Lagrangian Picture of Plasma Physics. Part 2

By introducing a Lagrangian transformation such that the space coordinates follow the fluid motion, a range of nonlinear problems in fluid dynamics and plasma theory can be either solved or at least simplified. This can often be done without recourse to an amplitude expansion. Although the idea of using Lagrangian coordinates in hydrodynamics is one of the oldest in theoretical mechanics, most results in plasma physics are of recent date. Somewhat surprisingly, so are some relatively simple examples in fluid dynamics. Similarly, Lagrangian coordinate methods used in a statistical description of a fluid can also be extended to plasma physics. Other problems such as the folding of contours and multi-valuedness, can be treated by introducing approximate Lagrangian coordinates that no longer follow the fluid motion exactly. Some possible future lines of research are indicated at the end. It is hoped that this article will help reawaken interest in using Lagrangian coordinates in other branches of classical physics, especially in analytic considerations. So as to widen the appeal of the article, heavy and technical calculations have been relegated to the Appendices. For Part 1 see 38, 607-645, 1997. (author)