The DC magnetization and AC complex magnetic susceptibilities were measured for MgB2 single crystals, unsubstituted and carbon substituted with the composition of Mg(B_0.94C_0.06)2. The measurements were performed in AC and DC magnetic fields oriented parallel to the c-axis of the crystals. From the DC magnetization loops and the AC susceptibility measurements, critical current densities (Jc) were derived as a function of temperature and the DC and AC magnetic fields. Results show that the substitution with carbon decreases Jc at low magnetic fields, opposite to the well known effect of an increase of Jc at higher fields. AC magnetic losses were derived from the AC susceptibility data as a function of amplitude and the DC bias magnetic field. The AC losses were determined for temperatures of 0.6 and 0.7 of the transition temperature Tc, so close to the boiling points of LH2 and LNe, potential cooling media for magnesium diboride based composites. The results are analyzed and discussed in the context of the critical state model.
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