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

Otsuki, Mamoru

doi:10.51094/jxiv.284

##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

This paper demonstrates that it is possible to induce axisymmetric magnetic fields by a poloidal flow to determine the effect on the magnetic field caused by a certain flow of a conductive fluid. Using a simultaneous equation expressed by inductances induced from the induction equation expressed by a vector potential and treating the current as an eigenvalue problem, it is shown that different current modes can exist. While there are many different expressions of the electromagnetic induction equation, the use of the simultaneous equation expressed by inductances is novel. Each mode varies according to its eigenvalue, which can be positive under certain conditions, resulting in an eigenvector that increases over time, thereby maintaining a magnetic field, at least in a poloidal flow. Several case studies based on the dimensions and plasma properties of a star are reviewed; however, there are no dimensional restrictions to the provided equations, which are expected to be appropriate for various applications. For example, the proposed methodology could be applied to enhance the understanding of specific phenomena occurring in celestial bodies (planets and stars).

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

J. Larmor, Reports Br. Assoc. 87, 159–160 (1919).

H. K. Moffat, Field Generation in Electrically Conducting Fluids. Cambridge University Press (1978).

G. Rüdiger, R. Hollerbach, The Magnetic Universe. First Edition. Wiley-VCH, Weinheim, Germany (2004).

M. M. Adams, D. R. Stone, D. S. Zimmerman, and D. P. Lathrop, Prog. Earth Planet. Sci. 2, 1–18 (2015).

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

P. H. Roberts and G. A. Glatzmaier, Rev. Mod. Phys. 72(4), 1081–1123 (2000).

A. Brandenburg, Astrophys. J. 465(2), L115-118 (1996).

R. Kaiser and A. Tilgner, SIAM J. Appl. Math. 74(2), 571–597 (2014).

J. J. Love, Geophys. Res. Lett. 23(8), 857–860 (1996).

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).

B. F. Farrel and P. J. Ioannou, Astrophys. J. 522(2), 1079–1087 (1999).

K. H. Burrell and J. D. Callen, Phys. Plasmas 28(6), 1–28 (2021).

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