An 8.3 hour observation of the Abell 2256 galaxy cluster using the Rossi X-ray Timing Explorer ( RXTE ) proportional counter array ( PCA ) produced a high quality spectrum in the 2 - 30 keV range . Joint fitting with the 0.7 - 11 keV spectrum obtained with the Advanced Satellite for Astrophysics and Cosmology ( ASCA ) Gas Imaging spectrometer ( GIS ) gives an upperlimit of \sim 2.3 \times 10 ^ { -7 } photons cm ^ { -2 } sec ^ { -1 } keV ^ { -1 } for non-thermal emission at 30 keV . This yields a lower limit to the mean magnetic field of 0.36 \mu G and an upperlimit of 1.8 \times 10 ^ { -13 } ergs cm ^ { -3 } for the cosmic-ray electron energy density . The resulting lower limit to the central magnetic field is \sim 1 - 3 \mu G. While a magnetic field of \sim 0.1 - 0.2 \mu G can be created by galaxy wakes , a magnetic field of several \mu G is usually associated with a cooling flow or , as in the case of the Coma cluster , a subcluster merger . However , for A2256 , the evidence for a merger is weak and the main cluster shows no evidence of a cooling flow . Thus , there is presently no satisfactory hypothesis for the origin of an average cluster magnetic field as high as > 0.36 \mu G in the A2256 cluster .