Turbulence and scaling laws for energy confinement

Abstract

Energy loss in magnetic confinement devices is often anomalously high and explanations in terms of turbulence due to instabilities are normally sought. The difficulties inherent in identifying the particular mechanism and then performing an explicit calculation for the energy loss encourage the search for a more general alternative approach. In this paper the invariance properties of the equations governing the turbulence are exploited. The essential idea is that, if these equations are invariant under a particular set of scale transformations, then a confinement time calculated from them (no matter how difficult the calculation) must exhibit these same invariance properties. This imposes constraints on the expression for the confinement time which are characteristic of the governing equations. By defining the geometry of the confinement device and the nature of the loss mechanism sufficiently precisely it may be possible to completely determine the confinement time scaling by invariance arguments alone. A discussion of such a case, namely losses due to pressure driven resistive fluid turbulence, is given in detail, followed by a brief description of an application in drift wave turbulence.