Energy fluxes in helical magnetohydrodynamics and dynamo action

Abstract

Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is to first-order in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to nonhelical interactions, and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a premitive model for galactic dynamo has been constructed. Our calculations yields dynamo time-scale for a typical galaxy to be of the order of 10 8 years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.

Dynamo transition in low-dimensional models

“…Clearly α is optimal if H K < 0 and H J > 0. Similar features are observed in flux calculation of Verma [22]. These conditions are satisfied in the helical model indicating a certain internal consistency with the results of Pouquet et al [20], and Chou [21].…”

Taylor's Frozen-in Hypothesis for Magnetohydrodynamic turbulence and Solar Wind

“…However, MHD turbulence has two diffusion parameters, viscosity and magnetic diffusivity, that depend on the cross helicity, Alfvén ratio, and mean magnetic field. We do not yet have general formulas for these renormalized parameters, even though they have been solved for special cases (see Verma 25,26,27 ). In this paper, we simplify the calculation by assuming that both the renormalized parameters are equal (i.e., ν(k) = η(k)), and that for Kolmogorov-like phenomenology,…”

Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

“…In the presence of mean magnetic field, Teaca et al [20] and Sundar et al [21] computed the corresponding energy fluxes. Verma [6,22,23,24] computed the energy fluxes using field-theoretic formalism. In addition, Verma [9] also described several exact relations among these fluxes using the analytical formalism of variable energy flux.…”