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Plasma flow in a curved magnetic field

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Abstract

A beam of collisionless plasma is injected along a longitudinal magnetic field into a region of curved magnetic field. Two unpredicted phenomena are observed: The beam becomes deflected in the directionopposite to that in which the field is curved, and itcontracts to a flat slab in the plane of curvature of the magnetic field.

The plasma is produced by a conical theta-pinch gun and studied by means of high speed photography, electric and magnetic probes, ion analyser, and spectroscopy.

The plasma beam is collisionless and its behaviour is, in principle, understood on the basis of gyro-centre drift theory. A fraction of the transverse electric fieldE=−v×B, which is induced when the beam enters the curved magnetic field, is propagated upstream and causes the reverse deflection byE×B drift. The upstream propagation of the transverse electric field is due to electron currents.

The circuit aspect on the plasma is important. The transverse polarization current in the region with the curved field connects to a loop of depolarization currents upstream. The loop has limited ability to carry current because of the collisionless character of the plasma; curlE is almost zero and electric field components arise parallel to the magnetic field. These play an essential role, producing runaway electrons, which have been detected. An increased electron temperature is observed when the plasma is shot into the curved field. Runaway electrons alone might propagate the electric field upstream in case the electron thermal velocity is insufficient.

The phenomenon is of a general character and can be expected to occur in a very wide range of ensities. The lower density limit is set by the condition for self-polarization,nm i /ɛ 0 B 2≫ 1 or, which is equivalent,c 2/v 2A ≫;1, wherec is the velocity of light, andv A the Alfvén velocity. The upper limit is presumably set by the requirement ω e τ e ≫ 1.

The phenomenon is likely to be of importance, for example, for the injection of plasma into magnetic bottles and in space and solar physics. The paper illustrates the complexity of plasma flow phenomena and the importance of close contact between experimental and theoretical work.

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References

  • Alfvén, H.: 1940, ‘On the Motion of a Charged Particle in a Magnetic Field’,Ark. Mat. Astron: Fys., Swedish Academy of Science,27A, Stockholm.

    Google Scholar 

  • Alfvén, H.: 1968,Ann. Géophys. 24, 1.

    Google Scholar 

  • Alfvén, H.: 1971,Science 172, 991.

    Google Scholar 

  • Alfvén, H.: 1977,Rev. Geophys. Space Phys. 15, 271.

    Google Scholar 

  • Alfvén, H. and Fälthammar, C.-G.: 1963,Cosmical Electrodynamics, Clarendon Press, Oxford.

    Google Scholar 

  • Alfvén, H. and Arrhenius, G.: 1976,Evolution of the Solar System, NASA SP-345, U.S. Gov. Printing Office, Washington, D.C.

    Google Scholar 

  • Baker, D.A.: 1962, Los Alamos Sci. Lab. Res. Rept.

  • Baker, D. A. and Hammel, J. E.: 1962,Phys. Rev. Letters 8, 157.

    Google Scholar 

  • Baker, D. A. and Hammel, J. E.: 1965,Phys. Fluids 8, 713.

    Google Scholar 

  • Barney, F. O.: 1969,Phys. Fluids 12, 2429.

    Google Scholar 

  • Beckers, J. M.: 1968,Solar Phys. 3, 367.

    Google Scholar 

  • Bieger, W., Gresser, H., Noll, P. and Tuczek, H. I.: 1963,Z. Naturforsch. 18a, 453.

    Google Scholar 

  • Block, L. P.: 1972,Cosmic Electrodyn. 3, 349.

    Google Scholar 

  • Block, L. P.: 1977, ‘A Double Layer Review’, Royal Inst. of Technology, Stockholm, TRITA-EPP-77-16 (submitted toAstrophys. Space Sci.).

  • Block, L. P. and Fälthammar, C.-G.: 1976,Ann. Géophys. 32, 161.

    Google Scholar 

  • Carlqvist, P.: 1969,Solar Phys. 7, 377.

    Google Scholar 

  • Carlqvist, P.: 1972,Cosmic Electrodyn. 3, 377.

    Google Scholar 

  • Colomès, J. and Véron, D.: 1969,Phys. Fluids 12, 1717.

    Google Scholar 

  • Danielsson, L.: 1973,Astrophys. Space Sci. 24, 459.

    Google Scholar 

  • Danielsson, L. and Brenning, N.: 1975,Phys. Fluids 18, 661.

    Google Scholar 

  • Demidenko, I. I., Lomino, N. S., Padalka, V. O., Safronov, B. O. and Sinelnikov, K. D.: 1966,J. Nucl. Energy, C. Plasma Physics 8, 433.

    Google Scholar 

  • Demidenko, I. I., Lomino, N. S., Padalka, V. O., Rutkevich, B. N. and Sinelnikov, K. D.: 1969,Zh. Tekhn. Fiz. 39, 27 (Soviet Phys.-Techn. Phys. 14, 16).

    Google Scholar 

  • Demidenko, I. I., Lomino, N. S. and Padalka, V. O.: 1971,Zh. Tekhn. Fiz. 41, 1392 (Soviet Phys.-Techn. Phys. 16, 1096, 1972).

    Google Scholar 

  • Ejima, S., Marshall, T. C., and Schlesinger, S. P.: 1974,Phys. Fluids 17, 163.

    Google Scholar 

  • Eubank, H. P. and Wilkerson, T. D.: 1961,Phys. Fluids 4, 1407.

    Google Scholar 

  • Eubank, H. P. and Wilkerson, T. D.: 1963a,Phys. Fluids 6, 914.

    Google Scholar 

  • Eubank, H. P. and Wilkerson, T. D.: 1963b,Rev. Sci. Instr. 34, 12.

    Google Scholar 

  • Fälthammar, C.-G.: 1977,Rev. Geophys. Space Phys. 15, 457.

    Google Scholar 

  • Hallén, E.: 1963,Electromagnetic Theory, Chapman and Hall, London.

    Google Scholar 

  • Hammel, J. E. and Baker, D. A.: 1966,Proc. Conf. on Plasma Physics and Controlled Nuclear Fusion Res. Culham 1965, IAEA Vienna.

  • Karlson, E.: 1973, ‘Plasma Stream in an Inhomogeneous Transverse Magnetic Field’, Royal Inst. of Technology, Stockholm, TRITA-EPP-73-08; abbreviated version publ. inProc. 6th European Conf. on Controlled Fusion and Plasma Physics, Moscow, 1973, p. 397.

  • Khiznyak, N. A.: 1965,Zh. Tekhn. Fiz. 35, 847, (Soviet Phys.-Techn. Phys. 10, 655, 1965).

    Google Scholar 

  • Komori, A., Sato, N., Sugai, H. and Hatta, Y.: 1977,Plasma Phys. 19, 283.

    Google Scholar 

  • Kopp, R. A. and Kuperus, M.: 1968,Solar Phys. 4, 212.

    Google Scholar 

  • Landau, L. D. and Lifshitz, E. M.: 1960,Electrodynamics of Continuous Media, Pergamon Press.

  • Lindberg, L.: 1976, ‘Injection of Plasma into a Transverse Magnetic Field’, Royl Inst. of Technology, Stockholm, TRITA-EPP-76-01.

    Google Scholar 

  • Lindberg, L. and Kristoferson, L.: 1971,Cosmic Electrodyn. 2, 305.

    Google Scholar 

  • Lindberg, L. and Kristoferson, L.: 1972, ‘Reverse Deflection and Contraction of a Plasma Beam Entering a Curved Magnetic Field’, Royal Inst. of Technology, Stockholm, TRITA-EPP-72-32.

    Google Scholar 

  • Marković, P. D. and Scott, F. R.: 1971,Phys. Fluids 14, 1742.

    Google Scholar 

  • Neugebauer, M. and Snyder, C. W.: 1966,J. Geophys. Res. 71, 4469.

    Google Scholar 

  • Niedermeyer, H.: 1967, ‘Ein Elektrostatischer Analysator zur Messung der Energie von Ionen und Elektronen aus heissen Plasmen’, Garching Res. Rept IPP 1/66.

  • Öhman, Y. (ed.): 1968, Nobel Symposium 9,Mass Motions in Solar Flares and Related Phenomena, Almqvist and Wiksell, Stockholm.

    Google Scholar 

  • Raadu, M. A.: 1975, ‘Critical Ionization Velocity and Electrostatic Instabilities’, Royal Inst. of Technology, Stockholm, TRITA-EPP-75-28.

    Google Scholar 

  • Raadu, M. A.: 1977, ‘The Role of Electrostatic Instabilities’, Royal Inst. of Technology, Stockholm, TRITA-EPP-75-28.

    Google Scholar 

  • Raadu, M. A.: 1977, ‘The Role of Electrostatic Instabilities in the Critical Ionization Velocity Mechanism’, Royal Inst. of Technology, Stockholm, TRITA-EPP-77-18 (to be published inAstrophys. Space Sci.).

    Google Scholar 

  • Schmidt, G.: 1960,Phys. Fluids 3, 961.

    Google Scholar 

  • Shawhan, S. D., Fälthammar, C.-G. and Block, L. P.: 1977, ‘On the Nature of Large Auroral Zone Electric Fields at OneR E Altitude’, Royal Inst. of Technology, Stockholm, TRITA-EPP-77-09; also in University of Iowa, U.S.A., Rept. 77-25.

    Google Scholar 

  • Sherman, J. C.: 1973,Astrophys. Space Sci. 24, 487.

    Google Scholar 

  • Tanaka, Y., Oya, K., Okuda, T., and Yamamoto, K.: 1972,J. Phys. Soc. Japan 32, 510.

    Google Scholar 

  • Torvén, S. and Babić, M.: 1975, ‘Current Chopping Space Charge Layers in a Low Pressure Arc Plasma’,Proc. 12th Int. Conf. on Phenomena in Ionized Gases, Eindhoven, I, North-Holland/Elsevier, p. 124.

  • Trivelpiece, A. W. and Gould, R. W.: 1959,J. Appl. Phys. 30, 1784.

    Google Scholar 

  • Wahlberg, C.: 1974, ‘Electron Plasma Oscillations in a Static Electric Field’, Royal Inst. of Technology, Stockholm, TRITA-EPP-74-21.

    Google Scholar 

  • Wahlberg, C.: 1976a, ‘Electron Oscillations of a Hot Collisionless Plasma in a Static Electric Field’, Royal Inst. of Technology, Stockholm, TRITA-EPP-76-03.

    Google Scholar 

  • Wahlberg, C.: 1977,J. Plasma Phys. 18, 415.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Dept of Plasma Physics, Royal Institute of Technology, Stockholm, Sweden

    Lennart Lindberg

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  1. Lennart Lindberg
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Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978

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Lindberg, L. Plasma flow in a curved magnetic field. Astrophys Space Sci 55, 203–225 (1978). https://doi.org/10.1007/BF00642589

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  • DOI: https://doi.org/10.1007/BF00642589

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