JMP  Vol.1 No.5 , November 2010
Slow Plasma Dynamo Driven by Electric Current Helicity in Non-Compact Riemann Surfaces of Negative Curvature
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

Cite this paper
nullL. Andrade, "Slow Plasma Dynamo Driven by Electric Current Helicity in Non-Compact Riemann Surfaces of Negative Curvature," Journal of Modern Physics, Vol. 1 No. 5, 2010, pp. 324-327. doi: 10.4236/jmp.2010.15046.
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