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.