We develop a novel maximum-a-posteriori method to measure magnetic power spectra from Faraday rotation data and implement it in the REALMAF code .
A sophisticated model for the magnetic autocorrelation in real space permits us to alleviate previously required simplifying assumptions in the processing .
We also introduce a way to treat the divergence relation of the magnetic field with a multiplicative factor in Fourier space , with which we can model the magnetic autocorrelation as a spherically symmetric function .
Applied to the dataset of Hydra A north , we find a power law power spectrum on spatial scales between 0.3 kpc and 8 kpc , with no visible turnover at large scales within this range and a spectral index consistent with a Kolmogorov-like power law regime .
The magnetic field strength profile seems to follow the electron density profile with an index \alpha = 1 .
A variation of \alpha from 0.5 to 1.5 would lead to a spectral index between 1.55 and 2.05 .
The extrapolated magnetic field strength in the cluster centre highly depends on the assumed projection angle of the jet .
For an angle of 45 ^ { o } we derive extrapolated 36 \mu G in the centre and directly probed 16 \mu G at 50 kpc radius .