Two-loop turbulent helical magnetohydrodynamics: Large-scale dynamo and energy spectrum.

Abstract

We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable "masslike" term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to ∇×b (b= magnetic field). Its presence destabilizes the trivial ground state 〈b〉=0 and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external masslike parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfvén modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, -11/3+2γ_{b★} (with γ_{b★}=-0.1039-0.4202ρ^{2}, for |ρ|⩽1 as the degree of helicity), compared to the Kolmogorov velocity spectrum of -11/3, thereby breaking equipartition.