Modelling of the Thermodynamic Properties

A. S. Polyukhin

Russian journal of nonlinear dynamics, Tome 17 (2021) no. 1, pp. 49-57.

Résumé

Numerical modelling of the thermodynamic properties of plasma mixture is performed using the Thomas – Fermi model with two different approaches. For this purpose, a numerical algorithm, as well as program realization, is developed to solve the Thomas – Fermi equations with quantum-exchange corrections. For the first time a comparison between different methods for taking account of the heterogeneous composition of plasma is made and an algorithm for estimating the corrections for mixtures is developed.

Détail

Keywords: computational model, magnetized plasma, numerical method, thermodynamic property.

Bibliographie

[1] Zel'dovich, Ya. B. and Raizer, Yu. P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover, New York, 2002, 178 pp.

[2] Ryzhkov, S. V. and Chirkov, A. Yu., Alternative Fusion Fuels and Systems, CRC Press, Taylor Francis Group, Boca Raton, Fla., 2019, 210 pp.

[3] Shemyakin, O. P., Levashov, P. R., and Krasnova, P. A., “TFmix: A High-Precision Implementation of the Finite-Temperature Thomas – Fermi Model for a Mixture of Atoms”, Comput. Phys. Commun., 235 (2019), 378–387 | DOI

[4] Kuzenov, V. V. and Shumaev, V. V., “Description of the Thermodynamic Properties of Plasma in Saha and Thomas – Fermi Models”, Prikl. Fiz., 2015, no. 2, 32–36 (Russian)

[5] Nikiforov, A. F., Novikov, V. G., and Uvarov, V. B., Quantum-Statistical Models of Hot Dense Matter: Methods for Computation Opacity and Equation of State, Progr. Math. Phys., 37, Birkhäuser, Basel, 2005, 34 pp. | MR | Zbl

[6] Zh. Èksper. Teoret. Fiz., 32:1 (1957), 115–123 (Russian) | MR | Zbl

[7] Belov, A. A., Golovanov, R. V., Kalitkin, N. N., Kozlitin, I. A., Koryakin, I. A., and Kuzmina, L. V., TEFIS Database. Thermodynamic Functions of Substances, Preprint No. 219, KIAM, Moscow, 2018, 20 pp. (Russian)

[8] Kuzenov, V. V. and Ryzhkov, S. V., “Calculation of Plasma Dynamic Parameters of the Magneto-Inertial Fusion Target with Combined Exposure”, Phys. Plasmas, 26:9 (2019), 092704 | DOI

[9] Kuzenov, V. V., Ryzhkov, S. V., and Shumaev, V. V., “Computer Analysis of Transport, Optical and Thermodynamic Properties of Plasma”, High Temp. Mater. Process., 18:1–2 (2014), 99–109 | DOI

[10] Kuzenov, V. V. and Ryzhkov, S. V., “Radiation-Hydrodynamic Modeling of the Contact Boundary of the Plasma Target Placed in an External Magnetic Field”, Prikl. Fiz., 2014, no. 3, 26–30 (Russian)

[11] Kuzenov, V. V. and Ryzhkov, S. V., “Mathematical Modeling of Plasma Dynamics for Processes in Capillary Discharges”, Russian J. Nonlinear Dyn., 15:4 (2019), 543–550 | MR | Zbl

[12] Uspekhi Fiz. Nauk, 165:2 (1995), 121–142 (Russian) | DOI | DOI

[13] Golovanov, R. V. and Lutskii, K. I., “Computation of the Integral Fermi – Dirac Function”, Math. Models Comput. Simul., 4 (2012), 464–470 | DOI | MR

[14] Dyachkov, S. A. and Levashov, P. R., “Region of Validity of the Finite-Temperature Thomas – Fermi Model with Respect to Quantum and Exchange Corrections”, Phys. Plasmas, 21:5 (2014), 052702, 6 pp. | DOI

[15] Kuzenov, V. V., Ryzhkov, S. V., and Shumaev, V. V., “Numerical Thermodynamic Analysis of Alloys for Plasma Electronics and Advanced Technologies”, Probl. Atom. Sci. Tech., 98:4 (2015), 53–56

[16] Kuzenov, V. V., Ryzhkov, S. V., and Shumaev, V. V., “Thermodynamic Properties of Magnetized Plasma Evaluated by Thomas – Fermi Model”, Prikl. Fiz., 2014, no. 3, 22–25