Magnetohydrodynamics in turbulent dynamo regime: the stability problem
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866915907903684608 |
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| author | Hnatič, Michal Lučivjanský, Tomáš Mižišin, Lukáš Molotkov, Yurii Ovsiannikov, Andrei |
| author_facet | Hnatič, Michal Lučivjanský, Tomáš Mižišin, Lukáš Molotkov, Yurii Ovsiannikov, Andrei |
| contents | This paper investigates stochastic solenoidal magnetohydrodynamics within the field-theoretic Martin-Siggia-Rose-De Dominicis-Janssen formalism, with a specific focus on the stability of the system when spatial mirror (parity) symmetry is explicitly broken. Under helical forcing, the one-particle-irreducible magnetic response function already at one loop contains a curl-type contribution that dominates the bare resistive term in the infrared limit, leading to exponential instability of the trivial state $\langle \mathbf{b} \rangle = \mathbf{0}$. We re-examine a stabilization mechanism proposed
in [L. T. Adzhemyan, et al., Theor. Math. Phys. 72, 940-950 (1987)], in which the system evolves into a phase with a dynamically spontaneously broken rotational symmetry and a generated mean magnetic field
$\langle \mathbf{b} \rangle = \mathbf{B}_0$. By deriving a self-consistency condition for $ \mathbf{B}_0$, we show that for any physically admissible (infrared) form of the pumping function, the model admits only a singular solution. We illustrate this with the standard power-law and "massive" pumping functions. We further show
that previous claims of a finite $ \mathbf{B}_0$ arose from an inconsistent truncation of asymptotic expansions. We argue that a consistent physical resolution requires including
a bare curl term in the stochastic induction equation, which naturally arises from a parity-violating modification of Ohm's law. With this modification, stabilization of the system by spontaneous symmetry breaking becomes a viable field-theoretic description of large-scale mean-field generation (turbulent dynamo) in helical turbulent
magnetohydrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10683 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magnetohydrodynamics in turbulent dynamo regime: the stability problem Hnatič, Michal Lučivjanský, Tomáš Mižišin, Lukáš Molotkov, Yurii Ovsiannikov, Andrei Plasma Physics Statistical Mechanics This paper investigates stochastic solenoidal magnetohydrodynamics within the field-theoretic Martin-Siggia-Rose-De Dominicis-Janssen formalism, with a specific focus on the stability of the system when spatial mirror (parity) symmetry is explicitly broken. Under helical forcing, the one-particle-irreducible magnetic response function already at one loop contains a curl-type contribution that dominates the bare resistive term in the infrared limit, leading to exponential instability of the trivial state $\langle \mathbf{b} \rangle = \mathbf{0}$. We re-examine a stabilization mechanism proposed in [L. T. Adzhemyan, et al., Theor. Math. Phys. 72, 940-950 (1987)], in which the system evolves into a phase with a dynamically spontaneously broken rotational symmetry and a generated mean magnetic field $\langle \mathbf{b} \rangle = \mathbf{B}_0$. By deriving a self-consistency condition for $ \mathbf{B}_0$, we show that for any physically admissible (infrared) form of the pumping function, the model admits only a singular solution. We illustrate this with the standard power-law and "massive" pumping functions. We further show that previous claims of a finite $ \mathbf{B}_0$ arose from an inconsistent truncation of asymptotic expansions. We argue that a consistent physical resolution requires including a bare curl term in the stochastic induction equation, which naturally arises from a parity-violating modification of Ohm's law. With this modification, stabilization of the system by spontaneous symmetry breaking becomes a viable field-theoretic description of large-scale mean-field generation (turbulent dynamo) in helical turbulent magnetohydrodynamics. |
| title | Magnetohydrodynamics in turbulent dynamo regime: the stability problem |
| topic | Plasma Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2603.10683 |