Geodesic
On the calculation of radiative heat transfer in a composite Z-pinch
Matematičeskoe modelirovanie, Tome 34 (2022) no. 9, pp. 21-36.

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A method for calculating the radiative energy transfer in the Schuster-Schwarzschild approximation, which is used for numerical simulation of the implosion of a composite shell-like Z-pinch under the action of the magnetic field of a high-current generator, is discussed. A significant part of the kinetic energy of the accelerated plasma shell, upon impact with the central insert, is converted into the energy of soft thermal X-ray radiation. The key element of the technique necessary for optimizing the conditions of the experiment on the conversion of the kinetic energy of the plasma shell into thermal radiation is the scheme for calculating radiant heat transfer in a medium with opacity that varies greatly in space and time. The numerical technique proposed for multiparameter computational experiments makes it possible to obtain the dependence of the radiation energy density in the form of a quadrature on the opacity coefficient and plasma emissivity. In the two-temperature model of magnetic plasma implosion, this determines the contribution of radiant heat transfer to the energy balance of the electronic component.
Keywords: mathematical model, current-carrying plasma, Z-pinch, energy transfer by radiation. 
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V. A. Gasilov; A. Yu. Krukovskiy. On the calculation of radiative heat transfer in a composite Z-pinch. Matematičeskoe modelirovanie, Tome 34 (2022) no. 9, pp. 21-36. http://geodesic.mathdoc.fr/item/MM_2022_34_9_a1/

[1] S. G. Alikhanov, L. I. Rudakov, V. P. Smirnov, I. R. Yampolskiy, “Primenenie metodov rentgenovskoi i VUF spektroskopii dlia diagnostiki impulsnykh plazmennykh istochnikov”, Pisma v ZhTF, 5 (1979), 1395

[2] V. N. Mokhov i dr., “O vozmozhnosti resheniia problemy upravliayemogo termoiadernogo sinteza na osnove magnitogazodinamicheskoi kumuliatsii energii”, DAN SSSR, 247 (1979), 83

[3] R. B. Spielman et al, “Increased X-ray power generated from low-mass large-number aluminum wire-array Z-pinch implosions”, J. Appl. Phys., 57 (1985), 830 | DOI

[4] D. B. Sinars et al, “Review of pulsed power-driven high energy density physics research on Z at Sandia”, Phys. Plasmas, 27 (2020), 070501 | DOI

[5] K. N. Mitrofanov et al, “Progress in researching the implosion of nested arrays of mixed composition and the generation of soft x-ray power pulse”, Plasma Phys. Control. Fusion, 64 (2022), 045007 | DOI

[6] Ya. B. Zel'dovich, Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Dover Books on Phys., N.Y., 2012, 653 pp.

[7] V. A. Gasilov, S. V. Zakharov, V. P. Smirnov, “O generatsii moshchnykh potokov izlucheniia i poluchenii megabarnykh davlenii v lainernykh sistemakh”, Pisma v ZhETF, 53:2 (1991), 15–18

[8] V. A. Gasilov, S. V. Zakharov, A. Yu. Krukovskiy, “Generatsiia intensivnykh potokov izlucheniia i megabarnykh udarnykh voln szhimaiushchimisia lainerami”, Fizika plazmy, 21:5 (1995), 399–406

[9] A. A. Samarskiy, Yu. P. Popov, Raznostnye metody resheniia zadach gazovoi dinamiki, Uchebnoe posobie: Dlia vuzov, 2-e izd., dop., Nauka. Fizmatlit, M., 424 pp. | MR

[10] B. N. Chetverushkin, Matematicheskoe modelirovanie zadach dinamiki izluchaiushchego gaza, Nauka, M., 1985, 304 pp.

[11] A. S. Boldarev, V. A. Gasilov, A. Yu. Krukovskiy, Yu. A. Poveshchenko, “The Technique of Solving Magnetohydrodynamic Problems in Quasi-Lagrangian Variables”, Mathematical Models and Computer Simulations, 14:1 (2022), 10–18 | DOI | MR | Zbl

[12] V. A. Gasilov, A. S. Chuvatin, A. Yu. i dr. Krukovskiy, “Kompleks programm “Razriad”: Modelirovanie uskoreniia plazmy v silnotochnykh impulsnykh sistemakh”, Matem. modelirovaniye, 15:9 (2003), 107–124 | Zbl

[13] R. M. More, K. H. Warren, D. A. Young, G. B. Zimmerman, “A new quotidian equation of state (QEOS) for hot dense matter”, Phys. Fluids, 31 (1988), 3059 | DOI | Zbl

[14] V.G. Novikov, A.D. Solomiannaia, I.Iu. Vichev, A.S. Grushin, Svidetelstvo o gosudarstvennoi registratsii programmy dlia EVM. THERMOS: Biblioteka funktsii dlia rascheta radiatsionnykh i termodinamicheskikh svoistv razlichnykh veshchestv i smesei v shirokoi oblasti temperatur i plotnostei, pravoobladatel IPM im. M.V. Keldysha RAN, No 2013616315; zaiavl. 27.05.2013; zareg. 03.07.2013

[15] P. Feautrier, “Sur la resolution numerique de l'equation de transfert”, Comptes Rendus Academie des Sciences Paris, 258 (1964), 3189

[16] G. B. Rybicki, “A modified Feautrier method”, J. Quant. Spectrosc. Radiat. Transfr., 11 (1971), 589–595 | DOI

[17] A. Benuzzi-Mounaix, M. Koenig, A. Ravasio et al., “Laser-driven shock waves for the study of extreme matter states”, Plasma Phys. Control. Fusion, 48 (2006), B347–B358 | DOI