Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T06:45:14.407Z Has data issue: false hasContentIssue false

Minimum dissipative relaxed states applied to laboratory and space plasmas

Published online by Cambridge University Press:  01 April 2009

B. DASGUPTA
Affiliation:
Institute of Geophysics and Planetary Physics (IGPP), University of California, Riverside, CA 92521, USA ([email protected])
DASTGEER SHAIKH
Affiliation:
Institute of Geophysics and Planetary Physics (IGPP), University of California, Riverside, CA 92521, USA ([email protected])
Q. HU
Affiliation:
Institute of Geophysics and Planetary Physics (IGPP), University of California, Riverside, CA 92521, USA ([email protected])
G. P. ZANK
Affiliation:
Institute of Geophysics and Planetary Physics (IGPP), University of California, Riverside, CA 92521, USA ([email protected])

Abstract

The usual theory of plasma relaxation, based on the selective decay of magnetic energy over the (global) magnetic helicity, predicts a force-free state for a plasma. Such a force-free state is inadequate to describe most realistic plasma systems occurring in laboratory and space plasmas as it produces a zero pressure gradient and cannot couple magnetic fields with flow. A different theory of relaxation has been proposed by many authors, based on a well-known principle of irreversible thermodynamics, the principle of minimum entropy production rate which is equivalent to the minimum dissipation rate of energy. We demonstrate the applicability of minimum dissipative relaxed states to various self-organized systems of magnetically confined plasma in the laboratory and in the astrophysical context. Such relaxed states are shown to produce a number of basic characteristics of laboratory plasma confinement systems and solar arcade structure.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amari, T. and Luciani, J. F. 2000 Helicity redistribution during relaxation of astrophysical plasmas. Phys. Rev. Lett. 84, 11961199.CrossRefGoogle ScholarPubMed
Antoni, V., Martini, S., Ortolini, S. and Paccagnella, R. 1983 Workshop on Mirror-based and Field-reversed Approaches to Magnetic Fusion, International School of Plasma Physics, Varenna, Italy, p. 107.Google Scholar
Bhattacharya, R., Janaki, M. S. and Dasgupta, B. 2000 Tokamak, reversed field pinch and intermediate structures as minimum-dissipative relaxed states. Phys. Plasmas 7, 48014804.CrossRefGoogle Scholar
Bhattacharya, R., Janaki, M. S. and Dasgupta, B. 2001 Field-reversed configuration (FRC) as a minimum-dissipative relaxed state. Phys. Lett. A 291A, 291295.CrossRefGoogle Scholar
Bhattacharya, R., Janaki, M. S. and Dasgupta, B. 2003 Relaxation phenomenon in the field reversed configuration. Plasma Phys. Control. Fusion 45, 6370.CrossRefGoogle Scholar
Bhattacharya, R. and Janaki, M. S. 2004 Dissipative relaxed states in two-fluid plasma with external drive. Phys. Plasmas 11, 56155619.CrossRefGoogle Scholar
Bhattacharya, R., Janaki, M. S., Dasgupta, B. and Zank, G. P. 2007 Solar arcades as possible minimum dissipative relaxed states. Solar Phys. 240, 6376.CrossRefGoogle Scholar
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Bouzat, S. and Farengo, R. 2006 Analytical solutions for minimum dissipation states: flux core spheromak sustained by helicity injection. J. Plasma Phys. 72, 443456.CrossRefGoogle Scholar
Chandrasekhar, S. and Kendall, P. C. 1957 On force-free magnetic fields. Astrophys. J. 126, 457459.CrossRefGoogle Scholar
Chandrasekhar, S. and Woltjer, L. 1958 On force-free magnetic fields. Proc. Natl. Acad. Sci. USA 44, 285289.CrossRefGoogle ScholarPubMed
Dasgupta, B., Dasgupta, P., Janaki, M. S., Watanabe, T. and Sato, T. 1998 Relaxed states of a magnetized plasma with minimum dissipation. Phys. Rev. Lett. 81, 31443147.CrossRefGoogle Scholar
Dasgupta, B., Janaki, M. S., Bhattacharya, R., Dasgupta, P., Watanabe, T. and Sato, T. 2002 Spheromak as a relaxed state with minimum dissipation. Phys. Rev. E E65, 046405 16.Google Scholar
Dasgupta, B., Sato, T., Hayashi, T., Watanabe, K. and Watanabe, T.-H. 1995 Formation of a field reversed configuration by coalescence of Spheromaks. Trans. Fusion Technol. 27, 374377.CrossRefGoogle Scholar
Farengo, R. and Caputi, K. I. 2002 Relaxed, minimum dissipation states, for a flux core spheromak sustained by helicity injection. Plasma Phys. Control. Fusion 44, 17071722.CrossRefGoogle Scholar
Farengo, R. and Sobehart, J. R. 1994 Minimum ohmic dissipation and DC helicity injection in tokamak-like plasmas. Plasma Phys. Control. Fusion 36, 16911700.CrossRefGoogle Scholar
Farengo, R. and Sobehart, J. R. 1995 Determination of minimum-dissipation states with self-consistent resistivity in magnetized plasma. Phys. Rev. E 52, 21022105.Google Scholar
Guo, H. Y., Hoffman, A. L., Steinhauer, L. C. and Miller, K. E. 2005 Observations of improved stability and confinement in a high-β self-organized spherical-torus-like field-reversed configuration. Phys. Rev. Lett. 95, 175001, 14.CrossRefGoogle Scholar
Guo, H. Y., Hoffman, A. L., Steinhauer, L. C., Miller, K. E. and Milroy, R. D. 2006 Evidence of relaxation and spontaneous transition to a high-confinement state in high-β steady-state plasmas sustained by rotating magnetic fields. Phys. Rev. Lett. 97, 235002, 14.CrossRefGoogle Scholar
Hart, G. W., Chin-Fatt, C., deSilva, A. W., Goldenbaum, G. C., Hess, R. and Shaw, R. S. 1983 Finite-pressure-gradient influences on ideal spheromak equilibrium. Phys. Rev. Lett. 51, 15581561.CrossRefGoogle Scholar
Hu, Q. and Dasgupta, B. 2008 An improved approach to non-force-free coronal magnetic field extrapolation. Sol. Phys. 247, 87101.CrossRefGoogle Scholar
Hu, Q., Dasgupta, B. and Choudhary, D. P. 2007 Application of the principle of minimum dissipation rate to solar coronal magnetic field extrapolation. In Proc. 6th Annual International Astrophysics Conference: Turbulence and Nonlinear Processes in Astrophysical Plasmas, 16–22 March, Hawaii (AIP Conf. Proc., 932, American Institute of Physics, ed. Shaikh, D. and Zank, G. P.), pp. 376381.Google Scholar
Lahiri, S., Iyenger, A. N., Mukhopadhyay, S. and Pal, R. 1996 Accessibility of very low q a (VLQ) and ultra-low q a (ULQ) discharges in SINP tokamak. Nucl. Fusion 36, 254257.CrossRefGoogle Scholar
Montgomery, D. and Phillips, L. 1988 Minimum dissipation rates in magnetohydrodynamics. Phys. Rev. A 38, 29532964.CrossRefGoogle ScholarPubMed
Ono, Y., Morita, A., Katsurai, and Yamada, M. 1993 Experimental investigation of three-dimensional magnetic reconnection by use of two colliding spheromaks. Phys. Fluids B B5, 36913701.CrossRefGoogle Scholar
Ortolani, S. and Schnack, D. D. 1993 Magnetohydrodynamics of Plasma Relaxation. Singapore: World Scientific.CrossRefGoogle Scholar
Prigogine, I. 1946 Etude Thermodynamique des Phénomènes Irreversibles. Liège: Editions Desoer.Google Scholar
Rayleigh 1873 Proc. Math Soc. London 363, 357.Google Scholar
Rosenbluth, M. N. and Bussac, M. N. 1979 MHD stability of spheromak. Nucl. Fusion 19, 489498.CrossRefGoogle Scholar
Sato, T. and Complexity Simulation Group 1996 Complexity in plasma: from self-organization to geodynamo. Phys. Plasmas. 3, 21352142.CrossRefGoogle Scholar
Shaikh, D., Dasgupta, B., Zank, G. P. and Hu, Q. 2008 Theory and simulations of principle of minimum dissipation rate. Phys. Plasmas. 15, 012306 15.CrossRefGoogle Scholar
Taylor, J. B. 1974 Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33, 11391141.CrossRefGoogle Scholar
Turner, L. 1986 Hall effects on magnetic relaxation. IEEE Trans. Plasma Sci. 14, 849857.CrossRefGoogle Scholar
Tuszewski, M. 1988 Field reversed configurations. Nucl. Fusion 28, 20332092.CrossRefGoogle Scholar
Watanabe, T.-H., Sato, T. and Hayashi, T. 1997 Magnetohydrodynamic simulation on co- and counter-helicity merging of spheromaks and driven magnetic reconnection. Phys. Plasmas 4, 12971307.CrossRefGoogle Scholar
Yamada, H., Kusano, K., Kamada, Y., Utsumi, H., Yoshida, Z. and Inoue, N. 1987 Nucl. Fusion 27, 1169.CrossRefGoogle Scholar
Yoshida, Z., Ishida, S., Hattori, K., Murakami, Y., Morikawa, J., Nehei, N. and Inoue, N. 1986 Remarks on relaxation phenomenon in toroidal discharge. J. Phys. Soc. Japan 55, 450453.CrossRefGoogle Scholar
Zhu, S., Horiuchi, R. and Sato, T. 1995 Non-Taylor magnetohydrodynamic self-organization. Phys. Rev. E 51, 60476056.Google ScholarPubMed