Many-particle (meaning 1000's) charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. This paper emphasizes the development of PIC computer experiments since the 1950's starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. The finite-size particle-in-mesh (finite DELTA-x, DELTA-t) theory of Langdon [51]-[53] is presented in part to display the effects of too small lambda-D/DELTA-x, even for Maxwellian velocity distributions, as a caution, for example, when some ions are cooled to background gas temperatures by charge exchange. Early work on adding collisions to 1-D charge-sheet models by Burger [28] and Shanny et al. [76] are presented, with many of the elements of current Monte Carlo codes. Bounded plasma modeling is presented with electrode charges and external R, L, C, and V(t), I(t) sources now in use on fast desktop computers as real-time computer experiments, complementing analytic modeling and laboratory experiments. The addition of Monte Carlo collisions (usually done with irregular timesteps) to PIC (usually done with uniform DELTA-t's) is displayed as a developing art, relying on experimental total cross sections and approximate analytical differential cross sections to produce changes in charged-particle speed and direction due to collisions with neutrals, so far including elastic, excitation, ionization, charge exchange, and attachment processes.
