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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.

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.

The measurement of two-phase flow parameters has never been an easy task in the experimental thermal-hydraulics and the need of such measurements in the SPES3 facility has led to investigation of different possibilities and evaluation methods to determine mass flows and energies. This paper deals with the theoretical prediction of the two-phase mass flow rate by the development of a mathematical model for a spool piece, consisting of a drag disk, a turbine and a void fraction detector. Data obtained by simulation of DBAs in the SPES3 facility, with the RELAP5 thermal-hydraulic code, have provided the reference conditions for defining the main thermal-hydraulic parameter ranges and selecting a set of instruments potentially suitable to measure and derive the required quantities. The governing equation and the instrumentation output are defined for each device. Three different turbine models (Aya, Rouhani and volumetric) have been studied to understand which one better adapts to two-phase flow conditions and to investigate the best instrument combination. The mathematical model has been tested versus the RELAP5 results with a reverse process where calculated variables, like void fraction, quality and slip ratio, are given as input to a specifically developed program to get back the mass flow rate. The analytical results, verified versus the DVI break transient, well agree with the RELAP5 mass flow rate. Specific tests on proper experimental loops are required to verify the analytical studies.Copyright © 2010 by ASME

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 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.

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.

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.