Theory and simulation of the test particle Debye cloud

The Debye screening of a test particle by plasma is well known to every student of plasma physics. It forms an important cornerstone of plasma theory, but can not be directly measured in the laboratory. The measurement of such a subtle effect on the computer is made possible by a subtraction technique in which we perform the simulation twice, once with the test particle and once again without it. Subtracting the potentials from the two runs gives the plasma response due to a single particle. Thus we have a "microscope" for the examination of fundamental plasma behavior. For unmagnetized plasmas, this technique is a significant improvement over previous diagnostics. More importantly, it enables one to see magnetized Debye clouds for the first time.; Our work proceeds systematically from one dimensional plasmas to two dimensional unmagnetized plasmas, and finally to the two dimensional magnetized plasmas. For each case, the subtraction technique is able to give clear pictures of the Debye cloud for various test particle velocities. The results are then compared to those obtained from kinetic theory. The 1-D unmagnetized simulation shows excellent agreement with the prediction of kinetic theory of finite size particles. The 2-D unmagnetized simulation potential contours agree qualitatively with the point particle kinetic theory.; The inclusion of a dc magnetic field introduces new complexity due to the particles' Larmor gyration, and correspondingly increases the computational investment required for both the simulation and the analytic treatment. The simulation measurement is performed in the particle's frame of reference to produce a clear picture of the Debye cloud. The analytic expression for the cloud involves products of the Bessel functions, and the evaluation of these consumes more computer time than the particle simulation. A series of case studies has demonstrated interesting behavior of the cloud.