  Young massive star clusters inhabit regions of star formation and play an
essential role in the galactic evolution. They are sources of both thermal and
non-thermal radiation, and they are effective cosmic ray accelerators. We
present the 3D magnetohydrodynamic (MHD) modeling of the plasma flows in a
young compact cluster at the evolutionary stage comprising multiple interacting
supersonic winds of massive OB and WR stars. The modeling allows studying the
partitioning of the mechanical energy injected by the winds between the bulk
motions, thermal heating and magnetic fields. Cluster-scale magnetic fields
reaching the magnitudes of $\sim$ 300 $\mu$G show the filamentary structures
spreading throughout the cluster core. The filaments with the high magnetic
fields are produced by the Axford-Cranfill type effect in the downstream of the
wind termination shocks, which is amplified by a compression of the fields with
the hot plasma thermal pressure in the central part of the cluster core. The
hot ($\sim$ a few keV) plasma is heated at the termination shocks of the
stellar winds and compressed in the colliding postshock flows. We also discuss
a possible role of the thermal conduction effects on the plasma flow, analyse
temperature maps in the cluster core and the diffuse thermal X-ray emission
spectra. The presence of high cluster-scale magnetic fields supports the
possibility of high-energy cosmic ray acceleration in clusters at the given
evolutionary stage.
