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arXiv · 2506.20578

Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum

Michal Hnatič·Tomáš Lučivjanský·Lukáš Mižišin·Yurii Molotkov·Andrei Ovsiannikov
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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 $\boldsymbol{\nabla} \times \boldsymbol{b}$ ($\boldsymbol{b} =$ magnetic field). Its presence destabilizes the trivial ground state $\langle \boldsymbol{b} \rangle = 0$ 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, $-11/3 + 2γ_{b\star}$ (with $γ_{b\star} = -0.1039 - 0.4202ρ^2$, for $|ρ| \leqslant 1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

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BibTeXRIS

Michal Hnatič, Tomáš Lučivjanský, Lukáš Mižišin, Yurii Molotkov, Andrei Ovsiannikov. 2025-06-25. Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum. https://doi.org/10.1103/xhzb-5hr4

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