A simple analytical relation of form \alpha = 2 \kappa - 1 between the magnetic energy spectral exponent \alpha of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent \kappa , 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 \alpha < -1 where \kappa \rightarrow 0 as \alpha \rightarrow - \infty .
The observationally derived upper limit of 0.38 on \kappa implies \alpha < -0.24 in the granular size range , apparently at odds with a small scale dynamo driven in the inertial range .