  We propose a novel method of determination of the dust particle spatial
distribution in dust clouds that form in three-dimensional (3D) complex plasmas
under microgravity conditions. The method utilizes the data obtained during the
3D scanning of a cloud and provides a reasonably good accuracy. Based on this
method, we investigate the particle density in a dust cloud realized in gas
discharge plasma in the PK-3 Plus setup onboard the International Space
Station. We find that the treated dust clouds are both anisotropic and
inhomogeneous. One can isolate two regimes, in which a stationary dust cloud
can be observed. At low pressures, the particle density decreases monotonically
with the increase of the distance from the discharge center; at higher
pressures, the density distribution has a shallow minimum. Regardless of the
regime, we detect a cusp of the distribution at the void boundary and a slowly
varying density at larger distances (in the foot region). A theoretical
interpretation of obtained results is developed that leads to reasonable
estimates of the densities for both the cusp and foot. The modified ionization
equation of state, which allows for violation of the local quasineutrality in
the cusp region, predicts the spatial distributions of ion and electron
densities to be measured in future experiments.
