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Turbulent magnetic energy spectrum and the cancellation function of solar photospheric magnetic fields

A simple analytical relation of form α = 2 κ -1 between the magnetic energy spectral exponent α of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent κ, valid under certain restrictive assumptions, is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial "magnetograms" are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain α < -1 where κ ---> 0 as α ---> - infinity. The observationally derived upper limit of 0.38 on κ implies α < -0.24 in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range.