Influence of small-scale EM and HM on the growth of large-scale magnetic field

We investigated the influence of small-scale magnetic energy (E-M) and magnetic helicity (H-M) on the growth rate (gamma) of (B) over bar field (large-scale magnetic field). H-M that plays a key role in magnetohydrodynamic (MHD) dynamo is a topological concept describing the structural properties of magnetic fields. Since E-M is a prerequisite of H-M, it is not easy to differentiate the intrinsic properties of H-M from the influence of E-M. However, to understand MHD dynamo, the features of helical and non-helical magnetic field should be made clear. For this, we made a detour: we gave each simulation set its own initial condition (IC, same E-M(0) and specific H-M(0) at the forced wavenumber k(f) = 5), and then drove the system with positive helical kinetic energy(k(f) = 5). According to the simulation results, E-M(0), whether or not helical, increases the growth rate of (B) over bar. The positive H-M(0) boosts the increased growth rate, but the negative H-M(0) decreases it. To explain these results, two coupled equations of H-M and E-M were derived and solved using a simple approximate method. The equations imply that helical magnetic field evolves into the total (helical and non-helical) magnetic field but quenches itself. Non-helical magnetic field also evolves into the total magnetic field but quenches itself. The initially given E-M(0) modifies the electromotive force (EMF, < u x b > and generates new terms. The effects of these terms depend on the magnetic diffusivity eta, position of initial conditions k(f), and magnetic diffusion time. But the influence disappears exponentially as time passes, so the saturated magnetic fields are eventually independent of the pre-existing initial conditions.