Magnetic Field Amplification and Reconstruction in Rotating Astrophysical Plasmas: Verifying the Roles of $\alpha$ and $\beta$ in Dynamo Action

TL;DR

This study investigates the roles of alpha and beta effects in magnetic field amplification within rotating astrophysical plasmas, revealing that beta diffusion dominates overall while alpha is crucial for nonlinear field sustenance.

Contribution

The paper introduces a comprehensive analysis of alpha and beta effects using multiple approaches and demonstrates the importance of turbulent magnetic field contributions in nonlinear regimes.

Findings

Beta diffusion dominates magnetic field evolution.

Alpha effect is minor in kinematic but essential in nonlinear regimes.

Adding turbulent magnetic field effects suppresses unbounded growth.

Abstract

We investigated the $\alpha$ and $\beta$ effects in a rotating spherical plasma system relevant to astrophysical environments. These coefficients were derived using three different approaches based on the large-scale magnetic field $\overline{\mathbf{B}}$, turbulent velocity $\mathbf{u}$, and turbulent magnetic field $\mathbf{b}$, yielding $\alpha_{\mathrm{EM-HM}}$, $\beta_{\mathrm{EM-HM}}$, $\beta_{\mathrm{vv-vw}}$, and $\beta_{\mathrm{bb+jb}}$. Using raw data from direct numerical simulations (DNS), we constructed the magnetic induction equation incorporating the $\alpha$ and $\beta$ coefficients. We then reproduced the $\overline{\mathbf{B}}$ field and compared the results with the DNS data. In the kinematic regime, where $\overline{\mathbf{B}}$ is weak, all models exhibit good agreement with the DNS results. However, in the nonlinear regime, the $\overline{\mathbf{B}}$ field, reproduced using $\beta_{\mathrm{vv-vw}}$, deviates from the DNS and exhibits unbounded growth. To address this discrepancy, we added $\beta_{\mathrm{bb+jb}}$, which represents the contribution of turbulent magnetic fields, to $\beta_{\mathrm{vv-vw}}$. This addition suppresses the divergent growth of $\overline{\mathbf{B}}$ in the nonlinear regime. We then assessed the actual influence of $\alpha$ and $\beta$ on the evolution of $\overline{\mathbf{B}}$ by applying weighted combinations of the two coefficients. Our results show that magnetic $\beta$ diffusion plays a dominant role throughout the entire process. In contrast, the $\alpha$ effect is minor in the kinematic regime but becomes essential for sustaining the $\overline{\mathbf{B}}$ field in the nonlinear regime. We also discussed the underlying physical mechanism responsible for this behavior.