Transport in complex magnetic geometries: 3D modelling of ergodic edge plasmas in fusion experiments

Runov, A.; Kasilov, Sergei; Reiter, D.; McTaggart, N.; Bonnin, X.; Schneider, R.

doi:10.1016/s0022-3115(02)01500-3

Cited by 11 publications

(15 citation statements)

References 12 publications

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“…[1], [6]. Formally, in fluid dynamics we deal with this convection-conduction differential equation for some generalised "fluid quantity" u in the form of a conservation law:…”

Section: New Parallel Coordinatementioning

confidence: 99%

“…[6] to build the coordinate system -it remains the surface ϕ = const. Let us check here the properties of the new coordinates.…”

Section: New Parallel Coordinatementioning

confidence: 99%

“…In [6] we proposed some optimizations of the coordinate system for the stellarator case. Here, we present further optimisation of the numerical procedure which improves the efficiency of the algorithm fundamentally: The restriction on the time step in Monte Carlo is obvious -a single particle step must be small compared to the gradient length of the diffusion coefficient.…”

Section: Introductionmentioning

confidence: 99%

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Extensions of the 3‐Dimensional Plasma Transport Code E3D

Runov

Kasilov

Schneider

et al. 2004

Contrib. Plasma Phys.

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One important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2-D code packages like B2-Eirene or UEDGE are under development. A 3-dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm.The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x 3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra-variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better.

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“…[1], [6]. Formally, in fluid dynamics we deal with this convection-conduction differential equation for some generalised "fluid quantity" u in the form of a conservation law:…”

Section: New Parallel Coordinatementioning

confidence: 99%

“…[6] to build the coordinate system -it remains the surface ϕ = const. Let us check here the properties of the new coordinates.…”

Section: New Parallel Coordinatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extensions of the 3‐Dimensional Plasma Transport Code E3D

Runov

Kasilov

Schneider

et al. 2004

Contrib. Plasma Phys.

Self Cite

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show abstract

“…The price for such flexibility is clear: the system is non-periodic, i.e. the coordinate surfaces of neighbouring systems overlap arbitrarily at the interface between the two systems [24].…”

Section: Transport Codes For Ergodic Configurationsmentioning

confidence: 99%

“…The penalty one pays for this method is an unstructured mesh [24]. The solution is done by finite differences, where for the parallel terms only the 3 points located along the same fieldline are used.…”

Section: Transport Codes For Ergodic Configurationsmentioning

confidence: 99%

Comprehensive suite of codes for plasma-edge modelling

Schneider

Bonnin

McTaggart

et al. 2004

Computer Physics Communications

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Energy transport modelling including ergodic effects

McTaggart

Bonnin

Runov

et al. 2004

Contrib. Plasma Phys.

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The effect of ergodization (either by additional coils like in TEXTOR-DED or by intrinsic plasma effects like in W7-X) defines the need for transport models being able to describe this properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors. For these coordinates the full respective metric tensor has to be known. To study the energy transport in complex edge geometries (in particular for W7-X) we use a finite difference discretization of the transport equations on a custom-tailored grid in local magnetic coordinates. This grid is generated by field line tracing to guarantee an exact discretization of the dominant parallel transport (this also minimizes the numerical diffusion problem). The perpendicular fluxes are interpolated on cross-sectional planes (toroidal cuts), where a quasi-isotropic problem is solved by a constrained Delaunay triangulation (preserving magnetic surfaces where they exist), and discretization. All terms involving toroidal terms are discretized by finite differences. The first tests for W7X and NCSX were successfully performed.

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Transport in complex magnetic geometries: 3D modelling of ergodic edge plasmas in fusion experiments

Cited by 11 publications

References 12 publications

Extensions of the 3‐Dimensional Plasma Transport Code E3D

Extensions of the 3‐Dimensional Plasma Transport Code E3D

Comprehensive suite of codes for plasma-edge modelling

Energy transport modelling including ergodic effects

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