{ "id": "2502.01300", "version": "v1", "published": "2025-02-03T12:20:48.000Z", "updated": "2025-02-03T12:20:48.000Z", "title": "Magnetic field Amplification in a Rotating Astrophysical Plasma Sphere: $α$ and $β$ Effects", "authors": [ "Kiwan Park" ], "categories": [ "physics.plasm-ph", "astro-ph.SR", "physics.space-ph" ], "abstract": "We investigated the generation of the $\\alpha$ and $\\beta$ effects in a rotating spherical plasma system with oppositely polarized kinetic helicity in the northern and southern hemispheres and examined their contributions to the induction of magnetic fields. We found that the $\\alpha$ effect is relatively small, and its sign depends on the polarization of kinetic helicity. In contrast, the $\\beta$ effect remains negative regardless of the sign of kinetic helicity. Despite its small magnitude, the $\\alpha$ effect plays a crucial role in determining the polarity of helical magnetic structures, while a negative $\\beta$ indicates energy diffusion from turbulent regions into the large-scale magnetic field. We derived the $\\alpha$ and $\\beta$ effects with oppositely polarized kinetic helicity using different approaches, incorporating large-scale magnetic data and turbulent kinetic data. These were used to reproduce the large-scale magnetic field and compare it with DNS results. In the kinematic regime, where the magnetic field strength is weak, our results align well; however, in regions with strong nonlinear magnetic effects, the magnetic field reproduced using turbulent kinetic data diverges. This divergence is attributed to insufficient quenching of the $\\beta$ effect, suggesting that including the second-moment terms of velocity in the magnetic field effect would improve the accuracy of the $\\beta$ coefficient. In this study, we considered the case of a rotating plasma sphere with $Pr_M = 1$ and low Reynolds numbers. However, in reality, Reynolds numbers are much higher, and $Pr_M$ is much less than 1, which necessitates further studies on this topic. We plan to address this in future research.", "revisions": [ { "version": "v1", "updated": "2025-02-03T12:20:48.000Z" } ], "analyses": { "keywords": [ "rotating astrophysical plasma sphere", "magnetic field amplification", "large-scale magnetic field", "turbulent kinetic data", "oppositely polarized kinetic helicity" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }