Spatially periodic, force-free magnetic fields with resistive decay

Author:
Rudolf X. Meyer

Journal:
Quart. Appl. Math. **40** (1983), 377-384

MSC:
Primary 78A25; Secondary 78A55, 85A20

DOI:
https://doi.org/10.1090/qam/693873

MathSciNet review:
693873

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Abstract: Force-free magnetic fields, i.e. fields that are either parallel or antiparallel to the electric current, occur in the solar chromosphere and also have been used in certain magnetic confinement schemes in controlled thermonuclear fusion research. In this paper, we derive a general expression for force-free fields that decay resistively and are spatially periodic.

**[1]**S. Chandrasekhar and P. C. Kendall,*On force-free magnetic fields*, Astrophys. J.**126**(1957), 457–460. MR**0088988**, https://doi.org/10.1086/146413**[2]**D. Voslamber and D. K. Callebaut,*Stability of force-free magnetic fields*, Phys. Rev. (2)**128**(1962), 2016–2021. MR**0144722****[3]**A. B. Severnyi,*Magnetic fields at various depths in the solar atmosphere*, Astronomicheskii Zhurnal**43**, 465-479 (1966), translated in Soviet Astronomy AJ.**10**(3) (1966)**[4]**Y. Nakagawa, M. A. Raadu, D. E. Billings, and D. McNamara,*On the topology of filaments and chromospheric fibrils near sunspots*, Solar Physics**19**, 72-85 (1971)**[5]**S. Lundquist,*Magneto-hydrostatic fields*, Ark. Fys.**2**(1950), 361–365. MR**0040994****[6]**A. D. Jette,*Force-free magnetic fields in resistive magnetohydrostatics*, J. Math. Anal. Appl.**29**, 109-122 (1970). See also A. D. Jeete and S. R. Sreenivasan,*Resistive force-free magnetic fields*, Phys. Fluids**12**, 2544-2547 (1969)**[7]**R. Courant and D. Hilbert,*Methods of mathematical physics*, vol. 2, Interscience Publishers, New York, 1962, p. 199**[8]**James Serrin,*Mathematical principles of classical fluid mechanics*, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959, pp. 125–263. MR**0108116**

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DOI:
https://doi.org/10.1090/qam/693873

Article copyright:
© Copyright 1983
American Mathematical Society