Three-dimensional fluid simulations of tokamak edge turbulence

Zeiler, A.; Biskamp, D.; Drake, J. F.; Guzdar, P. N.

doi:10.1063/1.871630

Cited by 83 publications

(140 citation statements)

References 28 publications

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“…[21][22][23][24][25] Furthermore, the periodic axial boundary conditions used in the LAPD turbulence simulation are obviously unphysical, and more realistic boundary conditions may change the parallel dynamics disallowing an exact n 6 ¼ 0 $ n ¼ 0 path.…”

Section: Linear Versus Nonlinear Instability Drivementioning

confidence: 99%

“…They are after all, not essential to the otherwise similar nonlinear drift-like instabilities in the tokamak edge simulations. [21][22][23][24][25] Now, there are a few ways to eliminate the flute modes in the simulation, such as eliminating one of the nonlinearities that is essential to the nonlinear instability process described in Fig. 5.…”

Section: Linear Versus Nonlinear Instability Drivementioning

confidence: 99%

“…This has been explored in tokamak edge simulations in which linear ballooning instability drive is overtaken in the saturated phase by a nonlinear drift-wave drive. [21][22][23][24][25] Finally, it is often found that a particular linear instability is enhanced, depressed, and/or modified in the saturated phase by a nonlinear instability with a similar mechanism as the linear instability. In some of these cases, nonlinear wavenumber transfers can increase or cause drive, 26,27 while in other cases zonal flow effects decrease drive.…”

Section: Introductionmentioning

confidence: 99%

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Energy dynamics in a simulation of LAPD turbulence

et al. 2012

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Energy dynamics calculations in a 3D fluid simulation of drift wave turbulence in the linear Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875] illuminate processes that drive and dissipate the turbulence. These calculations reveal that a nonlinear instability dominates the injection of energy into the turbulence by overtaking the linear drift wave instability that dominates when fluctuations about the equilibrium are small. The nonlinear instability drives flutelike (k k ¼ 0) density fluctuations using free energy from the background density gradient. Through nonlinear axial wavenumber transfer to k k 6 ¼ 0 fluctuations, the nonlinear instability accesses the adiabatic response, which provides the requisite energy transfer channel from density to potential fluctuations as well as the phase shift that causes instability. The turbulence characteristics in the simulations agree remarkably well with experiment. When the nonlinear instability is artificially removed from the system through suppressing k k ¼ 0 modes, the turbulence develops a coherent frequency spectrum which is inconsistent with experimental data. This indicates the importance of the nonlinear instability in producing experimentally consistent turbulence. V C 2012 American Institute of Physics. [http://dx

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Section: Linear Versus Nonlinear Instability Drivementioning

confidence: 99%

Section: Linear Versus Nonlinear Instability Drivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energy dynamics in a simulation of LAPD turbulence

et al. 2012

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“…More recently [23], the ballooning paradigm was extended to situations including the two fluid Ohm's law (i.e., the adiabatic response), leading to the ballooning mode approach to edge turbulence [3,4,5], coinciding with the development of the earliest treatments of flux tube geometry, which were originally constructed with ballooning modes specifically in mind [24,25].…”

Section: Introduction -More Than One Eigenmode In Turbulencementioning

confidence: 99%

“…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.…”

Section: Introduction -More Than One Eigenmode In Turbulencementioning

confidence: 99%

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

2005

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The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift wave character, qualitatively identical to simple two dimensional slab models. The underlying cause is the nonlinear vorticity advection through which the self sustained drift wave turbulence supersedes the linear instabilities, scattering them apart before they can grow, imposing its own physical character on the dynamics. This vorticity advection catalyses the gradient drive, while saturation occurs solely through turbulent mixing of pressure disturbances. This situation persists in the whole of tokamak edge parameter space. Both simplified isothermal models and complete warm ion models are treated.

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Plasma Edge Physics with B2‐Eirene

Schneider

Bonnin

Borraß

et al. 2006

Contrib. Plasma Phys.

473

426

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The B2‐Eirene code package was developed to give better insight into the physics in the scrape‐off layer (SOL), which is defined as the region of open field‐lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma‐wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape‐off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices. The paper presents the basic equations for the plasma transport and the basic models for the neutral transport. This defines the basic ingredients for the SOLPS (Scrape‐Off Layer Plasma Simulator) code package. A first level of understanding is approached for pure hydrogenic plasmas based both on simple models and simulations with B2‐Eirene neglecting drifts and currents. The influence of neutral transport on the different operation regimes is here the main topic. This will finish with time‐dependent phenomena for the pure plasma, so‐called Edge Localised Modes (ELMs). Then, the influence of impurities on the SOL plasma is discussed. For the understanding of impurity physics in the SOL one needs a rather complex combination of different aspects. The impurity production process has to be understood, then the effects of impurities in terms of radiation losses have to be included and finally impurity transport is necessary. This will be introduced with rising complexity starting with simple estimates, analysing then the detailed parallel force balance and the flow pattern of impurities. Using this, impurity compression and radiation instabilities will be studied. This part ends, combining all the elements introduced before, with specific, detailed results from different machines. Then, the effect of drifts and currents is introduced and their consequences presented. Finally, some work on deriving scaling laws for the anomalous turbulent transport based on automatic edge transport code fitting procedures will be described. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Three-dimensional fluid simulations of tokamak edge turbulence

Cited by 83 publications

References 28 publications

Energy dynamics in a simulation of LAPD turbulence

Energy dynamics in a simulation of LAPD turbulence

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

Plasma Edge Physics with B2‐Eirene

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