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Boozer addressed the role of magnetic helicity in dynamos [Phys Fluids\textbf{B},(1993)]. He pointed out that the magnetic helicity conservationimplies that the dynamo action is more easily attainable if the electricpotential varies over the surface of the dynamo. This provided us withmotivation to investigate dynamos in Riemannian curved surfaces [Phys Plasmas\textbf{14}, (2007);\textbf{15} (2008)]. Thiffeault and Boozer [Phys Plasmas(2003)] discussed the onset of dissipation in kinematic dynamos. When curvatureis constant and negative, a simple simple laminar dynamo solution is obtainedon the flow topology of a Poincare disk, whose Gauss curvature is $K=-1$. Byconsidering a laminar plasma dynamo [Wang et al, Phys Plasmas (2002)] theelectric current helicity ${\lambda}\approx{2.34m^{-1}}$ for a Reynoldsmagnetic number of $Rm\approx{210}$ and a growth rate of magnetic field$|{\gamma}|\approx{0.022}$. Negative constant curvature non-compact$\textbf{H}^{2}$, has also been used in one-component electron 2D plasma byFantoni and Tellez (Stat Phys, (2008)). Chicone et al (CMP (1997)) showed fastdynamos can be supported in compact $\textbf{H}^{2}$. PACS: 47.65.Md. Key-word:dynamo plasma.

Slow plasma dynamo driven by electric current helicity in non-compact Riemann surfaces of negative curvature