$\alpha$ 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 ${\bf \overline{B}}$ and current density ${\bf \overline{}}$ as follows : $\langle {\bf u}\times {\bf b} \rangle = \alpha {\bf \overline{B}}-\beta {\nabla\times \bf \overline{B}}$.} In astrophysical plasmas, high fluid Reynolds numbers ($Re$) and magnetic Reynolds numbers ($Re_\mathrm{M}$) drive turbulence, where $Re$ governs flow dynamics and $Re_\mathrm{M}$ 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.