Fluctuation--dissipation theorem and kinematic-dynamo activity

Using the dispersion relation obtained elsewhere describing the regeneration of large-scale magnetic fields under isotropic velocity turbulence, we set up the equations describing the response of the system to an arbitrary externally applied current distribution. We demonstrate that the absorption coefficient (which characterizes the rate at which the impressed current supplies power) may be either positive or negative depending on the level of turbulence. A positive absorption coefficient corresponds to a system in which the turbulent generation of field (through the action of the Lorentz force V X B) is not rapid enough to overcome resistive losses, while a negative absorption coefficient implies that regeneration by the turbulent Lorentz force exceeds resistive losses. We have done this calculation to simplify the "search" criteria that must otherwise be employed (for given, but arbitrary, forms of the correlation function describing the isotropic turbulent velocity pattern) when one is interested in determining whether a particular correlation function gives rise to regenerative kinematic-dynamo action.