Paraxial WKB description of short wavelength eigenmodes in a tokamak

A novel asymptotic approach for solving the eigenvalue problem in the short -wavelength limit is developed. This approach, called the paraxial WKB meth od, is presented and applied to the analysis of gradient-driven instabiliti es in a tokamak. In some respects, the paraxial WKB method is more general than the ballooning representations usually used for this problem. For inst ance, the paraxial WKB method can describe drift-ballooning instabilities i n the presence of sheared plasma rotation when the ballooning representatio n fails. Being different from other techniques, the paraxial WKB method not only sheds new light on the physics of drift-ballooning instabilities, but also provides a description for short-wave instabilities of other types. O ther possible extensions of the paraxial WKB technique, such as the applica tion to three-dimensional systems like stellarators, are briefly discussed. Finally, advantages and disadvantages of the paraxial WKB method in compar ison with the ballooning representation are considered. (C) 2001 American I nstitute of Physics.