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Kinetic simulation of plasmas in which equilibrium occurs over ion time scales poses a computational challenge due to disparity with electron time scales. Hybrid electrostatic particle-in-cell (PIC) algorithms are presented in which most of the electrons reach thermodynamic equilibrium [Maxwell–Boltzmann (MB) distribution function] each time step. Conservation of charge enables convergence of the nonlinear Poisson equation. Energy conservation is used to determine the temperature of the Boltzmann species. This article first develops an algorithm where all the electrons have a MB energy distribution, either with a full MB distribution or with a truncation of the high energy tail. Second, high energy PIC electrons are added to the truncated distribution so that high energy electrons are modeled kinetically by PIC and low energy electrons (the majority) are modeled by the MB distribution. Collisions for PIC electrons are included via a Monte Carlo model, while for the MB electrons, the distributions are integrated with energy dependent cross sections. The MB model is not constrained by the electron time scale which decreases the required computer time by about the square root of the mass ratio of ion to electron. However, the hybrid boundary conditions are more complex and the simulation is not quite self-consistent. Comparison between full PIC and the PIC–MB hybrid is made for simulations of photo-ionized sustained discharges and current-driven dc discharges.

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