Tokamak Edge Plasma Research Articles

Modeling of velocity distributions of dust in tokamak edge plasmas and dust–wall collisions

Velocity distribution functions of dust particles of various sizes are simulated in different regions of a tokamak using the DUSTT code. It is shown that dust particles accelerated by plasma flows can reach very high speed >1 km/s at the terminal stages of vaporization. Collisions of beryllium and tungsten dust particles with beryllium wall are modeled with the LS-DYNA material structural analysis code. It is demonstrated that the collisions at high speed ∼1 km/s can cause significant damage to the wall or complete dust destruction depending on dust and wall material parameters.

Scaling properties of intermittent edge plasma turbulence

The intermittency model of She–Leveque–Dubrulle in three dimensions has been extended to the edge magnetized plasma at moderate Reynolds numbers. The model depends on one parameter that is linked to anomalous scaling laws of one-dimension (filament-like) dissipative structures when characteristic scale l → 0 . A comparison with data from edge tokamak plasma shows that it is a workable model describing experimental scaling law. Within the framework of this model, dissipative structures of tokamak edge plasma turbulence in the scrape-off-layer are 1D filament-like.

Publisher’s Note: “Characterization of intermittency of impurity turbulent transport in tokamak edge plasmas” [Phys. Plasmas 15, 072506 (2008)

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Evidence from Numerical Simulations of Transport-Barrier Relaxations in Tokamak Edge Plasmas in the Presence of Electromagnetic Fluctuations

The dynamics of transport barriers in fusion plasmas is studied in the presence of electromagnetic fluctuations. The work is based on numerical simulations using a new three-dimensional electromagnetic fluid turbulence code (EMEDGE3D). In these simulations, the transport-barrier exhibits intermittent relaxation cycles. It is found that magnetic fluctuations have a negligible influence on the relaxation process while the magnetic activity is enhanced during these relaxations, in agreement with experimental observations.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfvén Brésilien [R. M. O. Galvão et al., Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Effects of the parallel electron dynamics and finite ion temperature on the plasma blob propagation in the scrape-off layer

A new three-dimensional model for the warm-ion turbulence at the tokamak edge plasma and in the scrape-off layer is proposed, and used to study the dynamics of plasma blobs in the scrape-off layer. The model is based on the nonlinear interchange mode, coupled with the nonlinear resistive drift mode, in the presence of the magnetic curvature drive, the density inhomogeneity, the electron dynamics along the open magnetic field lines, and the electron-ion and electron-neutral collisions. Within the present model, the effect of the sheath resistivity decreases with the distance from the wall, resulting in the bending and the break up of the plasma blob structure. Numerical solutions exhibit the coupling of interchange modes with nonlinear drift modes, causing the collapse of the blob in the lateral direction, followed by a clockwise rotation and radial propagation. The symmetry breaking, caused both by the parallel resistivity and the finite ion temperature, introduces a poloidal component in the plasma blob propagation, while the overall stability properties and the speed are not affected qualitatively.

Processes with neutral hydrogen and deuterium molecules relevant to edge plasma in tokamaks

Neutral hydrogen molecule is an important constituent of edge plasma in tokamak reactors. These molecules are continuously produced by ion neutralisation and recombination on plasma walls and are subsequently reemitted in the plasma. We initiated an experimental program to study processes in which vibrationally excited hydrogen molecules are involved. Two specific experimental techniques have been developed, one for vibrational spectroscopy of hydrogen molecules (H2 and D2) and another one for H and D depth profiling in materials. New information has been acquired on hydrogen recombination on tungsten and also on dissociative electron attachment in hydrogen, both relevant to edge plasma. Experimental setups are shortly presented as well as some of the results on above processes.

Characterization of intermittency of impurity turbulent transport in tokamak edge plasmas

The statistical properties of impurity transport of a tokamak edge plasma embedded in a dissipative drift-wave turbulence are investigated using structure function analysis. The impurities are considered as a passive scalar advected by the plasma flow. Two cases of impurity advection are studied and compared: A decaying impurities case (given by a diffusion-advection equation) and a driven case (forced by a mean scalar gradient). The use of extended self-similarity enables us to show that the relative scaling exponent of structure functions of impurity density and vorticity exhibit similar multifractal scaling in the decaying case and follows the She–Lévêque model. However, this property is invalidated for the impurity driven advection case. For both cases, potential fluctuations are self-similar and exhibit a monofractal scaling in agreement with Kolmogorov–Kraichnan theory for two-dimensional turbulence. These results obtained with a passive scalar model agree also with test-particle simulations.

Spontaneous rotation sources in a quiescent tokamak edge plasma

Spontaneous rotation sources in a quiescent tokamak edge plasma are studied without an external momentum source, such as, beam injected or wall-born neutrals. Discussions are based upon example neoclassical solutions from an edge gyrokinetic particle code. The main study is performed in a DIII-D plasma [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] with the ion Grad-B drift directed toward the single-null divertor. Comparison with a reversed Grad-B drift case is also shown. It is found that there is a robust spontaneous co-current toroidal plasma rotation source in the far scrape-off plasma due to the wall sheath effect. As the edge pedestal width becomes narrower, the co-current rotation in the far scrape-off becomes weaker, but there appears a stronger co-current rotation in the pedestal top/shoulder from the X-point orbit loss effect, possibly providing a co-rotation boundary condition to the core plasma. Reversal of the magnetic field and plasma current brings down the overall co-rotation, especially in the far scrape-off plasma.

On the first derivative probe method for electron energy distribution function measurements in tokamak edge plasma

The applicability of the first derivative Langmuir probe method in strongly magnetized tokamak plasmas is discussed. The method is used for processing the electron part of the current-voltage (IV) probe characteristics measured in the CASTOR tokamak edge plasma (Institute of Plasma Physics, Association EURATOM-IPP, Prague, Czech Republic). The comparison of the results obtained with the results given by the Stangeby method yields a satisfactory agreement.

Simulation of Small Size Divertor Tokamak Plasma Edge Including Self-Consistent Electric Fields

The B2.SOLPES.0.5.2D code (Braams, Contrib Plasma Phys 36:276, 1996; Rozhansky and Tendler, Rev Plasma Phys 19:147, 1996) is applied for modeling SOL (Scrape off Layer) plasma in the small size divertor tokamak. Detailed distributions of the plasma heat flux and other plasma parameters in SOL, especially at the target plate of the divertor are found by modeling. The modeling results show that most of the electron heat flux and small part of ion heat flux arrive at target plate of the divertor, while, a large part of the ion heat flux and part of electron heat flux arrive at the outer wall. Also analysis of the role of poloidal E × B drifts in the redistribution of edge plasma is fulfilled.

Dynamics and generation mechanisms of mesoscale structures in tokamak edge plasmas

Intermittent convective-like plasma transport associated with mesoscale coherent structures extended along the magnetic field lines (“blobs”) is often dominant at the edge of tokamaks, stellarators, and linear devices. Blobs can travel a large distance toward the wall (∼10 cm and larger) and strongly enhance both edge plasma energy and particle transport and plasma-wall interactions. The dynamics of blobs and blob generation mechanisms are discussed in this paper.

Current in the Edge of Small Size Divertor Tokamak

The scheme of poloidal (parallel) currents calculation is presented and compared to the two-dimensional code results both for the core region and for the Scrape-Off layer (SOL). A method of reduction of the two-dimensional equation for potential to one-dimensional ordinary differential equation is suggested. Also the impact of neutral beam injection (NBI) in plasma edge of small size divertor tokamak (SSDT) is studied.

On the Mechanisms of Generation of Meso‐Scale Convective Structures in Tokamak Edge Plasma

AbstractMeso‐scale structures, driven by curvature and gradB effects, like blobs and ELMs play a very important role in edge and SOL plasma transport in tokamaks. Here we discuss rather simple model describing the formation of blobs. The model is based on coupled drift‐wave and ballooning effects. Both analytic and preliminary numerical results are reported. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Progress in Kinetic Simulation of Edge Plasmas

AbstractKinetic codes are required for quantitative simulation of edge plasmas of most tokamaks, because orbit widths can be comparable to radial scale lengths and because mean free paths can be comparable to scale lengths along the magnetic field. However, the edge presents special challenges for edge simulation, both in terms of formulation and implementation. There are two major approaches to kinetic simulation, namely particle‐based and continuum‐ (high‐dimensional fluid‐) based. The edge presents challenges common to both approaches as well as ones that are unique to each approach. In this paper we review these challenges, and survey how they are being addressed in current edge kinetic simulation projects, as well as the status and accomplishments of those projects. We discuss in some detail the status and recent accomplishments of the U.S. Edge Simulation Laboratory (ESL), a project based on the continuum approach. The ESL currently consists of a main‐line effort to develop a code based on high‐order conservative finite‐volume discretization, as well as two prototype activities, TEMPEST and EGK. These prototype codes are exploring issues attached to energy‐magnetic moment and parallel velocity‐magnetic moment representations, respectively, as well as physics issues associated with simulation in a steep radial gradient region and a domain that includes both open field lines and closed flux surfaces. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Suite of Verification Test Problems for Edge Turbulence Simulations

AbstractWe present a suite of test problems that are used for verification of the edge turbulence code BOUT. BOUT is an electromagnetic fluid turbulence code for tokamak edge plasma that performs time integration of reduced Braginskii plasma fluid equations, using spatial discretization in realistic geometry and employing a standard ODE integration package PVODE. Recently the code underwent a substantial redesign and extensive verification testing. In the verification process, a series of linear and nonlinear test problems was applied to BOUT targeting different subgroups of physical terms. The tests include reproducing basic electrostatic and electromagnetic plasma modes in simplified geometry, axisymmetric benchmarks against the 2D edge code UEDGE in the actual DIII‐D tokamak divertor geometry. Successful passing of these tests by BOUT gives strong evidence that equations in the code are solved correctly. Although the tests were developed specifically for the BOUT code they can well be applied for verification of other codes used for simulations of edge turbulence. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Ion Particle Transport in the Tokamak Edge Plasma

AbstractA generalized pinch‐diffusion transport relation previously derived from momentum conservation is combined with the continuity equation to derive a “generalized diffusion theory” for ion particle transport in the tokamak plasma edge inside the separatrix. The resulting generalized diffusion coefficients are evaluated for a representative experiment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiscaling Dynamics of Impurity Transport in Drift-Wave Turbulence

Intermittency effects and the associated multiscaling spectrum of exponents are investigated for impurities advection in tokamak edge plasmas. The two-dimensional Hasagawa-Wakatani model of resistive drift-wave turbulence is used as a paradigm to describe edge tokamak turbulence. Impurities are considered as a passive scalar advected by the plasma turbulent flow. The use of the extended self-similarity technique shows that the structure function relative scaling exponent of impurity density and vorticity follows the She-Leveque model. This confirms the intermittent character of the impurities advection in the turbulent plasma flow and suggests that impurities are advected by vorticity filaments.

Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics

The electric potential plays a key role in the confinement properties of tokamak plasmas, with the subsequent impact on the performances of fusion reactors. Understanding its structure in the peripheral plasma -- interacting with solid materials -- is of crucial importance, since it governs the boundary conditions for the burning core plasma. This paper aims at highlighting the dedicated impact of the plasma-wall boundary layer on this peripheral region. Especially, the physics of plasma-wall interactions leads to non-linear constraints along the magnetic field. In this framework, the existence and uniqueness of the electric potential profile are mathematically investigated. The working model is two-dimensional in space and time evolving.

Study of three dimensional zonal flows characteristic and novel probe design in HL-2A

Three dimensional(3-D) features of geodesic acoustic mode zonal flows (GAMZF) were first determined with novel three-step zonal flow probes (TSZFP) at the edge of the HL-2A Tokamak plasmas. Three arrays of TSZFP were located 65mm and 800mm apart. The poloidal mode (m～0) and toroidal mode (n～0) of electric potential and field perturbations were simultaneously determined for the first time. Corresponding frequencies were estimated as 7kHz，which are in good agreement with theoretical prediction. The radial scale lengths of ZF were 24—42cm. The formation mechanism of the flows is identified to be nonlinear three wave coupling between high frequency turbulent fluctuations and the flows. The regulating effect of the flows on the ambient turbulent fluctuations was also demonstrated. The Reynolds stress driven by edge fluctuation is one of the main reasons driving the poloidal flow. It is also verified that the radial gradient of Reynolds stress can drive zonal flows.