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ALMA (Anti-symmetric, Large-Moment, Accelerated) is a fast, flexible, and scalable toolkit designed to solve hyperbolic conservation law systems in hybrid supercomputers. This manuscript describes the theoretical background and implementation of ALMA , which uses the anti-symmetric formulation of fluids to obtain simple, robust, and easily paralellizable code. Practical GPU acceleration is realized on entire applications with an overall gain factor of 2 to 4. ALMA also provides a parallel, GPU accelerated sparse solver based on geometric multigrid, capable of diagonalizing linear systems with 239 unknowns. We demonstrate ALMA 's scaling and performance in petascale supercomputers and use standard fluid models to verify the overall approach with canonical benchmark problems.

We describe a new version of GBS, a 3D global, flux-driven plasma turbulence code to simulate the turbulent dynamics in the tokamak scrape-off layer (SOL), superseding the code presented by Ricci et al. (2012) [14]. The present work is driven by the objective of studying SOL turbulent dynamics in medium size tokamaks and beyond with a high-fidelity physics model. We emphasize an intertwining framework of improved physics models and the computational improvements that allow them. The model extensions include neutral atom physics, finite ion temperature, the addition of a closed field line region, and a non-Boussinesq treatment of the polarization drift. GBS has been completely refactored with the introduction of a 3-D Cartesian communicator and a scalable parallel multigrid solver. We report dramatically enhanced parallel scalability, with the possibility of treating electromagnetic fluctuations very efficiently. The method of manufactured solutions as a verification process has been carried out for this new code version, demonstrating the correct implementation of the physical model. (C) 2016 Published by Elsevier Inc.

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator ( ∇ · v + v · ∇ ) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass ( ρ), momentum ( ρ v), and pressure ( p). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.

This paper presents two discretisation schemes for the parallel gradient operator used in scrape-off layer plasma turbulence simulations. First, a simple model describing the propagation of electrostatic shear-Alfven waves, and retaining the key elements of the parallel dynamics, is used to test the accuracy of the different schemes against analytical predictions. The most promising scheme is then tested in simulations of limited scrape-off layer turbulence with the flux-driven 3D fluid code GBS (Ricci et al., 2012): the new approach is successfully benchmarked against the original parallel gradient discretisation implemented in GBS. Finally, GBS simulations using a radially varying safety profile, which were inapplicable with the original scheme are carried out for the first time: the well-known stabilisation of resistive ballooning modes at negative magnetic shear is recovered. The main conclusion of this paper is that a simple approach to the parallel gradient, namely centred finite differences in the poloidal and toroidal direction, is able to simulate scrape-off layer turbulence provided that a higher resolution and higher convergence order are used.

We investigate the question of how plasma currents circulate and close in the scrape-off-layer (SOL) of convection-limited tokamak plasmas. A simplified two-fluid model describes how currents must evacuate charge at the sheaths due to cross-field currents that are not divergence-free. These include turbulence-driven polarization currents and poloidally asymmetric equilibrium diamagnetic currents. The theory provides an estimate for the radial profile of the floating potential, which reveals a dipolar structure like the one observed experimentally. Simulations with a fluid turbulence code provide evidence for the predicted behaviour of currents and floating potential.

To investigate the mechanisms leading to the heat deposition onto the first wall in the Scrape-Off Layer (SOL), we perform dedicated numerical non-linear simulations of the SOL plasma dynamics of a TCV discharge using the GBS code. The simulated parallel heat flux profiles on the limiter agree qualitatively with the experimental ones obtained by means of infrared thermography, showing a double scale length. Non-ambipolar currents are found to flow to the limiter, consistently with the experiments. The contribution of the latter to the total heat flux is discussed. The results of a second simulation identical to the first one but with 40 times higher resistivity are also discussed. Keywords: Plasma, Scrape-Off Layer, TCV, GBS simulations heat flux

In inboard-limited plasmas, the Scrape-Off Layer (SOL) shows two regions: the near SOL, extending a few mm from the Last Closed Flux Surface (LCFS), characterized by a steep gradient of the parallel heat flux radial profile, and a far SOL, typically some cm wide, with flatter heat flux profiles. The physics of the near SOL is investigated in TCV with two series of experiments featuring deuterium and helium plasmas, in which the plasma current, density and elongation have been varied. The parallel heat flux profiles are measured on the limiter by means of infrared thermography. For the first time, the near SOL is reported to disappear for low plasma current or at high density, for values of the SOL collisionality νlowast corresponding to a conduction-limited regime. The power in the near SOL ∆PSOL is shown to decrease with the normalized Spitzer resistivity ν as ∆PSOL ν−1. The floating potential profiles, measured at the limiter using flush-mounted Langmuir probes (LP), show the presence of non-ambipolar currents, and their relation to the presence of a velocity shear layer is discussed. The shearing rate is shown to strictly correlate with the power in the near SOL ∆PSOL, consistently with a recent theoretical model. Measurements of the near SOL on the Low Field Side (LFS) are performed using a reciprocating Langmuir probe (RP). The near SOL is reported to vanish simultaneously at the LFS and at the limiter. The near and far SOL widths are compared with the predictions from existing theoretical models, to which empirical corrections with resistivity and elongation are proposed.

A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter Δ ′ is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

We derive a set of fluid moment equations with inherent consistency and numerical stability, conceived by exploiting the anti-symmetric nature of the plasma flow operator (∇·v+v·∇). The obtained equations can be interpreted as an alternative to the traditional Eulerian and Lagrangian representations—one in which plasma flows generate infinitesimal rotations of generalized fluid moments n, nv, and p. The continuous model has a discrete analog with exact mass, momentum, and energy conservation, which is achieved by construction through vanishing integrals of the anti-symmetric flow terms. Positivity preservation is obtained through the use of the generalized moment quantities. The conservation properties of the approach are illustrated in simulations of seeded blob propagation, where we verify numerical conservation to machine accuracy.

The properties of plasma turbulence in a poloidally limited scrape-off layer (SOL) are addressed, with focus on ISTTOK, a large aspect ratio tokamak with a circular cross section. Theoretical investigations based on the drift-reduced Braginskii equations are carried out through linear calculations and non-linear simulations, in two-and three-dimensional geometries. The linear instabilities driving turbulence and the mechanisms that set the amplitude of turbulence as well as the SOL width are identified. A clear asymmetry is shown to exist between the low-field and the high-field sides of the machine. While the comparison between experimental measurements and simulation results shows good agreement in the far SOL, large intermittent events in the near SOL, detected in the experiments, are not captured by the simulations., United States. Department of Energy (Grant DE-FG02-91ER54109)

A numerical study of pressure driven magnetohydrodynamic (MHD) instabilities in a low-shear tight aspect ratio configuration is presented. When the magnetic shear is sufficiently small over an extended region in the core, enhanced instability occurs due to the coupling to poloidal sidebands, which itself occurs due to toroidicity. Numerical simulations have been performed with the initial value code XTOR-2F both in the ideal and resistive MHD frame. Two-fluid effects (plasma diamagnetic flows) have been retained as well. The predictions of the XTOR-2F code on the amplitude of the growth rate, and on the rotation frequency of the modes, have been compared with analytic linear theory of infernal modes. Qualitative agreement has been found between numerical and analytical results, in spite of the tight aspect ratio configuration. The intermediate scaling gamma similar to S-3/8, predicted by the linear theory (Brunetti et al 2014 Plasma Phys. Control. Fusion 56 075025), is recovered by the numerical results. A study of the nonlinear evolution of the magnetic island of the tearing sideband has been performed and the results from the simulations are compared with Rutherford's theory.

© 2015 IOP Publishing Ltd. We carry out a quantitative comparison between gas puff imaging (GPI) turbulence measurements in Alcator C Mod inner wall limited discharges (Zweben et al 2009 Phys. Plasmas 18 082505) and 3D flux driven drift reduced Braginskii turbulence simulations of scrape off layer dynamics. The comparison is carried out for a series of inner wall limited discharges where the magnetic field and the density are varied. The comparison between GPI data and non linear simulations yields overall good agreement for several observables such as the Da emission levels and intermittency the radial and poloidal correlation lengths and propagation velocities and the power and frequency spectral density.

Tokamaks with weak to moderate reversed central shear in which the minimum inverse rotational transform (safety factor) qmin is in the neighbourhood of unity can trigger bifurcated magnetohydrodynamic equilibrium states, one of which is similar to a saturated ideal internal kink mode. Peaked prescribed pressure profiles reproduce the ‘snake’ structures observed in many tokamaks which has led to a novel explanation of the snake as a bifurcated equilibrium state. Snake equilibrium structures are computed in simulations of the tokamak `a configuration variable (TCV), DIII-D and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma–vacuum interface which is more sensitive to ripple and resonant magnetic perturbations. On the other hand, the external perturbations do not alter the helical core deformation in a significant manner. The confinement of fast particles in MAST simulations deteriorate with the amplitude of the helical core distortion. These three-dimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations.

The narrow power decay-length ($\lambda_q$), recently found in the scrape-off layer (SOL) of inner-wall limited (IWL) discharges in tokamaks, is studied using 3D, flux-driven, global two-fluid turbulence simulations. The formation of the steep plasma profiles measured is found to arise due to radially sheared $\vec{E}\times\vec{B}$ poloidal flows. A complex interaction between sheared flows and outflowing plasma currents regulates the turbulent saturation, determining the transport levels. We quantify the effects of sheared flows, obtaining theoretical estimates in agreement with our non-linear simulations. Analytical calculations suggest that the IWL $\lambda_q$ is roughly equal to the turbulent correlation length., Comment: 5 pages, 5 figures

The long-term dynamics of the internal kink mode are studied using the non-linear, two-fluid magnetohydrodynamics (MHD) code XTOR-2F (Lutjens et al 2010 J. Comput. Phys. 229 8130). The dynamics of the internal kink are studied in resistive MHD plus transport, and, in addition, also including some two-fluid effects. The simulation results yield a pattern of kink cycles or stationary states with m/n = 1/1 helicity. The threshold for sustained (non-decaying) kink cycles, which characterize sawtooth oscillations, is shown to depend on the plasma pressure, the current and energy diffusion times, and the ion and electron diamagnetic drifts. In particular, the diamagnetic flow stabilization extends the cyclic kink regime into a parameter space that is adequate to carry out studies of sawtooth oscillations in ohmic tokamak discharges.

The International Tokamak Physics Activity Topical Group on scrape-off layer and divertor physics has amassed a database comprising hundreds of reciprocating Langmuir probe measurements of the main scrape-off layer heat-flux width lambda(q) in inner-wall limited discharges. We have carried out an analysis, based on turbulent transport theory, of the variation of lambda(q) with respect to the dimensionless plasma parameters. Restricting our analysis to circular plasmas, we find that a model based on non-linearly saturated turbulence can well reproduce the lambda(q) values found in the database.

Ion temperature has been measured to be of the same order, or higher, than the electron temperature in the scrape-off layer (SOL) of tokamak machines, questioning its importance in determining the SOL turbulent dynamics. Here, we present a detailed analysis of finite ion temperature effects on the linear SOL instabilities, such as the resistive and inertial branches of drift waves and ballooning modes, and a discussion of the properties of the ion temperature gradient (ITG) instability in the SOL, identifying the gi 1⁄4 Ln=LTi threshold necessary to drive the mode unstable. The non-linear analysis of the SOL turbulent regimes by means of the gradient removal theory is performed, revealing that the ITG plays a negligible role in limited SOL discharges, since the ion temperature gradient is generally below the threshold for driving the mode unstable. It follows that the resistive ballooning mode is the prevailing turbulence regime for typical limited SOL parameters. The theoretical estimates are confirmed by non-linear flux-driven simulations of SOL plasma dynamics.

We develop a predictive theory applicable to the scrape off layer (SOL) of inner wall limited plasmas. Using the non linear flattening of the pressure profile as a saturation mechanism for resistive ballooning modes we are able to demonstrate and quantify the increase of the SOL width with plasma size connection length plasma ß and collisionality. Individual aspects of the theory such as saturation physics parallel dynamics and system size scaling are tested and verified using non linear 3D flux driven SOL turbulence simulations. Altogether very good agreement between theory and simulation is found. © 2014 IAEA Vienna.

The propagation of blobs structures of localized enhanced plasma pressure is studied in global three dimensional simulations of a simple magnetized torus. In particular we carry out single seeded blob simulations to explore the dependence of the blob velocity with respect to its size. It is found that the velocity scaling for two dimensional blobs is satisfied in the parameter space where polarization currents are the dominant damping mechanism. On the other hand three dimensional blobs propagate faster than their two dimensional counterparts in the parallel current damping regime. A detailed analysis of the charge and current balance reveals that in fact the difference in speed is due to an overestimation of the strength of the sheath current term in the two dimensional model compared to the self consistent three dimensional model. © 2014 Euratom.

The effect of the limiter position on the scrape-off layer (SOL) width, radial electric field and intrinsic flows is investigated via global, three-dimensional turbulence simulations in four different limiter configurations. The limiter position affects the SOL dynamics in a number of ways, for example by changing the effective connection length or by modifying the unstable modes present in the system. The simulations show that the SOL width is much smaller and less poloidally asymmetric when the plasma is limited on the low-field side than on the high-field side, which can be explained by a change in the turbulence regime between the two configurations. The radial electric field is determined by the combined effect of the sheath physics and the electron adiabaticity condition, and its poloidal structure depends on the limiter position, as it can be fairly well explained through an analytical model. Intrinsic parallel flows established in the SOL, typically leading to co-current toroidal rotation with a magnitude that strongly depends on the limiter position, can also be fairly well reproduced analytically for each limiter configuration.

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω = ∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

The cycling dynamics of the internal kink mode, which drives sawtooth oscillations in tokamak plasmas, is studied using the three dimensional, non-linear magnetohydrodynamic (MHD) code XTOR-2F [H. Lütjens and J.-F. Luciani, J. Comput. Phys. 229, 8130 (2010)]. It is found that sawtooth cycling, which is characterized by quiescent ramps and fast crashes in the experiment, can be recovered in two-fluid MHD provided that a criterion of diamagnetic stabilization is fulfilled. The simulation results indicate that diamagnetic effects alone may be sufficient to drive sawteeth with complete magnetic reconnection in high temperature Ohmic plasmas.

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phy...

Predictive simulations of ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)], discharges are carried out for the 15MA high confinement mode (H-mode) scenario using PTRANSP, the predictive version of the TRANSP code. The thermal and toroidal momentum transport equations are evolved using turbulent and neoclassical transport models. A predictive model is used to compute the temperature and width of the H-mode pedestal. The ITER simulations are carried out for neutral beam injection (NBI) heated plasmas, for ion cyclotron resonant frequency (ICRF) heated plasmas, and for plasmas heated with a mix of NBI and ICRF. It is shown that neutral beam injection drives toroidal rotation that improves the confinement and fusion power production in ITER. The scaling of fusion power with respect to the input power and to the pedestal temperature is studied. It is observed that, in simulations carried out using the momentum transport diffusivity computed using the GLF23 model [R. Waltz et al., Phys. Plasm...

Time-dependent integrated predictive modelling is carried out using the PTRANSP code to predict fusion power and parameters such as alpha particle density and pressure in ITER H-mode plasmas. Auxiliary heating by negative ion neutral beam injection and ion-cyclotron heating of He3minority ions are modelled, and the GLF23 transport model is used in the prediction of the evolution of plasma temperature profiles. Effects of beam steering, beam torque, plasma rotation, beam current drive, pedestal temperatures, sawtooth oscillations, magnetic diffusion and accumulation of He ash are treated self-consistently. Variations in assumptions associated with physics uncertainties for standard base-line DT H-mode plasmas (withIp= 15 MA,BTF= 5.3 T and Greenwald fraction = 0.86) lead to a range of predictions for DT fusion powerPDTand quasi-steady state fusionQDT(≡PDT/Paux). Typical predictions assumingPaux= 50–53 MW yieldPDT= 250–720 MW andQDT= 5–14. In some cases wherePauxis ramped down or shut off after initial flat-top conditions, quasi-steadyQDTcan be considerably higher, even infinite. Adverse physics assumptions such as the existence of an inward pinch of the helium ash and an ash recycling coefficient approaching unity lead to very low values forPDT. Alternative scenarios with different heating and reduced performance regimes are also considered including plasmas with only H or D isotopes, DT plasmas with toroidal field reduced 10% or 20% and discharges with reduced beam voltage. In full-performance D-only discharges, tritium burn up is predicted to generate central tritium densities up to 1016 m−3and DT neutron rates up to 5 × 1016 s−1, compared with the DD neutron rates of 6 × 1017 s−1. Predictions with the toroidal field reduced 10% or 20% below the planned 5.3 T and keeping the sameq98, Greenwald fraction and βnindicate that the fusion yieldPDTandQDTwill be lower by about a factor of two (scaling asB3.5).

A comparison is made between two versions of the Weiland model for computing anomalous transport driven by drift modes such as the ion temperature gradient (ITG) and trapped electron mode (TEM) in tokamak plasmas. Both are quasilinear fluid models that include physical effects resulting from finite β, magnetic shear, electron-ion collisions, impurities, and fast ions. An outline of the derivation is presented for the newer Weiland19 model, which includes a more accurate description of the effects of finite β, low and negative magnetic shear, plasma elongation, varying correlation lengths, particle pinch, and momentum transport. It is shown that the two models produce nearly the same ion thermal diffusivity as a function of normalized temperature gradient in a circular plasma with moderate magnetic shear, low β, and moderately low density gradient. The models differ significantly at low magnetic shear and in elongated plasmas with high β. In addition, the two models differ significantly in the behavior of ...

The ISLAND module in the National Transport Code Collaboration (NTCC) Module Library computes the saturated widths of multiple magnetic islands due to neoclassical tearing modes by implementing a quasi-linear model that includes the effects of arbitrary aspect ratio. cross-sectional shape, and plasma beta. This paper presents a significantly improved version of the module available at the NTCC Library. The model was updated to include the distortion of islands caused by the radial variation of the perturbed magnetic field near the mode rational surface. The computer algorithm implemented by the module was redesigned to increase its speed, reliability and accuracy. The new module has been successfully interfaced with the BALDUR integrated modeling code, where it is used to compute the saturated widths of multiple islands in tokamak discharges.

A revised version of the ISLAND module [C. N. Nguyen et al., Phys. Plasmas 11, 3604 (2004)] is used in the BALDUR code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)] to carry out integrated modeling simulations of DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus (JET) [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)], and ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)] tokamak discharges in order to investigate the adverse effects of multiple saturated magnetic islands driven by neoclassical tearing modes (NTMs). Simulations are carried out with a predictive model for the temperature and density pedestal at the edge of the high confinement mode (H-mode) plasma and with core transport described using the Multi-Mode model. The ISLAND module, which is used to compute magnetic island widths, includes the effects of an arbitrary aspect ratio and plasma cross sectional shape, the effect of the neoclassical bootstrap current, and the effect of the distortion ...

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio. (C) 2014 AIP Publishing LLC.

Motivated by the wide range of physical parameters characterizing the scrape-off layer (SOL) of existing tokamaks, the regimes of low-frequency linear instabilities in the SOL are identified by numerical and analytical calculations based on the linear, drift-reduced Braginskii equations, with cold ions. The focus is put on ballooning modes and drift wave instabilities, i.e., their resistive, inertial, and ideal branches. A systematic study of each instability is performed, and the parameter space region where they dominate is identified. It is found that the drift waves dominate at high R/L-n, while the ballooning modes at low R/L-n; the relative influence of resistive and inertial effects is discussed. Electromagnetic effects suppress the drift waves and, when the threshold for ideal stability is overcome, the ideal ballooning mode develops. Our analysis is a first stage tool for the understanding of turbulence in the tokamak SOL, necessary to interpret the results of non-linear simulations. [http://dx.doi.org/10.1063/1.4758809]

The mechanism regulating the equilibrium electrostatic potential in the scrape-off layer (SOL) of magnetic confinement devices is elucidated. Based on a generalized Ohm's law and the boundary conditions at the magnetic presheath entrance, an analytical expression for the equilibrium electrostatic potential is derived. Results imply that the relative importance of the plasma dynamics at the sheath and far away from the wall in setting the value of the electrostatic potential depends on the density and temperature drops that are established between the two regions. Global, three-dimensional fluid simulations of tokamak SOL turbulence in a simple configuration are performed, confirming the validity of our predictions. The results presented here are general and can be applied to other open-field-line configurations, including linear devices and simple magnetized toroidal devices.

A theory based scaling for the characteristic length of a circular limited tokamak scrape off layer (SOL) is obtained by considering the balance between parallel losses and non linearly saturated resistive ballooning mode turbulence driving anomalous perpendicular transport. The SOL size increases with plasma size resistivity and safety factor q. The scaling is verified against flux driven non linear turbulence simulations which reveal good agreement within a wide range of dimensionless parameters including parameters closely matching the TCV tokamak. An initial comparison of the theory against experimental data from several tokamaks also yields good agreement. © 2013 IAEA Vienna.

We identify the turbulent regimes in the tokamak scrape-off layer as a function of plasma resistivity, electron to ion mass ratio, safety factor, and magnetic shear. We find that two main instabilities drive turbulence in the SOL: Drift Waves, with their resistive and inertial branches, and the Ballooning instabilities, with their resistive, ideal, and inertial branches. First, we identify how the linear growth rate, and the properties of these instabilities depend on the system physical parameters. Then, according to the gradient removal saturation mechanism, we use the fact that the transport is dominated by the mode with the highest growth rate divided by the poloidal wave number and the non-linear saturated pressure scale length is proportional to this ratio. This allows us to evaluate the non-linear saturated pressure gradient and the poloidal wavenumber of the dominating mode as a function of the resistivity, the mass ratio, the safety factor, and the magnetic shear . We can therefore define the non-linear instability phase space, locating the regions in which each instability is influencing transport the most. In order to validate our calculations, we run non-linear SOL simulations and we compare the plasma pressure scale length and the mode characteristics to the prediction provided by the phase space description. The non-linear simulations are performed using the GBS code, which solves the drift-reduced Braginskii equations evolving self-consistently equilibrium and fluctuations in three-dimensional geometry. The non-linear simulations are interpreted in light of our non-linear analysis and confirm its validity.

A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism.

The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Braginskii-type fluid simulations, and check this against a first-principles theoretical model. The analysis of the numerical simulations indicates that the probability distribution function of the intermittent process contains strong exponential tails, as predicted by the analytical theory.

Based on the drift-reduced Braginskii equations, the Global Braginskii Solver, GBS, is able to model the scrape-off layer (SOL) plasma turbulence in terms of the interplay between the plasma outflow from the tokamak core, the turbulent transport, and the losses at the vessel. Model equations, the GBS numerical algorithm, and GBS simulation results are described. GBS has been first developed to model turbulence in basic plasma physics devices, such as linear and simple magnetized toroidal devices, which contain some of the main elements of SOL turbulence in a simplified setting. In this paper we summarize the findings obtained from the simulation carried out in these configurations and we report the first simulations of SOL turbulence. We also discuss the validation project that has been carried out together with the GBS development.

Bridging the gap between plasma physics and other scientific domains, in particular, the computational fluid dynamics community, a general, rigorous, and simple-to-apply methodology is presented for both the verification of the correct implementation of the model equations (code verification) and numerical error quantification (solution verification). The proposed code verification procedure consists in using the method of manufactured solutions and executing an order-of-accuracy test, assessing the rate of convergence of the numerical solution to the manufactured one. For the solution verification, the numerical error is quantified by applying the Richardson extrapolation, which provides an approximation of the analytical solution, and by using the grid convergence index to estimate the numerical uncertainty affecting the simulation results. The methodology is applied to verify the correct implementation of the drift-reduced Braginskii equations into the GBS code, and to estimate the numerical error affecting the GBS solutions. The GBS code is successfully verified, and an estimate of the numerical error affecting the simulation results is provided.

A region of steep plasma gradients, the so-called "narrow-feature," has been found in the near scrape-off layer (SOL) of inner-wall limited (IWL) discharges. Dedicated IWL discharges were carried out in Alcator C-Mod [Marmar et al., Nucl. Fusion 55, 104020 (2015)] to study this phenomenon, allowing detailed observations of the plasma profiles and fluctuations. Langmuir probe (LP) measurements show a clear two-decay length ne and T-e profile structure at the outer midplane. The Gas-Puff Imaging (GPI) diagnostic shows large turbulent fluctuations across the last closed flux-surface, hence supporting the hypothesis that turbulent phenomena play a role in setting the profile steepness. Flux-driven non-linear turbulence simulations of two C-Mod discharges have been carried out, allowing a three-way comparison between LP, GPI, and simulation data. Observations and simulations correlate the steep gradient region characterizing the narrow feature with sheared poloidal flows and a deviation of the plasma potential from its floating value. The E x B shear rate exceeds the linear ballooning growth rate, indicating that the narrow feature could result from the effects of sheared flows, although causality could not be established. The fluctuation level in the narrow feature remains of order unity across the entire SOL, indicating that the transport reduction in the near-SOL cannot result from a simple quench rule. Published by AIP Publishing.

Heat flux profiles inferred from a reciprocating probe at the outer midplane of the TCV tokamak during inner wall limited discharges feature radial fall-off lengths that shorten near the last closed flux surface (LCFS) consistent with the so-called narrow feature. The narrow feature is significantly wider on the outboard side compared with that measured on the inner wall by infrared thermography, so it is difficult to discern from the main scrape-off layer feature. After small shifts were applied for alignment, the fraction of the power contained in the narrow feature matches between inboard and outboard measurements, and they scale together with plasma current Ip, suggesting that we are observing the same phenomenon. The outboard side fall-off length within the narrow feature is found to scale closely with the radial correlation length of the edge turbulence as expected if the narrow feature arises due to radially sheared E × B flows. This is found to hold true even for cases where the narrow feature is ...

To investigate blob properties in the tokamak scrape-off layer (SOL), we perform dedicated numerical nonlinear simulations of plasma turbulence in the SOL of a TCV discharge using the Global Braginskii Solver code. A blob detection technique is used for the first time in a three-dimensional (3D) full-turbulence simulation to track the motion of the filaments in the SOL. The specific size, density amplitude and radial velocity of the blobs are computed, with the typical values being 7.4 rho(s), 0.33 n(e) and 0.016 c(s), respectively. The analysis of blob structure in the parallel direction shows that the blobs are partially detached from the limiter. The cross correlation analysis shows how the blobs are born all along the entire field line, not being generated primarily on the low field side SOL and expanding towards the limiter. The blob radial velocity agrees well with the inertial branch of the existing scaling law. The radial particle and heat fluxes given by blobs are shown to be responsible of up to 100% and 70% of the turbulent particle and heat flux in the far SOL, respectively. The results of a second simulation with a 40 times higher resistivity are also discussed.

In the present work, a Verification and Validation procedure is presented and applied showing, through a practical example, how it can contribute to advancing our physics understanding of plasma turbulence. Bridging the gap between plasma physics and other scientific domains, in particular, the computational fluid dynamics community, a rigorous methodology for the verification of a plasma simulation code is presented, based on the method of manufactured solutions. This methodology assesses that the model equations are correctly solved, within the order of accuracy of the numerical scheme. The technique to carry out a solution verification is described to provide a rigorous estimate of the uncertainty affecting the numerical results. A methodology for plasma turbulence code validation is also discussed, focusing on quantitative assessment of the agreement between experiments and simulations. The Verification and Validation methodology is then applied to the study of plasma turbulence in the basic plasma physics experiment TORPEX [Fasoli et al., Phys. Plasmas 13, 055902 (2006)], considering both two-dimensional and three-dimensional simulations carried out with the GBS code [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. The validation procedure allows progress in the understanding of the turbulent dynamics in TORPEX, by pinpointing the presence of a turbulent regime transition, due to the competition between the resistive and ideal interchange instabilities.

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer (SOL) of tokamaks is investigated both analytically and through numerical simulations. It is shown that the equilibrium poloidal E x B flow, the sheath physics, and the presence of poloidal asymmetries in the pressure profile act as sources of momentum, while turbulence provides the mechanism for the radial momentum transport. An equation for the radial and poloidal dependence of the equilibrium parallel ion flow is derived, and a simple analytical solution is presented. This solution reproduces and explains the main experimental trends for the Mach number found in the SOL of tokamaks. Global, three-dimensional fluid simulations of SOL turbulence in different limiter configurations confirm the validity of the analytical theory.