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We investigate the magnetic field power spectrum in the cool core galaxycluster A2199 by analyzing the polarized emission of the central radio source3C338. The polarized radiation from the radio emitting plasma is modified bythe Faraday rotation as it passes through the magneto-ionic intraclustermedium. We use Very Large Array observations between 1665 and 8415 MHz toproduce detailed Faraday rotation measure and fractional polarization images ofthe radio galaxy. We simulate Gaussian random three-dimensional magnetic fieldmodels with different power-law power spectra and we assume that the fieldstrength decreases radially with the thermal gas density as n_e^{\eta}. Bycomparing the synthetic and the observed images with a Bayesian approach, weconstrain the strength and structure of the magnetic field associated with theintracluster medium. We find that the Faraday rotation toward 3C338 in A2199 isconsistent with a magnetic field power law power spectrum characterized by anindex 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 theradio galaxy lobes, we find a magnetic field strength of <B_0>=(11.7 \pm 9.0)\mu G at the cluster center. Further out, the field decreases with the radiusfollowing the gas density to the power of \eta=(0.9 \pm 0.5).

The intracluster magnetic field power spectrum in A2199