Moment approach to deriving parallel heat flow for general collisionality

Abstract

In the moment approach, a parallel electron heat flux density is obtained for arbitrary collisionality in the transport ordering. The parallel moment equations are derived from the drift kinetic equation with the exact linearized Landau operator and analytically solved for the heat flux in integral form. Quantitative analysis of the integral heat flux for sinusoidal temperature profiles shows that the number of moments required for convergence increases as collision length increases. The integral heat flux well agrees with the Braginskii heat flux and the collisionless heat flux for high and low collisionalities, respectively. Incorrect application of the Braginskii heat flux in moderately collisional or nearly collisionless plasmas often leads higher heat flux than the integral closure. This fact is consistent with numerical studies of electron heat confinement in the sustained spheromak physics experiment [Hooper et al., Nucl. Fusion 39, 863 (1999)] which show a modest (6%) increase in core temperature when the integral heat flux is adopted.