The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries

Tamain, P.; Bufferand, Hugo; Ciraolo, Guido; Colin, C.; Galassi, D.; Ghendrih, Ph.; Schwander, F.; Serre, Éric

doi:10.1016/j.jcp.2016.05.038

Cited by 127 publications

(164 citation statements)

References 27 publications

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“…The form of the diamagnetic current, in terms of a magnetic drift V mag , is used here because it is more easily implemented in terms of fluxes through cell faces than the standard form, and hence suitable for the conservative numerical schemes described in section 3: The flow speed depends only on the local temperature, rather than on pressure gradients, and this has been found to improve numerical stability. This approach has also been used in the TOKAMX code [10].…”

Section: Hermes Model Equationsmentioning

confidence: 99%

“…Unfortunately in general geometry it is extremely difficult to ensure that the resulting numerical method conserves particles since these terms must combine so as to obey the analytic integral relation. Here we adopt the approach also used in [10], and write the advection in flux-conservative form: The first two terms describe the drift-plane motion, which is calculated using the scheme illustrated in figure 1. The third term describes radial flow due to poloidal electric fields, whilst the fourth (last) term describes poloidal flow due to radial electric fields.…”

Section: Poloidal Flowsmentioning

confidence: 99%

“…One of the uncertainties in making these predictions is the transport across the magnetic field, which is not well described by diffusion [4,5], and is thought to be turbulent [6]. Since the fluctuations can be of similar spatial scales and magnitude to average profiles, significant effort has been devoted to developing and testing 3D flux-driven fluid turbulence simulation codes, including GBS [7,8], TOKAM-3D [9] and TOKAM3X [10].…”

Section: Introductionmentioning

confidence: 99%

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Hermes: global plasma edge fluid turbulence simulations

Dudson

Leddy

2017

Plasma Phys. Control. Fusion

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Abstract. The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the self-consistent evolution of plasma fluctuations, global profiles and flows, but the numerical tools capable of doing this in realistic (diverted) geometry are only now being developed.Here a 5-field reduced 2-fluid plasma model for the study of instabilities and turbulence in magnetised plasmas is presented, built on the BOUT++ framework. This cold ion model allows the evolution of global profiles, electric fields and flows on transport timescales, with flux-driven cross-field transport determined self-consistently by electromagnetic turbulence. Developments in the model formulation and numerical implementation are described, and simulations are performed in poloidally limited and diverted tokamak configurations.

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Section: Hermes Model Equationsmentioning

confidence: 99%

Section: Poloidal Flowsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hermes: global plasma edge fluid turbulence simulations

Dudson

Leddy

2017

Plasma Phys. Control. Fusion

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“…Eqs. (3)(4)(5)(6)(7)(8) are solved by the GBS code using a second order finite difference scheme, except for the [A 1 , A 2 ] operators that are discretized by using the Arakawa scheme [22]. Time integration is carried out with the classical Runge-Kutta method [23].…”

Section: Turbulent Sol Simulations and Comparison With The Simple Twomentioning

confidence: 99%

“…A number of simulation codes were developed in the past years to carry out these simulations, such as BOUT++ [3], GBS [4,5], GRILLIX [6], and TOKAM3X [7]. However, their development is still ongoing and turbulence simulations remain computationally very expensive.…”

Section: Introductionmentioning

confidence: 99%

A comparison between a refined two-point model for the limited tokamak SOL and self-consistent plasma turbulence simulations

Wersal

Ricci

Loizu

2017

Plasma Phys. Control. Fusion

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A refined two-point model is derived from the drift-reduced Braginskii equations for the limited tokamak scrape-off layer (SOL) by balancing the parallel and perpendicular transport of plasma and heat and taking into account the plasma-neutral interaction. The model estimates the electron temperature drop along a field line, from a region far from the limiter to the limiter plates. Self-consistent first-principles turbulence simulations of the SOL plasma including its interaction with neutral atoms are performed with the GBS code and compared to the refined two-point model. The refined two-point model is shown to be in very good agreement with the turbulence simulation results.

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Effect of the Boussinesq approximation: Turbulence studies with GRILLIX in slab geometry

Ross

Stegmeir

Coster

2018

Contributions to Plasma Physics

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The drift‐reduced global Braginskii system is implemented in GRILLIX, a plasma turbulence code that is able to treat diverted geometries by using the flux‐coordinate independent approach (FCI). We solve a four‐field model, evolving the density, the electron temperature, the vorticity, and parallel ion momentum. The difference between the system with the Boussinesq approximation (BS) and the full system (FS) is investigated. The Boussinesq approximation is widely used as it reduces the numerical and computational complexity significantly. In order to understand the impact of the Boussinesq approximation, a periodic flux tube geometry is chosen as the computational domain. The conservation of energy and particles is derived and tested within the code, both in FS and BS. Moreover, we will discuss how the Boussinesq approximation has subtle effects on the energy theorem of the model, and a conserved energy‐like quantity is only obtained if the Boussinesq approximation is applied in a consistent way. We will also present numerical and computational techniques in order to relax the Boussinesq approximation. The code is verified by the method of manufactured solutions, which yields the expected order of accuracy. A fundamental result found in the paper is that the Boussinesq approximation only has a minor effect on non‐linear simulations, at least in the regime studied here.

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The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries

Cited by 127 publications

References 27 publications

Hermes: global plasma edge fluid turbulence simulations

Hermes: global plasma edge fluid turbulence simulations

A comparison between a refined two-point model for the limited tokamak SOL and self-consistent plasma turbulence simulations

Effect of the Boussinesq approximation: Turbulence studies with GRILLIX in slab geometry

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