Evolution of Kinetic and Magnetic Energy in a Large Magnetic Prandtl Number System

Abstract

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 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.