A FAST DYNAMO OF ALPHA-OMEGA-TYPE

We introduce a fast dynamo model of alpha omega-type, involving applic ation of a uniform shear and a Beltrami wave, which models cyclonic ev ents. We simulate magnetic field numerically in the given dow, with we ak molecular diffusion, but no prescribed transport effects, that is, no alpha-effect nor eddy diffusivity. We verify the Parker picture of propagating dynamo waves, and find that the growth rate and frequency tend to constants independent of magnetic Reynolds number Rm for large Rm. We give approximate analysis of growth rates and frequencies, whi ch behave as root k for small wavenumbers k, and assess the validity o f approximations commonly used in solar modelling. In particular we fi nd that small wavelength modes grow more quickly than one would expect based on standard estimates of eddy diffusivity. We then identify a p arameter range where our theory does not yield an alpha omega-model in mean-field form, indicating a breakdown of the conventional picture i n the limit of large Rm.