Symbolic Vector Analysis in Plasma Physics
Authors: H. Qin, W.M. Tang, and G. Rewoldt
Many problems in plasma physics involve substantial amounts of analytical vector calculation. The complexity usually originates from both the vector operations themselves and the choice of underlying coordinate system. A computer algebra package for symbolic vector analysis in general coordinate systems, GeneralVectorAnalysis (GVA), is developed using Mathematica. The modern viewpoint for 3D vector calculus, differential forms on 3-manifolds, is adopted to unify and systematize the vector calculus operations in general coordinate systems. This package will benefit physicists and applied mathematicians in their research where complicated vector analysis is required. It will not only save a huge amount of human brain-power and dramatically improve accuracy, but this package will also be an intelligent tool to assist researchers in finding the right approaches to their problems. Several applications of this symbolic vector analysis package to plasma physics are also given.