$\alpha$ Effect and Magnetic Diffusivity $\beta$ in Helical Plasma under Turbulence Growth

Abstract

We investigate the transport coefficients $\alpha$ and $\beta$ in plasma systems with varying Reynolds numbers while maintaining a unit magnetic Prandtl number. {The $\alpha$ and $\beta$ tensors parameterize the turbulent electromotive force (EMF) in terms of the large-scale magnetic field $\overline{\mathbf{B}}$ and current density $\overline{}$ as follows : $⟨\mathbf{u}\times \mathbf{b}⟩=\alpha \overline{\mathbf{B}}-\beta \nabla \times \overline{\mathbf{B}}$.} In astrophysical plasmas, high fluid Reynolds numbers ($Re$) and magnetic Reynolds numbers ($R{e}_{\mathrm{M}}$) drive turbulence, where $Re$ governs flow dynamics and $R{e}_{\mathrm{M}}$ controls magnetic field evolution. The coefficients ${\alpha }_{\text{semi}}$ and ${\beta }_{\text{semi}}$ are obtained from large-scale magnetic field data as estimates of the $\alpha$ and $\beta$ tensors, while ${\beta }_{\text{theo}}$ is derived from turbulent kinetic energy data. The reconstructed large-scale field $\overline{B}$ agrees with simulations, confirming consistency among $\alpha$, $\beta$, and $\overline{B}$ in weakly nonlinear regimes. This highlights the need to incorporate magnetic effects under strong nonlinearity. To clarify $\alpha$ and $\beta$, we introduce a field structure model, identifying $\alpha$ as the electrodynamic induction effect and $\beta$ as the fluid-like diffusion effect. The agreement between our method and direct simulations suggests that plasma turbulence and magnetic interactions can be analyzed using fundamental physical quantities. Moreover, ${\alpha }_{\text{semi}}$ and ${\beta }_{\text{semi}}$, which successfully reproduce the numerically obtained magnetic field, provide a benchmark for future theoretical studies.

arXiv commentPublished in Universe

References in corpus (20)

• Astrophysical magnetic fields and nonlinear dynamo theory
• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Nonhelical inverse transfer of a decaying turbulent magnetic field
• An Incoherent $\alpha -\Omega$ Dynamo in Accretion Disks
• Collapse and Fragmentation of Rotating Magnetized Clouds. I. Magnetic Flux - Spin Relation
• Advances in mean-field dynamo theory and applications to astrophysical turbulence
• Magnetic Fields from QCD Phase Transitions
• The Search for a Primordial Magnetic Field
• A note on shell models for MHD Turbulence
• Inverse cascade behavior in freely decaying two-dimensional fluid turbulence
• Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment
• Large-scale dynamo action due to $\alpha$ fluctuations in a linear shear flow
• Simulations of a Magnetic Fluctuation Driven Large Scale Dynamo and Comparison with a Two-scale Model
• Study on the large scale dynamo transition
• The mean electromotive force resulting from magnetic buoyancy instability
• Comparison Between Turbulent Helical Dynamo Simulations and a Nonlinear Three-Scale Theory
• On the Inverse Transfer of (Non-)Helical Magnetic Energy in a Decaying Magnetohydrodynamic Turbulence
• Iterative removal of sources to model the turbulent electromotive force
• Negative Magnetic Diffusivity beta replacing alpha effect in Helical Dynamo
• Magnetic Effect on Potential Barrier for Nucleosynthesis II