Breakdown of Onsager Symmetry in Neoclassical Transport Theory

Neoclassical transport theory is developed in a Lagrangian rather than the usual Eulerian formulation. We show that an underlying asymmetry exists in the neoclassical pinch and bootstrap effects and demonstrate the physical basis of the Onsager symmetry relationship in the pinch-bootstrap duality. A simple model calculation shows that low frequency turbulence can destroy the bootstrap current at levels, eb/T, ~ 10, too low to affect the Ware pinch. Neoclassical transport theory ' has long predicted the existence of a "bootstrap current " driven by the radial density gradient and a pinch effect driven by the toroidal electric field. In addition to the substantial practical importance of these phenomena in fusion devices, they provide a sensitive test of neoclassical theory. In fact, they point out a substantial discrepancy between theory and experimental observation. Although a pinch effect has been observed,2 there is strong if indirect evidence' that the bootstrap current6 does not exist.4 This is particularly surprising because the pinch and bootstrap currents are Onsager conjugates. The object of this Comment is to demonstrate an underlying asymmetry in these processes, to identify the physical basis for suppression of the bootstrap current and to present the results of a calculation of the effect of turbulence on the pinch and bootstrap transport coefficients. This paper considers the questions of Onsager symmetry and the nonobservance of the bootstrap current in light of a recently developed Lagrangian formulation of neoclassical theory.7 This formulation has the virtue of being a direct expression of the elementary kinematics and collision processes, allowing the various flows to be identified at th