Context :

Aims : We investigate the magnetic field power spectrum in the cool core galaxy cluster A2199 by analyzing the polarized emission of the central radio source 3C 338 .

Methods : The polarized radiation from the radio emitting plasma is modified by the Faraday rotation as it passes through the magneto-ionic intracluster medium .
We use Very Large Array observations between 1665 and 8415 MHz to produce detailed Faraday rotation measure and fractional polarization images of the radio galaxy .
We simulate Gaussian random three-dimensional magnetic field models with different power-law power spectra and we assume that the field strength decreases radially with the thermal gas density as n _ { e } ^ { \eta } .
By comparing the synthetic and the observed images with a Bayesian approach , we constrain the strength and structure of the magnetic field associated with the intracluster medium .

Results : We find that the Faraday rotation toward 3C 338 in A2199 is consistent with a magnetic field power law power spectrum characterized by an index n = ( 2.8 \pm 1.3 ) between a maximum and a minimum scale of fluctuation of \Lambda _ { max } = ( 35 \pm 28 ) kpc and \Lambda _ { min } = ( 0.7 \pm 0.1 ) kpc , respectively .
By including in the modeling X-ray cavities coincident with the radio galaxy lobes , we find a magnetic field strength of \langle B _ { 0 } \rangle = ( 11.7 \pm 9.0 ) \mu G at the cluster center .
Further out , the field decreases with the radius following the gas density to the power of \eta = ( 0.9 \pm 0.5 ) .

Conclusions :