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

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(v)(similar to 1/k(v)). However, the magnetic field extends the viscous scale to the magnetic diffusivity one l eta(similar to 1/k(eta)) yielding a unique energy spectrum. Numerical simulation shows that kinetic and magnetic energy spectrum are E-v similar to k(-3.7) and E-M similar to 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) similar to 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 similar to k(-3.8) -k(-3.07) and E-M similar to k(-2.17) - k(-0.27) with large magnetic Prandtl number.

Automated summary

The article examines the energy spectrum of hot, magnetized, and ionized X-ray emitting plasmas in various regions of the universe through numerical simulations. The results demonstrate the significant influence of magnetic fields on the viscous scale and the unique energy spectrum it yields. Furthermore, the study investigates the spectrum relation between kinetic and magnetic energy, as well as the effect of helical energy on the spectrum steepness.