An algorithm for calculating the plasma composition based on the improved Raizer method is described in detail. The results of calculations by this method and by solving the system of the Saha equations, taking into account the degeneracy of electrons, are compared. A method of solution of scalar equation is proposed, which is just as reliable as the dichotomy method and is faster than the Brent method in calculating the composition of a multicomponent plasma. Formulas for calculation of thermodynamic functions of the plasma are given.
A semiempirical mathematical model of motion of the center of mass of a spinning projectile in the atmosphere is proposed. This model takes into account the effects of the derivation and change in the frontal resistance due to variation in the angle of attack. These effects are accounted for without a detailed description of spinning in our model, which allows using a large integration step and provides the capability of real-time computation of ballistic corrections. The selection procedure of the model parameters for real weapon systems is described in detail.
We propose a new mathematical technique for processing of experimental data measured with large errors. The method is applied to all available experiments on 4 major thermonuclear reactions taken into account in simulations of deuterium and deuterium-tritium fusion targets. We present new approximations for the dependence of the cross sections on energy and for the dependence of the reaction rates on temperature. Along with these approximations, we propose a procedure allowing to estimate their confidence belts. Such estimations were not known before. New approximations provide error similar to 0.3% for the cross sections and similar to 4% for the reaction rates. The present data are up to similar to 5 times more accurate than reported in literature.
A database on the thermodynamic properties of materials under extreme conditions is described. The first version of the base includes tables of pressure, energy, and entropy for 103 elements of the Periodic system in wide ranges of temperature and density. The database is developed at the Keldysh Institute of Applied Matematics, Russian Academy of Sciences, and can be accessed via links http://tefis.keldysh.ru and http://tefis.ru.
The equation of state for gaseous plasma is well described bу the Saha model. In this work, accounting for the finite ion core volume is included in this model. This improvement allows the expansion of the Saha model to superhigh densities and moderate temperatures, where plasma can be considered as a liquid. In this domain, the thermodynamics of the Saha model is quite close to that of the Thomas–Fermi model with corrections (TFC), which is conventionally used for condensed matter. This improved the agreement of the theory with experimental data. Using a special interpolation, the Saha model and the TFC model are united in a single equation of state, in which the strict thermodynamic consistency of all quantities is provided. The latter is very important for the application of the equation of state in gasdynamic calculations.
Analyzing the results of ballistic experiments often brings up the problem of restoring the input computation parameters of the exterior ballistics of a body (the ballistic coefficient, the initial velocity, the environment temperature, the pressure, etc.) by the results of trajectory measurements (the reverse problem of exterior ballistics). It is found that without a priori information on unknown parameters, the problem in question cannot have a unique solution. We propose a procedure of solving the reverse problem with a priori information at hand; this procedure rests on the least-squares method and the maximum-likelihood method. An algorithm for solving the reverse problem is described in detail (the described algorithm implements the proposed procedure). We consider applying this procedure to the problem of restoring the initial departure conditions and atmospheric parameters, as well as to the problem of simultaneously determining the initial velocity of the body and its ballistic coefficient.
Modern gas dynamic codes use equations of state (EOS) of substances. These EOS must have good accuracy in a wide range of temperatures and densities and must be thermodynamically self-consistent. In the present paper, we describe new improvements of the ionization equilibrium model for plasma. They account for finite volumes of ion cores and partial electron degeneration. This permits to expand this model to the super high densities and low temperatures. Thus, the enhanced Saha model becomes a wide range EOS itself.
A plasma equation of state in a gas domain is derived from Saha model accounting for ion cores. Calculations for Cu are performed using the stiff ion core model for densities of up to 106 g/cm3. A compressible ion core model is also developed. The Tomas–Fermi model is applied to condensed plasma. Both models are unified into a thermodynamically consistent equation of state.
A model of the ionization equilibrium of plasma (the Saha model) is constructed while taking into account the degeneracy of free electrons and the inherent volume of ion cores. The absence of corrections on the charge-particle interaction (the corrections on nonideality) is substantiated. The calculations showed that taking into account the inherent volume of ion cores explains the phenomenon of ionization by compression at high density and taking into account the degeneracy substantially improves the accuracy of thermodynamic functions in this region. All this makes it possible to advance the model of ionization equilibrium far beyond the gas region and extend it into the region of liquid plasma.
The Holtsmark distribution is simulated by the Monte Carlo method. Convergence of the Monte Carlo calculation to this distribution is estimated empirically. The problem of the infinite density of energy in the Holtsmark model is considered and ways to solve it are discussed.
An original model of a plasma microfield constructed from first principles is much more advantageous than the earlier ones. The validity of the model is confirmed by optical measurements. The thermodynamics of a gaseous plasma is qualitatively described by a new ionization equilibrium model in which the interaction between charged particles is accounted for by means of a self-consistent plasma microfield. Numerical simulations show that, in this new model, nonideal effects are insignificant even at high plasma densities, and there are no phase transitions in a gaseous plasma, a conclusion that agrees with experimental data. The model is tested against the popular models of nonideal plasma and the SESAM database.
A compensated microfield model of plasma nonideality is proposed as an improvement of the traditional microfield models. In this model, a double contribution of a microfield to the truncation of statistical sums removed. The new method of truncation of the statistical sums of atoms or ions is compared with the results of experiments and computations performed by well-known Debye-type and other models. It is shown that only the microfield model correctly describes experiments. Ionization of Li and Hg atoms is calculated. The effect of metallization of plasma—an abrupt increase of ionization from zero to a single ionization at low temperatures and nearly normal densities—is qualitatively described. The results of calculation of Hg vapor ionization qualitatively agree with known experimental results on the measurement of electric conductivity of this vapor.
A self-consistent model with compensation for strongly coupled plasma is described. The effective algorithm to solve the equations of this model is proposed. The calculation of the ionization tables is performed. This model is compared with the Thomas-Fermi model with quantum and exchange corrections (TFC) and with the self-consistent model of ionization equilibrium without compensation. It is established that the model is in agreement with the TFC model for rarefied and rather dense plasma and differs from it for condensed matter. The effects of plasma non-ideality and electron degeneration are considered.
An efficient and reliable algorithm for selecting the optimal exposure in video cameras of technicalvision systems is proposed. The algorithm is based on the Otsu binarization method. A theoretical justification of the convergence of the proposed algorithm is given. At the end of the paper, we discuss software and hardware aspects of a real-world implementation of our algorithm, which confirmed its efficiency and stability.
