Skip to main content
SpringerLink
Log in

Nonlocal transport in hot plasma. Part I

  • Transport Processes
  • Published:
Plasma Physics Reports Aims and scope Submit manuscript

Abstract

The problem of describing charged particle transport in hot plasma under the conditions in which the ratio of the electron mean free path to the gradient length is not too small is one of the key problems of plasma physics. However, up to now, there was a deficit of the systematic interpretation of the current state of this problem, which, in most studies, is formulated as the problem of nonlocal transport. In this review, we fill this gap by presenting a self-consistent linear theory of nonlocal transport for small plasma perturbations and an arbitrary collisionality from the classical highly collisional hydrodynamic regime to the collisionless regime. We describe a number of nonlinear transport models and demonstrate the application of the nonclassical transport theory to the solution of some problems of plasma physics, first of all for plasmas produced by nanosecond laser pulses with intensities of 1013–1016 W/cm2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Shvarts, in Laser-Plasma Interactions 3 (Proceedings of the 29th Scottish Universities Summer School in Physics, St. Andrews, 1985), Ed. by H. B. Hooper (Scottish Universities Summer School in Physics Publications, Edinburgh, 1986), p 105.

  2. L. Spitzer and R. Harm, Phys. Rev. 89, 977 (1953).

    Article  ADS  MATH  Google Scholar 

  3. S. I. Braginskii, JETP 6, 358 (1958).

    MathSciNet  ADS  Google Scholar 

  4. J. J. Duderstadt and G. A. Moses, Inertial Confinement Fusion (Wiley, New York, 1982).

    Google Scholar 

  5. W. I. Kruer, The Physics of Laser-Plasma Interactions (Addison-Wesley, New York, 1988).

    Google Scholar 

  6. R. Balescu, Transport Processes in Plasmas: Classical Transport Theory (Elsevier Science, Amsterdam, 1988).

    Google Scholar 

  7. J. F. Luciani, P. Mora, and J. Virmont, Phys. Rev. Lett. 51, 1664 (1983).

    Article  ADS  Google Scholar 

  8. J. R. Albritton, E. A. Williams, I. B. Bernstein, and K. Swarty, Phys. Rev. Lett. 57, 1887 (1986).

    Article  ADS  MATH  Google Scholar 

  9. J. S. De Groot, K. G. Estabrook, S. H. Glenzer, et al., Bull. Am. Phys. Soc. 42, 1993 (1997).

    Google Scholar 

  10. R. E. Harrington, J. Appl. Phys. 37, 2028 (1966).

    Article  ADS  Google Scholar 

  11. N. G. Basov, P. P. Volosevich, E. G. Gamalii, et al., J. Russ. Laser Res. 10, 438 (1989).

    Article  Google Scholar 

  12. G. Schurtz, S. Gary, S. Hulin, et al., Phys. Rev. Lett. 98, 095002 (2007).

    Article  ADS  Google Scholar 

  13. M. D. Rosen, H. A. Scott, D. E. Hinkel, et al., High Energy Density Phys. 7, 180 (2012).

    Article  ADS  Google Scholar 

  14. V. Yu. Bychenkov and V. T. Tikhonchuk, in Nuclear Fusion by Inertial Confinement: A Comprehensive Treatise, Ed. by G. Velarde, V. Ronen, and J. M. Martinzval (CRC Press, Boca Raton, FL, 1993), p. 73.

  15. R. C. Malone, R. L. McCrory, and R. L. Morse, Phys. Rev. Lett. 34, 721 (1975).

    Article  ADS  Google Scholar 

  16. D. W. Forslund, J. Geophys. Res. 17, 75 (1970).

    Google Scholar 

  17. P. B. Snyder, G. W. Hammet, and W. Dorland, Phys. Plasmas 4, 3974 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  18. E. Furkal, A. I. Smolyakov, and A. Hirose, Phys. Rev. E 58, 965 (1998).

    Article  ADS  Google Scholar 

  19. Z. Chang and J. D. Callen, Phys. Fluids B 4, 1167 (1992).

    Article  ADS  Google Scholar 

  20. O. V. Batishchev, S. I. Krasheninnikov, P. J. Catto, et al., Phys. Plasmas 4, 1672 (1997).

    Article  ADS  Google Scholar 

  21. V. Yu. Bychenkov, W. Rozmus, V. T. Tikhonchuk, and A. V. Brantov, Phys. Rev. Lett. 75, 4405 (1995).

    Article  ADS  Google Scholar 

  22. A. F. Alexandrov, L. S. Bogdankevich, and A. A. Rukhadze, Principles of Plasma Electrodynamics (Vysshaya Shkola, Moscow, 1978; Springer-Verlag, Berlin, 1984).

    Google Scholar 

  23. V. P. Silin and A. A. Rukhadze, Electromagnetic Properties of Plasmas and Plasmalike Media (Gosatomizdat, Moscow, 1961) [in Russian].

    Google Scholar 

  24. I. P. Shkarofsky, T. W. Johnston, and M. P. Bachynskii, The Particle Kinetics of Plasmas (Addison-Wesley, Reading, 1966).

    Google Scholar 

  25. V. P. Silin, Phys. Usp. 45, 955 (2002).

    Article  ADS  Google Scholar 

  26. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Nauka, Moscow, 1979; Pergamon, Oxford, 1981).

    Google Scholar 

  27. M. Opher, G. J. Morales, and J. N. Leboeuf, Phys. Rev. E 66, 032702 (2002).

    Article  Google Scholar 

  28. V. Yu. Bychenkov, V. T. Tikhonchuk, and W. Rozmus, Phys. Plasmas 4, 4205 (1997).

    Article  ADS  Google Scholar 

  29. V. Yu. Bychenkov, Plasma Phys. Rep. 24, 801 (1998).

    ADS  Google Scholar 

  30. R. A. Koch, Phys. Fluids 18, 861 (1975).

    Article  ADS  Google Scholar 

  31. J. R. Penano, G. J. Morales, and J. E. Maggs, Phys. Plasmas 4, 555 (1997).

    Article  ADS  Google Scholar 

  32. A. V. Brantov, V. Yu. Bychenkov, W. Rozmus, and C. Capjack, JETP 100, 1159 (2005).

    Article  ADS  Google Scholar 

  33. A. V. Brantov, V. Yu. Bychenkov, W. Rozmus, and C. E. Capjack, IEEE Trans. Plasma Sci. 13, 738 (2006).

    Article  ADS  Google Scholar 

  34. E. M. Epperlein, Phys. Rev. Lett. 65, 2145 (1990).

    Article  ADS  Google Scholar 

  35. V. Yu. Bychenkov, W. Rozmus, A. V. Brantov, and V. T. Tikhonchuk, Phys. Plasmas 7, 1511 (2000).

    Article  ADS  Google Scholar 

  36. S. Chapman and T. G. Cowling, Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1952).

    MATH  Google Scholar 

  37. R. Landshoff, Phys. Rev. 76, 904 (1949).

    Article  ADS  MATH  Google Scholar 

  38. R. Landshoff, Phys. Rev. 82, 442 (1951).

    Article  ADS  Google Scholar 

  39. A. V. Brantov, V. Yu. Bychenkov, V. T. Tikhonchuk, and W. Rozmus, JETP 83, 716 (1996).

    ADS  Google Scholar 

  40. R. J. Bickerton, Nucl. Fusion 13, 457 (1973).

    Article  Google Scholar 

  41. W. L. Kruer, Comm. Plasma Phys. 5, 69 (1979).

    Google Scholar 

  42. J. Delettrez, Can. J. Phys. 64, 932 (1986).

    Article  ADS  Google Scholar 

  43. R. Benattar, C. Popovics, R. Sigel, and J. Virmont, Phys. Rev. Lett. 42, 766 (1979).

    Article  ADS  Google Scholar 

  44. W. B. Fechner, C. L. Shephard, G. E. Busch, et al., Phys. Fluids 27, 1552 (1984).

    Article  ADS  Google Scholar 

  45. A. W. Ehler, J. Appl. Phys. 46, 2464 (1975).

    Article  ADS  Google Scholar 

  46. E. J. Baleo and I. B. Bernstein, Phys. Fluids 19, 1348 (1976).

    Article  ADS  Google Scholar 

  47. E. M. Campbell, R. R. Johnson, F. J. Mayer, et al., Phys. Rev. Lett. 39, 274 (1977).

    Article  ADS  Google Scholar 

  48. B. Yaakobi and T. C. Bristow, Phys. Rev. Lett. 38, 350 (1977).

    Article  ADS  Google Scholar 

  49. B. Yaakobi, T. Boehly, P. Bourke, et al., Opt. Commun. 39, 175 (1981).

    Article  ADS  Google Scholar 

  50. G. H. Dahlbacka, Bull. Am. Phys. Soc. 21, 1028 (1976).

    Google Scholar 

  51. F. Amiranoff, R. Fabbro, E. Fabre, et al., Phys. Rev. Lett. 43, 522 (1979).

    Article  ADS  Google Scholar 

  52. F. C. Young, R. R. Whitlock, R. Decoste, et al., Appl. Phys. Lett. 30, 45 (1978).

    Article  ADS  Google Scholar 

  53. W. C. Mead, E. M. Campbell, K. G. Estabrook, et al., Phys. Rev. Lett. 47, 1289 (1981).

    Article  ADS  Google Scholar 

  54. B. Yaakobi, J. Delettrez, L. M. Goldman, et al., Phys. Fluids 27, 516 (1984).

    Article  ADS  Google Scholar 

  55. A. Hauer, W. C. Mead, O. Willi, et al., Phys. Rev. Lett. 53, 2563 (1984).

    Article  ADS  Google Scholar 

  56. R. A. Haas, W. C. Mead, W. L. Kruer, et al., Phys. Fluids 20, 322 (1977).

    Article  ADS  Google Scholar 

  57. C. Garban-Labaune, E. Fabre, C. E. Max, et al., Phys. Rev. Lett. 48, 1018 (1982).

    Article  ADS  Google Scholar 

  58. B. Yaakobi, J. Delettrez, R. L. McCrory, et al., in Proceedings of the 6th International Workshop on Laser Interaction and Related Plasma Phenomena, Monterey, CA, 1982, Ed. by H. Hora and H. Miley, p. 731.

  59. J. N. Rogers, J. S. De Groot, Z. Abbou-Assaleh, et al., Phys. Fluids B 1, 741 (1989).

    Article  ADS  Google Scholar 

  60. D. G. Colombant, W. M. Manheimer, and M. Busquet, Phys. Plasmas 12, 072702 (2005).

    Article  ADS  Google Scholar 

  61. G. Gregori, S. H. Glenzer, J. Knight, et al., Phys. Rev. Lett. 92, 205006 (2004).

    Article  ADS  Google Scholar 

  62. R. J. Mason, Phys. Rev. Lett. 47, 652 (1981).

    Article  ADS  Google Scholar 

  63. S. A. Bel’kov, A. V. Bessarab, I. N. Voronich, et al., Sov. Phys. JETP 74, 43 (1992).

    Google Scholar 

  64. D. S. Montgomery, O. L. Landen, R. P. Drake, et al., Phys. Rev. Lett. 73, 2055 (1994).

    Article  ADS  Google Scholar 

  65. D. W. Forslund and J. U. Brackbill, Phys. Rev. Lett. 48, 1615 (1982).

    ADS  Google Scholar 

  66. C. E. Max, W. M. Manheimer, and J. J. Thomson, Phys. Fluids 21, 128 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  67. R. P. J. Town, M. D. Rosen, P. A. Michel, et al., Phys. Plasmas 18, 056302 (1994).

    Article  ADS  Google Scholar 

  68. V. V. Aleksandrov, N. G. Koval’skii, and V. P. Silin, Sov. Phys. JETP 52, 432 (1980).

    ADS  Google Scholar 

  69. R. J. Mason, Phys. Rev. Lett. 43, 1795 (1979).

    Article  ADS  Google Scholar 

  70. E. V. Mishin, Sov. Phys. Doklady 19, 140 (1974).

    ADS  Google Scholar 

  71. A. A. Galeev and A. M. Natanson, in Handbook of Plasma Physics, Ed. by A. Rubenchik and S. Witkowski (North-Holland, Amsterdam, 1991), Vol. 3, p. 549.

  72. G. P. Zimmerman and W. L. Kruer, Comm. Plasma Phys. Controlled Fusion 2, 51 (1975).

    Google Scholar 

  73. I. P. Shkarofsky, Phys. Rev. Lett. 42, 1342 (1979).

    Article  ADS  Google Scholar 

  74. J. R. Albritton, I. B. Bernstein, E. J. Valeo, and E. A. Williams, Phys. Rev. Lett. 39, 1536 (1977).

    Article  ADS  Google Scholar 

  75. A. V. Gurevich and Ya. N. Istomin, Sov. Phys. JETP 50, 470 (1979).

    ADS  Google Scholar 

  76. D. R. Gray, J. D. Kilkenny, M. S. White, et al., Phys. Rev. Lett. 39, 1270 (1977).

    Article  ADS  Google Scholar 

  77. W. M. Manheimer, Phys. Fluids 20, 256 (1977).

    ADS  Google Scholar 

  78. E. L. Lindman, J. Phys. Colloq. (Paris) 38(C6), 9 (1977).

    ADS  Google Scholar 

  79. V. Yu. Bychenkov and V. P. Silin, Sov. Phys. JETP 55, 1086 (1982).

    Google Scholar 

  80. V. Yu. Bychenkov, O. M. Gradov, and V. P. Silin, Sov. Phys. JETP 56, 1202 (1982).

    Google Scholar 

  81. D. Shvarts, J. Delettrez, R. L. McCrory, and C. P. Verdon, Phys. Rev. Lett. 47, 247 (1981).

    Article  ADS  Google Scholar 

  82. D. R. Gray and J. D. Kilkenny, Plasma Phys. 22, 81 (1980).

    Article  ADS  Google Scholar 

  83. A. R. Bell, R. G. Evans, and D. J. Nicholas, Phys. Rev. Lett. 46, 243 (1981).

    Article  ADS  Google Scholar 

  84. P. Mora and H. Yahi, Phys. Rev. A 26, 2259 (1982).

    Article  ADS  Google Scholar 

  85. P. Mora and J. E. Luciani, Laser Part. Beams 12, 387 (1994).

    Article  ADS  Google Scholar 

  86. J. P. Matte and J. Virmont, Phys. Rev. Lett. 49, 1936 (1982).

    Article  ADS  Google Scholar 

  87. J. R. Albritton, Phys. Rev. Lett. 50, 2078 (1983).

    Article  ADS  Google Scholar 

  88. J. P. Matte, T. W. Johnston, J. Delettrez, and R. L. McCrory, Phys. Rev. Lett. 53, 1461 (1984).

    Article  ADS  Google Scholar 

  89. A. R. Bell, Phys. Fluids 28, 2007 (1985).

    Article  ADS  Google Scholar 

  90. T. H. Kho and M. G. Haines, Phys. Rev. Lett. 55, 825 (1985).

    Article  ADS  Google Scholar 

  91. T. H. Kho and M. G. Haines, Phys. Fluids 29, 2665 (1986).

    Article  ADS  Google Scholar 

  92. P. Nicolai, M. Vandenboomgaerde, B. Canaud, and F. Chaigneau, Phys. Plasmas 7, 4250 (2000).

    Article  ADS  Google Scholar 

  93. E. M. Epperlein, G. J. Rickard, and A. R. Bell, Phys. Rev. Lett. 61, 2453 (1988).

    Article  ADS  Google Scholar 

  94. G. P. Schurtz, Ph. D. Nicolai, and M. Busquet, Phys. Plasmas 7, 4238 (2000).

    Article  ADS  Google Scholar 

  95. A. Sunahara, K. Mima, T. Johzaki, and H. Nagatomo, J. Phys. IV France 133, 193 (2006).

    Article  Google Scholar 

  96. E. M. Epperlein, Laser Part. Beams 12, 257 (1994).

    Article  ADS  Google Scholar 

  97. O. V. Batishchev, V. Yu. Bychenkov, F. Detering, et al., Phys. Plasmas 9, 2302 (2002).

    Article  ADS  Google Scholar 

  98. A. G. R. Thomas, M. Tzoufras, A. P. L. Robinson, et al., J. Comput. Phys. 231, 1051 (2012).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  99. M. Tzoufras, A. R. Bell, P. A. Norreys, and F. S. Tsung, J. Comput. Phys. 230, 6475 (2011).

    Article  ADS  MATH  Google Scholar 

  100. F. L. Lindman and D. Shwartz, Phys. Fluids 29, 2657 (1986).

    Article  ADS  Google Scholar 

  101. J. F. Luciani and P. Mora, Phys. Fluids 28, 835 (1985).

    Article  ADS  MATH  Google Scholar 

  102. A. Bendib, J. F. Luciani, and J. P. Matte, Phys. Fluids 31, 711 (1988).

    Article  ADS  Google Scholar 

  103. N. N. Ljepojevic and P. MacNeice, Phys. Rev. A 40, 981 (1989).

    Article  ADS  Google Scholar 

  104. F. Minotti and C. F. Fontan, Phys. Fluids B 2, 1725 (1990).

    Article  ADS  Google Scholar 

  105. E. M. Epperlein and R. W. Short, Phys. Fluids B 3, 3092 (1991).

    Article  ADS  Google Scholar 

  106. S. J. Krasheninnikov, Phys. Fluids B 5, 74 (1993).

    Article  ADS  Google Scholar 

  107. E. D. Held, J. D. Callen, C. C. Hegna, et al., Phys. Plasmas 11, 2419 (2004).

    Article  ADS  Google Scholar 

  108. W. Manheimer, D. Colombant, and V. Goncharov, Phys. Plasmas 15, 083103 (2008).

    Article  ADS  Google Scholar 

  109. Y. Kishimoto and K. Mima, J. Phys. Soc. Jpn. 52, 3389 (1983).

    Article  ADS  Google Scholar 

  110. I. P. Shkarofsky, Phys. Fluids 23, 52 (1980).

    Article  ADS  MATH  Google Scholar 

  111. A. V. Maksimov, V. P. Silin, and M. V. Chegotov, Sov. J. Plasma Phys. 16, 331 (1990).

    Google Scholar 

  112. K. N. Ovchinnikov, V. P. Silin, and S. A. Uryupin, Sov. J. Plasma Phys. 17, 748 (1991).

    Google Scholar 

  113. D. Colombant and W. Manheimer, Phys. Plasmas 15, 083104 (2008).

    Article  ADS  Google Scholar 

  114. S. G. Krasheninnikov, Sov. Phys. JETP 67, 2483 (1988).

    Google Scholar 

  115. S. A. Uryupin, S. Kato, and K. Mima, Phys. Plasmas 2, 3100 (1995).

    Article  ADS  Google Scholar 

  116. V. Yu. Bychenkov, W. Rozmus, and R. Teshima, Phys. Plasmas 9, 2872 (2002).

    Article  ADS  Google Scholar 

  117. S. G. Bochkarev, V. Yu. Bychenkov, and W. Rozmus, Phys. Plasmas 11, 3997 (2004).

    Article  ADS  Google Scholar 

  118. P. A. Holstein, J. Delettrez, S. Skupsky, and J. P. Matte, J. Appl. Phys. 60, 2296 (1986).

    Article  ADS  Google Scholar 

  119. M. K. Prasad and D. S. Kershaw, Phys. Fluids B 1, 2430 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  120. M. K. Prasad and D. S. Kershaw, Phys. Fluids B 3, 3087 (1991).

    Article  ADS  Google Scholar 

  121. F. Vidal, J. P. Matte, M. Casanova, and O. Larroche, Phys. Plasmas 2, 1412 (1995).

    Article  ADS  Google Scholar 

  122. G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990).

    Article  ADS  Google Scholar 

  123. G. W. Hammett, W. Dorland, and F. W. Perkins, Phys. Fluids B 4, 2052 (1992).

    Article  ADS  Google Scholar 

  124. A. V. Maksimov and V. P. Silin, JETP 76, 39 (1993).

    ADS  Google Scholar 

  125. A. V. Maksimov and V. P. Silin, JETP Lett. 58, 271 (1993).

    ADS  Google Scholar 

  126. A. V. Maximov and V. P. Silin, Phys. Lett. A 173, 83 (1993).

    Article  ADS  Google Scholar 

  127. A. V. Maksimov and V. P. Silin, JETP 78, 669 (1994).

    ADS  Google Scholar 

  128. V. P. Silin, JETP 79, 756 (1994).

    ADS  Google Scholar 

  129. K. Bendib and A. Bendib, Phys. Plasmas 6, 1500 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  130. A. Tahraoui and A. Bendib, Phys. Plasmas 9, 3089 (2002).

    Article  ADS  Google Scholar 

  131. S. Brunner and E. Valeo, Phys. Plasmas 9, 923 (2002).

    Article  ADS  Google Scholar 

  132. S. Brunner, E. Valeo, and J. A. Krommes, Phys. Plasmas 6, 4504 (1999).

    Article  ADS  Google Scholar 

  133. S. Brunner, E. Valeo, and J. A. Krommes, Phys. Plasmas 7, 2810 (2000).

    Article  ADS  Google Scholar 

  134. V. Yu. Bychenkov, J. Myatt, W. Rozmus, and V. T. Tikhonchuk, Phys. Plasmas 1, 2419 (1994).

    Article  ADS  Google Scholar 

  135. A. V. Brantov, V. Yu. Bychenkov, V. T. Tikhonchuk, and W. Rozmus, Phys. Plasmas 5, 2742 (1998).

    Article  ADS  Google Scholar 

  136. A. V. Brantov and V. Yu. Bychenkov, Plasma Phys. Rep. 21, 991 (1995).

    ADS  Google Scholar 

  137. A. V. Brantov, V. Yu. Bychenkov, and W. Rozmus, JETP 106, 983 (2008).

    Article  ADS  Google Scholar 

  138. N. Mattor and S. E. Parker, Phys. Rev. Lett. 79, 3419 (1997).

    Article  ADS  Google Scholar 

  139. R. D. Hazeltine, Phys. Plasmas 5, 3282 (1998).

    Article  MathSciNet  ADS  Google Scholar 

  140. Zh. Zheng, W. Rozmus, V. Yu. Bychenkov, et al., Plasma Phys. 16, 102301 (2009).

    Article  Google Scholar 

  141. A. Bendib, G. Matthieussent, and F. Bouzid, Phys. Plasmas 9, 35 (2002).

    Article  ADS  Google Scholar 

  142. A. V. Brantov, V. Yu. Bychenkov, W. Rozmus, and C. E. Capjack, Phys. Rev. Lett. 93, 125002 (2004).

    Article  ADS  Google Scholar 

  143. E. M. Epperlein, Phys. Plasmas 1, 109 (1994).

    Article  ADS  Google Scholar 

  144. S. I. Braginskii, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p 205.

  145. V. Yu. Bychenkov, V. N. Novikov, and V. T. Tikhonchuk, JETP 87, 916 (1998).

    Article  ADS  Google Scholar 

  146. V. Yu. Bychenkov, J. F. Myatt, W. Rozmus, and V. T. Tikhonchuk, Phys. Rev. E 52, 6759 (1995).

    Article  ADS  Google Scholar 

  147. T. Ditmire, E. T. Gumbrell, R. A. Smith, et al., Phys. Rev. Lett. 80, 720 (1998).

    Article  ADS  Google Scholar 

  148. M. D. Tracy, E. A. Williams, K. G. Estabrook, et al., Phys. Fluids B 5, 1420 (1993).

    Article  ADS  Google Scholar 

  149. A. V. Brantov, V. Yu. Bychenkov, and W. Rozmus, Phys. Rev. Lett. 108, 205001 (2012).

    Article  ADS  Google Scholar 

  150. W. Rozmus, J. Plasma Phys. 22, 41 (1979).

    Article  ADS  Google Scholar 

  151. V. L. Ginzburg, The Propagation of Electromagnetic Waves in Plasmas (Nauka, Moscow, 1967; Pergamon, Oxford, 1970).

    Google Scholar 

  152. G. A. Moses and J. J. Duderstadt, Phys. Fluids 20, 764 (1977).

    ADS  Google Scholar 

  153. S. Yu. Gus’kov, N. N. Demchenko, V. B. Rozanov, et al., Quant. Electron. 33, 95 (2003).

    Article  ADS  Google Scholar 

  154. A. V. Brantov, V. Yu. Bychenkov, O. V. Batishchev, and W. Rozmus, in Proceedings of the 30th EPS Conference on Controlled Fusion and Plasma Physics, St. Petersburg, 2003, ECA 27A, P–4.151 (2003).

    Google Scholar 

  155. A. V. Brantov, V. Yu. Bychenkov, O. V. Batishchev, and W. Rozmus, Comput. Phys. Commun. 164, 67 (2004).

    Article  ADS  Google Scholar 

  156. V. Yu. Bychenkov, S. G. Bochkarev, W. Rozmus, et al., Proc. SPIE 5228, 510 (2003).

    Article  ADS  Google Scholar 

  157. A. A. Batishcheva, O. V. Batishchev, M. M. Shoucri, et al., Phys. Plasmas 3, 1634 (1996).

    Article  ADS  Google Scholar 

  158. K. Otani, K. Shigemori, T. Kadono, et al., Phys. Plasmas 17, 016407 (2010).

    Google Scholar 

  159. D. Salzmann, Atomic Processes in Hot Plasmas (Oxford University Press, Oxford, UK, 1998).

    Google Scholar 

  160. E. M. Epperlein, G. J. Rickard, and A. R. Bell, Comput. Phys. Commun. 52, 7 (1988).

    Article  ADS  Google Scholar 

  161. R. P. J. Town, A. R. Bell, and S. J. Rose, Phys. Rev. E 50, 1413 (1994).

    Article  ADS  Google Scholar 

  162. K. Mima, V. Tikhonchuk, and M. Perlado, Nucl. Fusion 51, 094004 (2011).

    Article  ADS  Google Scholar 

  163. S. G. Garanin, S. A. Bel’kov, and S. V. Bondarenko, XXXIX International Zvenigorod Conference on Plasma Physics and Controlled Fusion, Zvenigorod, 2012, Book of Abstracts, p. 17.

  164. D. E. Hinkel, M. D. Rosen, E. A. Williams, et al., Phys. Plasmas 18, 056312 (2011).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskiii pr. 53, Moscow, 119991, Russia

    A. V. Brantov & V. Yu. Bychenkov

  2. Dukhov All-Russia Research Institute of Automatics, Mospochtamt a/ya 918, Moscow, 101000, Russia

    A. V. Brantov & V. Yu. Bychenkov

Authors
  1. A. V. Brantov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Yu. Bychenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Brantov.

Additional information

Original Russian Text © A.V. Brantov, V.Yu. Bychenkov, 2013, published in Fizika Plazmy, 2013, Vol. 39, No. 9, pp. 786–836.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brantov, A.V., Bychenkov, V.Y. Nonlocal transport in hot plasma. Part I. Plasma Phys. Rep. 39, 698–744 (2013). https://doi.org/10.1134/S1063780X13090018

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X13090018

Keywords

Search

Navigation