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

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.