Full kinetic partiele-in-cell model of dusty plasma has been built. It takes into account the collisions of electrons and ions with dust grains. This permits to study the dynamics of grain charging and mechanisms of interaction etween grains. The model is implemented in a frame of 3D kinetic object oriented code. As an illustration test problems of grain charging and two grain interaction were solved. The results were in a good agreement with theoretical predictions. In addition, the ions with finite trajectories were detected. This work is partly supported by Russian Ministry of Science, grant N 01.99.00.07938.

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