  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.
