Clusters of galaxies are among the best candidates for particle acceleration sources in the universe , a signature of which is non-thermal hard X-ray emission from the accelerated relativistic particles . We present early results on Suzaku observations of non-thermal emission from Abell 3376 , which is a nearby on-going merger cluster . Suzaku observed the cluster twice , focusing on the cluster center containing the diffuse radio emission to the east , and cluster peripheral region to the west . For both observations , we detect no excess hard X-ray emission above the thermal cluster emission . An upper limit on the non-thermal X-ray flux of 2.1 \times 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ( 15–50 keV ) at the 3 \sigma level from a 34 \times 34 arcmin ^ { 2 } region , derived with the Hard X-ray Detector ( HXD ) , is similar to that obtained with the BeppoSAX/PDS . Using the X-ray Imaging Spectrometer ( XIS ) data , the upper limit on the non-thermal emission from the West Relic is independently constrained to be < 1.1 \times 10 ^ { -12 } erg s ^ { -1 } cm ^ { -2 } ( 4 - 8 keV ) at the 3 \sigma level from a 122 arcmin ^ { 2 } region . Assuming Compton scattering between relativistic particles and the cosmic microwave background ( CMB ) photons , the intracluster magnetic field B is limited to be > 0.03 \mu G ( HXD ) and > 0.10 \mu G ( XIS ) .