Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Plasma Physics
Volume 67, Number 15
Monday–Friday, October 17–21, 2022; Spokane, Washington
Session GO05: MFE: Analytical and Computational TechniquesLive Streamed
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Chair: Mark Cianciosa, Oak Ridge National Lab Room: Ballroom 111 B |
Tuesday, October 18, 2022 9:30AM - 9:42AM |
GO05.00001: Improved Darwin PIC algorithm Daniel C Barnes The application of the Darwin field algorithm to PIC simulation presents two challenges: 1) Coulomb gauge must be achieved to high accuracy; 2) time centering is not natural (as in the case of EM PIC). Using the previously-reported [1] solenoidal FE representation, Coulomb gauge is point-wise satisfied. Extending this previous work, the general scheme of Lapenta [2] and Markedis for “Energy-conserving PIC” is adapted to the time-stepping issue. The resulting algorithm is time-centered, almost energy-conserving, and absolutely stable. In contrast to the method of Ref. 2, the issue of charge conservation is moot, i.e. charge is exactly conserved by the Darwin separation of ES and MS components. 2D tests with time steps beyond explicit stability limits repeating the successful tests of Ref. 1.are reported. Extensions to arbitrary-magnetization, multi-species, 3D, and to hybrid models with some or all fluid species are discussed. |
Tuesday, October 18, 2022 9:42AM - 9:54AM |
GO05.00002: An implicit, conservative, asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas Luis Chacon, Guangye Chen, Oleksandr Koshkarov, Lee Ricketson We present a new full-orbit electrostatic particle-in-cell algorithm able to use large timesteps compared to particle gyro-period in arbitrary magnetic fields [1]. The algorithm extends earlier electrostatic fully implicit PIC implementations [2] with a new asymptotic-preserving (AP) particle-push scheme [3] (recently endowed with a very fast Picard nonlinear solver [4]) that allows timesteps much larger than particle gyroperiods. The AP integrator preserves all the averaged particle drifts in the large-timestep limit, while recovering resolved particle orbits with small timesteps. The scheme allows for a seamless, efficient treatment of particles with arbitrary magnetization, conserves energy and charge exactly, and does not spoil implicit solver performance. We demonstrate by numerical experiment with several strongly magnetized problems (diocotron instability, modified two-stream instability, and drift-wave instability) that two orders of magnitude wall-clock-time speedups are possible vs. the standard fully implicit electrostatic PIC algorithm without sacrificing solution quality and while preserving strict charge and energy conservation. |
Tuesday, October 18, 2022 9:54AM - 10:06AM |
GO05.00003: Fundamental limits in a magnetically confined thermonuclear fusion reactor Chiping Chen, James Becker, James Farrell A theory is presented for quantitative calculations of confinement time limits for plasma thermal energies in magnetically confined thermonuclear fusion reactors [1]. The theory is based on radiation reaction associated with spontaneous electron cyclotron radiation as described by the Larmor formula. Good agreement is found between the theory and the measurements of energy confinement times from the early TFTR D-T fusion experiment [2] and the recent Wendelstein 7-X hydrogen plasma experiment [3]. A new, advanced Lawson criterion for D-T ignition is derived. A fundamental limit of fusion energy gain is predicted, which is consistent with the latest magnetically confined D-T fusion energy record achieved experimentally at JET [4]. |
Tuesday, October 18, 2022 10:06AM - 10:18AM |
GO05.00004: Multi-species magnetized plasma fluid simulations with BOUT++/Hermes Benjamin Dudson, Kaden Loring, Hasan Muhammed, John T Omotani Magnetized laboratory and space plasmas of scientific and practical interest contain multiple ionized and neutral ion species. We present a new simulation tool to study turbulence and transport in these plasmas, with examples in 1D, 2D and 3D involving mixed hydrogenic, helium and neon plasmas. Our motivation is the study of transport and turbulence in the edge and divertor of tokamak fusion reactors, but the applications of BOUT++/Hermes are broader and offer opportunities to validate and improve our models. |
Tuesday, October 18, 2022 10:18AM - 10:30AM |
GO05.00005: Can drift-ordered fluid models be made fully consistent? Federico D Halpern, Ronald E Waltz, Tess Bernard Although drift-ordered fluid models based on the Braginskii equations are widely used in plasma turbulence codes, no single implementation of these models conserves energy – except in extremely limiting cases where density and magnetic gradients are completely neglected. The main reason for this is the difficulty of obtaining a closed-form expression for the polarization flux and its relation to the vorticity. Our objective is to provide a simple and practical expression for the polarization flux, applicable to drift-Braginskii models. The lowest order form of the model, which truncates the perpendicular kinetic energy flux, results in a closed form for the polarization velocity as a sum of drifts. This result mainly stems from considering a generalized vorticity function related to the curl of the momentum. The resulting vorticity equation is formulated in divergence form, which ensures charge conservation and can be adapted to different numerical schemes. However, the correct kinetic energy flux can only be reconstructed by defining the polarization flux recursively – which yields a challenging 3D vector equation to solve. This poses the question of whether drift-ordered fluid models can ever be made energy-consistent in a practical manner. |
Tuesday, October 18, 2022 10:30AM - 10:42AM |
GO05.00006: A Multi-Region Multi-Timescale Burning Plasma Dynamics Model for Tokamaks Zefang Liu, Weston M Stacey A multi-region multi-timescale transport model is developed to simulate burning plasma dynamics in tokamaks. Deuterium-tritium fusion generates 3.5 MeV alpha particles, which transfer their energy mainly to core electrons. The heated electrons and lower-energy fusion alpha particles then heat core ions, which will increase the fusion reaction rate and may conceivably lead to a thermal runaway instability. Meanwhile, core energy is transported to the edge and radiated to the wall. The timescales of such processes determine the burning plasma dynamics. Our transport model considers the core, edge, scrape-off layer, and divertor as separate nodes. Alpha heating with a time delay between electrons and ions is computed. Electron cyclotron and impurity radiations are evaluated. Ion orbit loss as an edge plasma effect is also included. Diffusivity parameters in internodal transport times are calculated by machine learning algorithms. This model is validated against various DIII-D non-fusion plasmas and applied for multiple ITER operation scenarios. Simulation results indicate that radiation and transport can promptly remove extra heat from the core plasma and thereby inhibit the thermal runaway instability from fusion alpha heating in ITER. |
Tuesday, October 18, 2022 10:42AM - 10:54AM |
GO05.00007: A predictor-corrector scheme for hybrid fluid-PIC electrostatic plasma simulation Logan Meredith, Davide Curreli Computational plasma physicists typically must choose between fluid models, which are fast but can fail in certain physical regimes, and particle models, which are slower and noisier but more widely applicable. Many hybrid schemes have been developed to combine the two models. Notably, delta-f schemes model deviations from a Maxwellian distribution as particles. However, this introduces negative-weight particles to the simulation, complicating collisional models. In this work, we present a hybrid scheme for simulations of electrostatic plasmas utilizing both a discontinuous Galerkin discretization of the Euler fluid equations and a particle-in-cell (PIC) method. We implement this in the hPIC2 unstructured PIC code leveraging the MFEM finite element method library, perform verification studies, and evaluate its performance on massively parallel, heterogeneous computers. The hybrid coupling allows hPIC2 to model the Maxwellian bulk of a species as a fluid and kinetic perturbations as PIC, all while allowing typical collisional models. |
Tuesday, October 18, 2022 10:54AM - 11:06AM |
GO05.00008: A Learned Fluid Closure for Phase Mixing Applied to a Turbulent Gradient-Driven Gyrokinetic System in Simple Geometry Akash Shukla, David R Hatch, William D Dorland, Craig Michoski We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system - temperature gradient driven turbulence in an unsheared slab. The closure is motivated by the observation that in a turbulent system the nonlinearity continually perturbs the system away from the linear solution, thus demanding versatility in the closure scheme. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition (SVD). Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with several other closures schemes over a broad range of the relevant 2D parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase mixing rates much lower than the linear expectations. In contrast with the other closures, the LMM closure is able to capture this reduction. In comparisons of heat fluxes, the LMM closure exhibits errors substantially lower than the other closures. |
Tuesday, October 18, 2022 11:06AM - 11:18AM |
GO05.00009: Anisotropic Elastic Scattering Models of Neutral Fusion-Relevant Species for Monte Carlo Plasma Modeling Mark C Zammit, Ryan M Park, Brett Scheiner, James Colgan, Christopher J Fontes, William Kupets, Eddy M Timmermans, Xianzhu Tang, Nathan Garland Accurate elastic differential cross sections are essential for modeling many plasma scenarios, particularly in low temperature plasma technologies or the cooler edge regions of tokamaks. Currently, few models have reported the ability to accurately predict elastic electron scattering from neutral targets at low energies. Here we present an alternative analytic approach that is applicable to H, He, H2 and the respective isotopes across a wide-range of energies. It is shown that the current model reliably predicts elastic anisotropic scattering, while also offering straightforward analytic expressions that can be implemented efficiently in particle-in-cell (PIC) / Monte Carlo (MC) modeling. |
Tuesday, October 18, 2022 11:18AM - 11:30AM |
GO05.00010: Gaussian Process Regression for Equilibrium Reconstruction of DIII-D Plasmas Jarrod Leddy, Sandeep Madireddy, Eric C Howell, Scott E Kruger, Cihan Akcay, Lang L Lao, Joseph T McClenaghan, David Orozco, Sterling P Smith, Torrin A Bechtel, Alexei Pankin Gaussian Process Regression is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community for its many advantages over traditional fitting techniques. For kinetic EFIT reconstructions on DIII-D, data from magnetic probes and flux loops, motional Stark effect diagnostics, and plasma density and temperature profile measurements from Thomson scattering and charge exchange recombination diagnostics are critical for obtaining accurate reconstructions. Each of these data sources contain unique challenges for proper analysis that can be aided by using the GPR techniques within the magnetic equilibrium reconstruction process. Here, we review our progress on applying these GPR techniques to experimental data within the EFIT workflow, and contrast with similar efforts within the fusion community. |
Tuesday, October 18, 2022 11:30AM - 11:42AM |
GO05.00011: Model Order Reduction of the Plasma Equilibrium Reconstruction framework EFIT with Deep Neural Networks Jaehoon Koo, Sandeep Madireddy, Cihan Akcay, Torrin A Bechtel, Scott E Kruger, Yueqiang Liu, Xuan Sun, Prasanna Balaprakash, Lang L Lao We present a model order reduction (MOR) of magnetics-only EFITs with neural network (EFIT-MORNN) surrogates that have been trained on the 2019 DIII-D data. Our neural networks reconstruct DIII-D equilibria, given an input space comprising external measurements of the poloidal magnetic field, poloidal flux, plasma current, and currents in the external poloidal-field coils. A total of 160 thousand magnetic equilibria from 2019 were used. First, we built a physics-informed machine-learning (ML) surrogate based on a combination of a convolutional neural network and a multi-layer perceptron (MLP) used to concurrently predict the equilibrium poloidal magnetic flux y and the toroidal current density Jf. Next, two additional MLP-based surrogate models were built and trained to reconstruct the plasma boundary shape and global quantities including the normalized beta, the internal inductance, and the edge safety factor. These trained networks were then used to infer plasma equilibria for 4 different types of DIII-D discharges: high poloidal beta, hybrid, super H-mode, and negative triangularity. Performance of EFIT-MORNN was compared to offline-EFIT as well as real time (RT) EFIT. The trained EFIT-MORNN reconstructed y with better than 99% accuracy and Jf better than 98% accuracy, showing an improvement over RT-EFIT reconstructions, with a reconstruction speed per time slice that is at least comparable to that of RT-EFIT. The offline-EFIT-like accuracy and RT-EFIT-like speed offer the possibility of turning EFIT-MORNN into a real-time tool. We also present a new framework that initializes the EFIT iteration loop with an equilibrium generated by EFIT-MORNN to increase the accuracy of RT-EFITs. |
Tuesday, October 18, 2022 11:42AM - 11:54AM |
GO05.00012: Adaptive toroidal equilibrium code ATEQ and the X- point effects on the external MHD modes Linjin Zheng, Michael T Kotschenreuther, Francois Waelbroeck, Yasushi Todo A newly developed adaptive toroidal equilibrium code (ATEQ) is presented (Phys. Plasmas {\bf 29} (7), 2022). Comparisons with existing codes, such as TOQ, VMEC, EFIT etc., as well as the Solov\'ev equilibrium solution with X-points, are detailed. An important feature of ATEQ is that the edge safety factor can reach several thousands for configurations with X-points. With ATEQ equilibrium, it then becomes possible to examine the X-points effects on the external MHD modes. The adaptive stability code AEGIS is used for this purpose. The coupling between the external and internal Fourier components is studied for different edge q values by cutting off proper edge portion. The impacts both on the equilibrium and subsequent stability properties with the adaptive equilibrium computation by ATEQ will be discussed. |
Tuesday, October 18, 2022 11:54AM - 12:06PM |
GO05.00013: XGC Gyrokinetic simulations of coupled core delta-f and edge total-f models with a canonical maxwellian in the core* Pallavi Trivedi, Julien Dominski, Choongseok Chang, Robert Hager, Seung Hoe Ku, Aaron Scheinberg, Amitava Bhattacharjee One of the goals of the Exascale High-Fidelity Whole Device Modeling (ECP-WDM) project is to model the whole device of Tokamaks with core-edge coupled gyrokinetic simulations. This coupling of core delta-f and edge total-f gyrokinetic models [1] could enable a significant simulation speed-up. In particular, coupling core delta-f with edge total-f simulations, which raises many issues including the coupling of different gyrokinetic model equations together [2]. Therefore, we made the choice of solving the same equations but using different background f0 in the core and the edge. The goal being to avoid the background neoclassical drive in the core, as it drives large amplitude (GAM-like) perturbation. Our background Maxwellian is thus a linear combination of a canonical (fcm) in the core with a local (flm) Maxwellian in the edge, f = wfcm + (1 − w)flm. Preliminary electrostatic and electromagnetic simulations using this new core-edge model will be presented. |
Tuesday, October 18, 2022 12:06PM - 12:18PM |
GO05.00014: Plasma-wave interaction modelling in magnetic confined devices with the finite element method Ruben Otin, Guillaume Urbanczyk, Wouter Tierens Plasma-wave interaction is a broad topic that includes many different phenomena. In the Scrape-Of-Layer (SOL) of tokamak plasmas, different modes of electromagnetic waves can be found, resonances, reflections, scattering and the interaction of these fields with the wall. The study of these phenomena is important for the correct operation of future nuclear fusion reactors because electromagnetic waves are commonly used to stabilize and heat the plasma. Without the proper understanding and modelling, the integrity of the machine could be endangered (e.g., due to the creation of hot-spots caused by RF-DC sheath rectification [1]) and limit the maximum heating power that can be safely sent to the plasma. |
Tuesday, October 18, 2022 12:18PM - 12:30PM |
GO05.00015: A phase-shift-periodic parallel boundary condition for low-magnetic-shear scenarios Denis A St-Onge, Michael Barnes, Felix I Parra We formulate a generalized periodic boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift is shown to have measurable effects in periodic gyrokinetic simulations, and can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa-Wakatani system. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios which, while more straightforward, can be computationally demanding. |
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