Applications of Beltrami functions in plasma physics

Nonlinear Analysis, Theory, Methods and Applications

Volumn 30, Issue 6, 1997, Pages 3617-3627

  Yoshida, Zensho ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Beltrami field; Chaos; Cohomology class; Dynamo theory; Eigenfunction expansion; Helicity; Invariant measure; Plasma physics; Reduced model; Self organization; Singular perturbation; Statistical equilibrium

Indexed keywords

EID: 0012378238     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(97)00262-9     Document Type: Article

References (23)

1. LADYZHENSKAYA O. A. & SOLONNIKOV V. A., The linearization principle and invariant manifolds for problems of magnetohydrodynamics, J. Soviet Math. 8, 384-422 (1977).
2. YOSHIDA Z. & GIGA Y., On the Ohm-Navier-Stokes system in magnetohydrodynamics, J. Math. Phys. 24, 2860-2864 (1983).
3. YOSHIDA Z., A remark on the Hamiltonian form of the magnetic-field-line equations, Phys. Plasmas 1, 208-209 (1994).
4. GRAD, H. & RUBIN, H., Hydromagnetic equilibria and force-free fields, in Second United Nation Conference on the Peaceful Uses of Atomic Energy, Vol. 31, pp. 190-197. IAEA, Geneva (1958).
5. YOSHIDA Z., Beltrami functions: a paradigm of streamline chaos, in Current Topics in the Physics of Fluids, Vol. 1, pp. 155-178. Council of Scientific Information, Trivandrum (1994).
6. VAINSHTEIN S. I., SAGDEEV R. Z., ROSNER R. & KIM E.-K., On the fractal properties of the stretch-twist-fold magnetic dynamo, Phys. Rev. E 53, 4729-4744 (1996).
7. WOLTJER L., A theorem on force-free magnetic fields, Proc. Natl. Acad. Sci. U.S.A. 44, 489-491 (1958).
8. TAYLOR J. B., Relaxation of toroidal plasma and generation of reversed magnetic fields, Phys. Rev. Lett. 33, 1139-1141 (1974); Relaxation and magnetic reconnection in plasmas, Rev. Mod. Phys. 58, 741-763 (1986).
9. TAYLOR J. B., Relaxation of toroidal plasma and generation of reversed magnetic fields, Phys. Rev. Lett. 33, 1139-1141 (1974); Relaxation and magnetic reconnection in plasmas, Rev. Mod. Phys. 58, 741-763 (1986).
10. HASEGAWA A., Self-organization processes in continuous media, Adv. Phys. 34, 1-42 (1985).
11. RUSSEL C. T., Reconnection at the earth's magnetopause: magnetic field observations and flux transfer events, in Magnetic Reconnection in Space and Laboratory Plasmas, (Ed. E. W. Hones), pp. 124-138. American Geophysics Union, Washington DC (1984).
12. KÖNIGL A. & CHOUDHURI A. R., Force-free equilibria of magnetized jets, Astrophys. J. 289, 173-187 (1985).
13. YOSHIDA Z., Direct ion heating through MHD relaxation, Nucl. Fusion 31, 386-390 (1991).
14. YOSHIDA Z. & HASEGAWA A., Transit-time magnetic pumping by spontaneous fluctuations in a magnetohydrodynamic relaxation process, Phys. Fluids B 4, 3013-3015 (1992).
15. YOSHIDA Z. & GIGA Y., Remarks on spectra of operator rot, Math. Z. 204, 235-245 (1990).
16. TEMAM R., Navier-Stokes Equations, North-Holland, Amsterdam (1984).
17. MONTGOMERY D., TURNER L. & VAHALA G., Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry, Phys. Fluids 21, 757-764 (1978).
18. CHANDRASEKHAR S. & KENDALL P. C., On force-free magnetic fields, Astrophys. J. 126, 457-460 (1957).
19. ITO N. & YOSHIDA Z., Statistical mechanics of magnetohydrodynamics, Phys. Rev. E 53, 5200-5206 (1996).
20. BOOZER A. H., Ohm's law for mean magnetic fields, J. Plasma Phys. 35, 133-139 (1986).
21. STRAUSS H. A., Hyper-resistivity produced by tearing mode turbulence, Phys. Fluids 29, 3668-3671 (1986).
22. YOSHIDA Z. & HASEGAWA A., Anomalous transports associated with the helicity transport in a plasma, Phys. Fluids B 3, 3059-3064 (1991).
23. YOSHIDA Z., SAKURAGI Y. & YAMAKOSHI Y, A reduced model of chaotic magnetic fluctuations in a tokamak plasma, J. Plasma Phys. 49, 403-411 (1993).