Scaling laws for trace impurity confinement: a variational approach

A variational approach is outlined for the deduction of impurity confinement scaling laws. Given the forms of the diffusive and convective components to the impurity particle flux, we present a variational principle for the impurity confinement time in terms of the diffusion time scale and the convection parameter, which is a non-dimensional measure of the size of the convective flux relative to the diffusive flux. These results are very general and apply irrespective of whether the transport fluxes are of theoretical or empirical origin. The impurity confinement time scales exponentially with the convection parameter in cases of practical interest. (orig.)