Existence of a turbulent dynamo in mirror-symmetric (ρ = 0) MHD

Determine whether a large-scale turbulent dynamo—i.e., spontaneous generation of a nonzero mean magnetic field—can arise in incompressible stochastic magnetohydrodynamics when the helicity parameter ρ equals zero (mirror-symmetric turbulence).

Background

Based on two-loop analysis, the authors argue that helicity appears fundamental for the turbulent dynamo; however, they observe that one-loop results for the spontaneous field are independent of helicity and the two-loop helical contribution is small, prompting the question of dynamo existence at ρ = 0.

They note that local stability analysis is inconclusive and state there is no known global criterion to decide between the locally stable states ⟨b⟩ = 0 and ⟨b⟩ = B, leaving the question open as it has been for decades.