We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a mechanically forced plasma system. Also, we show how helical magnetic energy is inversely cascaded (α effect) toward large scale magnetic eddies in a mechanically or magnetically forced system. We, then, compare the simulation results with the model qualitatively for the verification of the model. In addition to these intuitive and numerical approaches, we show how to get α and β coefficient semi-analytically from the temporally evolving large scale magnetic energy and magnetic helicity.
Many regions of the universe are in a state of hot, magnetized, and ionized X-ray emitting plasmas. We numerically simulated the energy spectrum of this highly viscous and conductive system. Without magnetic field, the fluctuating plasma motion decays in a relatively large viscous scale l ν (∼1/k ν ). However, the magnetic field extends the viscous scale to the magnetic diffusivity one l η (∼1/k η ) yielding a unique energy spectrum. Numerical simulation shows that kinetic and magnetic energy spectrum are E V ∼ k −3.7 and E M ∼ k −0.85 in the extended viscous scale regime. To explain this extraordinary power law, we set up two simultaneous differential equations for E V and E M and solved them using Eddy Damped Quasi Normal Markovianized approximation. Focusing on the most dominant terms, we analytically derived the spectrum relation E M 2 ∼ k 2 E V consistent with the simulation data. We also simulated the same system with helical energy. The inversely cascaded magnetic energy makes the spectrum steeper. This inverse energy transfer, in addition to the external magnetic field and instabilities, provides us a clue to the diversified spectra characterized by E V ∼ k −3.8 − k −3.07 and E M ∼ k −2.17 − k −0.27 with large magnetic Prandtl number.
We have studied the large-scale dynamo forced with helical magnetic energy. Compared to the kinetic forcing process, the magnetic process is not clearly observed nor intuitive. However, it may represent the actual B field amplification in the stellar corona, accretion disk, plasma lab, or other magnetically dominated systems where the strong kinetic effect does not exist. The interaction between the magnetic field and the plasma is essentially nonlinear. However, when the plasma system is driven by helical energy, whether kinetic or magnetic, the nonlinear process can be linearized with pseudotensors a, β and the large-scale magnetic field B ¯ . Conventionally, the α effect is thought to be the main dynamo effect converting kinetic energy into magnetic energy and transferring it to the large-scale regime. In contrast, β effect has been thought to diffuse magnetic energy. However, these conclusions are not based on the exact definition of α and β. In this paper, instead of the analytic definition of α and β, we derive a semi-analytic equation and apply it to the simulation data. The half analytic and numerical result shows that the averaged α effect is not so important in amplifying the B ¯ field. Rather, it is the negative β effect combined with the Laplacian (∇2 → −k 2) that plays a key role in the dynamo process. Further, the negative magnetic diffusivity accounts for the attenuation of the plasma kinetic energy E ¯ V in large scales. We discuss this process using the theoretical method and the intuitive field structure model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.