Connecting Dynamo Theory with DNS Data: A Computational Analysis of $α$ and $β$ Effects

RESUMO

We investigate the influence of current helicity on the turbulent magnetic diffusivity $\beta$ using three complementary derivations of the $\alpha$ and $\beta$ coefficients, based on the large-scale magnetic field $\overline{\mathbf{B}}$, the turbulent velocity $\mathbf{u}$, and the turbulent magnetic field $\mathbf{b}$. Applying these coefficients to raw DNS data, we reconstruct $\overline{\mathbf{B}}$ and compare the results with the original simulations. In the kinematic regime all models agree well with the DNS data. In the nonlinear regime, however, $\beta_{\mathrm{vv-vw}}$ alone produces unbounded growth of $\overline{\mathbf{B}}$. Including the contribution from turbulent magnetic fields ($\beta_{\mathrm{bb+jb}}$) suppresses this unphysical growth and restores agreement with the DNS results. We find that kinetic helicity drives $\beta$ more negative, while current helicity shifts it back toward zero. Weighted combinations of the coefficients further show that the $\beta$ effect dominates the evolution of $\overline{\mathbf{B}}$ throughout, whereas the $\alpha$ effect becomes important mainly for sustaining the field in the nonlinear regime. The corresponding IDL analysis scripts are provided to facilitate practical implementation of the theoretical models.