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  1. MHD modeling of shattered pellet injection in JET

    Abstract Nonlinear 3D MHD simulations of shattered-pellet injection (SPI) in JET show prototypical SPI- driven disruptions using the M3D-C1 and NIMROD extended-MHD codes. Initially, radiation-driven thermal quenches are accelerated by MHD activity as the pellet crosses rational surfaces, leading to a radiation spike, global stochasticization of the magnetic field, and a complete thermal quench. Eventually, current quenches, preceded by a current spike are seen as the Ohmic heating becomes equal to the radiative cooling. The results are qualitatively similar for both a single monolithic pellet, pencil-beam model, and a realistic shatter to represent the SPI plume. A scan in viscositymore » from 500-2000 m2/s for MHD simulations finds that reducing viscosity increases MHD activity and decreases thermal quench time 1slightly. A realistic cloud of fragments modeling shows that mixed-D-Ne pellet travels deeper into the plasma core before the thermal quench. At the slow pellet speeds, the pellet is found to be moving slowly enough inward that even the 5% neon in the mixed pellet is enough to effectively radiate the thermal energy available. Radiation toroidal peaking is predicted to be at levels consistent with experimental observations and reduced as the pellet travels deeper into the plasma. These simulations lay the ground work for more-sophisticated validative and predictive modeling of SPI in JET using both M3D-C1 and NIMROD« less
  2. Self-consistent investigation of density fueling needs on ITER and CFETR utilizing the new Pellet Ablation Module

    Absmore » tract Self-consistent modeling using the stability, transport, equilibrium, and pedestal (STEP) workflow in the OMFIT integrated modeling framework (predicting pedestal with EPED, core profiles with TGYRO, current profile with ONETWO, and EFIT for equilibrium) suggests ITER and future devices such as China Fusion Engineering Test Reactor (CFETR) Zhuang et al (2019 Nucl. Fusion 59 112010) will benefit from high-density operation (Greenwald limit fraction f g w 0.7−1.3). Regimes with an operational density near the Greenwald limit will likely need peaked density profiles so that the pedestal density remains below the Greenwald limit. Peaked density profiles can be achieved with the help of pellet injection. A flexible Pellet Ablation Module (PAM), which predicts the density source based on a comprehensive analytical pellet ablation model, has been developed for predicting pellet fueling for transport studies, and has been incorporated into the STEP workflow for predictive modeling. This workflow is applied to DIII-D and finds good agreement with experiments. On ITER the effect of pellet fueling is examined in an advanced inductive scenario, where a fusion gain of up to Q  = 9 is predicted with strong central pellet fueling. On CFETR, with a mid-radius density source, an average of 1.5 × 10 22 electrons s −1 are required to achieve the density and temperature profiles necessary for the 1000 MW advanced scenario with a tritium burn-up fraction of 3 % .« less
  3. Surrogate models for plasma displacement and current in 3D perturbed magnetohydrodynamic equilibria in tokamaks

    Abstract A numerical database of over one thousand perturbed three-dimensional (3D) equilibria has been generated, constructed based on the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) computed plasma response to the externally applied 3D field sources in multiple tokamak devices. Perturbed 3D equilibria with the n = 1–4 ( n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations formore » the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first five eigenstates, achieving a relative error (RE) below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3D equilibria, based on the two-dimensional equilibrium input and the 3D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% RE. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.« less
  4. Transition from ITG to MTM linear instabilities near pedestals of high density plasmas

    Here, investigation of linear gyrokinetic ion-scale modes ( k θ ρ s = 0.3) finds that a transition from ion temperature gradient to microtearing mode (MTM) dominance occurs as the density is increased near the pedestal region of a parameterized DIII-D sized tokamak. H-modes profile densities, temperatures, and equilibria are parameterized utilizing the OMFIT PRO_create module. With these profiles, linear gyrokinetic ion-scale instabilities are predicted with CGYRO. This transition (nMTM) has a weak dependence on radial location in the region near the top of the pedestal ( ρ = 0.7 – 0.9), which allows simulating single radii to examine themore » approximate scaling of nMTM with global parameters. The critical nMTM is found to scale with plasma current. Additionally, increasing the minor radius by decreasing the aspect ratio and increasing the major radius are found to reduce nMTM. However, any relationship between nMTM and density limit physics remains unclear as nMTM increases relative to the Greenwald density with larger minor radius and with larger magnetic field, suggesting that the transport due to MTM may be less important for a reactor. Additionally, nMTM is sensitive to the pedestal temperature, the local electron and ion gradients, the ratio of ion to electron temperature T i / T e, and the current profile. MTMs are predicted to be the dominant instability in the core at similar Greenwald fractions for DIII-D, NSTX, and NSTX-U H-mode experiments, supporting the results of the parameterized study. Additionally, MTMs continue to be the dominant linear instability in a DIII-D L-mode after an H–L transition as the plasma approaches a density limit disruption despite the large change in plasma profiles.« less
  5. Implementing Faraday effect measurement constraints into the Grad–Shafranov equilibrium fitting code EFIT

    A new tool for the exploration and diagnosis of the internal magnetic field of plasmas in the DIII-D tokamak in the form of a constraint on the EFIT (Equilibrium Fitting) Grad–Shafranov code based on the Faraday-effect Radial Interferometer-Polarimeter (RIP) diagnostic is presented, including description, verification, and sample application. The physics underlying the diagnostic and its implementation into EFIT are discussed, and the results showing the verification of the model are given, and the model’s limitations are discussed. The influence of the diagnostic’s input on the resulting equilibrium parameters is characterized. Furthermore, the effect of electron density profile refinement is evaluatedmore » and found to be negligible. A sample application of the diagnostic is shown, indicating that the RIP constraint has similar effects on the equilibrium as motional Stark effect constraints do.« less
  6. Simulation of runaway electron production with CQL3D coupled to NIMROD

    Abstract A coupling between two distinctly different codes—one magnetohydrodynamic (MHD) and another kinetic—is achieved and applied for simulation of runaway electron (RE) production. The 3D initial value MHD code NIMROD simulates a DIII-D pure neon shattered pellet injection plasma quench including the propagation and ablation of the fragments, ionization and recombination of the impurities, and the radiated and transported energies. The field data from NIMROD is then used by the bounce-averaged Fokker–Planck Collisional QuasiLinear 3D (CQL3D) kinetic code to simulate the production of REs and their radial transport. The coupling procedure involves mapping of data between different grids and adjustmentmore » of the NIMROD toroidal electric field when REs appear. It is shown that without the radial transport, a large RE current is generated, up to 30% of the pre-pellet ohmic current. However, when the radial transport is included in CQL3D, the RE current is reduced to undetectable level, consistent with experiment. Various forms of the radial diffusion are surveyed to determine conditions when the fast electrons would not have time to be accelerated to relativistic energies before they are lost to chamber wall.« less
  7. Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

    New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflowmore » utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.« less
  8. Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

    Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. A neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets withmore » encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.« less
  9. Toroidal modeling of runaway electron loss due to 3-D fields in DIII-D and COMPASS

    The 3-D field induced relativistic runaway electron (RE) loss has been simulated for DIII-D, COMPASS and ITER plasmas, utilizing the MARS-F code incorporated with the recently developed and updated RE orbit module (REORBIT). Modeling shows effectively 100% loss of a post-disruption, high-current runaway beam in DIII-D, due to the 1 kG level of magnetic field perturbation produced by a fast growing n = 1 resistive kink instability. The RE loss is shown to be independent of the particle energy or the initial location of particles in the configuration space. Applied resonant magnetic perturbation (RMP) fields from in-vessel coils are notmore » effective for RE beam mitigation in DIII-D, but do produce finite (>10%) RE loss in COMPASS, consistent with experimental observations in above two devices. The major reasons for this difference in RE control by RMP between these two devices are (i) the coil proximity to the RE beam and (ii) the effective coil current scaling versus the machine size and the toroidal magnetic field. About 10% RE loss fraction is also predicted for an ITER 15 MA scenario with pre-disruption plasma, highlighting the role of the plasma response. Up to 30% loss is computed, however, by artificially scaling the equilibrium pressure to zero. This is due to the more resistive plasma response and stronger resulting field line stochasticity. Distributions of the lost REs to the limiting surface show poloidally peaked profile near the high-field-side in both DIII-D and COMPASS, covering about 100o poloidal angle. Higher perturbation field level and/or higher particle energy also result in REs being lost to the low-field-side of the limiting surface of these two devices, increasing the effective wetted area. Finally, for the modeled ITER plasmas, the applied RMP field, with optimal poloidal spectrum that maximizes the edge localized mode control, leads to REs being lost to the lower divertor region of the limiting surface within a narrow poloidal band.« less
  10. Advances in physics understanding of high poloidal beta regime toward steady-state operation of CFETR

    Experimental and modeling investigations of the high βp scenarios on the DIII-D and EAST tokamaks show advantages in high energy confinement, avoidance of n = 1 MHD, and core-edge integration with reduced heat flux, making this scenario an attractive option for CFETR steady-state operation. Experiments show that plasmas with high confinement and high density can be achieved with neutral beam injection on DIII-D (βp ~ 2.2, βN ~ 3.5, fBS ~ 50%, fGw ~ 1.0, H98y2 ~ 1.5) and pure RF power on EAST (βP ~ 2.0, βN ~ 1.6, fBS ~ 50%, fGw ~ 0.8, H98y2 > 1.3). Bymore » tailoring the current density profile, a q-profile with local (off-axis) negative shear is achieved that yields improved confinement and MHD stability. Transport analysis and simulation suggest that the combination of high density gradient and high Shafranov shift allows turbulence stabilization and higher confinement. Using on-axis ECH injection, tungsten accumulation is avoided on EAST, and this is reproduced in modeling. Reduced heat flux (by >40%) and maintenance of high core confinement is achieved with active feedback control of the radiated divertor, an important result for long pulse operation in tokamaks. In conclusion, the improved physics understanding and validated modeling tools are used to design a 1GW steady-state scenario for CFETR.« less
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