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A time-explicit formula that describes the time evolution of velocity distribution functions of gases and plasmas is derived from the Boltzmann equation. The formula can be used to construct collision simulation algorithms. Specialization of the formula to the case of the Coulomb interaction shows that the previous method [K. Nanbu, Phys. Rev. E 55, 4642 (1997)] for a Coulomb collision simulation is a solution method of the Landau-Fokker-Planck equation in the limit of a small time step. Also, a collision simulation algorithm for multicomponent plasmas is proposed based on the time-explicit formula derived.

The structures of the CF4 radio-frequency discharge between parallel electrodes are clarified by the use of the particle-in-cell/Monte Carlo method. The simulation is performed based on the most reliable collision data, i.e., detailed cross-section data for electron–CF4 collision, measured rate for positive–negative ion recombination, and the newly developed ion–CF4 collision model for endothermic reactions. Reactive collisions between positive ions (especially CF3+) and CF4 molecules are found to be important. The major loss process of negative ions is the recombination with positive ions. It is also found that the discharge sustaining mechanism is the ionization, not the electron detachment from negative ions.