α Effect and Magnetic Diffusivity β in Helical Plasma Under Turbulence Growth

We investigate the transport coefficients α and β in plasma systems with varying Reynolds numbers while maintaining a unit magnetic Prandtl number (PrM). The α and β tensors parameterize the turbulent electromotive force (EMF) in terms of the large-scale magnetic field B¯ and current density as follows: ⟨u×b⟩=αB¯−β∇×B¯. In astrophysical plasmas, high fluid Reynolds numbers (Re) and magnetic Reynolds numbers (ReM) drive turbulence, where Re governs flow dynamics and ReM controls magnetic field evolution. The coefficients αsemi and βsemi are obtained from large-scale magnetic field data as estimates of the α and β tensors, while βtheo is derived from turbulent kinetic energy data. The reconstructed large-scale field B¯ agrees with simulations, confirming consistency among α, β, and B¯ in weakly nonlinear regimes. This highlights the need to incorporate magnetic effects under strong nonlinearity. To clarify α and β, we introduce a field structure model, identifying α as the electrodynamic induction effect and β 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, αsemi and βsemi, which successfully reproduce the numerically obtained magnetic field, provide a benchmark for future theoretical studies.