A comparison between a refined two-point model for the limited tokamak SOL and self-consistent plasma turbulence simulations

A refined two-point model is derived from the drift-reduced Braginskii equations for the limited tokamak scrape-off layer (SOL) by balancing the parallel and perpendicular transport of plasma and heat and taking into account the plasma–neutral interaction. The model estimates the electron temperature drop along a field line, from a region far from the limiter to the limiter plates. Self-consistent first-principles turbulence simulations of the SOL plasma including its interaction with neutral atoms are performed with the GBS code and compared to the refined two-point model. The refined two-point model is shown to be in very good agreement with the turbulence simulation results

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.Comment: 26 pages, 14 figure

A methodology for the rigorous verification of Particle-in-Cell simulations

A methodology to perform a rigorous verification of Particle-in-Cell (PIC) simulations is presented, both for assessing the correct implementation of the model equations (code verification), and evaluating the numerical uncertainty affecting the simulation results (solution verification). The proposed code verification methodology is a generalization of the procedure developed for plasma simulation codes based on finite difference schemes that was described by Riva et al. [Phys. Plasmas 21, 062301 (2014)] and consists of an order-of-accuracy test using the method of manufactured solutions. The generalization of the methodology for PIC codes consists of accounting for numerical schemes intrinsically affected by statistical noise and providing a suitable measure of the distance between continuous, analytical distribution functions and finite samples of computational particles. The solution verification consists of quantifying both the statistical and discretization uncertainties. The statistical uncertainty is estimated by repeating the simulation with different pseudorandom number generator seeds. For the discretization uncertainty, the Richardson extrapolation is used to provide an approximation of the analytical solution and the grid convergence index is used as an estimate of the relative discretization uncertainty. The code verification methodology is successfully applied to a PIC code that numerically solves the one-dimensional, electrostatic, collisionless Vlasov-Poisson system. The solution verification methodology is applied to quantify the numerical uncertainty affecting the two-stream instability growth rate, which is numerically evaluated thanks to a PIC simulation

Investigation of turbulent transport regimes in the tokamak edge by using two-fluid simulations

The results of flux-driven, two-fluid simulations in single-null configurations are used to investigate the processes determining the turbulent transport in the tokamak edge. Three turbulent transport regimes are identified: (i) a developed transport regime with turbulence driven by an interchange instability, which shares a number of features with the standard L-mode of tokamak operation, (ii) a suppressed transport regime, characterized by a higher value of the energy confinement time, low-amplitude relative fluctuations driven by a Kelvin-Helmholtz instability, a strong E x B sheared flow, and the formation of a transport barrier, which recalls the H-mode, and (iii) a degraded confinement regime, characterized by a catastrophically large interchange-driven turbulent transport, which reminds the crossing of the Greenwald density limit.We derive an analytical expression of the pressure gradient length in the three regimes. The transition from the developed to the suppressed transport regime is obtained by increasing the heat source or decreasing the collisionality and vice versa for the transition from the developed transport regime to the degraded confinement regime. An analytical expression of the power threshold to access the suppressed transport regime, linked to the power threshold for H-mode access, as well as the maximum density achievable before entering the degraded confinement regime, related to the Greenwald density, are also derived. The experimental dependencies of the power threshold for H-mode access on density, tokamak major radius, and isotope mass are retrieved. The analytical estimate of the density limit contains the correct dependence on the plasma current and on the tokamak minor radius

The TOKAM3X code for edge turbulence fluid simulations of tokamak plasmas in versatile magnetic geometries

International audienceThe new code TOKAM3X simulates plasma turbulence in full torus geometry including the open field lines of the Scrape-off Layer (SOL) and the edge closed field lines region in the vicinity of the separatrix. Based on drift-reduced Braginskii equations, TOKAM3X is able to simulate both limited and diverted plasmas. Turbulence is flux driven by incoming particles from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed so that interactions between large scale flows and turbulence are consistently treated. Based on a domain decomposition, specific numerical schemes are proposed using conservative finite-differences associated to a semi-implicit time advancement. The process computation is multi-threaded and based on MPI and OpenMP libraries. In this paper, fluid model equations are presented together with the proposed numerical methods. The code is verified using the manufactured solution technique and validated through documented simple experiments. Finally, first simulations of edge plasma turbulence in X-point geometry are also introduced in a JET geometry. (C) 2016 Elsevier Inc. All rights reserved

Numerical simulations and stochastic modeling of intermittent fluctuations in magnetized plasmas

The exhaust of particles and heat in the boundary of contemporary magnetic confinement experiments remains to this day a major obstacle on the road to commercially viable fusion energy production. It is recognized, that coherent structures of hot and dense plasma, called blobs or filaments, are the dominant mechanism for cross-field particle transport. These filaments are created by plasma turbulence at the outboard midplane and move radially outwards driven by interchange motions. This leads to high average particle densities and relative fluctuation levels in the scrape-off layer, which increases plasma-wall interactions. Time series of the plasma density measured at a fixed point using either Langmuir probes or gas puff imaging have shown highly intermittent fluctuations across a variety of devices, plasma parameters and confinement modes. Recent statistical analysis of measurement data time series has revealed that the fluctuations are well described as a superposition of uncorrelated exponential pulses with fixed duration and exponentially distributed pulse amplitudes, arriving according to a Poisson process. Due to the complexity of the physics involved in the boundary of fusion devices, numerical simulations are utilized to gain an accurate description of scrape-off layer plasmas. This approach requires a validation metric for simulations of plasma turbulence such as the statistical framework based on filtered Poisson processes. In this thesis, well-established models for scrape-off layer plasmas are analyzed. These models use two-fluid equations simulating plasma evolution in the two-dimensional plane perpendicular to the magnetic field. Time series of the plasma density are measured at a fixed point and their fluctuation statistics are compared to experimental measurements utilizing the statistical framework. This includes probability density functions, power spectral densities and conditionally averaged waveforms. In addition, simulations of a population of seeded blobs are performed in order to study the effects of blob interactions. It is shown that the fluctuation statistics of single-point measurements in simple numerical models stand in excellent agreement with their experimental counterparts. This work thereby sets a new standard and methodology for validating scrape-off layer turbulence simulations