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  1. Integrated Tokamak modeling: When physics informs engineering and research planning

    Modeling tokamaks enables a deeper understanding of how to run and control our experiments and how to design stable and reliable reactors. We model tokamaks to understand the nonlinear dynamics of plasmas embedded in magnetic fields and contained by finite size, conducting structures, and the interplay between turbulence, magneto-hydrodynamic instabilities, and wave propagation. This tutorial guides through the components of a tokamak simulator, highlighting how high-fidelity simulations can guide the development of reduced models that can be used to understand how the dynamics at a small scale and short time scales affects macroscopic transport and global stability of plasmas. Itmore » discusses the important role that reduced models have in the modeling of an entire plasma discharge from startup to termination, the limits of these models, and how they can be improved. It discusses the important role that efficient workflows have in the coupling between codes, in the validation of models against experiments and in the verification of theoretical models. Finally, it reviews the status of integrated modeling and addresses the gaps and needs towards predictions of future devices and fusion reactors.« less
  2. Regarding the optimization of O1-mode ECRH and the feasibility of EBW startup on NSTX-U

    Recently published scenarios for fully non-inductive startup and operation on the National Spherical Torus eXperiment Upgrade (NSTX-U) [Menard J et al 2012 Nucl. Fusion 52 083015] show Electron Cyclotron Resonance Heating (ECRH) as an important component in preparing a target plasma for efficient High Harmonic Fast Wave and Neutral Beam heating. The modelling of the propagation and absorption of EC waves in the evolving plasma is required to define the most effective window of operation, and to optimize the launcher geometry for maximal heating and current drive during this window. Here in this paper, we extend a previous optimization ofmore » O1-mode ECRH on NSTX-U to account for the full time-dependent performance of the ECRH using simulations performed with TRANSP. We find that the evolution of the density profile has a prominent role in the optimization by defining the time window of operation, which in certain cases may be a more important metric to compare launcher performance than the average power absorption. This feature cannot be captured by analysis on static profiles, and should be accounted for when optimizing ECRH on any device that operates near the cutoff density. Additionally, the utility of the electron Bernstein wave (EBW) in driving current and generating closed flux surfaces in the early startup phase has been demonstrated on a number of devices. Using standalone GENRAY simulations, we find that efficient EBW current drive is possible on NSTX-U if the injection angle is shifted below the midplane and aimed towards the top half of the vacuum vessel. However, collisional damping of the EBW is projected to be significant, in some cases accounting for up to 97\% of the absorbed EBW power.« less
  3. EC power management in ITER for NTM control: the path from the commissioning phase to demonstration discharges

    Time dependent simulations that evolve consistently the magnetic equilibrium and plasma pressure profiles and the width and frequency rotation of magnetic islands under the effect of the Electron Cyclotron feedback system are used to assess whether the control of NTMs on ITER is compatible with other simulataneous functionalities of the EC system, like core heating and current profile tailoring, or sawtooth control. Furthermore, results indicate that the power needs for control can be reduced if the EC power is reserved and if pre-emptive control is used as opposed to an active search for an already developed island.
  4. Rotation and neoclassical ripple transport in ITER

    Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria in the presence of toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Furthermore, neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planckmore » Iterative Neoclassical Conservative Solver (SFINCS).« less
  5. Electron Cyclotron power management for control of Neoclassical Tearing Modes in the ITER baseline scenario

    Time-dependent simulations are used to evolve plasma discharges in combination with a Modified Rutherford equation (MRE) for calculation of Neoclassical Tearing Mode (NTM) stability in response to Electron Cyclotron (EC) feedback control in ITER. The main application of this integrated approach is to support the development of control algorithms by analyzing the plasma response with physics-based models and to assess how uncertainties in the detection of the magnetic island and in the EC alignment affect the ability of the ITER EC system to fulfill its purpose. These simulations indicate that it is critical to detect the island as soon asmore » possible, before its size exceeds the EC deposition width, and that maintaining alignment with the rational surface within half of the EC deposition width is needed for stabilization and suppression of the modes, especially in the case of modes with helicity (2,1). A broadening of the deposition profile, for example due to wave scattering by turbulence fluctuations or not well aligned beams, could even be favorable in the case of the (2,1)-NTM, by relaxing an over-focussing of the EC beam and improving the stabilization at the mode onset. Pre-emptive control reduces the power needed for suppression and stabilization in the ITER baseline discharge to a maximum of 5 MW, which should be reserved and available to the Upper Launcher during the entire flattop phase. By assuming continuous triggering of NTMs, with pre-emptive control ITER would be still able to demonstrate a fusion gain of Q=10.« less
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  6. Multi-machine analysis of termination scenarios with comparison to simulations of controlled shutdown of ITER discharges

    To improve our understanding of the dynamics and control of ITER terminations, a study has been carried out on data from existing tokamaks. The aim of this joint analysis is to compare the assumptions for ITER terminations with the present experience basis. The study examined the parameter ranges in which present day devices operated during their terminations, as well as the dynamics of these parameters. The analysis of a database, built using a selected set of experimental termination cases, showed that, the H-mode density decays slower than the plasma current ramp-down. The consequential increase in f<sub>GW</sub> limits the duration ofmore » the H-mode phase or result in disruptions. The lower temperatures after the drop out of H-mode will allow the plasma internal inductance to increase. But vertical stability control remains manageable in ITER at high internal inductance when accompanied by a strong elongation reduction. This will result in ITER terminations remaining longer at low q (q<sub>95</sub>~3) than most present-day devices during the current ramp-down. A fast power ramp-down leads to a larger change in β<sub>p</sub> at the H-L transition, but the experimental data showed that these are manageable for the ITER radial position control. The analysis of JET data shows that radiation and impurity levels significantly alter the H-L transition dynamics. Self-consistent calculations of the impurity content and resulting radiation should be taken into account when modelling ITER termination scenarios. Here, the results from this analysis can be used to better prescribe the inputs for the detailed modelling and preparation of ITER termination scenarios.« less
  7. Formation and sustainment of internal transport barriers in the International Thermonuclear Experimental Reactor with the baseline heating mix

    Plasmas with internal transport barriers (ITBs) are a potential and attractive route to steady-state operation in ITER. These plasmas exhibit radially localized regions of improved confinement with steep pressure gradients in the plasma core, which drive large bootstrap current and generate hollow current profiles and negative magnetic shear. This work examines the formation and sustainment of ITBs in ITER with electron cyclotron heating and current drive. The time-dependent transport simulations indicate that, with a trade-off of the power delivered to the equatorial and to the upper launcher, the sustainment of steady-state ITBs can be demonstrated in ITER with the baselinemore » heating configuration.« less
  8. Fusion Energy Sciences Exascale Requirements Review. An Office of Science review sponsored jointly by Advanced Scientific Computing Research and Fusion Energy Sciences, January 27-29, 2016, Gaithersburg, Maryland

    The additional computing power offered by the planned exascale facilities could be transformational across the spectrum of plasma and fusion research — provided that the new architectures can be efficiently applied to our problem space. The collaboration that will be required to succeed should be viewed as an opportunity to identify and exploit cross-disciplinary synergies. To assess the opportunities and requirements as part of the development of an overall strategy for computing in the exascale era, the Exascale Requirements Review meeting of the Fusion Energy Sciences (FES) community was convened January 27–29, 2016, with participation from a broad range ofmore » fusion and plasma scientists, specialists in applied mathematics and computer science, and representatives from the U.S. Department of Energy (DOE) and its major computing facilities. This report is a summary of that meeting and the preparatory activities for it and includes a wealth of detail to support the findings. Technical opportunities, requirements, and challenges are detailed in this report (and in the recent report on the Workshop on Integrated Simulation). Science applications are described, along with mathematical and computational enabling technologies. Also see for more information.« less
  9. FY2014 FES (Fusion Energy Sciences) Theory & Simulation Performance Target, Final Report

    We report here the work done for the FY14 OFES Theory Performance Target as given below: "Understanding alpha particle confinement in ITER, the world's first burning plasma experiment, is a key priority for the fusion program. In FY 2014, determine linear instability trends and thresholds of energetic particle-driven shear Alfven eigenmodes in ITER for a range of parameters and profiles using a set of complementary simulation models (gyrokinetic, hybrid, and gyrofluid). Carry out initial nonlinear simulations to assess the effects of the unstable modes on energetic particle transport". In the past year (FY14), a systematic study of the alpha-driven Alfvenmore » modes in ITER has been carried out jointly by researchers from six institutions involving seven codes including the transport simulation code TRANSP (R. Budny and F. Poli, PPPL), three gyrokinetic codes: GEM (Y. Chen, Univ. of Colorado), GTC (J. McClenaghan, Z. Lin, UCI), and GYRO (E. Bass, R. Waltz, UCSD/GA), the hybrid code M3D-K (G.Y. Fu, PPPL), the gyro-fluid code TAEFL (D. Spong, ORNL), and the linear kinetic stability code NOVA-K (N. Gorelenkov, PPPL). A range of ITER parameters and profiles are specified by TRANSP simulation of a hybrid scenario case and a steady-state scenario case. Based on the specified ITER equilibria linear stability calculations are done to determine the stability boundary of alpha-driven high-n TAEs using the five initial value codes (GEM, GTC, GYRO, M3D-K, and TAEFL) and the kinetic stability code (NOVA-K). Both the effects of alpha particles and beam ions have been considered. Finally, the effects of the unstable modes on energetic particle transport have been explored using GEM and M3D-K.« less

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