Tokamak Edge Turbulence Research Articles

The effect of divertor particle sources on scrape-off-layer turbulence

Tokamak edge turbulence is crucial for the cross-field transport of particles and energy away from the separatrix. A better understanding of what affects the turbulence helps to control the heat flux to the divertor targets and the wall. One potentially important factor is the ion particle source in the divertor, as the neutral pathways and the ionisation source distributions are different depending on the divertor geometry, e.g. vertical- and horizontal-target configurations. Numerically, how to represent the sources and mimic the effects on the SOL in the simulations is still an open question. In this paper, we use a 3D turbulence code STORM, based on drift-reduced Braginskii equations, to study the effects of the divertor particle source distribution on turbulence in a simplified 3D slab geometry. The results show that it requires a large amount of divertor particle source to be peaked near the separatrix to alter the heat flux deposited on the target in attached conditions. This large non-uniform particle source can locally enhance the turbulence in the divertor volume, which redistributes the energy flux to the target and reduces the maximum amplitude. Meanwhile, the plasma profiles evaluated at the outboard midplane, such as the amplitudes and fluctuations of the density and temperature, are marginally changed. Another consequence of our results is that the prediction of the temperature difference between the outboard midplane and the target would be underestimated, if the calculation only considers the conductive heat flux and ignores this enhanced cross-field transport in the divertor.

Analysis of locally-aligned and non-aligned discretisation schemes for reactor-scale tokamak edge turbulence simulations

Edge turbulence codes will play a key role in the interpretation of ITER data and for reliable predictions of EU-DEMO. At present, such codes are not yet capable of routine simulations at reactor scale, and instead focus on smaller experiments like TCV or ASDEX Upgrade. Numerical methods have to be identified that scale to reactor size, and are able to cope with the highly anisotropic turbulent structures and simultaneously with the complex magnetic geometry in the edge with X-point(s), the vessel wall and divertor targets present. Particularly for such conditions two main approaches, non-aligned discretisation schemes and a locally-aligned discretisation scheme (commonly referred to as Flux-Coordinate Independent approach (FCI)), have emerged. We analyse both schemes concerning their applicability and scalability to next generation fusion reactors. We find that the ratio of the computational cost of a non-aligned scheme compared to aligned scheme scales as ∝(R0qρs)2 for shear Alfvén dynamics, and as (R0qρs)3 for electron heat conduction, where R0 is the major radius of a tokamak, q an estimate for the safety factor at the edge and ρs is the drift scale representing the typical size of turbulent structures to be resolved. Locally-aligned schemes can therefore be considered strongly favourable for reactor scale tokamaks concerning computational performance. On the other hand, locally-aligned schemes suffer from a more complex treatment of boundary conditions, for which an immersed boundary approach (IBA) was recently proposed. We demonstrate numerically the validity of this method in combination with the FCI approach. Finally, we present a first attempt of an ITER edge turbulence simulation with the FCI code GRILLIX at realistic parameters and in realistic geometry.

Drift-ordered fluid vorticity equation with energy consistency

Although drift-ordered fluid models are widely applied in tokamak edge turbulence simulations, the models used are acknowledged not to conserve energy or even electrical charge. The present paper aims to remove many of the existing pitfalls in drift-fluid models, however, with the objective of finding a solution simple enough to be implemented in numerical applications. Our main result is an improved version of the drift-Braginskii equations involving a generalized vorticity function. In the new drift-Braginskii system, the quasi-neutrality condition translates into a transport equation for a generalized vorticity, expressed in conservation form, and related to the total mass-weighted circulation. It is found that kinetic energy conservation can be achieved if the polarization flow is defined recursively. The resulting model conserves the kinetic energy associated with E×B and diamagnetic flows and retains the associated perpendicular kinetic energy flux.

A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between n=0, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. The proposed scheme can capture an interplay between n=1 global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.

Tomographic reconstruction of tokamak edge turbulence from single visible camera data and automatic turbulence structure tracking

Following the lead of Nguyen van Yen (2012 Nucl. Fusion 52 013005), this article tackles the problem of tomographic inversion with one camera assuming a constant emissivity of light along the magnetic field lines. In this way, the 3D problem reduces to 2D by helical symmetry, allowing for the reconstruction of any poloidal plane in the field of view of the camera. It is shown in this article that the complexity of using a wavelet basis for the reconstruction, as presented by Nguyen van Yen, is not necessary. The method is also validated by confronting it to 3D numerical data coming from the TOKAM3X code, for which the emissivity is slowly varying along the field lines (up to 20%), showing the robustness of the reconstruction. The technique is then applied to real camera data recorded during a D-shaped ohmic plasma shot realized in the COMPASS tokamak. The method is experimentally validated by comparing reconstructed data from camera and ion saturation currents measured by Langmuir probes in the divertor region. Finally, it is shown that automatic detection and tracking of structures visible in the reconstructed poloidal plane enables unique investigations of edge plasma physics and opens wide perspectives for this method.

Nonlinear gyrokinetic particle simulation of dissipative trapped electron mode

Electron turbulence induced by the trapped electron mode has been widely studied. The dissipative trapped electron mode (DTEM) is an important candidate for tokamak edge turbulence. Nonlinear gyrokinetic particle simulations based on edge parameters are carried out to investigate the collisional effects on the nonlinear transport of DTEM turbulence. It is found that the collisions can induce a low level radially inward electron transport for the DTEM turbulence, which is closely related to the phase difference between the radial turbulent motion and perturbed density fluctuation induced by collisional dissipation. We observe an inverse spectral cascade of the turbulence during the nonlinear DTEM saturation, which is caused by quasimode scattering induced by trapped electrons and important for determining the magnitude of turbulent transport. The nonlinear transport of DTEM is found to be inversely proportional to the collisional frequency by gyrokinetic simulation, which is consistent with the prediction of quasilinear theory.

Effect of magnetic shear on edge turbulence in SOL-like open field line configuration in QUEST

Intensity fluctuations are investigated using the fast camera imaging technique in the slab annular plasma as a function of magnetic shear and connection length in the spherical tokamak QUEST. Note that here QUEST is operated as a simple magnetized torus with a tight aspect ratio. Slab annular plasmas feature open magnetic field lines and can mimic the tokamak edge-scrape off layer (SOL)-like plasma attributes reasonably well. Three magnetic shear regimes are realized using three poloidal magnetic field (PF) coil pairs. A whole range of connection lengths (∼∞ ≥ Lc ≥ 5.5 m) is scanned by varying the PF strength for a given toroidal field for each magnetic shear regime. For the first time a systematic study of the effect of magnetic shear and field line pitch together on edge-SOL-like plasma fluctuations is being reported. Slab plasmas with intermediate magnetic shear are observed to be more susceptible to generate distinct blobs when Lc is reduced by increasing the PF strength. A distinct coherent mode appears only at the lowest magnetic shear slab featuring a deep potential well. Such mode is not apparent at other magnetic shear cases even at the same Lc. Finally, with a combination of PF coil pairs, both the features of intermediate and low magnetic shear slabs are shown to be realizable simultaneously. Significantly stronger blobs are observed with such combination of PF mirror ratios in the presence of a coherent mode. This study may provide better insight into the effect of magnetic configuration in the tokamak edge and SOL turbulence and can help in searching for better tools to control cross-field convective intermittent transport in tokamaks.

Observation of quasi-coherent edge fluctuations in Ohmic plasmas on National Spherical Torus Experiment

A quasi-coherent edge density mode with frequency fmode ∼ 40 kHz is observed in Ohmic plasmas in National Spherical Torus Experiment using the gas puff imaging diagnostic. This mode is located predominantly just inside the separatrix, with a maximum fluctuation amplitude significantly higher than that of the broadband turbulence in the same frequency range. The quasi-coherent mode has a poloidal wavelength λpol ∼ 16 cm and a poloidal phase velocity of Vpol ∼ 4.9 ± 0.3 km s−1 in the electron diamagnetic direction, which are similar to the characteristics expected from a linear drift-wave-like mode in the edge. This is the first observation of a quasi-coherent edge mode in an Ohmic diverted tokamak, and so may be useful for validating tokamak edge turbulence codes.

Nonlinear parallel momentum transport in strong electrostatic turbulence

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux- ⟨ṽrñũ∥⟩. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.

Boundary plasma turbulence simulations for tokamaks

The boundary plasma turbulence code BOUT models tokamak boundary-plasma turbulence in a realistic divertor geometry using modified Braginskii equations for plasma vorticity, density (ni), electron and ion temperature (T{sub e}; T{sub i}) and parallel momenta. The BOUT code solves for the plasma fluid equations in a three dimensional (3D) toroidal segment (or a toroidal wedge), including the region somewhat inside the separatrix and extending into the scrape-off layer; the private flux region is also included. In this paper, a description is given of the sophisticated physical models, innovative numerical algorithms, and modern software design used to simulate edge-plasmas in magnetic fusion energy devices. The BOUT code's unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics.

Boundary plasma turbulence simulations for tokamaks

The boundary plasma turbulence code BOUT models tokamak boundary-plasma turbulence in a realistic divertor geometry using modified Braginskii equations for plasma vorticity, density (ni), electron and ion temperature (T{sub e}; T{sub i}) and parallel momenta. The BOUT code solves for the plasma fluid equations in a three dimensional (3D) toroidal segment (or a toroidal wedge), including the region somewhat inside the separatrix and extending into the scrape-off layer; the private flux region is also included. In this paper, a description is given of the sophisticated physical models, innovative numerical algorithms, and modern software design used to simulate edge-plasmas in magnetic fusion energy devices. The BOUT code's unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics.

Nonadiabatic electron response in the Hasegawa-Wakatani equations

Tokamak edge turbulence is strongly influenced by parallel electron physics, which relaxes density and potential fluctuations towards electron adiabatic response. Beginning with the paradigmatic Hasegawa-Wakatani equations (HWEs) for resistive tokamak edge turbulence, a unique decomposition of the electric potential (φ) into adiabatic (a) and nonadiabatic (b) portions is derived, based on the requirement that a neither drive nor respond to the parallel current j∥. The form of the decomposition clarifies that, at perpendicular scales large relative to the sound radius, the electron adiabatic response controls the nonzonal φ, not the fluctuating density n. Simple energy balance arguments allow one to rigorously bound the ratio of rms nonzonal nonadiabatic fluctuations (b̃) relative to adiabatic ones (ã). The role of the vorticity nonlinearity in transferring energy between adiabatic and nonadiabatic fluctuations aids intuitive understanding of self-sustained turbulence in the HWEs. When the normalized parallel resistivity is weak, b̃ becomes effectively slaved, allowing the reduction to an approximate one-field model that remains valid for strong turbulence. In addition to guiding physical intuition, the one-field reduction should greatly ease further analytical manipulations. Direct numerical simulation of the 2D HWEs confirms the convergence of the asymptotic formula for b̃.

Spatial structures and interaction of multiple sheared flow populations in tokamak edge turbulence

The radial structures of multiple sheared flow populations and fluctuations are simultaneously measured using combinations of Langmuir probe arrays in the edge plasmas of the HL-2A tokamak with ohmic and electron cyclotron resonance heating (ECRH). The maximum of geodesic acoustic mode (GAM) amplitude locates at ∼2–3 cm inside the last close flux surface (LCFS). The low-frequency zonal flow (LFZF) and GAM tend to coexist in the inner region. The dependences of the amplitudes of the multiple sheared flows and turbulence on ECRH heating power are also investigated. The measured turbulent Reynolds stresses are shown to be strongly correlated with the sheared flows, as predicted by theory. The turbulence is modulated at the each frequency of the multiple sheared flows simultaneously, and the particle fluxes induced by the turbulence are significantly reduced near the LCFS and in the GAM peaking region. The analyses also show that the spatial structures of the turbulent envelopes at the LFZF and GAM frequencies are similar to those observed in LFZF and GAM.

Simulations of drift resistive ballooning L-mode turbulence in the edge plasma of the DIII-D tokamak

Results from simulations of electromagnetic drift-resistive ballooning turbulence for tokamak edge turbulence in realistic single-null geometry are reported. The calculations are undertaken with the BOUT three-dimensional fluid code that solves Braginskii-based fluid equations [X. Q. Xu and R. H. Cohen, Contrib. Plasma Phys. 36, 158 (1998)]. The simulation setup models L-mode edge plasma parameters in the actual magnetic geometry of the DIII-D tokamak [J. L. Luxon et al., Fusion Sci. Technol. 48, 807 (2002)]. The computations track the development of drift-resistive ballooning turbulence in the edge region to saturation. Fluctuation amplitudes, fluctuation spectra, and particle and thermal fluxes are compared to experimental data near the outer midplane from Langmuir probe and beam-emission-spectroscopy for a few well-characterized L-mode discharges in DIII-D. The simulations are comprised of a suite of runs in which the physics model is varied to include more fluid fields and physics terms. The simulations yield results for fluctuation amplitudes, correlation lengths, particle and energy fluxes, and diffusivities that agree with measurements within an order of magnitude and within factors of 2 or better for some of the data. The agreement of the simulations with the experimental measurements varies with respect to including more physics in the model equations within the suite of models investigated. The simulations show stabilizing effects of sheared E × B poloidal rotation (imposed zonal flow) and of lower edge electron temperature and density.

Nonlinear gyrofluid computation of edge localized ideal ballooning modes

Three dimensional electromagnetic gyrofluid simulations of the ideal ballooning mode blowout scenario for tokamak edge localized modes (ELMs) are presented. Special emphasis is placed on energetic diagnosis, examining changes in the growth rate in the linear, overshoot, and decay phases. The saturation process is energy transfer to self generated edge turbulence which exhibits an ion temperature gradient (ITG) mode structure. Convergence in the decay phase is found only if the spectrum reaches the ion gyroradius. The equilibrium is a self consistent background whose evolution is taken into account. Approximately two thirds of the total energy in the edge layer is liberated in the blowout. Parameter dependence with respect to plasma pressure and the ion gyroradius is studied. Despite the violent nature of the short-lived process, the transition to nonlinearity is very similar to that found in generic tokamak edge turbulence.

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell’s equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E×B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov–Maxwell system. Generalized ordering takes ρi⪡ρθi∼LE∼Lp⪡R [here ρi is the thermal ion Larmor radius and ρθi=B∕(Bθρi)], as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. k⊥ρi∼1 is assumed for generality, and the relative fluctuation amplitudes eδϕ∕Ti∼δB∕B are kept up to the second order. Extending the electrostatic theory in the presence of high E×B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pullback transformation from the gyro...

Edge turbulence and SOL transport in tokamaks

Some key topics in tokamak edge plasma transport and turbulence are reviewed. Multi-device results reveal a new paradigm of scrape-off layer (SOL) transport. Radial transport is driven by intermittency throughout the SOL, in between edge localized modes (ELMs) in H-mode, and comprised of plasma filaments that are generated near the last closed flux surface likely by interchange instability. The filaments travel radially at speeds of ∼1 km/s into the SOL and have a poloidal size of 1–3 cm in most devices. The radial transport in the SOL is poloidally asymmetric, by factors of 2–5, causing a pressure peak in the low field side. This asymmetry and other neo-classical terms, such as Pfirsch–Schlüter currents, are found to drive strong SOL flows. The intermittent particle flux, is 20% of the total, including ELMs, at low collisionality, becoming 70% of total at high collisionality. Numerical and analytical models can reproduce the scaling of intermittency with collisionality as well as many details of the filament dynamics in the SOL.

Status and verification of edge plasma turbulence code BOUT

The BOUT code is a detailed numerical model of tokamak edge turbulence based on collisional plasma fluid equations. BOUT solves for time evolution of plasma fluid variables: plasma density N i , parallel ion velocity V ‖ i , electron temperature T e , ion temperature T i , electric potential ϕ, parallel current j ‖ , and parallel vector potential A ‖ , in realistic 3D divertor tokamak geometry. The current status of the code, physics model, algorithms, and implementation is described. Results of verification testing are presented along with illustrative applications to tokamak edge turbulence.

Modelling of Lévy walk kinetics of charged particles in edge electrostatic turbulence in tokamaks

We model and discuss the possible types of motion that charged particles may undergo in a stationary and spatially periodic electrostatic potential and a homogeneous magnetic field. The model is considered to be the simplest approximation of more complex phenomena of plasma edge turbulence in tokamaks. Therein, low frequency turbulence appears in the plasma edge, resulting in a fluctuation of the electron density, and also in the generation of a turbulent electrostatic field. Typical parameters of this turbulent electrostatic field are an electrical potential amplitude of 10–100 V and wave numbers k≈103 m-1. In our model, we consider these regimes, together with a homogeneous magnetic field with a magnitude of 1 T. We investigate the dynamics of singly-ionized carbon ions – a typical plasma impurity – with kinetic energies on the order of 10 eV. Besides the obvious Larmor and drift motions, a motion of random-walk and of Levy walk character appear therein. All of these types of motion can play an important role in the modelling of the anomalous diffusion of particles from the plasma edge turbulence region. The dynamics mentioned will cause an inevitable escape of energetic particles and thus of power loss from the thermonuclear reactor. Moreover, Levy walk kinetics represents a very interesting kind of kinetics, currently of great interest, which was previously not so often discussed.

Disparate Scale Nonlinear Interactions in Edge Turbulence

AbstractIn this topical review, we explain the recent achievement in the study of nonlinear interactions, putting an emphasis on the relevance to edge turbulence. First, we start from the survey of the essence in the nonlinear theory of drift wave ‐zonal flows systems, and visit the experimental observations of the nonlinear interactions of tokamak edge turbulence. Secondly, the universality of intermittent convective transport in the SOL of different magnetic devices are shown. Then, we discuss evolution of collisional drift wave instability in the linear plasma configuration, which is bounded by end plates having analogy to SOL plasmas. By introducing the Numerical Linear Device, the intermittent evolution of large‐amplitude instabilities, generation mechanism of the poloidal flow and other nonlinear process are examined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)