Influence of small scale magnetic energy and helicity on the growth of large scale magnetic field

TL;DR

This paper investigates how initial small scale magnetic energy and helicity influence the growth of large scale magnetic fields in MHD dynamo processes, revealing that small scale energy boosts growth and helicity sign affects efficiency.

Contribution

It derives and solves equations showing the impact of initial small scale magnetic energy and helicity on large scale magnetic field growth in MHD dynamo theory, including simulation validation.

Findings

Small scale magnetic energy enhances large scale magnetic field growth.

Positive initial magnetic helicity is more effective than negative.

Small scale magnetic fields modify electromotive force and energy cascade.

Abstract

The influence of initially given small scale magnetic energy($E_M(0)$) and helicity($H_M(0)$) on the magnetohydrodynamics(MHD) dynamo was investigated. Equations for $E_M$(t), $H_M$(t), and electromotive force($\langle {\bf v}\times {\bf b}\rangle$, $EMF$) were derived and solved. The solutions indicate small scale magnetic field(${\bf b}_i$) caused by $E_M$(0) modifies $EMF$ and generates additional terms of which effect depends on magnetic diffusivity $\eta$, position of initial conditions($IC$s) $k_f$, and time ($\sim e^{-\eta k_f^2 t}$). ${\bf b}_i$ increases the inverse cascade of energy resulting in the enhanced growth of large scale magnetic field($\overline{{\bf B}}$). Simulation data show that $E_M$(0) in small scale boosts the growth rate, which also proportionally depends on $H_M(0)$. If $E_M$(0) is the same, positive $H_M(0)$ is more effective for MHD dynamo than negative $H_M(0)$ is. It was discussed why large scale magnetic helicity should have the opposite sign of the injected kinetic helicity.