Consistency in drift-ordered fluid equations

Abstract

We address several concerns related to the derivation of drift-ordered fluid equations. Starting from a fully Galilean invariant fluid system, we show how consistent sets of perturbative drift-fluid equations in the case of a isothermal collisionless fluid can be obtained. Treating all the dynamical fields on equal footing in the singular-drift expansion, we show under what conditions a set of perturbative equations can have a non-trivial quasi-neutral limit. We give a suitable perturbative setup where we provide the full set of perturbative equations for obtaining the first-order corrected fields and show that all the constants of motion are preserved at each order. With the dynamical field variables under perturbative control, we subsequently provide a quantitative analysis by means of numerical simulations. With direct access to first-order corrections the convergence properties are addressed for different regimes of parameter space and the validity of the first-order approximation is discussed in the three settings: cold ions, hot ions and finite charge density.

Collisional multispecies drift fluid model

“…The validity of the occurrence of the diamagnetic drift at this order is discussed in Ref. 18. As the polarization and viscosity drift are of higher order, the effect is expected to be small and therefore negligible, which has been confirmed by numerical experiments (see the last paragraph of Sec.…”

Multi-temperature generalized Zhdanov closure for scrape-off layer/edge applications

“…A partial solution for this system using transport coefficients obtained from the singletemperature Zhdanov closure is provided in [40], in which the parallel divergence of η α∥∥0 [ϵ ∥∥ + ϵ dia,∥∥ )] is neglected in equation ( 63), q α,dia is also neglected, and then a partial first solution is derived for the parallel divergence of π α∥∥ , which is included in the momentum equation. It is also worth noting that including q α,dia in such a manner, either in the momentum equation or the closure, or both, can lead to inconsistencies [41] such as summabilitity issues [42]. That is, if a species is split into two continuous portions all else being equal, the two split portions may not evolve together as the whole unsplit species would.…”

Effects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence

“…Since equations (42) are given in terms of analytical base functions we can numerically evaluate ψ p (R, Z) and I(ψ p ) and all their derivatives at arbitrary points to machine precision, which is simple to implement and fast to execute. This translates to an exact representation of the magnetic field and related quantities, for example curvature (23), in code. In particular, the X-point(s) and O-point can be determined to machine precision via a few Newton iterations.…”

“…Gyro-fluid models in general result from taking velocity space moments over an underlying gyro-kinetic model and share many of its advantages: finite Larmor radius corrections, consistent particle drifts, an energy and momentum theorem based on variational methods in the underlying gyro-kinetic model and an inherent symmetry in moment equations with regards to multiple ion species. These advantages are absent from so-called drift-fluid models that result from a drift-expansion of the Braginskii equations [20][21][22][23][24]. A downside of gyro-fluid models is that closed expressions for scattering collisions and plasma neutral interactions remain an open issue, despite recent formulations in the long wavelength limit [25].…”