DIFFUSION-APPROXIMATION PROBED WITH PARKER INSTABILITY SIMULATIONS

The diffusion approximation works with simple ''stress-strain'' relati ons with eddy diffusivities as scaling coefficients. Numerical simulat ions of the Parker instability are analysed with respect to the non-lo cal mean-field relation between magnetic field and turbulent EMF. The kernel in the convolution integral is expanded in a series of derivati ves of Dirac's delta functions. The diffusion approximation holds if t he coefficient of the first derivative (the traditional ''eddy diffusi vity'') dominates. In fact, all the considered simulations contain a d ominating eddy diffusivity but also the subsequent coefficient appears . The traditional diffusion approximation, therefore, only works for m ean magnetic fields with scares clearly exceeding the pressure-scale h eight. The turbulent-advection effect (the zero-order coefficient) pro ves to be very small.