Slow Plasma Dynamo Driven by Electric Current Helicity in Non-Compact Riemann Surfaces of Negative Curvature

Luiz Carlos Garcia de Andrade

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DOI: 10.4236/jmp.2010.15046                

Abstract

Boozer addressed the role of magnetic helicity in dynamos [1]. He pointed out that the magnetic helicity conservation implies that the dynamo action is more easily attainable if the electric potential varies over the surface of the dynamo. This provided motivated us to investigate dynamos in Riemannian curved surfaces [2]. Thiffeault and Boozer [3] discussed the onset of dissipation in kinematic dynamos. In this paper, when curvature is constant and negative, a simple laminar dynamo solution is obtained on the flow topology of a Poincare disk, whose Gauss curvature is K = –1. By considering a laminar plasma dynamo [4] the electric current helicity λ ≈ 2.34 m–1 for a Reynolds magnetic number of Rm ≈ 210 and a growth rate of magnetic field |γ| ≈ 0.022 are obtained. Negative constant curvature non-compact H2 manifold, has also been used in onecomponent electron 2D plasma by Fantoni and Tellez [5]. Chicone et al. (CMP (1997)) showed fast dynamos can be supported in compact H2. PACS: 47.65.Md.

Keywords

Plasma, Dynamos

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. H. Boozer, Physics of Fluids B, Vol. 7, 1993, p. 2271.
[2]	L. C. Garcia de Andrade, Physics of Plasmas, Vol. 15, 2008.
[3]	J. L. Thiffeault and A. D. Boozer, Physics of Plasmas, Vol. 10, No. 1, 2003, p. 259.
[4]	A. Wang, V. Pariev, C. Barnes and V. Barnes, Physics of Plasmas, Vol. 9, 2002, p. 1491.
[5]	R. Fantoni and G. Tellez, Journal of Statistical Physics, Vol. 133, 2008, p. 121.
[6]	J. L. Thiffeault, Journal of Physics A, Vol. 34, No. 29, 2001, p. 5575.
[7]	C. Chicone and Yu. Latushkin, “Evolution Semigroups in Dynamical Systems and Differential Equations,” American Mathematical Society, 1999.
[8]	B. Bayly, Physical Review Letters, Vol. 57, 1986, p. 2800.
[9]	A. Gilbert, Proceedings of the Royal Society London A, Vol. 433, 1993, p. 585.
[10]	V. Arnold, Ya. B. Zeldovich, A. Ruzmaikin and D. D. Sokoloff, JETP, Vol. 81, No. 6, 1981, p. 2052.
[11]	A. Shukurov, R. Stepanov and D. D. Sokoloff, “Dynamo Action in Moebius Flow,” Physical Review E, Vol. 78, 2008, p. 025301.
[12]	V. Pariev, S. Colgate and J. M. Finn, Astro-Physical Journal, Vol. 658, No. 128, 2007.
[13]	H. Busse, Physics of Fluids B, Vol. 14, 2003, p. 1301.