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Empirical Stationary Condition of Two-Dimensional Flows of Ionizing Hydrogen in the Plasma Accelerator Channel

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Abstract

Stationary and unstable pulsating flows of ionizing hydrogen in the channel of a quasi-stationary plasma accelerator are considered. Numerical studies of two-dimensional axisymmetric flows are carried out based on the modified magnetogasdynamic (MGD) equations in the approximation of local thermodynamic equilibrium, taking into account electrical conductivity, thermal conductivity, and radiation transport. The generalization of the calculation results led to the formulation of the empirical condition for the stationarity of two-dimensional flows of an ionizing gas.

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RЕFERENCES

  1. S. I. Braginskii, “Transfer phenomena in plasma,” in Problems in the Theory of Plasma, Issue 1, Ed. by M. A. Leontovich (Gosatomizdat, Moscow, 1963), pp. 183–272 [in Russian]; English transl.: S. I. Braginskii, “Transport processes in plasma,” in Reviews of Plasma Physics, Vol. 1, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1965), pp. 205–311.

  2. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Nauka, Moscow, 1966; Dover, Mineola, NY, 2002).

  3. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, New York, 1973).

  4. A. I. Morozov, Introduction to Plasma Dynamics (Fizmatlit, Moscow, 2008; CRC Press, Boca Raton, FL, 2013).

  5. A. I. Morozov, “Principles of coaxial (quasi)stationary plasma accelerators (QSPA),” Sov. J. Plasma Phys. 16, 63–78 (1990).

    Google Scholar 

  6. N. Klimov, V. Podkovyrov, A. Zhitlukhin, D. Kovalenko et al., “Experimental study of PFCs erosion under ITER-like transient loads at plasma gun facility QSPA,” J. Nucl. Mater. 390–391, 721–726 (2009). https://doi.org/10.1016/j.jnucmat.2009.01.197

    Article  Google Scholar 

  7. A. N. Kozlov, S. P. Drukarenko, N. S. Klimov, A. A. Moskacheva, and V. L. Podkovyrov, “The experimental research of the electric characteristics of discharge in the quasi-steady plasma accelerator with the longitudinal magnetic field,” Vopr. At. Nauki Tekh., Ser.: Fiz. Plazmy, No. 1, 92–94 (2009).

  8. N. S. Klimov, D. V. Kovalenko, V. L. Podkovyrov, D. M. Kochnev, A. D. Yaroshevskaya, R. V. Urlova, A. N. Kozlov, and V. S. Konovalov, “Experimental study of integrated characteristics of plasma stream and discharge of a quasi-stationary high-current plasma accelerator with its own magnetic field,” Vopr. At. Nauki Tekh., Ser.: Termoyad. Sint. 42 (3), 52–63 (2019). https://doi.org/10.21517/0202-3822-2019-42-3-52-63

  9. V. I. Tereshin, A. N. Bandura, O. V. Byrka, V. V. Chebotarev, I. E. Garkusha, I. Landman, V. A. Makhlaj, I. M. Neklyudov, D. G. Solyakov, and A. V. Tsarenko, “Application of powerful quasi-steady-state plasma accelerators for simulation of ITER transient heat loads on divertor surfaces,” Plasma Phys. Controlled Fusion 49 (5A), A231–A239 (2007). https://doi.org/10.1088/0741-3335/49/5A/S19

    Article  Google Scholar 

  10. I. E. Garkusha, V. V. Chebotarev, S. S. Herashchenko, V. A. Makhlaj, et al., “Novel test-bed facility for PSI issues in fusion reactor conditions on the base of next generation QSPA plasma accelerator,” Nucl. Fusion 57 (11), 116011 (2017). https://doi.org/10.1088/1741-4326/aa7924

    Article  Google Scholar 

  11. I. E. Garkusha, D. G. Solyakov, V. V. Chebotarev, V. A. Makhlay, and N. V. Kulik, “Experimental studies of high-energy quasi-steady plasma streams generated by a magnetoplasma analogue of the Laval nozzle in the compression and acceleration regimes,” Plasma Phys. Rep. 45 (2), 166–178 (2019). https://doi.org/10.1134/S1063780X19010057

    Article  Google Scholar 

  12. V. M. Astashynski, S. I. Ananin et al., “Materials surface modification using quasi-stationary plasma accelerators,” Surf. Coat. Technol. 180–181, 392–395 (2004). https://doi.org/10.1016/j.surfcoat.2003.10.098

    Article  Google Scholar 

  13. K. V. Brushlinskii and A. I. Morozov, “Calculation of two-dimensional plasma flows in channels,” in Reviews of Plasma Physics, Vol. 8, Ed. by M. A. Leontovich (Springer, New York, 1980), pp. 105–198. https://doi.org/10.1007/978-1-4615-7814-7_2

  14. K. V. Brushlinskii, A. M. Zaborov, A. N. Kozlov, A. I. Morozov, and V. V. Savelyev, “Numerical simulation of plasma flows in QSPA,” Sov. J. Plasma Phys. 16, 79–89 (1990).

    Google Scholar 

  15. A. N. Kozlov and V. S. Konovalov, “Numerical study of the ionization process and radiation transport in the channel of plasma accelerator,” Commun. Nonlinear Sci. Numer. Simul. 51, 169–179 (2017). https://doi.org/10.1016/j.cnsns.2017.04.014

    Article  Google Scholar 

  16. L. M. Biberman, V. S. Vorob’ev, and I. T. Yakubov, Kinetics of Nonequilibrium Low-Temperature Plasma (Na-uka, Moscow, 1982; Consultants Bureau (Plenum), New York, 1987).

  17. A. N. Kozlov, “Ionization and recombination kinetics in a plasma accelerator channel,” Fluid Dyn. 35 (5), 784–790 (2000). https://doi.org/10.1023/A:1026663520401

    Article  MATH  Google Scholar 

  18. A. A. Barmin and A. N. Kozlov, “Structure of a steady-state ionization front in the plasma accelerator channel,” Fluid Dyn. 48 (4), 556–566 (2013). https://doi.org/10.1134/S0015462813040157

    Article  MathSciNet  MATH  Google Scholar 

  19. A. N. Kozlov, I. E. Garkusha, V. S. Konovalov, and V. G. Novikov, “The radiation intensity of the Lyman alpha line at the ionization front in the quasi-steady plasma accelerator,” Vopr. At. Nauki Tekh., Ser.: Fiz. Plazmy, No. 1 (83), 128–130 (2013).

  20. A. I. Morozov and L. S. Solov’ev, “Steady-state plasma flows in a magnetic field,” in Reviews of Plasma Physics, Vol. 8, Ed. by M. A. Leontovich (Springer, New York, 1980), pp. 1–103. https://doi.org/10.1007/978-1-4615-7814-7_1

  21. K. V. Brushlinskii, Mathematical Foundations of Liquid, Gas, and Plasma Computational Mechanics (Intellekt, Dolgoprudnyi, 2017) [in Russian].

  22. A. N. Kozlov, “Influence of a longitudinal magnetic field on the Hall effect in the plasma accelerator channel,” Fluid Dyn. 38 (4), 653–661 (2003). https://doi.org/10.1023/A:1026342315743

    Article  MathSciNet  MATH  Google Scholar 

  23. A. N. Kozlov, “Dynamics of rotating flows in plasma accelerator channels with a longitudinal magnetic field,” Plasma Phys. Rep. 32 (5), 378–387 (2006). https://doi.org/10.1134/S1063780X06050035

    Article  Google Scholar 

  24. A. N. Kozlov, “Basis of the quasi-steady plasma accelerator theory in the presence of a longitudinal magnetic field,” J. Plasma Phys. 74 (2), 261–286 (2008). https://doi.org/10.1017/S0022377807006794

    Article  Google Scholar 

  25. K. V. Brushlinskii, N. S. Zhdanova, and E. V. Stepin, “Acceleration of plasma in coaxial channels with preshaped electrodes and longitudinal magnetic field,” Comput. Math. Math. Phys. 58 (4), 593–603 (2018). https://doi.org/10.1134/S0965542518040085

    Article  MathSciNet  MATH  Google Scholar 

  26. A. N. Kozlov, “Two-fluid magnetohydrodynamic model of plasma flows in a quasi-steady-state plasma accelerator with a longitudinal magnetic field,” J. Appl. Mech. Tech. Phys. 50 (3), 396–405 (2009). https://doi.org/10.1007/s10808-009-0053-7

    Article  MATH  Google Scholar 

  27. A. N. Kozlov, “Study of the near-electrode processes in quasi-steady plasma accelerators with impenetrable electrodes,” Plasma Phys. Rep. 38 (1), 12–21 (2012). https://doi.org/10.1134/S1063780X11120051

    Article  Google Scholar 

  28. A. N. Kozlov, “The study of plasma flows in accelerators with thermonuclear parameters,” Plasma Phys. Controlled Fusion 59 (11), 115004 (2017). https://doi.org/10.1088/1361-6587/aa86be

    Article  Google Scholar 

  29. A. I. Morozov and A. N. Kozlov, “Self-cleaning effect of hydrogen plasma flow in the QSPA accelerator,” in Physics of Extreme States of Matter, Ed. by V. E. Fortov (Inst. Probl. Khim. Fiz. Ross. Akad. Nauk, Chernogolovka, Moscow oblast, 2007), pp. 316–319 [in Russian].

    Google Scholar 

  30. K. V. Brushlinskii, A. N. Kozlov, and V. S. Konovalov, “Numerical models of steady-state and pulsating flows of self-ionizing gas in plasma accelerator channels,” Comput. Math. Math. Phys. 55 (8), 1370–1380 (2015). https://doi.org/10.1134/S0965542515080059

    Article  MathSciNet  MATH  Google Scholar 

  31. D. Mihalas, Stellar atmospheres (W. H. Freeman, San Francisco, 1978) [Part 1 of Russian translation].

  32. B. N. Chetverushkin, Mathematical Modeling of Problems of Radiating Gas Dynamics (Nauka, Moscow, 1985) [in Russian].

    MATH  Google Scholar 

  33. J. I. Castor, Lectures on Radiation Hydrodynamics (Lawrence Livermore National Laboratory, Livermore, CA, 2000).

    Google Scholar 

  34. A. F. Nikiforov, V. G. Novikov, and V. B. Uvarov, Quantum-Statistical Models of Hot Dense Matter: Methods for Computation Opacity and Equation of State (Fizmatlit, Moscow, 2000; Birkhäuser, Basel, 2005). https://doi.org/10.1007/b137687

  35. R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1972).

  36. E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow (Elsevier, New York, 1987).

  37. L. M. Degtyarev and A. P. Favorskii, “Flow variant of the sweep method for difference problems with strongly varying coefficients,” USSR Comput. Math. Math. Phys. 9 (1), 285–294 (1969). https://doi.org/10.1016/0041-5553(69)90021-4

    Article  Google Scholar 

  38. V. I. Lebedev, “Quadratures on a sphere,” USSR Comput. Math. Math. Phys. 16 (2), 10–24 (1976). https://doi.org/10.1016/0041-5553(76)90100-2

    Article  MathSciNet  MATH  Google Scholar 

  39. B. N. Chetverushkin, O. G. Olkhovskaya, and V. A. Gasilov, “Solution of the radiative transfer equation on parallel computer systems,” Dokl. Math. 92 (2), 528–531 (2015). https://doi.org/10.1134/S1064562415050038

    Article  MathSciNet  MATH  Google Scholar 

  40. V. A. Gasilov, A. S. Boldarev et al., “Program package MARPLE3D for simulation of pulsed magnetically driven plasma using high performance computing,” Mat. Model. 24 (1), 55–87 (2012).

    MATH  Google Scholar 

  41. O. Olkhovskaya, A. Kotelnikov, M. Yakobovskiy, and V. Gasilov, “Parallel ray tracing algorithm for numerical analysis in radiative media physics,” in Parallel Computing is Everywhere, EBook Ser.: Advances in Parallel Co-mputing 32 (IOS Press, Amsterdam, 2018), pp. 137–146. https://doi.org/10.3233/978-1-61499-843-3-137

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Kozlov, A.N., Konovalov, V.S. Empirical Stationary Condition of Two-Dimensional Flows of Ionizing Hydrogen in the Plasma Accelerator Channel. Math Models Comput Simul 15, 630–642 (2023). https://doi.org/10.1134/S2070048223040075

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