An 8.3 hour observation of the Abell 2256 galaxy cluster using the Rossi X-ray Timing Explorer proportional counter array 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 gas imaging spectrometer gives an upperlimit of 2.3x10^-7 photons/cm^2/sec/keV for non-thermal emission at 30 keV. This yields a lower limit to the mean magnetic field of 0.36 micro Gauss (uG) and an upperlimit of 1.8x10^-13 ergs/cm^3 for the cosmic-ray electron energy density. The resulting lower limit to the central magnetic field is ~1 - 3 uG While a magnetic field of ~0.1 - 0.2 uG can be created by galaxy wakes, a magnetic field of several uG 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 uG in the A2256 cluster.
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