Simulations of hot, dense iron plasma opacity at 89 eV and comparison with experiment

Predictions of hot, dense iron plasma opacity at 89 eV photon energy are compared with experimental determinations from the transmission of laser-heated iron to extreme ultra-violet (EUV) laser radiation. The EUV laser was pumped using six beams of an Nd-Yag laser in a refraction compensating geometry, while another beam irradiated a tamped solid iron target with an intensity of 10¹⁴ W cm⁻². The Ehybrid hydrodynamic and atomic physics code was used to predict temperatures, densities and ionisation throughout the evolving iron plasma. The iron opacities were deduced taking into account free–free, bound–free and bound–bound absorption. Bound–bound absorption was considered using atomic data generated by the Opacity Project. Reasonable overall agreement between theory and experiment was obtained for the iron layer transmission. The simulations indicated the dominance of bound–bound absorption throughout most regions of the iron plasma, but also the potential importance of photoionisation from core levels where energetically possible.     

Propagation of small disturbances in a relaxing and radiating diatomic gas in vibrational nonequilibrium

In radiation gasdynamical problems, where the primary object of investigation is a moving gas, the influence of radiation on the parameters of the gas flow is usually neglected to avoid overcomplication of the problem. The growth and behavior of initial disturbances in a scattering, radiating, absorbing, viscous, heat-conducting gas characterized by local thermodynamic equilibrium has been investigated previously [1]. However, for low pressures (p10^–4 to 10^–3 technical atm) and fairly high temperatures of the active molecular degrees of freedom (T10³ to 3·10³K) the distribution of the molecules among the vibrational levels can differ markedly from the equilibrium distribution due to the or der-of-magnitude closeness of the vibrational relaxation time _c associated with collisions and the radiative deactivation time * of excited molecules [2, 3]. We now analyze normal modes in a vibrationally nonequilibrium medium with allowance for radiation scattering in the vibrational-rotational band. We formulate a dispersion relation and discuss some limiting cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 168–171, September–October, 1976.The author is grateful to V. I. Kruglov, Yu. V. Khodyko, and M. A. El'yashevich for their interest and discussions.     

Pressure fluctuations and heating of a gas by the inflow of a supersonic jet into a cylindrical cavity

The formation of pressure fluctuations at the inflow of a jet into a cavity (or the so-called resonance tube) was first observed by Hartmann. Further investigations showed that at the same time there is a heating of the gas in the cavity [1, 2]. It was established in [1, 2] that at subsonic and slightly supersonic velocities (M < 2.0) the cavity air can be heated up to 500–700 °K. Further investigations [4, 6] showed that by using monatomic gases inside the cavity one can reach even higher temperatures (T 800–900 °K). The resonance tubes find an application as powerful sound sources. There is also a possibility of their use in thermochemistry, and for the plasma production [6], In the literature, there is an absence of data on the resonance tube characteristics for large Mach numbers. In the present work we investigate the resonance tubes for M = 3.2–4.0. These investigations have shown that pressure oscillations can occur at these Mach numbers with the peak-to-peak amplitude of P 0.4·P_o, where P_o is the total pressure in the inflowing jet. Depending on the clearance between the nozzle and the cavity, both low- and high-frequency oscillations can be set up. It is established that the most intense shock-wave heating of the gas takes place at high-frequency fluctuations, although their amplitude is smaller in comparison with the low-frequency ones. It is shown that the cold air inside the cavity can be heated by means of the fluctuations up to T 1600 °K or more.Translated from Izvestiya Akamemii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–111, September–October, 1977.     

Criteria for excitation of a shock wave and its intensity during an explosion in a rarefied gas

The effect of the initial pressure of the surrounding gas on the intensity of the shock wave (SW) formed during the dispersion of material vaporized by a powerful laser pulse is examined. The initial stage of expansion of the plasma generated through the focusing of powerful laser radiation on the surface of a solid material in air was studied experimentally in [1, 2]. The times of formation and the initial radii of the SW were recorded on the photo-scans of the SW front radiation presented in these reports. It is found that at an air pressure below 0.1 mm Hg the recordings of the intrinsic radiation of a flare do not differ from the corresponding recordings in a vacuum. For instance, in [2] a bright shock front was observed at a pressure of 0.18 mm Hg, while at a pressure of 0.1 mm Hg SW radiation was not detected. In [2] the hypothesis was made that at an air pressure below 0.1 mm Hg a SW is not formed and the interaction of the vaporized material with the surrounding gas has a diffusion nature. However, in [1] SW were detected by the Schlieren method at a considerably lower pressure, about 2 · 10^–2 mm Hg. It will be shown below that the sharp decrease observed in the brightness of the radiation of SW fronts generated during laser heating of a solid material in a rarefied gas is explained by the rapid decrease in the maximum SW velocity at a pressure below 0.1 mm Hg. The expansion of the vaporized material at a pressure of the surrounding gas much less than 0.1 mm Hg is also examined.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–51, September–October, 1973.     

Contraction of a highly nonequilibrium current-bearing plasma

Contracted is the term applied to that inhomogeneous state of a plasma in which it withdraws from the enclosing walls and concentrates in a more or less thin layer through which a current passes. Contraction is the result of instability developed in the original homogeneous state and may be related to the existence of a volt-ampere characteristic segment with negative differential conductivity. This phenomenon is known in semiconductor physics, and various instability mechanisms leading to contraction have been studied [1], Well known in a low-temperature plasma is thermal contraction connected with superheating instability of the electron gas [2–4]. In the present study we will consider a highly nonequilibrium plasma in which contraction may develop as a result of disproportion in the number of electrons, i.e., contraction of a recombination-ionization character. We consider below the homogeneous state of a nonequilibrium weakly ionized plasma with charged-particle concentration n_e- 10¹¹-10¹³ cm^–3 (electron temperature T of the order of thousands of degrees, with gas cold). Disequilibrium is produced by the departure of radiation beyond the limits of the plasma volume. Such a state will be considered with respect to the instability noted, but not studied, in [5]. As a consequence of this instability the plasma may transform to an inhomogeneous (contracted) state, which is considered under conditions such that Joulean electron heating is compensated by losses due to elastic collisions with atoms of the gas. Charge diffusion plays the basic role in establishing the boundaries dividing the currentbearing region from that without current. More complex is the situation where radiation losses of energy are also significant and superheating, as well as ionization instability, is possible. This case is evaluated briefly at the close of the study.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 45–54, January–February, 1975.     

Effect of precursor radiation on the flow structure and ionization behind the shock front in inert gases

The problem of the propagation of strong, intensely radiating shock waves in inert gases is considered. It is shown that the heating of the shock tube walls by the precursor radiation, accompanied by an increase in the temperature of the adjacent gas, leads to the transverse stratification of the medium and to the disturbance of the one-dimensionality of the flow of shock-heated gas behind the wave front. Ionization kinetics calculations which take this into account indicate an acceleration of ionization near the tube walls, which is consistent with experiment. On the basis of the gas heating values obtained it is possible to establish critical values of the gas pressures ahead of the front and the shock wave Mach numbers, transition through which is accompanied by a radical restructuring of the flow with the formation of a configuration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–131, May–June, 1991.     

Determination of laser plasma temperature from study of radiation in roentgen and visible regions of spectrum

A laser plasma temperature of T_e 20 eV is determined by the foil method from measurements in the region of soft roentgen radiation. Measurements of radiation intensity in the visible region of the continuous spectrum give values of the temperature of T 15 eV for the part of the plasma which is opaque in the visible region of the spectrum.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 114–117, January–February, 1972.The authors are grateful to V. E. Panchenko and M. Yu. Lel'chuk for aid in conducting the roentgen measurements, as well as to A. M. Orishich and A. I. Shusharo for participating in the experiments on optical diagnostics.     

Screening of selective radiation in a boundary layer

An analysis of numerous calculations of the flow and radiative-convective heat exchange in a hypersonic shock layer near a blunt body, both at an impermeable surface [1] and in the presence of ablation [1–4], made it possible to establish some relationships connected with the screening in the boundary layer of radiation from the high-temperature part of the shock layer. It was established that the dependence of the screening coefficient of the boundary layer, which consists of the ratio of the integral flux q⁺ _RW of radiation incident on the body to the flux q⁺ _RW arriving at the outer limit of the boundary layer from the high-temperature region behind the shock wave, on the radius has a nonmonotonic character. In this case the absolute value of the minimum _min is determined mainly by the temperature T_S behind the shock wave and by the injection velocityf _W = (v)_W/(v), while its position (R_min) is determined by the pressure P_S in the shock layer. An analysis of the spectral characteristics of the screening of the boundary layer showed that the region of wavelengths > 0.5 m is very important from the point of view of the radiative heating and destruction of the surface. Components which efficiently absorb high-temperature radiation in this spectral interval are absent from the gaseous products of the disintegration of specific heat-protection coatings. An analysis is made permitting an evaluation of the possibility of introducing into the coatings additives possessing those optical and thermochemical properties which would provide for screening of radiation in this part of the spectrum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 71–77, September–October, 1978.The authors thank A. B. Karasev for advice and a discussion.     

Calculation of a wall-stabilized argon arc with account for radiative energy transfer

It was shown experimentally in [1, 2] and in a study by E. I. Asinovskii and A. V. Kirillin reported at the Scientific Technical Conference of the High-Temperature Scientific Research Institute held in 1964 that the heat transfer mechanism in a wall-stabilized argon arc was not purely purely conductive at gas temperatures greater than 11 000° K. Asinovskii and Kirillin also showed that radiative energy transfer is the reason why similarity is lost when the current-voltage characteristics are constructed in dimensionless form. The radiation of an argon arc has been studied experimentally by a number of authors [3–5], Dautov [6] calculated an argon arc without allowing for radiation.In this article an argon arc stabilized by the cooled duct walls is calculated with account for radiation using theoretically computed relationships describing the transport properties of argon plasma. A large portion of the radiated energy pertains to spectral lines whose role has been studied by L. M. Biberman. The authors have used I. T. Yakubov's data on argon radiation published in the journal Optics and Spectroscopy. A method of calculation and data on argon plasma radiation are also given in [7].Reference [8] deals with the problem of the role of radiation in an arc burning in nitrogen. In particular, the above-mentioned loss of similarity follows from the results of this work. However, the relationships used in this article to describe the transport properties of nitrogen plasma were obtained experimentally in [9].Notation r₀ arc radius (cm) - r variablesradius (cm) - T temperature (°K) - heat transfer coefficient (ergcm^–1sec^–1deg^–1) - E electric field intensity (g^1/2cm^–1/2sec^–1) - electrical conductivity (sec^–1) - q₁ heat flux density due to conduction - q₂ heat flux density due to radiation - u divergence of radiative energy flux density in the transparent part of the spectrum (ergcm^–3sec^–1) - u₂ same for part of the spectrum where reabsorption is taken taken into account - m₀ atomic mass - m_e electronic mass - Stefan-Boltzmann constant - h Planck constant - k Boltzmann constant - e electronic charge - p pressure - degree of ionization - N_e electron concentration (cm^–3) - n₀ neutral atom concentration - Q_0e electron-neutral collision cross section - Q_ie electron-ion collision cross section (cm²) - ₀ line center frequency (sec^–1) - ₊ line halfwidth (distance from line center to contour for ) due to effects giving dispersion contour - k _v absorption coefficient (cm^–1) - energy radiated by a hemispherical volume - emissivity of hemispherical volume - radius of hemispherical volume - S line intensity The authorS thank I. T. Yakubov for allowing them to use his data on arc plasma radiation.     

Water vapor cooling when radiation of wavelength λ=2.8 μm is absorbed

Investigations of the processes arising under the influence of electromagnetic radiation on resonantly absorbing gaseous media have now been widely developed. Particular interest is shown in the penetration of a pulse of laser radiation through the atmosphere. The main component absorbing the radiation of both CO₂ and HF lasers (wavelengths, respectively, 10.6 and 2.8 m) in the earth's atmosphere is water vapor [1]. Numerous experimental investigations show that the integrated coefficient of laser radiation absorption by water vapor is fairly large [1–3], while at the same time the energy absorption leads to the heating of the medium in a channel around the beam and, as a consequence, to its defocusing. However, all these investigations were carried out with continuous sources of laser radiation or with pulses of fairly great duration. It will be shown below that gas cooling in the channel around the beam is possible when a pulse of radiation with wavelength 2.8 m whose duration is less than the vibrational-translational (V-T) relaxation time of the energy absorbed by the H₂O molecules passes through a stationary medium containing water vapor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 141–151, May–June, 1986.     

Distribution of the electron concentration and wave processes in a pulsed discharge

A quantitative Schlieren method for measuring the electron-density gradient using a laser source in the infrared range is described, which guarantees measurement of densities above 10¹⁴ cm^–2; a detailed observation of the profile of the gas ionization in a pulsed discharge is likewise described. Certain results are presented of a study of the distribution of the electron concentration over the cross section of the discharge tube in a straight argon discharge during the flow of discharge current and also during the subsequent stages of the process. In order to perform time measurement of the electron-density gradients and to construct an overall picture of the plasma distribution, the Schlieren method with a CO₂ laser (10.6 ) as a light source was used. The measurements that were carried out revealed a complex picture involving the formation of a series of successive radial compression waves that exist during a fairly long period after completion of the discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 15–20, March–April, 1971.     

Experimental investigation of return currents in electrogasdynamic flows

An investigation is made of return electric currents in electrogasdynamic flows for laboratory sources of unipolar charged particles. These currents play an important role in the process of airplane electrification as a result of the work of jet engines. Models have been built, making it possible to study the behavior of return currents outside and inside an axisymmetric electrogasdynamic flow, in the absence (single-contour source) and the presence (double contour source) of an external annular neutral jet. It is shown that a rise in the return current J^– outside an electrogasdynamic jet is accompanied by a decrease in the take-off current J °. A decrease in the relative distance L from the source to an external grounded surface and an increase in the ratiov of the velocity of the external neutral jet to the velocity of the electrogasdynamic flow lowers J^– in both grounded and insulated models; in the latter case, where J ° J°0, there is an appreciable return current outside the jet. With an increase in the potential of the source from =0 to the floating potential, the current J^– rises, attaining a maximum, and then decreases. This effect is observed also when J^–=0 in both grounded and insulated models. For the case L–1,v=1, the theoretical and experimental dependences of J^– on the potential of the source , retarding the charged particles of the flow under transitional conditions, are in satisfactory agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 127–134, January–February, 1978.In conclusion, the authors thank A. B. Vatazhin for his interest in the work, and A. P. Strekal and V. F. Kudryashov for their participation in the experiments.     

Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection)

An analysis is carried out to study the effects of localized heating (cooling), suction (injection), buoyancy forces and magnetic field for the mixed convection flow on a heated vertical plate. The localized heating or cooling introduces a finite discontinuity in the mathematical formulation of the problem and increases its complexity. In order to overcome this difficulty, a non-uniform distribution of wall temperature is taken at finite sections of the plate. The nonlinear coupled parabolic partial differential equations governing the flow have been solved by using an implicit finite-difference scheme. The effect of the localized heating or cooling is found to be very significant on the heat transfer, but its effect on the skin friction is comparatively small. The buoyancy, magnetic and suction parameters increase the skin friction and heat transfer. The positive buoyancy force (beyond a certain value) causes an overshoot in the velocity profiles.A mass transfer constant - B magnetic field - C_fx skin friction coefficient in the x-direction - C_p specific heat at constant pressure, kJ.kg^–1.K - C_v specific heat at constant volume, kJ.kg^–1.K^–1 - E electric field - g acceleration due to gravity, 9.81 m.s^–2 - Gr Grashof number - h heat transfer coefficient, W.m².K^–1 - Ha Hartmann number - k thermal conductivity, W.m^–1.K - L characteristic length, m - M magnetic parameter - Nu_x local Nusselt number - p pressure, Pa, N.m^–2 - Pr Prandtl number - q heat flux, W.m^–2 - Re Reynolds number - Re_m magnetic Reynolds number - T temperature, K - T_o constant plate temperature, K - u,v velocity components, m.s^–1 - V characteristic velocity, m.s^–1 - x,y Cartesian coordinates - thermal diffusivity, m².s^–1 - coefficient of thermal expansion, K^–1 - , transformed similarity variables - dynamic viscosity, kg.m^–1.s^–1 - ₀ magnetic permeability - kinematic viscosity, m².s^–1 - density, kg.m^–3 - buoyancy parameter - electrical conductivity - stream function, m².s^–1 - dimensionless constant - dimensionless temperature, K - w, conditions at the wall and at infinity     

Diagnosis of a hydrogen plasma by beams of helium atoms of different energy

The underlying theory is described for a method of diagnosing a hydrogen plasma by means of beams of helium atoms of different energy. The range of measured density is 10¹⁴ to 10¹⁶ cm^–3 with a length of plasma section probed 10 cm. The highest accuracy ( ± 20%) is attained in the middle of the range. The accuracy in measuring electron temperature from 10 to 50 eV is no worse than 10–30%. Higher temperatures can be determined with an accuracy of the same order. Methods have been developed in recent years for active diagnosis of a high-temperature plasma using beams of fast neutral particles [1–5]. These methods, in spite of involving somewhat unwieldy apparatus, promise to permit the study of a plasma in the range of parameters difficult to investigate by traditional methods (probes, microwave equipment, and so on). In addition, they have relatively high timewise and spatial resolutions and are noncontact methods in practice.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 11, no. 2, pp. 7–11, March–April, 1970.     

Low-density jets beyond a sonic nozzle at large pressure drops

The gas-dynamical structure of jets of a low-density diatomic gas beyond a sonic nozzle at large pressure drops under conditions of a transition from continuous medium processes to rarefied gas processes is examined on the basis of experimental data obtained in low-density gas-dynamical tubes using electron-beam diagnostics and the Pitot tube method. Isomorphism is shown in the density distribution and total pressure in all cross sections of the jet with respect to pressures at a constant value of the complex R_L=R_*/N^1/2(R_* is the Reynolds number in the critical cross section of the nozzle, and N is the ratio of the Pitot pressure and the pressure in the discharge chamber). It is shown on the basis of a comparison of local Reynolds numbers for all zones of the jet that this is an analog complex. The experimental data on the variation in the jet structure are presented as a function of the number R_L in the range of 5–600. For R_L> 100 the flow in the jet can be considered as continuous; for R_L< 5–10 the flow corresponds to a scattering process; the range of 5–10< R_L< 100 corresponds to a transitional state. Ranges of isomorphism of the jet with respect to R_* and N are indicated. Based on the results of the measurements, it is shown that the flow behind a Mach disk for R_L> 200 remains subsonic on the axis to a distance of several lengths of the primary cycle. A transition to supersonic velocity on the jet axis can occur with a decrease in the numbers R_L owing to ejection acceleration by the supersonic ring-shaped compressed layer.This word is apparently interchangeable with self-similarity-Translator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–73, March–April, 1973.     

Radiational properties of the decomposition products of a model around which flows a subsonic high-temperature plasma stream

Models made of an asbestos plastic were tested in a subsonic jet of air heated to T = 8500 °K with p = 1 atm. The multicomponent thermal boundary layer arising at the decomposing surface of the model has a complex structure. At the surface of the model, in the critical region of the boundary layer, there is a sublayer with an extension of 1.5-2 mm where the temperature of the gas is constant and its composition is unchanged to a great degree and is mainly determined by the decomposition products of the asbestos plastic. In this region the spectral distribution of the intensity of the radiation of the vapors of the asbestos plastic was obtained in a range of 0.3-0.9, which makes it possible to calculate the spectral coefficients of absorption for a temperature of 3500 °K. The radiating power of the vapors is compared with the radiation of an air plasma of the oncoming flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 76– 80, November–December 1978.The authors are indebted to Yu. K. Rulev for his aid in carrying out the experiment.     

Nonmagnetic containment of a dense plasma

A study is made of the possibility of confining a thermonuclear plasma with temperature T 10⁴ eV and density n 10¹⁸ cm^-3, not by magnetic field pressure, but by hard walls of a chamber (nonmagnetic containment). This method of plasma containment has some specific features: the occurrence of plasma flow, formation of a dense layer at the wall, increased importance of radiative losses from the plasma, and more. A numerical solution of the plasma-transport equations is used to investigate the influence of these features on the energy lifetime of the plasma. The results indicate that the additional energy losses by the plasma are not catastrophically large, and, in principle, nonmagnetic containment of a dense plasma is possible.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 3–13, November–December, 1974.     

Radiative heat transfer in an emitting,absorbing, and scattering compressed layer

The aim of the paper is to investigate the screening of radiation from the high-temperature part of the compressed layer by the two-phase ablation products of a graphite axisymmetric body moving under the following conditions through a hypersonic air flow: V = 12–18 km/sec, p_s = 10⁵ Pa, R = 1–3 m, and /₀ = (2.54–5.73)·10^–4. Steady and unsteady sublimation regimes of graphite ablation with strong blowing are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1984.     

Interferometric study of natural convection in rectangular air cavities of various orientations

The results of an experimental investigation into the temperature profiles and heat transfer associated with natural convection in rectangular air cavities are presented, the angle of inclination varying from 0 (heating at the bottom) to 180° (heating at the top). The range of Rayleigh numbers was R=2.68·10³–2.57·10⁵, and n=H/d=5.06–18.3. The investigation was carried out by an optical method, using an IZK-454 interferometer. For a horizontal orientation of the cavity the heat-transfer data satisfy the relation N=0.216 R^0.25, for a vertical orientation N=0.144 R^0.3h^–0.129, where N is the Nusselt number. In the region of an inclination of 30° the heat transfer passes through a maximum under all conditions studied.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 89–93, July–August, 1972.     

Screening of a surface vaporizing under laser bombardment,at temperature and ionization disequilibrium

The kinetics of the process through which vapor released from the surface of a solid is heated by laser radiation are calculated. The data indicate the existence of temperature and ionization disequilibrium (for Al at incident flux densities q over 50 MW/cm² in times of the order of 1sec or less). Treatment of this disequilibrium lowers the critical flux density q_* corresponding to the onset of screening within a specified time t, or within the time t_* required for screening to develop at a specified flux density q, appreciably, as compared to the values obtained in the equilibrium theory of the process. Some of the other physical processes that might have some effect on flare behavior are also discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 35–45, September–October, 1971.In conclusion, the authors express their thanks to A. I. Petrukhin and V. I. Bergel'son for valuable discussions and for kindly making available experimental and theoretical data, to V. A. Onishchuk for performing calculations of the absorption coefficients, and to V. V. Novikov for helpful assistance in the calculations.