Turbulent dynamos at low magnetic Prandtl number

Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. Plasmas in stellar interiors and conducting fluids in planetary cores and liquid sodium experiments are characterized by a magnetic Prandtl number PM (the ratio of the kinematic viscosity ν to the magnetic diffusivity η) much smaller than one. As a few examples, the magnetic Prandtl number in the solar convective region is estimated to be PM ≈ 10−5 − 10−6, and in the Earth’s core PM ≈ 10−5. While numerical simulations of dynamo action in these objects are available, the large values of the kinetic (RV) and magnetic (RM) Reynolds numbers forbid a study using realistic values of PM. Simulations of the geodynamo or the solar convective region are often done for PM ∼ 1. While the proper separation of the kinetic and magnetic dissipation scales cannot be achieved in these simulations, values of PM much smaller than one can be reached under more idealized conditions. Pseudospectral methods in periodic boxes give an excellent tool to study the behavior of magnetohydrodynamic (MHD) turbulence in the regime PM < 1. In this talk, we review recent results from simulations of helical and non-helical dynamos at PM < 1 using pseudospectral codes in periodic boxes [1, 2, 3, 4]. To extend the range in PM in the simulations