  Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are
investigated analytically by decomposition of the velocity and magnetic fields
in Fourier space into helical modes. Steady solutions of the dynamical system
which governs the evolution of the helical modes are determined, and a
stability analysis of these solutions is carried out. The interpretation of the
analysis is that unstable solutions lead to energy transfer between the
interacting modes while stable solutions do not. From this, a dependence of
possible interscale energy and helicity transfers on the helicities of the
interacting modes is derived. As expected from the inverse cascade of magnetic
helicity in 3D MHD turbulence, mode interactions with like helicities lead to
transfer of energy and magnetic helicity to smaller wavenumbers. However, some
interactions of modes with unlike helicities also contribute to an inverse
energy transfer. As such, an inverse energy cascade for nonhelical magnetic
fields is shown to be possible. Furthermore, it is found that high values of
the cross-helicity may have an asymmetric effect on forward and reverse
transfer of energy, where forward transfer is more quenched in regions of high
cross-helicity than reverse transfer. This conforms with recent observations of
solar wind turbulence. For specific helical interactions the relation to dynamo
action is established.

Fluid Dynamics;Cosmology and Nongalactic Astrophysics;Chaotic Dynamics