  We apply a novel technique of Faraday Rotation measure (RM) map analysis to
three galaxy clusters, Abell 400, Abell 2634 and Hydra A, in order to estimate
cluster magnetic field strengths, length scales and power spectra. This
analysis is based on the assumption that the magnetic fields are statistically
isotropically distributed across the Faraday screen. We investigate the
difficulties involved in the application of the analysis to observational data.
We derive magnetic power spectra for the three clusters and discuss influences
on their shapes. We show that magnetic fluctuations are probed on length scales
ranging over at least one order of magnitude. Using this range for the
determination of central cluster magnetic field strength yields 3 muG in Abell
2634, 6 muG in Abell 400 and 12 muG in Hydra A. The magnetic field
autocorrelation length was determined to be 4.9 kpc for Abell 2634, 3.6 kpc for
Abell 400 and 0.9 kpc for Hydra A. We show that the RM autocorrelation length
is larger than the magnetic field autocorrelation length. We investigate in a
response analysis if it is possible to determine spectral slopes of the power
spectra. We find that integrated numbers can be determined from this analysis
but differential parameters such as spectral slopes have to be treated
differently. Our response analysis results in spectral slopes of the power
spectra of spectral indices alpha = 1.6 to 2.0 suggesting that Kolmogorov
spectra are possible but flatter spectral slopes than alpha = 1.3 can be
excluded.
