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

We investigate the α and β 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 β. These coefficients were modeled using three complementary theoretical approaches. Direct numerical simulation (DNS) data (large-scale magnetic field B¯, turbulent velocity u, and turbulent magnetic field b) were then used to obtain the actual values of αEM−HM, βEM−HM, βvv−vw, and βbb+jb. Using these coefficients, we reconstructed B¯ and compared it with the DNS results. In the kinematic regime, where B¯ remains weak, all models agree well with DNS. In the nonlinear regime, however, the field reconstructed with βvv−vw alone deviates from DNS and grows without bound. Incorporating the turbulent magnetic diffusion term βbb+jb suppresses this unphysical growth and restores consistency. Specifically, B¯DNS saturates at approximately 0.23 in the nonlinear regime. The reconstructed B¯ using βEM−HM saturates at B¯∼0.3. When βvv−vw+bb+jb(=βvv−vw+βbb+jb) is used, B¯ varies from about 0.3 to 0.23. These results indicate that kinetic helicity reduces β (or provides a negative contribution), thereby amplifying B¯, whereas turbulent current helicity, together with turbulent magnetic and kinetic energies, enhances β, thus suppressing B¯ in the nonlinear regime. In this respect, the new form of β differs from the conventional one, which acts solely to diffuse the magnetic field.