Three-dimensional computation of drift Alfvén turbulence

Abstract

A transcollisional, electromagnetic fluid model, incorporating the parallel heat flux as a dependent variable, is constructed to treat electron drift turbulence in the regime of tokamak edge plasmas at the L-H transition. The resulting turbulence is very sensitive to the plasma beta throughout this regime, with the scaling with rising beta produced by the effect of magnetic induction to slow the Alfvénic parallel electron dynamics and thereby leave the turbulence in a more robust, non-adiabatic state. Magnetic flutter and curvature have a minor qualitative effect on the turbulence mode structure and on the beta scaling, even when their quantitative effect is strong. Transport by magnetic flutter is small compared to that by the E × B flow eddies. Fluctuation statistics show that while the turbulence shows no coherent structure, it is coupled strongly enough so that neither density nor temperature fluctuations behave as passive scalars. Both profile gradients drive the turbulence, with the total thermal energy transport varying only weakly with the gradient ratio, d log T /d log n. Scaling with magnetic shear is pronounced, with stronger shear leading to lower drive levels. Scaling with either collision frequency or magnetic curvature is weak, consistent with their weak qualitative effect. The result is that electron drift turbulence at L-H transition edge parameters is drift Alfvén turbulence, with both ballooning and resistivity in a clear secondary role. The contents of the drift Alfvén model will form a significant part of any useful first-principles computation of tokamak edge turbulence.

Drift wave versus interchange turbulence in tokamak geometry: Linear versus nonlinear mode structure

“…The physics of turbulence cannot be assessed from transport scalings or pictorial morphology; quantitative diagnostics of the amplitude, energy, and energetics spectra, as well as several cross-variable statistical measurements relating the transported quantities to the ExB flows that transport them, are needed [1,2,10,11,27,33,38,41]. In the present case, the diagnosis of the energy transfer channels between the equations for p e and φ are among the more important.…”

“…The most basic model of ExB drift turbulence containing both drift wave and interchange physics is a four field model in tokamak flux tube geometry which we call DALF3, for three dimensional drift Alfvén turbulence [2]. The magnetic geometry is assumed to be a set of nested, toroidal, axisymmetric flux surfaces, on which one can define a globally consistent flux tube [12]; this is a matter of defining Hamada coordinates aligned to the equilibrium magnetic field B for which there is only one nonvanishing contravariant component, which is a flux function, and applying the parallel boundary condition after one connection length L , ensuring that all degrees of freedom in the flux tube actually exist on the flux surface for which it is a model.…”

“…This is even true in two dimensional slab turbulence, where there is also dependence on dimensionless parameters such as the collisionality [10]. In three dimensional electromagnetic computations, a finite plasma beta was found to enhance the nonlinear drift wave as well as the interchange (ideal ballooning) effects [2]. It therefore becomes crucial to resolve ρ s in any computation of tokamak edge turbulence, and crucial further to use a formulation of the magnetic geometry which represents both slab and toroidal mode structure equally well.…”

“…Edge turbulence in tokamak flux tube geometry has been treated by models working from a drift wave [1,2] or resistive ballooning [3,4,5] paradigm. Beyond computing edge transport, the main purpose of these computations is to understand the underlying physical character of the turbulence: drive and saturation mechanisms and free energy transfer channels.…”

Ideal ballooning modes in the tokamak scrape-off layer

“…As a matter of fact, the key characteristics of the scrape-off layer turbulent phase space appear to be captured by the electromagnetic fluid drift turbulence theory (see, for example, Refs. 8,[15][16][17][18][19][20][21].…”