To determine the properties of the Faraday screen and the magnetic field near the central region of the Galaxy, we measured the Faraday rotation measure (RM) towards 60 background extragalactic source components through the -6 deg < l <6 deg, -2 deg < b < 2 deg region of the Galaxy using the 4.8 and 8.5 GHz bands of the ATCA and VLA. Here we use the measured RMs to estimate the systematic and the random components of the magnetic fields. The measured RMs are found to be mostly positive for the sample sources in the region. This is consistent with either a large scale bisymmetric spiral magnetic fields in the Galaxy or with fields oriented along the central bar of the Galaxy. The outer scale of the RM fluctuation is found to be about 40 pc, which is much larger than the observed RM size scales towards the non-thermal filaments (NTFs). The RM structure function is well-fitted with a power law index of 0.7 +/- 0.1 at length scales of 0.3 to 100 pc. If Gaussian random processes in the ISM are valid, the power law index is consistent with a two dimensional Kolmogorov turbulence. If there is indeed a strong magnetic field within 1 degree (radius 150 pc) from the GC, the strength of the random field in the region is estimated to be 20 microGauss. Given the highly turbulent magnetoionic ISM in this region, the strength of the systematic component of the magnetic fields would most likely be close to that of the random component. This suggests that the earlier estimated milliGauss magnetic field near the NTFs is localised and does not pervade the central 300 pc of the Galaxy.
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