  A parallel, relativistic, three-dimensional particle-in-cell code SPACE has
been developed for the simulation of electromagnetic fields, relativistic
particle beams, and plasmas. In addition to the standard second-order
Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to
resolve atomic physics processes such as multi-level ionization of plasma
atoms, recombination, and electron attachment to dopants in dense neutral
gases. SPACE also contains a highly adaptive particle-based method, called
Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems.
It eliminates the traditional Cartesian mesh of PIC and replaces it with an
adaptive octree data structure. The code's algorithms, structure, capabilities,
parallelization strategy and performances have been discussed. Typical examples
of SPACE applications to accelerator science and engineering problems are also
presented.
