V. G. Novikov

Study of the radiation spectra of fast Z-pinches formed during the implosion of wire arrays in the Angara-5-1 facility

Results are presented from measurements of the radiation spectra of the Z-pinch tungsten plasma produced during the implosion of cylindrical wire arrays with a linear mass of 200–400 μg/cm and an initial diameter of 12–20 mm at a current of ∼3 MA in the experiments performed at the Angara-5-1 facility. The radiation spectra in the photon energy range of 50–900 eV were recorded on a UF-4 X-ray film by using a spectrograph with a transmission grating. The radiation spectrum in the photon energy range of 1–3 keV was recorded using a crystalline panoramic spectrograph. A curtain shutter was used to protect the transmission grating from fast microparticles produced due to the erosion of high-voltage electrodes. The total radiation yield was measured with a thermocouple calorimeter. It is shown that most of the tungsten plasma radiation energy is emitted in the photon energy range of 80–300 eV. Measurements of the spectral intensity of pinch radiation with a spatial resolution along the pinch radius showed that the effective transverse diameter of the pinch did not exceed 2 mm, which agrees with independent current measurements of the pinch size. The results of measurements of the spectral intensity of pinch radiation were compared with calculations per-formed under the assumption of a stationary homogeneous plasma.

Calculations of the equation of state by the Liberman mode

The algorithm of the calculation of self-consistent atomic potential accounting for resonant states of electrons is developed by the Liberman model. The resonant states are related to quasi-stationary states of electrons and appear at the squeezing of bound levels of energy into continuum accompanied by an increase in the density of a substance. Such states play an important role in calculations of thermodynamic functions of substance, since they facilitate the smooth dependences of pressure and internal energy on density. Appropriate software (RESEOS) was developed and calculations of the equations of state of aluminum and uranium were performed in a wide range of temperatures and densities. The resulted shock adiabats were compared with the experimental data.

Modeling of the emission spectra of tungsten plasma

A model of nonequilibrium radiating multicharge ion plasma, which takes into account the radiation transport and level kinetics of electrons, is constructed. The model allows one to obtain the properties of plasma with arbitrary optical thickness. On the basis of this model, emission spectra of tungsten plasma were calculated, which are of interest in connection with studying high-current multiwire liners. Computations were carried out by the THERMOS & BELINE program package for plane and cylindrical plasma layers at temperatures T = 30–150 eV and densities ρ = 0.01–0.03 g/cm3. In a number of the most important cases, the computation results were corrected both for the spectral line positions and a more realistic geometry of the liner.

Soft X-ray spectrum of laser-produced aluminum plasma

Soft X-ray spectra (30–70 Å) of aluminum plasma have been measured in experiments carried out at the Kanal-2 laser facility at laser intensities of (1–7) × 1013 W/cm2. It is shown that the measured spectra satisfactory agree with those calculated using the RADIAN numerical code.

Methods and results of studies of the radiation spectra of megampere Z-pinches at the angara-5-1 facility

Methods and results of studies of the radiation spectra of high-current Z-pinches with different elemental compositions are presented. To examine a wide spectral range (Ehν = 30–3000 eV), two diagnostics tools were used—a transmission grating and a reflecting mica crystal. The radiation characteristics of the pinch are determined by its elemental composition. For currents of 2–3 MA and low-Z elements (aluminum), the hard end of the radiation spectrum is represented by spectral lines with clearly pronounced K lines, while for high-Z elements (tungsten), the spectrum lies in the softer photon energy range and is quasi-continuous. Two methods of spectrum processing were used to determine the plasma parameters. The parameters of aluminum plasma were traditionally determined from the intensity ratios of the K lines taking into account the plasma transparency for these lines. The spectra of tungsten plasma were compared with the results of computer simulations of pinch compression with allowance for both magnetohydrodynamic and plasma radiation processes. The applicability of these methods of spectral analysis is discussed.

Mesh-ray model and method for calculating the laser radiation absorption

The present paper puts forward a mathematical model of laser radiation absorption in a laser target, which combines approximations of geometrical and wave optics and the corresponding numerical algorithm. This model depends on the principles of geometrical optics in the range of weak variation of the plasma refractive index on the scale of the wave length. This enables one to describe the refraction of the radiation. A transition to wave approximation is carried out near the surface of critical density, where the approximation of the geometrical optics is a fortiori inapplicable. For this aim, the plasma medium is approximately represented as a set of plane layers, on which the one-dimensional Helmholtz equation is solved. This makes it possible to construct a simple and relatively accurate method for calculating the absorption and reflection of laser radiation near the critical density surface in order to effectively take into account the dependence of the interaction of radiation with matter on the polarization direction, etc. The proposed model is adapted for implementation in the radiation gas dynamics (RGD) code. A numerical computation subroutine is presented based on the analytical solution of the differential equations corresponding to the optical ray model of the laser radiation energy flux. This solution is obtained under the assumption that the squared gradient of the refractive index is constant in any cell of the mesh. The convergence rates of the proposed algorithms are estimated using the data obtained in the numerical experiments.

Peculiarities of calculating entropy in self-consistent field models

The calculation of entropy in the self-consistent field models faces some difficulties related to the entropy behavior peculiarities at low temperatures in the models with different degrees of specification of the electron energy spectrum. This paper considers the behavior of the electron entropy in two self-consistent field models that have been widely used lately, namely the Liberman model and the quasi-zone model. Special attention is focused on low temperatures. In particular, it is shown that the entropy of electrons in the Liberman model at low densities and the temperature T = 0 takes on nonzero values which differ in the relativistic and nonrelativistic versions of the model. The electron entropy in the quasi-zone model at low densities of the matter and T = 0 is zero. In addition, it is shown that at low temperatures and high densities the entropy in the Liberman model smoothly turns to the asymptotic form of the Thomas-Fermi (TF) model, while such a smooth transition to the TF asymptotic form is not always observed in the quasi-zone model.

3D simulation of the impact made by a noncentral laser pulse on a spherical tin target

A mathematical model for plasma dynamics is described based on a fully conservative difference scheme for three-dimensional equations of radiation gas dynamics. The model has been implemented using a 3DLINE code for calculations of the physical processes for a target exposed to central and noncentral laser pulses in order to obtain a radiation source with prespecified properties.

Calculation of output power and X-ray spectrum of Z-pinches based on multiwire arrays

We present mathematical models and methods of the computational experiment using a three-dimensional RMHD model simulating the implosion of Z-pinches formed by an imploding cylindrical array of thin tungsten wires. The calculations take into account the discrete structure of the array and the extended plasma formation at the evaporation of the wire material and they yield the estimated values of the output power and X-ray spectrum. The data are presented on the spatio-temporal distribution in the parameters of the Z-pinch plasma, including the velocity, electron and ion temperatures, ionization degree, and the power output integrated over space. We have also calculated the characteristics of the Z- pinch X-ray spectrum depending on the photon energy at different times after the discharge current starts. It has been found that the trailing mass of tungsten on the periphery affects the emission intensity of the central part of the pinch in the radial direction, which can be explained by the emission absorption in the peripheral plasma layers of the trailing tungsten mass. A detailed model has been constructed of the central pinch formed by the electric current implosion of the material of multiwire tungsten arrays. This model enables one to calculate the intensity of the soft X-ray emission with a temporal, spatial, angular, and spectral resolution for specific experiments on the Angara-5-1 experimental complex intended to study the implosion of cylindrical multiwire arrays, for which there is sufficient information about the time profile of the absolute emission intensity in the low-energy range of the X-ray emission. The obtained numerical results can be directly compared with the experimental values. The RMHD model simulating the implosion of Z-pinches has been verified by comparing its results with the experimental implosion indicators.

Numerical modeling of a pinch in a vacuum diode with laser ignition

The present paper is concerned with the mathematical model and methods of numerical analysis of processes in plasma created in a vacuum chamber by means of a discharge initiated on a cathode by a pulsed laser. The model is capable of describing in a two-dimensional approximation the formation of a plume’ of laser plasma and the magneto-hydrodynamic effects (pinching, etc.) due to the current in the plasma. The results of the first numerical experiments with this model are presented.