Magnetic Field Amplification and Reconstruction in Rotating Astrophysical Plasmas: Verifying the Roles of α and β in Dynamo Action

We investigate the $\alpha$ and $\beta$ effects in a rotating spherical plasma system relevant to astrophysical contexts. In particular, we focus on how kinetic and magnetic (current) helicities influence the magnetic diffusivity $\beta$. These coefficients were modeled using three complementary theoretical approaches. Direct numerical simulation (DNS) data (large-scale magnetic field $\overline{\mathbf{B}}$, turbulent velocity $\mathbf{u}$, and turbulent magnetic field $\mathbf{b}$) were then used to obtain the actual values of ${\alpha }_{\mathrm{EM}-\mathrm{HM}}$, ${\beta }_{\mathrm{EM}-\mathrm{HM}}$, ${\beta }_{\mathrm{vv}-\mathrm{vw}}$, and ${\beta }_{\mathrm{bb}+\mathrm{jb}}$. Using these coefficients, we reconstructed $\overline{\mathbf{B}}$ and compared it with the DNS results. In the kinematic regime, where $\overline{\mathbf{B}}$ remains weak, all models agree well with DNS. In the nonlinear regime, however, the field reconstructed with ${\beta }_{\mathrm{vv}-\mathrm{vw}}$ alone deviates from DNS and grows without bound. Incorporating the turbulent magnetic diffusion term ${\beta }_{\mathrm{bb}+\mathrm{jb}}$ suppresses this unphysical growth and restores consistency. Specifically, ${\overline{B}}_{DNS}$ saturates at approximately 0.23 in the nonlinear regime. The reconstructed $\overline{B}$ using ${\beta }_{EM-HM}$ saturates at $\overline{B}$∼0.3. When ${\beta }_{vv-vw+bb+jb}$$(={\beta }_{vv-vw}+{\beta }_{bb+jb})$ is used, $\overline{B}$ varies from about 0.3 to 0.23. These results indicate that kinetic helicity reduces $\beta$ (or provides a negative contribution), thereby amplifying $\overline{\mathbf{B}}$, whereas turbulent current helicity, together with turbulent magnetic and kinetic energies, enhances $\beta$, thus suppressing $\overline{\mathbf{B}}$ in the nonlinear regime. In this respect, the new form of $\beta$ differs from the conventional one, which acts solely to diffuse the magnetic field.