  Particle acceleration physics at supernova remnant (SNR) shocks is one of the
most intriguing problems in astrophysics. SNR RCW~86 provides a suitable
environment for understanding the particle acceleration physics because one can
extract the information of both accelerated particles and acceleration
environment at the same regions through the bright X-ray emission. In this
work, we study X-ray proper motions and spectral properties of the southwestern
region of RCW~86. The proper motion velocities are found to be $\sim
300$--2000~km~s$^{-1}$ at a distance of 2.8~kpc. We find two inward-moving
filaments, which are more likely reflected shocks rather than reverse shocks.
Based on the X-ray spectroscopy, we evaluate thermal parameters such as the
ambient density and temperature, and non-thermal parameters such as the
power-law flux and index. From the flux decrease in time of several non-thermal
filaments, we estimate the magnetic field amplitudes to be $\sim
30$--100~$\mu$G. Gathering the physical parameters, we then investigate
parameter correlations. We find that the synchrotron emission from
thermal-dominated filaments is correlated with the ambient density $n_{\rm e}$
as $\text{(power-law flux)} \propto n_{\rm e}^{1.0 \pm 0.2}$ and
$\text{(power-law index)} \propto n_{\rm e}^{0.38 \pm 0.10}$, not or only
weakly with the shock velocity and shock obliquity. As an interpretation, we
propose a shock-cloud interaction scenario, where locally enhanced magnetic
turbulence levels have a great influence on local acceleration conditions.
