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Evolution of Mirror Axion Solitons

P. M. Akhmetiev, M. S. Dvornikov

TL;DR

This work analyzes axion solitons in magnetohydrodynamics, focusing on mirror-symmetric configurations and their phase transition to helical, mirror-asymmetric states. By incorporating a spatially inhomogeneous axion field and a gamma-term into the mean-field induction equation, the authors connect an IK-dominated initial regime to a Kolmogorov-like regime after symmetry breaking, enabling transfer of axionic energy into magnetic energy and helicity. A key result is the identification of a characteristic wave-number $k_{\max}$ with $k_{\max} = (16/(7\eta))^{2/3} \propto \eta^{-2/3}$ that marks where large-scale magnetic-field generation is most efficient. The paper also develops a simple statistical ensemble to project harmonics, discusses the growth of lateral harmonics signaling potential instabilities, and proves generalized Arnold-type inequalities linking magnetic energy and helicity, providing a theoretical framework for axion-driven dynamos and guiding future numerical exploration of the connection between axion clump scales and magnetic-field spectra.

Abstract

We study an axion soliton, which weakly interacts with background matter and magnetic fields. A mirror-symmetric soliton, for which the magnetic flow is due to secondary magnetic helicity invariant, is described by the Iroshnikov-Kreichnan spectrum. For a large scale magnetic field dynamo is not observed. In a mirror axionic soliton, a phase transition, which produces a magnetic helical flow, is possible. Using this transition, the soliton becomes mirror-asymmetric. When the mirror symmetry is broken, the axion soliton allows the magnetic energy, which is the result of the transformation of the axionic energy. In the main result, for an initial stage of the process, we calculate a scale for which the generation of large scale magnetic fields is the most intense. By making numerical simulations, we received that lower lateral harmonics of the magnetic field have greater amplitudes compared to higher ones. A simplest statistical ensemble, which is defined by the projection of all harmonics onto principal harmonics is constructed. We put forward an assumption that it was the indication to some instability in axionic MHD. Now, we can provide a possible explanation of this feature. When the mirror symmetry of the axion soliton is broken, the $γ$-term in the axionic mean field equation, which is related to the axion spatial inhomogeneity, interacts with principal harmonics. As the result, the axion soliton acquires the magnetic energy and becomes helical.

Evolution of Mirror Axion Solitons

TL;DR

This work analyzes axion solitons in magnetohydrodynamics, focusing on mirror-symmetric configurations and their phase transition to helical, mirror-asymmetric states. By incorporating a spatially inhomogeneous axion field and a gamma-term into the mean-field induction equation, the authors connect an IK-dominated initial regime to a Kolmogorov-like regime after symmetry breaking, enabling transfer of axionic energy into magnetic energy and helicity. A key result is the identification of a characteristic wave-number with that marks where large-scale magnetic-field generation is most efficient. The paper also develops a simple statistical ensemble to project harmonics, discusses the growth of lateral harmonics signaling potential instabilities, and proves generalized Arnold-type inequalities linking magnetic energy and helicity, providing a theoretical framework for axion-driven dynamos and guiding future numerical exploration of the connection between axion clump scales and magnetic-field spectra.

Abstract

We study an axion soliton, which weakly interacts with background matter and magnetic fields. A mirror-symmetric soliton, for which the magnetic flow is due to secondary magnetic helicity invariant, is described by the Iroshnikov-Kreichnan spectrum. For a large scale magnetic field dynamo is not observed. In a mirror axionic soliton, a phase transition, which produces a magnetic helical flow, is possible. Using this transition, the soliton becomes mirror-asymmetric. When the mirror symmetry is broken, the axion soliton allows the magnetic energy, which is the result of the transformation of the axionic energy. In the main result, for an initial stage of the process, we calculate a scale for which the generation of large scale magnetic fields is the most intense. By making numerical simulations, we received that lower lateral harmonics of the magnetic field have greater amplitudes compared to higher ones. A simplest statistical ensemble, which is defined by the projection of all harmonics onto principal harmonics is constructed. We put forward an assumption that it was the indication to some instability in axionic MHD. Now, we can provide a possible explanation of this feature. When the mirror symmetry of the axion soliton is broken, the -term in the axionic mean field equation, which is related to the axion spatial inhomogeneity, interacts with principal harmonics. As the result, the axion soliton acquires the magnetic energy and becomes helical.

Paper Structure

This paper contains 7 sections, 4 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Mean large scale magnetic flows of small-scale magnetic field could be differ from a flow of large scale field
  3. The Arnold inequalities in the case of bounded domains
  4. Mean-field equation with the axionic $\gamma$-term
  5. Conclusion
  6. The generalized Arnold inequality in the case of random distributions of magnetic fields
  7. The Biot-Savart's law: A particular case of Maxwell Theorem on multipoles

Key Result

Theorem 1

Let ${\bf B}({\bf x})$ be a magnetic field in a domain $\Omega$, which is tangent to the boundary surface in the case $\partial(\Omega) \ne \emptyset$. The following inequality is satisfied: where $C$ is a positive constant of the dimension $\text{cm}^{-1}$, which depends only on a size and of a form of the domain $\Omega$. For a domain of the diameter $d$, one can put $C = d^{-1}$. In a special

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Corollary 3
  • Lemma 4