ON STANDARD FORMS FOR TRANSPORT-EQUATIONS AND QUASI-LINEAR FLUXES

Quasilinear expressions for anomalous particle and energy fluxes arising from electrostatic plasma turbulence in a Tokamak are reviewed yet again. Further clarifications are made, and the position taken in a previous report (Ross, 1989, Comments Plasma Phys. Contr. Fusion 12, 155) is modified. There, the total energy flux, Q(j), and the conductive heat flux, q(j), were correctly defined, and the anomalous Qj was correctly calculated. It was shown that the anomalous energy transport can be described by nabla.Q(j)*, where Q(j)* = 3/5Q(j), with all remaining source terms such as <p(j) approximately nabla.V(j) approximately> cancelling. Here, a revised discussion is given of the identification of the anomalous conductive flux, q(j), in which the distinction between Q(j) and Q(j)* is reconsidered. It is shown that there is more than one consistent way to define q(j). Transport calculations involving only theoretical electrostatic turbulent fluxes are unaffected by these distinctions since Q(j) or Q(j)*, rather than q(j), is the quantity naturally calculated in theory. However, an ambiguity remains in experimental transport analysis if the measured particle flux GAMMA(j) = n(j)V(j) is to be used in the energy equation to identify the convective terms. This is because we cannot be sure in general how properly to treat the source terms p(j) nabla.V(j) or <p(j) approximately nabla.V(j) approximately>.