  While the particle-in-cell (PIC) method is quite mature, verification and
validation of both newly developed methods and individual codes has largely
focused on an idiosyncratic choice of a few test cases. Many of these test
cases involve either one- or two-dimensional simulations. This is either due to
availability of (quasi) analytic solutions or historical reasons. Additionally,
tests often focus on investigation of particular physics problems, such as
particle emission or collisions, and do not necessarily study the combined
impact of the suite of algorithms necessary for a full featured PIC code. As
three dimensional (3D) codes become the norm, there is a lack of benchmarks
test that can establish the validity of these codes; existing papers either do
not delve into the details of the numerical experiment or provide other
measurable numeric metrics (such as noise) that are outcomes of the simulation.
This paper seeks to provide several test cases that can be used for validation
and bench-marking of particle in cell codes in 3D. We focus on examples that
are collisionless, and can be run with a reasonable amount of computational
power. Four test cases are presented in significant detail; these include,
basic particle motion, beam expansion, adiabatic expansion of plasma, and two
stream instability. All presented cases are compared either against existing
analytical data or other codes. We anticipate that these cases should help fill
the void of bench-marking and validation problems and help the development of
new particle in cell codes.
