RSS feeds
РусскийEnglish
Issue 4, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2026

 / 

March

←  →

Reviews of topical problems


Simulations of Z-pinches

† ,
Russian Federal Nuclear Center - All-Russian Research Institute of Experimental Physics, prosp. Mira 37, Sarov, Nizhny Novgorod region, 607188, Russian Federation

Studies of the development of a 'sausage' instability of Z-pinch in the MHD-approximation and the account for the development of two-dimensional turbulence have shown that turbulence development prevents the formation of the neck with an infinitely decreasing radius. Under the neck compression in this approximation there is also no generation of high voltages near the axis that could contribute to the formation of ion beams and neutrons generation due to the beam-target mechanism. Thus, to describe neutron generation in the beam—target mechanism, it is necessary to take into account the kinetic processes of high voltage generation in plasma. 2D MHD-computations with the account for kinetic processes in the phenomenological form of anomalous resistivity make it possible to achieve for a number of plasma focus configurations and gas puff Z-pinch an agreement with experimental data on current, voltage and neutron measurements. 2D kinetic computations of the plasma focus carried out for the final phase of pinch formation agree with experimental data on the neutron yield and distribution of ions in the resulting beams and confirm that the anomalous plasma resistivity may be due to lower hybrid drift instability, which was assumed in phenomenological MHD-computations that describe neutron generation in Z-pinch and plasma focus.

Typically, an English full text is available in about 1 month from the date of publication of the original article.

Keywords: MHD-simulations, plasma dynamics, 'sausage' instability, Z-pinch, plasma focus
PACS: 52.30.Cv, 52.35.Py, 52.58.Lq (all)
DOI: 10.3367/UFNe.2025.08.039998
URL: https://ufn.ru/en/articles/2026/3/a/
Citation: Garanin S F, Dolinskii V Yu "Simulations of Z-pinches" Phys. Usp. 69 (3) (2026)

Received: 10th, June 2025, revised: 7th, August 2025, 8th, August 2025

Оригинал: Гаранин С Ф, Долинский В Ю «Расчетное моделирование Z-пинчей» УФН 196 222–237 (2026); DOI: 10.3367/UFNr.2025.08.039998

References (74) ↓ Similar articles (20)

  1. D’yachenko V F, Imshennik V S Voprosy Teorii Plazmy Vyp. 8 (Pod red. M A Leontovicha) (M.: Atomizdat, 1974) p. 164; Per. na angl. yaz., D’yachenko V F, Imshennik V S Reviews Plasma Physics Vol. 8 (Ed. M A Leontovich) (Boston, MA: Consultants Bureau, 1980) p. 199
  2. Vikhrev V V, Braginskii S I Voprosy Teorii Plazmy Vyp. 10 (Pod red. M A Leontovicha) (M.: Atomizdat, 1980) p. 243; Per. na angl. yaz., Vikhrev V V, Braginskii S I Review Plasma Physics Vol. 10 (Ed. M A Leontovich) (New York: Consultants Bureau, 1986) p. 243
  3. Ryutov D D, Derzon M S, Matzen M K Rev. Mod. Phys. 72 167 (2000)
  4. Haines M G Plasma Phys. Control. Fusion 53 093001 (2011)
  5. Ise J, Pyle R V Conf. On Controlled Thermonuclear Reactions, Princeton Univ., 17-20 October 1955, TID-7503 (Washington, DC: USAEC, 1955) p. 218
  6. Artsimovich L A i dr Atomnaya Energiya 1 (3) 84 (1956); Artsimovich L A et al Sov. J. Atom. Energy 1 375 (1956)
  7. Gilbert F C et al. Conf. On Controlled Thermonuclear Reactions, Gaitlinburg, TN, 4-7 June 1956 TID-7520 Pt. 1 (Washington, DC: USAEC, 1956) p. 144; Dunaway R Conf. On Controlled Thermonuclear Reactions, Gaitlinburg, TN, 4-7 June 1956 TID-7520 Pt. 1 (Washington, DC: USAEC, 1956) p. 127
  8. Filippov N V, Filippova T I, Vinogradov V P Nucl. Fusion Suppl. 2 577 (1962)
  9. Mather J W Phys. Fluids Suppl. 7 5 (1964)
  10. Makeev N G, Rumyantsev V G, Maslov V V Entsiklopediya nizkotemperaturnoi plazmy Ser. B, T. IX-3 (Pod red. V A Gribkova) (M.: Yanus, 2007) p. 176
  11. Makeev N G, Rumyantsev V G, Cheremukhin G N Fizika i tekhnika impul’snykh istochnikov ioniziruyushchikh izluchenii dlya issledovaniya bystroprotekayushchikh protsessov (Pod red. N G Makeeva) (Sarov: RFYaTs-VNIIEF, 1996) p. 281
  12. Batyunin A V i dr Fizika Plazmy 16 1027 (1990); Batyunin A V et al Sov. J. Plasma Phys. 16 597 (1990)
  13. Klir D et al Plasma Phys. Control. Fusion 52 065013 (2010)
  14. Lee S, Serban A IEEE Trans. Plasma Sci. 24 1101 (1996)
  15. Mikhailov Yu V, Lemeshko B D, Prokuratov I A Fizika Plazmy 45 323 (2019); Mikhailov Yu V, Lemeshko B D, Prokuratov I A Plasma Phys. Rep. 45 334 (2019)
  16. Gribkov V A et al J. Phys. D 40 3592 (2007)
  17. Ablesimov V E i dr Fizika Plazmy 36 396 (2010); Ablesimov V E et al Plasma Phys. Rep. 36 403 (2010)
  18. Klir D et al Phys. Plasmas 15 032701 (2008)
  19. Klir D et al New J. Phys. 20 053064 (2018)
  20. Klir D et al Matter Radiat. Extremes 5 026401 (2020)
  21. Velikovich A L et al Phys. Plasmas 14 022701 (2007)
  22. Coverdale C A et al Phys. Plasmas 14 022706 (2007)
  23. Coverdale C A et al Phys. Plasmas 14 056309 (2007)
  24. Stanislawski J et al Nucleonika 46 S73 (2001)
  25. Milanese M M Rev. Sci. Instrum. 77 036106 (2006)
  26. Grabovskii E V i dr Voprosy Atomnoi Nauki Tekhniki. Ser. Termoyadernyi Sintez 45 (1) 119 (2022)
  27. Trubnikov B A, Zhdanov S K Pis’ma ZhETF 41 (7) 292 (1985); Trubnikov B A, Zhdanov S K JETP Lett. 41 358 (1985)
  28. Zhdanov S K, Trubnikov B A Zh. Eksp. Teor. Fiz. 90 1380 (1986); Zhdanov S K, Trubnikov B A Sov. Phys. JETP 63 809 (1986)
  29. Garanin S F, Chernyshev Yu D Fizika Plazmy 13 974 (1987)
  30. Garanin S F Fizicheskie Protsessy v Sistemakh MAGO-MTF (Sarov: FGUP RFYaTs-VNIIEF, 2012); Garanin S F "Physical processes in the MAGO/MTF systems" LA-UR-13-29094 (Los Alamos, 2013)
  31. Vikhrev V V Fizika Plazmy 12 454 (1986); Vikhrev V V Sov. J. Plasma Phys. 12 735 (1986)
  32. Trubnikov B A Fizika Plazmy 12 468 (1986); Trubnikov B A Sov. J. Plasma Phys. 12 271 (1986)
  33. Yan’kov V V Fizika Plazmy 17 521 (1991); Yan’kov V V Sov. J. Plasma Phys. 17 305 (1991)
  34. Shan B, Lee P, Lee S Sing. J. Phys. 16 25 (2000)
  35. Lee S J. Fusion Energy 33 319 (2014)
  36. Schmidt A et al Phys. Plasmas 21 102703 (2014)
  37. Offermann D T et al Phys. Rev. Lett. 116 195001 (2016)
  38. Bennett N et al Phys. Plasmas 24 012702 (2017)
  39. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982); Per. na angl. yaz., Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (New York: Pergamon Press, 1984)
  40. Trubnikov B A Fizika Plazmy i Problema Upravlyaemykh Termoyadernykh Reaktsii Vol. 1 (Otv. red. M A Leontovich) (M.: Izd-vo AN SSSR, 1958) p. 289
  41. Kruskal M, Schwarzschild M Proc. R. Soc. London A 223 348 (1954)
  42. Shafranov V D Atom. Energiya 1 (5) 38 (1956); Shafranov V D Sov. J. Atom. Energy 1 709 (1956)
  43. Book D L, Ott E, Lampe M Phys. Fluids 19 1982 (1976)
  44. Yan’kov V V Preprint IAE-4218/7 (M.: Institut atomnoi energii imeni I.V. Kurchatova, 1985)
  45. Lebedev S V, Frank A, Ryutov D D Rev. Mod. Phys. 91 025002 (2019)
  46. Garanin S F, Mamyshev V I Fizika Plazmy 34 695 (2008); Garanin S F, Mamyshev V I Plasma Phys. Rep. 34 639 (2008)
  47. Garanin S F i dr Fizika Plazmy 46 890 (2020); Garanin S F et al Plasma Phys. Rep. 46 978 (2020)
  48. Garanin S F, Dolinskii V Yu Fizika Plazmy 47 728 (2021); Garanin S F, Dolinskii V Yu Plasma Phys. Rep. 47 814 (2021)
  49. Kadomtsev B B Voprosy Teorii Plazmy Vyp. 2 (Pod red. M A Leontovicha) (M.: Gosatomizdat, 1963) p. 132; Per. na angl. yaz., Kadomtsev B B Reviews Of Plasma Physics Vol. 2 (Ed. M A Leontovich) (New York: Consultants Bureau, 1966) p. 153
  50. Braginskii S I Voprosy Teorii Plazmy Vyp. 1 (Pod red. M A Leontovicha) (M.: Gosatomizdat, 1963) p. 183; Per. na angl. yaz., Braginskii S I Reviews In Plasma Physics Vol. 1 (Ed. M A Leontovich) (New York: Consultants Bureau, 1965) p. 183
  51. Lifshits E M, Pitaevskii L P Fizicheskaya Kinetika (M.: Nauka, 1979); Per. na angl. yaz., Lifshitz E M, Pitaevskii L P Physical Kinetics (Oxford: Pergamon Press, 1981)
  52. Davidson R C, Gladd N T Phys. Fluids 18 1327 (1975)
  53. Krall N A, Liewer P C Phys. Rev. A 4 2094 (1971)
  54. Gudblud I P, Pyatak A I, Sizonenko V L Zh. Eksp. Teor. Fiz. 64 2084 (1973); Goedbloed J P, Pyatak A I, Sizonenko V L Sov. Phys. JETP 37 1051 (1973)
  55. Sasorov P V Fizika Plazmy 18 275 (1992); Sasorov P V Sov. J. Plasma Phys. 18 143 (1992)
  56. Kadomtsev B B Kollektivnye Yavleniya v Plazme (M.: Nauka, 1976); Per. na angl. yaz., Kadomtsev B B Reviews Of Plasma Physics Vol. 22 (Ed. V D Shafranov) (New York: Kluwer Acad. Plenum Publ., 2001) p. 1
  57. Trubnikov B A Teoriya Plazmy (M.: Energoatomizdat, 1996)
  58. Chadwick M B et al Nucl. Data Sheets 107 2931 (2006)
  59. Fletcher K Vychislitel’nye metody v dinamike zhidkostei T. 1 Osnovnye polozheniya i obshchie metody (M.: Mir, 1991); Per. s angl. yaz., Fletcher C A J Computational Techniques For Fluid Dynamics Vol. 1 Fundamental And General Techniques (Berlin: Springer, 1988)
  60. Samarskii A A, Popov Yu P Raznostnye Metody Resheniya Zadach Gazovoi Dinamiki (M.: Nauka, 1992)
  61. Gaganov V V, Garanin S F, Dolinskii V Yu Fizika Plazmy 49 332 (2023); Gaganov V V, Garanin S F, Dolinskii V Yu Plasma Phys. Rep. 49 428 (2023)
  62. Zav’yalov N V i dr Fizika Plazmy 39 276 (2013); Zavyalov N V et al Plasma Phys. Rep. 39 243 (2013)
  63. Sohrabi M, Zarinshad A, Habibi M Sci. Rep. 6 38843 (2016)
  64. Ito H, Nishino Y, Masugata K J. Korean Phys. Soc. 59 3674 (2011)
  65. Dolinskii V Yu et al Proc. of the 16th Intern. Conf. on Megagauss Magnetic Field Generation and Related Topics, Kashiwa, 2018 p. 131
  66. Garanin S F i dr XLVI Mezhdunarodnaya Zvenigorodskaya konf. po fizike plazmy i upravlyaemomu termoyadernomu sintezu, ICPAF-2019, 18-22 marta 2019, g. Zvenigorod (M.: PLAZMAIOFAN, 2019) p. 122
  67. Sasorov P V Fizika Plazmy 16 1236 (1990)
  68. Garanin S F, Mamyshev V I Fizika Plazmy 16 1218 (1990)
  69. Ananyev S S, Suslin S V Fusion Eng. Design 137 338 (2018)
  70. Garanin S F, Buiko A M, Yakubov V B Prikladnaya Mekhanika Tekhnicheskaya Fizika 58 (5) 26 (2017); Garanin S F, Buyko A M, Yakubov V B J. Appl. Mech. Tech. Phys. 58 779 (2017)
  71. Liskien H, Paulsen A Atom. Data Nucl. Data Tables 11 569 (1973)
  72. Garanin S F, Dolinskii V Yu Fizika Plazmy 50 887 (2024); Garanin S F, Dolinskii V Yu Plasma Phys. Rep. 50 948 (2024)
  73. Schmidt A, Tang V, Welch D Phys. Rev. Lett. 109 205003 (2012)
  74. Schmidt A et al Phys. Rev. E 89 061101 (2014)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions