On standard forms for transport equations and quasilinear fluxes

Quasilinear expressions for anomalous particle and energy fluxes arising from electrostatic plasma turbulence in a Tokamak are reviewed. 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 Q j was correctly calculated. It was shown that the anomalous energy transport can be described by Del .Q j *, where Q j *= 3 / 5 Q j , with all remaining source terms such as (p j Del .V j ) cancelling. 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 the author cannot be sure in general how properly to treat the source terms p j Del .V j or (p j Del .V j ).