sense of physical theory and in the sense of developing new approaches to the mathematical modeling of the corresponding problems. The capabilities of modern computer technology make it possible to carry out numerical experiments in two-dimensional and three-dimensional setups and analyze the features of the new numerical methods. Presently, numerous methods with many modifications are used in practice. This review focuses on the most promising among them.

The compression and burning of a fusion target ignited by a focused shock wave produced at the action of a time-profiled second harmonic laser pulse of a Nd laser have been calculated and theoretically studied. The main energy features of the shock ignition scheme have been considered. The use of the second harmonic radiation corresponds to a higher energy and a longer laser pulse necessary for ignition by this method compared to the use of the third harmonic radiation. Nevertheless, the method of ignition by the focused shock wave with the second harmonic radiation makes it possible to reach the fusion target gain that is two or three times higher than that at the traditional spark ignition with the laser pulse energy higher than in the former case by a factor of 1.5. The numerical calculations have been performed with one-dimensional hydrodynamic codes.

The influence of heating homogeneity violations in a laser thermonuclear target designed for shock ignition on the target compression and burning has been studied. We have performed our studies based on two-dimensional hydrodynamic simulations when modeling the target heating homogeneity violations due to various factors of symmetry violation of the target irradiation by a finite number of laser beams. The gains have been calculated at various perturbation amplitudes of the spatial distribution of absorbed energy in the target for two characteristic cases—low and high dominant perturbation modes. The first and second cases refer, respectively, to the factors of regular irradiation homogeneity violation due to a finite number of laser beams and a target offset from the focusing point and the factors of stochastic irradiation homogeneity violation related to laser beam energy imbalance, beam mispointing, and beam mistiming. We show that for a target designed for shock ignition the factors of regular irradiation homogeneity violation are much more dangerous than those for a spark ignition target.

The results of numerical and theoretical studies of the gain of direct-drive inertial confinement fusion (ICF) target, which includes a kinetic description of energy transfer by laser-accelerated fast electrons, are presented. The range of initial temperature of fast electrons and fraction of laser energy contained in these particles were chosen based on the results of recent experiments at the National Ignition Facility (NIF).The effect of 'wandering' of fast electrons is taken into account. It is due to a remoteness of the region of fast electron generation from the ablation surface of imploded target. As a result a significant fraction of particles do not fall into the compressed part of target. The `wandering' effect leads to decreasing the negative effect of fast electron generation on the target's gain.

We have studied the dependence of the compression and burning of a spherical direct-drive fusion target on the nonuniformity of its heating caused by the asynchronous arrival of laser beams under conditions of irradiation by a modern laser system with a total energy of 2 MJ intended for the fuel ignition and fusion energy evolution equal to the absorbed laser energy. The investigation is performed by numerical simulation based on 2D hydrodynamic codes. It is established that the limiting permissible spread of the moments of laser pulse action on the target for ignition significantly exceeds the level that can be ensured using modern methods of controlled temporal synchronization of laser beams.

In this work, we investigate the formation of a converging shock wave in a homogeneous spherical target, whose outer layer was heated by a flux of monoenergetic fast electrons of a given particle energy. Ablation pressure generating the wave forms at spherical expansion of a layer of a heated substance, whose areal density remains constant throughout the entire heating process and equal to the product of the initial heating depth and density of the target. The studies are carried out based on numerical calculations using a one-dimensional hydrodynamic code as applied to ignition of a precompressed target by a shock wave (shock ignition), one of the most promising techniques of laser fusion ignition.

Processes of explosion and expansion of laser targets, experiments with which could clarify the reason for the observed asymmetric distribution of matter in a remnant cloud of some supernovae (e.g., the Cassiopeia A supernova), have been simulated. By analyzing criteria of hydrodynamic similarity of conditions characteristic of an astrophysical object and experiment, targets for absorbed laser energies in the range of 1–100 kJ have been proposed. This work continues a series of previous studies of supernovae and the possibility of simulating a number of processes observed at the explosion of supernovae such as the motion of a shock wave in matter, development of hydrodynamic instabilities at interfaces between shells with different densities, and largescale mixing of layers of the central region of a star with elements initially located at the periphery of the remnant cloud under laboratory conditions with high-power lasers. The studies are based on the numerical simulation of the explosion and explosion of targets using one- and two-dimensional hydrodynamic programs.

It is shown that fast ignition can ensure the combustion of asymmetrically compressed targets for inertial confinement fusion with an efficiency close to the combustion of one-dimensionally compressed targets. This statement is valid not only for targets specially designed for fast ignition. Fast heating by an external energy source can ensure the ignition of a target designed for spark ignition, but where this ignition does not occur because inhomogeneities are formed in the temperature and density distributions owing to the development of hydrodynamic instabilities. The condition for ignition is the fast heating of the plasma in the combustion initiation region whose size is comparable with the sizes of compression inhomogeneities. Thus, fast ignition not only significantly reduces the ignition energy, but also is possibly a necessary stage in the inertial confinement fusion scheme when the spherically symmetric compression of a target requires very high engineering and financial expenses. The studies are based on the numerical simulation of the compression and combustion of inertial confinement fusion targets with one- and two-dimensional hydrodynamic codes.

Direct-drive fusion targets are considered at present as an alternative to targets of indirect compression at a laser energy level of about 2 MJ. In this approach, the symmetry of compression and ignition of thermonuclear fuel play the major role. We report on the results of theoretical investigation of compression and burning of spherical direct-drive targets in the conditions of spatial nonuniformity of heating associated with a shift of the target from the beam center of focusing and possible laser radiation energy disbalance in the beams. The investigation involves numerous calculations based on a complex of 1D and 2D codes RAPID, SEND (for determining the target illumination and the dynamics of absorption), DIANA, and NUT (1D and multidimensional hydrodynamics of compression and burning of targets). The target under investigation had the form of a two-layer shell (ablator made of inertial material CH and DT ice) filled with DT gas. We have determined the range of admissible variation of compression and combustion parameters of the target depending on the variation of the spatial nonuniformity of its heating by a multibeam laser system. It has been shown that low-mode (long-wavelength) perturbations deteriorate the characteristics of the central region due to less effective conversion of the kinetic energy of the target shell into the internal energy of the center. Local initiation of burning is also observed in off-center regions of the target in the case of substantial asymmetry of irradiation. In this case, burning is not spread over the entire volume of the DT fuel as a rule, which considerably reduces the thermonuclear yield as compared to that in the case of spherical symmetry and central ignition.

We propose a model for the explosion of a supernova and the expansion of its ejecta in the presence of a strong initial asymmetry (at the explosion time) in the central part of the star (core) and a possible smallscale asymmetry in the peripheral regions. The Chandra and NuSTAR observations of ejecta in the Cassiopeia A supernova remnant are analyzed. Based on our 1D and 2D numerical simulations performed using the DIANA and NUTCY codes, we propose a model for the explosion and expansion of ejecta that explains the observed experimental data where the materials initially located in the central region of the star end up on the periphery of the cloud of ejecta.

The role of energy transfer by fast electrons, which is responsible for the positive effect of increasing the ablative pressure and the negative effect of preheating, on the implosion and thermonuclear gain of the target designed for shock ignition is investigated in comparison with the target designed for traditional spark ignition. On the base of one-dimensional hydrodynamic simulations with kinetic description of fast electron transfer it is shown, that depending on the characteristics of fast electron flux, in shock ignition target are manifested to varying degree both effects the positive and negative ones. This is a distinguishing feature of a shock ignition target compared to a traditional spark ignition target, in which only the negative effect of fast electron energy transfer takes place. In a shock ignition target up to temperatures of 50–60 keV, the positive effect is dominant and provides high gain. With an increase in the fast electron temperature, the role of the negative preheating effect increases, that ultimately leads to the ignition failure as temperature exceeding 90–100 keV.

A theoretical model is proposed for computing simulations of laser radiation interaction with inhomogeneous foam materials doped with heavy elements and undoped materials. The model satisfactorily describes many experiments on the interaction of the first and third harmonics of a 200 J pulsed PALS iodine laser with low-density porous cellulose triacetate targets. The model can be used to analyze experimental data and estimate the reality of experimental results.

Central ignition of a thin two-layer-shell fusion target that is directly driven by a 2-MJ profiled pulse of Nd laser second-harmonic radiation has been studied. The parameters of the target were selected so as to provide effective acceleration of the shell toward the center, which was sufficient for the onset of ignition under conditions of increased hydrodynamic stability of the ablator acceleration and compression. The aspect ratio of the inner deuterium-tritium layer of the shell does not exceed 15, provided that a major part (above 75%) of the outer layer (plastic ablator) is evaporated by the instant of maximum compression. The investigation is based on two series of numerical calculations that were performed using one-dimensional (1D) hydrodynamic codes. The first 1D code was used to calculate the absorption of the profiled laser-radiation pulse (including calculation of the total absorption coefficient with allowance for the inverse bremsstrahlung and resonance mechanisms) and the spatial distribution of target heating for a real geometry of irradiation using 192 laser beams in a scheme of focusing with a cubo-octahedral symmetry. The second 1D code was used for simulating the total cycle of target evolution under the action of absorbed laser radiation and for determining the thermonuclear gain that was achieved with a given target.

The burning efficiency of a preliminarily compressed inertial confinement fusion (ICF) target with a solid noncryogenic fuel (deuterium-tritium beryllium hydride) upon fast central ignition by a fast ion beam is studied. The main aim of the study was to determine the extent to which the spatial temperature distribution formed under the heating of an ICF target by ion beams with different particle energy spectra affects the thermonuclear gain. The study is based on a complex numerical modeling including computer simulations of (i) the heating of a compressed target with a spatially nonuniform density and temperature distributions by a fast ion beam and (ii) the burning of the target with the initial spatial density distribution formed at the instant of maximum compression of the target and the initial spatial temperature distribution formed as a result of heating of the compressed target by the ion beam. The threshold energy of the igniting ion beam and the dependence of the thermonuclear gain on the energy deposited in the target are determined.

In the previous works (Rozanov et al., 2013; 2015) we have performed one-dimensional (1D) numerical simulations of the target compression and burning at the absorbed energy of ~1.5 MJ. As a result, the target was chosen to have a low initial aspect ratio in order to be less sensitive to the influence of such parameters as laser pulse duration, total laser energy, and equations of state model. The simulation results demonstrated a higher probability of ignition and effective burning of such a system. In the present work we discuss the impact of irradiation asymmetry on this baseline target implosion. The details of the 1D compression and a possible influence of 2D and 3D effects due to the hydrodynamic instability and mixing have been described. In accordance with the 2D calculations the target is still ignited, however, the symmetry analysis of 3D ones gives reasons to further reduce the efficiency of conversion of kinetic energy into potential energy.

We present the results of a large number of 2D and 3D simulations of the Rayleigh–Taylor instability development. The simulations were made with the help of the EGAK code developed at RFNC–VNIIEF and performed using fine grids (for 2D, 1000 × 2000; for 3D, 10003) for two ideal fluids of different densities in the gravitational field with different initial perturbations at the interface. We present an analysis of the results of 2D and 3D simulations compared with the evolutionary model of a turbulent mixing layer. This theoretical approach is based on the idea of a “perturbation age” where the age of a perturbation is the product of its height and the wave number. The “critical age” represents the boundary between the linear and nonlinear stages of the instability development (a boundary that is different for 2D and 3D problems). Central in this model is information on the initial perturbation spectra and their role in the appearance of low wave-number modes at a later stage of the turbulent mixing layer evolution. The instability evolution model enables an adequate interpretation of various peculiarities in the development of a turbulent layer.

Turbulent Richtmyer--Meshkov instability (RMI) is investigated through a series of high resolution three dimensional smulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm, and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regime combined. Overall, the growth rate exponent is determined as $\theta=0.292 \pm 0.009$, in good agreement with prior studies; however, the exponent is decaying slowly in time. $\theta$ is shown to be relatively insensitive to the choice of mixing layer width measurement. The asymptotic integral molecular mixing measures $\Theta=0.792\pm 0.014$, $\Xi=0.800 \pm 0.014$ and $\Psi=0.782\pm 0.013$ which are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49\% and 66\% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single $\theta$. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research., Comment: 50 pages

We investigate the ignition and burning of a precompressed laser fusion target when it is rapidly heated by an ion beam with the formation of a temperature peak in the central part of the target. We present the results of our comprehensive numerical simulations of the problem that include the following components: (1) the target compression under the action of a profiled laser pulse, (2) the heating of the compressed target with spatially nonuniform density and temperature distributions by a beam of high-energy ions, and (3) the burning of the target with the initial spatial density distribution formed at the instant of maximum target compression and the initial spatial temperature distribution formed as a result of the compressed-target heating by an ion beam. The dependences of the threshold energies of the igniting ion beam and the thermonuclear gain on the width of the Gaussian beam ion energy spectrum have been established. The peculiarities of fast ignition by an ion beam related to the spatial distribution of parameters for the target precompressed by a laser pulse are discussed.

We study the possibility of laboratory modeling of some processes that are intrinsic to supernova (SN) explosion by means of powerful lasers (the so-called laboratory astrophysics); in particular, the possibility of reproducing astrophysical data via numerical models was originally aimed at laser plasma simulation. First of all, we analyze hydrodynamic similarity criteria for the considered processes. Then, we conduct 1D and 2D hydrodynamic simulations to model the expansion dynamics of the SN remnant (the progenitor mass is ∼5–15 that of the Sun) during several hundreds of seconds after the explosion, including initially asymmetric configurations. Basing on the similarity criteria, we consider possible laser targets – simulators for a supernova, which mimic some processes inherent in astrophysical phenomenon, such as shock wave propagation through a medium, the development of hydrodynamic instabilities at contact boundaries of shells of different densities, etc. We present a simple solution to the problem of blast wave propagation in a medium with density distributed according to a decreasing power law, which is a good approximation for the density distribution in a supernova progenitor.

Results are presented from theoretical analysis and numerical simulations aimed to clarify specific features of Rayleigh-Taylor instability in 2D and 3D geometries. Two series of simulations, one with an isolated single-mode perturbation of the interface and the other with a random density perturbation, were performed. It is shown that the relative evolutions of integral characteristics for the first and the second series are different in 2D and 3D geometries. An attempt is made to interpret this result in the framework of the previously developed evolutionary approach based on the concept of the “critical age” of the perturbation (where, by the age is meant the product of the wavenumber and amplitude). The critical age corresponds to the destruction of the main mushroom-like structure formed during the development of Rayleigh-Taylor instability due to the onset of the secondary Kelvin-Helmholtz instability.

The possibility of simulating the processes during supernova explosions in laboratory conditions using powerful lasers (laboratory astrophysics) is investigated. The Chandra observations of ejecta in the Cassiopeia A supernova remnant are analyzed. Based on the DIANA and NUTCY numerical codes, we have performed 1D and 2D hydrodynamic simulations of the ejecta expansion dynamics for a supernova with a mass of ∼5–15 solar masses within several hundred seconds after its explosion, including an initial asymmetry. We propose a model for the explosion and expansion of ejecta that illustrates strong inhomogeneities in the distribution of material to the extent that the Fe, Si, and S material from the stellar center turns out to be ejected to the periphery, the “star turns inside out,” in agreement with observations. Based on hydrodynamic similarity criteria, we consider possible supernova-simulating laser targets that will allow one to reproduce the physical processes that take place during the explosion of an astrophysical object, such as the shock propagation through the material, the growth of hydrodynamic instabilities at the boundaries of envelopes with different densities, etc.

Variants of a target with a solid thermonuclear fuel in the form of deuterium-tritium hydrides of light metals for an inertial fusion have been proposed. The laser-pulse-induced compression of non-cryogenic targets, as well as ignition and combustion of such targets, has been examined. The numerical calculations show that, despite a decrease in the caloric content of the fuel and an increase in the energy losses on intrinsic radiation in the target containing deuterium-tritium hydrides of light metals as compared to the target containing deuterium-tritium ice, the non-cryogenic target can ensure the fusion gain sufficient for its use in the energy cycle of a thermonuclear power plant based on the inertial plasma confinement method.

We develop a BIN computer code for simulating the interaction of a monochromatic ion beam with a plasma, which takes into account changes in the spatial distribution of the heated-plasma temperature. This enables us to calculate the heating of both homogeneous and inhomogeneous plasmas with parameters corresponding to their real spatial distributions at the time of maximum compression of the inertial confinement fusion (ICF) target. We present the results of a numerical simulation using the BIN code for the heating of a homogeneous deuterium–tritium plasma by a short pulse of monochromatic ions at various ion velocity and plasma–electron thermal velocity ratios. We also present the results of calculations for the heating of an inhomogeneous plasma of a non-cryogenic target formed as a beryllium deuteride–tritide shell by beams of light, medium, and heavy ions. As the initial distributions, we use the results of numerical simulations for such a target, precompressed by a laser pulse (carried out at the M. V. Keldysh Institute of Applied Mathematics using the DIANA code). We demonstrate the possibility of forming the central ignitor with the parameters sufficient for igniting the targets by beams of ions with energies E ~ 100 − 400 MeV/u and specific energy densities of the beam Q ∼ 5−20 GJ/cm2. The required specific energy density drops with increase in the ion energy; however, due to the increased path length, larger-charge ions have to be used.

Fast ignition of a precompressed inertial confinement fusion (ICF) target by a hydrodynamic material flux is investigated. A model system of hydrodynamic objects consisting of a central deuterium-tritium (DT) ball and a concentric two-layer shell separated by a vacuum gap is analyzed. The outer layer of the shell is an ablator, while the inner layer consists of DT ice. The igniting hydrodynamic flux forms as a result of laser-driven acceleration and compression of the shell toward the system center. A series of one-dimensional numerical simulations of the shell implosion, the collision of the shell with the DT ball, and the generation and propagation of thermonuclear burn waves in both parts of the system are performed. Analytic models are developed that describe the implosion of a thin shell onto a central homogeneous ball of arbitrary radius and density and the initiation and propagation of a thermonuclear burn wave induced by such an implosion. Application of the solution of a model problem to analyzing the implosion of a segment of a spherical shell in a conical channel indicates the possibility of fast ignition of a spherical ICF target from a conical target driven by a laser pulse with an energy of 500–700 kJ.

The turbulent mixing (TM) of different DT-fuel areas (cold with hot) and of DT-fuel with ablator is one of the deciding factors, determining the neutron yield from compressing laser fusion, and, more generally, inertial confinement fusion (ICF) targets. A lower than predicted neutron yield gained in experiments is not studied comprehensively, but can be caused by the mixing processes. A study of mixing in the ICF problem is complicated by density gradients, spherical convergence, compression, etc., so we suppose the fundamental understanding of the mixing processes must be acquired first in the problem of classical Rayleigh-Taylor (RT) instability in plain geometry. In our work we present results, obtained by the supercomputer numerical modeling of RT-induced TM processes with different initial conditions in 2D and 3D geometries conditions on a high-resolution meshes. For analysis of the modeling results we use an evolutionary model of singular perturbation development, including linear and non-linear stages. This theoretical approach allows us to obtain highly detailed view of the mixing zone evolution along with possibility to trace the initial conditions influence on the mixing late stages.

We investigate the efficiency of inertial fusion target compression, where at the initial time moment the thermonuclear fuel is in a two-phase state and has the form of two adjacent layers — the external DT-liquid layer and the internal DT-ice layer. We study this problem for the fast ignition targets, where the ultimate final density of the thermonuclear matter is of a special importance. We take the simplest type of a fast ignition target, which corresponds to the technical justification of the HiPER Project aimed at demonstrating fast ignition at the compressing laser pulse energy ~100 kJ. Such a target presents a spherical DT-ice shell coated with a thin polymer film. We obtain the dependence of the final target density on the mass fraction of the DT-matter liquid phase and formulate the requirements on the admissible concentration of liquid phase if the decrease in the DT-fuel final density does not exceed 10%. We find the criterion for choosing the laser-pulse duration which provides the minimum decrease in the final density of the target containing DT-matter in the initial two-phase state.

The heating of inertial confinement fusion (ICF) target by fast electrons, which are generated as a result of laser interaction with expanding plasma (corona) of a target, is investigated theoretically. It is shown that due to remoteness of the peripheral region, where electrons are accelerated, a significant portion of these particles, moving in corona and repeatedly crossing it due to reflection in a self-consistent electric field, will not hit into the compressed part of target. Using the modern models of fast electron generation, it is shown that in a typical target designed for spark ignition, the fraction of fast electrons that can pass their energy to compressed part of target is enough small. Only 12% of the total number of fast electrons can do it. Such an effect of 'wandering' of fast electrons in corona leads to a significant decrease in a negative effect of fast electrons on target compression. Taking into account the wandering effect, the distribution of energy transmitted by fast electrons to different parts of target and the resulting reduction of deuterium-tritium (DT) fuel compression are established.

We have analyzed and numerically simulated our experiments on the compression of DT-gas-filled glass capsules under irradiation by a small number of beams on the Iskra-5 facility (12 beams) at the second harmonic of an iodine laser (λ = 0.66 μm) for a laser pulse energy of 2 kJ and duration of 0.5 ns in the case of asymmetric irradiation and compression. Our simulations include the construction of a target illumination map and a histogram of the target surface illumination distribution; 1D capsule compression simulations based on the DIANA code corresponding to various target surface regions; and 2D compression simulations based on the NUTCY code corresponding to the illumination conditions. We have succeeded in reproducing the shape of the compressed region at the time of maximum compression and the reduction in neutron yield (compared to the 1D simulations) to the experimentally observed values. For the Iskra-5 conditions, we have considered targets that can provide a more symmetric compression and a higher neutron yield.

Determination of the spectra and yields of thermonuclear particles is an actual research line for inertial confinement fusion (ICF) in two areas: the development of diagnostic methods for ICF plasma and thermonuclear reactor design for energy production. The latter is particularly important for thermonuclear neutron emission, which contains the bulk of the evolving energy. This work is devoted to the determination and analysis of the energy spectrum composition of the emissions of thermonuclear neutrons, charged thermonuclear particles and recoil nuclei from ICF targets, which correspond to a laser pulse energy of ≈2 MJ and are designed for modern experiments to achieve a positive energy yield. The spectra are determined on the basis of hydrodynamic numerical simulations of ICF target burnup, modeling the generation of thermonuclear particles and their interaction with the target by means of the Monte Carlo method. The spectrum characteristics are discussed with reference to the problems of corpuscular diagnostics and radiation damage to the materials of thermonuclear reactor units.

This work is devoted to an optimization problem of a neutronless target DHe3. It reports the results of optimization for a gas-filled target DHe3 with the CH-shell in its irradiation by laser pulse with 5 MJ energy. The data of computational experiments are compared with the results of approximation theory [1].

A method for calculating the effective charge of fast ions decelerated in a hot dense plasma is proposed. The method is based on the known experimental dependence of the effective charge of an ion decelerated in cold matter on its velocity. The ion velocity in this dependence is replaced with the velocity of an ion relative to plasma electrons, averaged over the Fermi-Dirac distribution. Using results of numerical calculations performed in a wide range of plasma parameters (from a Maxwellian plasma to a fully degenerate one), a scale-invariant representation of the effective charge of a decelerating ion as a function of its initial velocity and the plasma temperature and density is obtained. An analytical formula fitting the calculated results to within 5% is derived. The obtained dependences of the effective charge are incorporated in the model describing deceleration of fast ions in plasma. Using this model, the stopping powers of krypton and lead ions in a relatively cold rarefied gas-discharge plasma and hot ICF plasma are calculated. The results of calculations are shown to agree satisfactorily with available experimental data.

The interaction of ultrashort relativistically intense laser pulses with plasma resulting in the forward-directed harmonics generation from the rear side of a target is investigated by particle-in-cell simulation [1]. The dependences of the spectral characteristics of the electro-magnetic radiation on the laser intensity, the laser pulse duration, and the polarization of the laser light, as well as the laser radiation geometry and the plasma thickness and density, are considered.

This paper is devoted to the analysis of a hyperbolic heat-transfer model, which takes into account the heat-flow relaxation. It is shown that heat-flow relaxation can have a significant impact on the nature of energy transfer in substances. The role of the relaxation heat transfer in the processes taking place in laser plasma is assessed. Some qualitative features are investigated with the help of solutions of gas-dynamics equations—both the automodel and running-wave type

The fast ignition as, possibly the most efficient method of inertial confinement fusion (ICF) is based on heating a small fusion initiation region (igniter) while the rest of the target is compressed by a compressing driver. We investigate the influence of two factors on the efficiency of fast ignition of ICF-targets. The first factor is the spatial distribution of thermonuclear-fuel parameters formed due to the ICF-target irradiation by the compressing driver. The second one is a mismatch in the time moments of the target maximum compression and the igniter heating by the igniting driver. The main characteristics of fast ignition, namely, the minimum energy of igniter needed to ignite the main ICF-target fuel (ignition energy) and the burn efficiency (ratio between the burnt and initial fuel masses), are investigated in view of numerical simulation. The scale-invariant dependences of the minimum ignition energy E ig and the burn efficiency are obtained. It is shown that the burn efficiency depends on the spatial heterogeneity of the thermonuclear-fuel parameters much weaker then the ignition energy, but a strong dependence of the burn efficiency on the mismatch in time moments of the maximum compression and ignition is found. In particular, the ignition before the time moment of the maximum compression is more favorable than the ignition at just this moment.

Based on many direct numerical simulations of the development of hydrodynamic instabilities upon compression of laser thermonuclear targets, an efficient model is developed for describing the width of the mixing region taking into account the influence of the initial conditions on the mixing process dynamics. Approaches are proposed which are based on the evolution theory of the development of hydrodynamic instabilities [1], which was specially elaborated to describe the compression of targets for inertial thermonuclear fusion.

Theoretical and experimental studies of radiative properties of hot dense plasmas that are used as soft X-ray sources have been carried out depending on the plasma composition. Important features of the theoretical model, which can be used for complex materials, are discussed. An optimizing procedure that can determine an effective complex material to produce optically thick plasma by laser interaction with a thick solid target is applied. The efficiency of the resulting material is compared with the efficiency of other composite materials that have previously been evaluated theoretically. It is shown that the optimizing procedure does, in practice, find higher radiation efficiency materials than have been found by previous authors. Similar theoretical research is performed for the optically thin plasma produced from exploding wires. Theoretical estimations of radiative efficiency are compared with experimental data that are obtained from measurements of X-pinch radiation energy yield using two exploding wire materials, NiCr and Alloy 188. It is shown that theoretical calculations agree well with the experimental data.

The energetic characteristics of the compression and burning of targets with beryllium and beryllium deuteride shells are compared. The characteristics considered include the hydrodynamic efficiency, the efficiency of energy transmission to the thermonuclear fuel, and the gain factor found from numerical simulation using the ‘Diana’ one-dimensional mathematical code. The calculations are carried out for direct-drive cryogenic laser targets with the ablator shells made of beryllium or beryllium deuteride with parameters corresponding to the third harmonic of energy of the neodymium-laser radiation with a pulse energy of 1–3 MJ. It is proved that the gain of beryllium hydride targets can be brought to the level of beryllium targets due to variations in the geometrical parameters of BeD2 targets. It is shown that the fission of BeD2 or BeDT ablators in reactor-scale targets could significantly contribute to the final thermonuclear yield.

Different designs of a green house target (GHT) were considered at 2 MJ laser pulse energy, in which the thermonuclear gain G achieved ∼20-30 in one-dimensional calculations. The GH targets were designed to attain a symmetrical compression and efficient thermonuclear burning of a target irradiated by a low number of laser beams (N = 2, 4, 6, 8...) by using a low-density foam-like absorber. But as compared to the earlier studied target designs, where the value of gain G achieved ∼8, the newly developed schemes are more risky, less reliable, and less experimentally verified. In the calculations, value G is increased as one employs a longer laser pulse for compression, the greater A = R 0 /ΔR 0 , the conversion ratio R 0 /R min , and the lesser value α = p/p F . It seems that all these changes correspond to a less stable regime of operation. A sensitivity of results to the elements of uncertainty in the physics of processes is discussed.

The possibility of efficient and symmetric compression of a target with a low-density structured absorber by a few laser beams is considered. An equation of state is proposed for a porous medium, which takes into account the special features of the absorption of high-power nanosecond laser pulses. The open version of this target is shown to allow the use of ordinary Gaussian beams, requiring no special profiling of the absorber surface. The conditions are defined under which such targets can be compressed efficiently by only two laser beams (or beam clusters). Simulations show that for a 2.1-MJ laser pulse, a seven-fold gain for the target under study is achieved.

Based on two-dimensional numerical simulations, a study was made of the radiation absorption, the energy transfer, and the plasma formation upon the interaction of a laser beam with a homogeneous medium consisting of light elements with a density not exceeding the critical plasma density, which corresponds to the plasma resonance for the wavelength of the driving laser radiation. The calculations were performed by the HEAT-3D code, which involved the solution of a two-dimensional heat conduction equation with an energy source describing the absorption of laser radiation due to inverse bremsstrahlung in the material. The simulations were performed of the interaction of laser beams of radii 10-2—6×10-2 cm, 1014—5×1015 W cm-2 in intensity, and with wavelengths of 1.053 and 0.527 μm with materials composed of light elements with densities of 1–10 mg cm-3. An analysis of the simulations showed that the spatial temperature distribution of the resultant plasma is determined by the anisotropy of energy transfer. In its turn, the degree of anisotropy depends on the relation between the beam radius and the laser radiation absorption length, which is a function of the density and the temperature of the resultant plasma. The results of simulations are compared with the findings of experiments on laser irradiation of targets composed of low-density materials.

The paper is devoted to recent results concerning investigation of physical processes occurring in a “laser greenhouse” target. Results of experimental and theoretical studies of laser-pulse interaction with a low-density absorber of the target, namely, with a porous substance having density close to the plasma critical density, are presented. On the basis of a vast cycle of experiments carried out in a number of laboratories, it is shown that the absorption of the laser radiation in porous media, including those with a density exceeding the critical one by at least a factor of 4 to 6, has a bulk nature and is distributed over the target depth. In particular, the laser-radiation absorption region in a porous substance with density 10−3–10−2 g/cm3 is extended into the target 400–100 μm, respectively. The coefficient of absorption of laser radiation with intensity 1014–1015 W/cm2 in porous substances, including those of the supercritical density, is 70–90%. Experiments have not shown enhanced (compared to a solid-state target) radiation intensity associated with a possible development of parametric instabilities in an extended laser plasma of low-density porous media, as well as noticeable contribution of fast electrons to the energy balance and their effect on the energy transfer. In this paper, theoretical models are developed explaining features of the laser-radiation absorption and energy transfer in porous media. These models are based on the phenomenon of laser-radiation interaction with solid components of a porous substance and plasma production inside pores and cells of the medium. The efficiency of energy conversion in the vicinity of the ignition threshold for the laser-greenhouse target is investigated in the case of an absorber having the above properties. Numerical calculations have shown that a thermonuclear-gain coefficient of 1 to 2 (with respect to the energy absorbed) is attained for a laser-radiation energy of 100 kJ.