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 ``mass-like'' term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\nabla \times \mathbf{b}$ ($\mathbf{b}=$ magnetic field). Its presence destabilizes the trivial ground state $⟨\mathbf{b}⟩=0$ 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 mass-like 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, $-11/3+2{\gamma }_{b\star }$ (with ${\gamma }_{b\star }=-0.1039-0.4202{\rho }^2$, for $|\rho |⩽1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

Accepted for publication in Physical Review E, 46 pages, 8 figures

References in corpus (18)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Experimental observation and characterization of the magnetorotational instability
• Anisotropic Thermal Conduction and the Cooling Flow Problem in Galaxy Clusters
• Magnetohydrodynamic experiments on cosmic magnetic fields
• Turbulence in the Interstellar Medium
• New developments in relativistic magnetohydrodynamics
• Intermittent magnetic field excitation by a turbulent flow of liquid sodium
• Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit
• Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
• Zonal shear and super-rotation in a magnetized spherical Couette flow experiment
• Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev--Kraichnan kinematic model
• Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
• Two-loop calculation of the turbulent Prandtl number
• Regulation of thermal conductivity in hot galaxy clusters by MHD turbulence
• Gauge fixing, BRS invariance and Ward identities for randomly stirred flows
• Comparative statistics of selected subgrid-scale models in large eddy simulations of decaying, supersonic MHD turbulence
• Anomalous scaling of a passive vector field in $d$ dimensions: Higher-order structure functions
• Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell