Plasma Science: From Fundamental Research to Technological Applications (1995)
Chapter: Boundary Layers
quantitative understanding. But nonlinear theory is of great intrinsic interest and is essential for the description of most important applications of plasma physics that involve magnetohydrodynamics, kinetic theory, turbulence, the interaction of charged particles with intense electromagnetic fields, and so on. Therefore, increased attention should be given to nonlinear theory aimed at the development of new analytical and numerical tools.
Numerical Simulation
A most promising area for the future is that of numerical simulation, driven by continuing dramatic advances in computational speed and computer organization, and decreases in the cost of hardware. These ongoing improvements in hardware, coupled with the parallel design of new and more efficient algorithms, should allow the solution of many of the nonlinear problems that currently defy direct analytical solution. Numerical computation offers the best hope of dealing meaningfully with the large problems in complex geometries that characterize so many of the significant applications of plasma physics. One anticipates the development of teams of computational specialists, theorists, experimentalists, and engineers, organized to optimize the solution of particular large technical problems. Training of students for this type of operation should be encouraged in universities.
Novel Analytical Techniques
The challenge of nonlinear theory suggests the adaptation or innovation of novel analytical techniques. The use of percolation theory for certain transport problems in plasmas appears to be promising. The development of modern statistical analyses, perhaps employing artificial intelligence (symbolic dynamics), may lead to greatly improved data analysis and new physical insights. The transfer from pure mathematics of well-developed areas such as wavelet theory, which are relatively unknown in physics and engineering, offers great promise.
Boundary Layers
Boundary layers are of great importance in plasmas. These occur in such diverse applications as the sheath region near the first wall of a fusion reactor, the region in a coronal hole where the solar wind is emitted as the system changes from collision-dominated to collision-free, and magnetic reconnection in plasmas of interest in space. They are often distinguished by the need for a full kinetic theory, and they will require a synthesis of analytical boundary layer techniques and advanced numerical methods.
