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The onset of dynamo action is investigated within the context of a newlydeveloped low Rossby, low magnetic Prandtl number, convection-driven dynamomodel. This multiscale model represents an asymptotically exact form of an$\alpha^2$ mean field dynamo model in which the small-scale convection isrepresented explicitly by finite amplitude, single mode solutions. Both steadyand oscillatory convection are considered for a variety of horizontalplanforms. The kinetic helicity is observed to be a monotonically increasingfunction of the Rayleigh number. As a result, very small magnetic Prandtlnumber dynamos can be found for sufficiently large Rayleigh numbers. Alldynamos are found to be oscillatory with an oscillation frequency thatincreases as the strength of the convection is increased and the magneticPrandtl number is reduced. Kinematic dynamo action is strongly controlled bythe profile of the helicity; single mode solutions which exhibit boundary layerbehavior in the helicity show a decrease in the efficiency of dynamo action dueto the enhancement of magnetic diffusion in the boundary layer regions. For agiven value of the Rayleigh number, lower magnetic Prandtl number dynamos areexcited for the case of oscillatory convection in comparison to steadyconvection. With regards to planetary dynamos, these results suggest that thelow magnetic Prandtl number dynamos typical of liquid metals are more easilydriven by thermal convection than by compositional convection.

Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: single mode solutions