  In this work we analyze the power scaling potential of amplifying multicore
fibers (MCFs) used in coherently-combined systems. In particular, in this study
we exemplarily consider rod-type MCFs with 2x2 up to 10x10 Ytterbium doped
cores arranged in a squared pattern. We will show that, even though increasing
the number of active cores will lead to higher output powers, particular
attention has to be paid to arising thermal effects, which potentially degrade
the performance of these systems. Additionally, we analyze the influence of the
core dimensions on the extractable and combinable output power and pulse
energy. This includes a detailed study on the thermal effects that influence
the propagating transverse modes and, in turn, the amplification efficiency,
the combining efficiency, the onset of nonlinear effect, as well as differences
in the optical path lengths between the cores. Considering all these effects
under rather extreme conditions, the study predicts that average output powers
higher than 10 kW from a single 1 m long Ytterbium-doped MCF are feasible and
femtosecond pulses with energies higher than 400 mJ can be extracted and
efficiently recombined in a filled-aperture scheme.
