An alternative justification for the stationary assumption made by many reduced models for nonlocal electron heat flow in plasmas

Abstract

Nonlocal models are widely used for approximating kinetic effects on electron heat flow in fusion-relevant plasmas. Almost universally, such models have no explicit time dependence and are designed to make heat flow predictions based directly on instantaneous profiles of macroscopic plasma parameters. While this is usually justified by the claim that transient effects fade before temperature profiles evolve appreciably, a more rigorous justification of the stationarity assumption in terms of kinetic theory is desirable. In this Letter, such a justification is provided by demonstrating that nonstationary effects related to the time dependence of the isotropic part of the electron distribution function vanish up to third order in Chapman–Enskog theory (irrespective of ion charge state or presence of magnetic fields). However, it is found that the electron inertia term (whose appearance in Ohm's law stems from the time derivative of the anisotropic part of the electron distribution function) does have a small but finite third order effect that is most prominent for plasmas with low average ion charges. This Letter additionally provides a convenient analytic inverse for the isotropic part of the Landau electron–electron collision operator.

A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas

“…The deviation from Maxwellian δf α and therefore transport fluxes are established on much faster, kinetic timescales than the characteristic timescales on which hydrodynamic quantities vary. The RKM then solves for δf α from only the instantaneous hydrodynamic profiles [34] by relaxing the kinetic equation (4) to the stationary state where ∂ t δf α = 0. This relaxed solution corresponds to the physical state for δf α for the input hydrodynamic profiles, even though the transient states that the DF evolves through in the RKM on the way to this relaxed state are not necessarily physical.…”