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BOOSTING THE MAGNETIC FIELD OF A TOROIDAL CONDUCTIVE FLUID BY A POLOIDAL FLOW

##article.authors##

  • Otsuki, Mamoru Independent

DOI:

https://doi.org/10.51094/jxiv.284

キーワード:

Poloidal flow、 dynamo theory、 electromagnetic induction、 inductance、 conductive fluid、 magnetohydrodynamics

抄録

Cowling's theorem asserts that applying the first-order derivative of the stream function of the magnetic field results in a value of zero and its second-order derivative does not result in a value of zero. Thus, a contradiction to the magnetic maximum or minimum pole in the electromagnetic induction equation occurs. However, a different interpretation of this assertion is presented in this paper. If Ohm's law in Cowling's theorem includes an electromotive force due to a vector potential, this equation can be satisfied, which is why the magnetic flux fluctuates. The self-excitation mechanism causes these fluctuations. In this paper, a theory that decomposes vector potential into inductance and current is introduced, and it is solved as an eigenvalue problem. Considering the suppression of convection by the Lorentz force is equally essential to understanding the stability of the magnetic fields.

利益相反に関する開示

The author has no conflicts of interest to declare. No funding was obtained for this work.

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引用文献

T. G. Cowling and Q. J. Mech. Appl. Math. 10(1), 129–136 (1957).

H. S. Reall, Mathematical Tripos Part IB: Electromagnetism [Internet]. Available from: www.damtp.cam.ac.uk/user/hsr1000/electromagnetism_lectures.pdf. Accessed 03/11/2022.

H. A. Haus and J. R. Melcher, Vector Potential and the Boundary Value Point of View. In: Electromagnetic Fields and Energy [Internet], Massachusetts Institute of Technology (1998). Available from: https://ocw.mit.edu/courses/res-6-001-electromagnetic-fields-and-energy-spring-2008/pages/chapter-8/. Accessed 03/11/2022.

A. Kanzawa, Netsu Bussei. 4(1), 3-11 (1990) (In Japanese).

R. Stieglitz, Nonlin. Proc. Geophys. 9, 165–170 (2002).

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投稿日時: 2023-02-13 11:54:06 UTC

公開日時: 2023-02-14 11:13:06 UTC — 2023-07-31 05:47:02 UTCに更新

バージョン

改版理由

An interpretation is added to the relationship between this thesis and Cowling's theorem.
研究分野
物理学