THE TURBULENT EMF AS A TIME-SERIES AND THE QUALITY OF DYNAMO CYCLES

Following earlier suggestions to replace the ensemble average used in the mean-field electrodynamics by an averaging over the azimuthal coor dinate, we consider the basic coefficients in the turbulent electromot ive force (EMF) as time-dependent functions. The well-known dynamo coe fficients alpha and eta(T) - both in the relevant tensorial formulatio ns - are derived from one and the same turbulence field with maximal h elicity so that in a local formulation the total turbulent EMF is desc ribed as a time series. The (kinematic) turbulence models have always the same intensity of similar or equal to 100 ms(-1) and the number of the eddies in the unit length is varied. The EMF-coefficients alpha a nd eta(T) are evaluated within the limit of high (microscopic) conduct ivity. Both coefficients prove to exhibit time series with remarkable fluctuations. The fluctuations are stronger for the alpha-effect compa red with the eddy diffusivity, and they are stronger if the number of cells is decreased. In general, we find fluctuations dominating the av erage for turbulence with only a few large cells. Even changes of the sign of the EMF coefficients occur for short periods. Application of t he resulting turbulence EMF-coefficients to an one-dimensional alpha(2 ) Omega-dynamo model leads to complicated time series for the resultin g magnetic held. It is oscillatory for an infinite number of cells and becomes more complex if less turbulence eddies are operating in the h ow. For decreasing eddy population the corresponding spectral line in the power spectrum of the magnetic cycles becomes more and more broad (the 'quality' of the cycle sinks) - but further reduction of the cell population leads to a chaotic character of the dynamo amplitude. Fina lly, the difference between oscillatory and stationary solutions of th e dynamo model seems to disappear. The observed quality of the solar c ycle might be produced by about 100 giant cells along the equator.