Bulletin of the American Physical Society
57th Annual Meeting of the APS Division of Plasma Physics
Volume 60, Number 19
Monday–Friday, November 16–20, 2015; Savannah, Georgia
Session GI2: MFE Model Development and SimulationInvited
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Chair: Andris Dimits, Lawrence Livermore National Laboratory Room: Chatham Ballroom C |
Tuesday, November 17, 2015 9:30AM - 10:00AM |
GI2.00001: Unification of Plasma Fluid and Kinetic Theory via Gaussian Radial Basis Functions Invited Speaker: J.M. Candy A fundamental macroscopic description of a magnetized plasma is the Vlasov equation supplemented by the nonlinear inverse-square force Fokker-Planck collision operator [Rosenbluth et al., Phys. Rev. 107, 1957]. The Vlasov part describes advection in a six-dimensional phase space whereas the collision operator contains friction and diffusion coefficients that are weighted velocity-space integrals of the particle distribution function. The Fokker-Planck collision operator is an integro-differential, nonlinear (bilinear) operator. Numerical discretization of the operator, in particular for collisions of unlike species, is extremely challenging. In this work, we describe a new approach to discretize the entire kinetic system based on an expansion in Gaussian Radial Basis functions (RBFs). This approach is particularly well-suited to treat the collision operator because the friction and diffusion coefficients can be analytically calculated. Although the RBF method is known to be a powerful scheme for the interpolation of scattered multidimensional data, Gaussian RBFs also have a deep physical interpretation in statistical mechanics and plasma physics as local thermodynamic equilibria. We outline the general theory, highlight the connection to plasma fluid theories, and also give 2D and 3D numerical solutions of the nonlinear Fokker-Planck equation. A broad spectrum of applications for the new method is anticipated in both astrophysical and laboratory plasmas. In particular, we believe that the RBF method may provide a new bridge between fluid and kinetic descriptions of magnetized plasma. [Preview Abstract] |
Tuesday, November 17, 2015 10:00AM - 10:30AM |
GI2.00002: Continuum Kinetic Modeling of the Tokamak Plasma Edge Invited Speaker: Mikhail Dorf The problem of edge plasma transport provides substantial challenges for analytical or numerical analysis due to (a) complex magnetic geometry including both open and closed magnetic field lines \textbf{B}, (b) steep radial gradients comparable to ion drift-orbit excursions, and (c) a variation in the collision mean-free path along \textbf{B }from long to short compared to the magnetic connection length. Here, the first 4D continuum drift-kinetic transport simulations that span the magnetic separatrix of a tokamak are presented, motivated in part by the success of continuum kinetic codes for core physics and in part by the potential for high accuracy. The calculations include fully-nonlinear Fokker-Plank collisions and electrostatic potential variations. ~The problem of intrinsic toroidal rotation driven by ion orbit loss is addressed in detail.~ The code, COGENT, developed by the Edge Simulation Laboratory collaboration, is distinguished by a fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex magnetic X-point divertor geometry with high accuracy. Previously, successful performance of high-order algorithms has been demonstrated in a simpler closed magnetic-flux-surface geometry for the problems of neoclassical transport and collisionless relaxation of geodesic acoustic modes in a tokamak pedestal, including the effects of a strong radial electric field under H-mode conditions. [Preview Abstract] |
Tuesday, November 17, 2015 10:30AM - 11:00AM |
GI2.00003: Validation of a coupled core-transport, pedestal-structure, current-profile and equilibrium model Invited Speaker: O. Meneghini The first workflow capable of predicting the self-consistent solution to the coupled core-transport, pedestal structure, and equilibrium problems from first-principles and its experimental tests are presented. Validation with DIII-D discharges in high confinement regimes shows that the workflow is capable of robustly predicting the kinetic profiles from on axis to the separatrix and matching the experimental measurements to within their uncertainty, with no prior knowledge of the pedestal height nor of any measurement of the temperature or pressure. Self-consistent coupling has proven to be essential to match the experimental results, and capture the non-linear physics that governs the core and pedestal solutions. In particular, clear stabilization of the pedestal peeling ballooning instabilities by the global Shafranov shift and destabilization by additional edge bootstrap current, and subsequent effect on the core plasma profiles, have been clearly observed and documented. In our model, self-consistency is achieved by iterating between the TGYRO core transport solver (with NEO and TGLF for neoclassical and turbulent flux), and the pedestal structure predicted by the EPED model. A self-consistent equilibrium is calculated by EFIT, while the ONETWO transport package evolves the current profile and calculates the particle and energy sources. The capabilities of such workflow are shown to be critical for the design of future experiments such as ITER and FNSF, which operate in a regime where the equilibrium, the pedestal, and the core transport problems are strongly coupled, and for which none of these quantities can be assumed to be known. Self-consistent core-pedestal predictions for ITER, as well as initial optimizations, will be presented. [Preview Abstract] |
Tuesday, November 17, 2015 11:00AM - 11:30AM |
GI2.00004: Self-organized stationary states of tokamaks Invited Speaker: Stephen Jardin We report here on a nonlinear mechanism that forms and maintains a self-organized stationary (sawtooth free) state in tokamaks. This process was discovered by way of extensive long-time simulations using the M3D-C1 3D extended MHD code in which new physics diagnostics have been added. It is well known that most high-performance modes of tokamak operation undergo ``sawtooth'' cycles, in which the peaking of the toroidal current density triggers a periodic core instability which redistributes the current density. However, certain modes of operation are known, such as the ``hybrid'' mode in DIII-D, ASDEX-U, JT-60U and JET, and the long-lived modes in NSTX and MAST, which do not experience this cycle of instability. Empirically, it is observed that these modes maintain a non-axisymmetric equilibrium which somehow limits the peaking of the toroidal current density. The physical mechanism responsible for this has not previously been understood, but is often referred to as ``flux-pumping,'' in which poloidal flux is redistributed in order to maintain q$_{0}$ \textgreater 1. In this talk, we show that in long-time simulations of inductively driven plasmas, a steady-state magnetic equilibrium may be obtained in which the condition q$_{0}$ \textgreater 1 is maintained by a dynamo driven by a stationary marginal core interchange mode. This interchange mode, unstable because of the pressure gradient in the ultra-low shear region in the center region, causes a (1,1) perturbation in both the electrostatic potential and the magnetic field, which nonlinearly cause a (0,0) component in the loop voltage that acts to sustain the configuration. This hybrid mode may be a preferred mode of operation for ITER. We present parameter scans that indicate when this sawtooth-free operation can be expected. [Preview Abstract] |
Tuesday, November 17, 2015 11:30AM - 12:00PM |
GI2.00005: Free-Boundary 3D Equilibria and Resistive Wall Instabilities with Extended-MHD Invited Speaker: N.M. Ferraro The interaction of the plasma with external currents, either imposed or induced, is a critical element of a wide range of important tokamak phenomena, including resistive wall mode (RWM) stability and feedback control, island penetration and locking, and disruptions. A model of these currents may be included within the domain of extended-MHD codes in a way that preserves the self-consistency, scalability, and implicitness of their numerical methods. Such a model of the resistive wall and non-axisymmetric coils is demonstrated using the M3D-C1 code for a variety of applications, including RWMs, perturbed non-axisymmetric equilibria, and a vertical displacement event (VDE) disruption. The calculated free-boundary equilibria, which include Spitzer resistivity, rotation, and two-fluid effects, are compared to external magnetic and internal thermal measurements for several DIII-D discharges. In calculations of the perturbed equilibria in ELM suppressed discharges, the tearing response at the top of the pedestal is found to correlate with the onset of ELM suppression. Nonlinear VDE calculations, initialized using a vertically unstable DIII-D equilibrium, resolve in both space and time the currents induced in the wall and on the plasma surface, and also the currents flowing between the plasma and the wall. The relative magnitude of these contributions and the total impulse to the wall depend on the resistive wall time, although the maximum axisymmetric force on the wall over the course of the VDE is found to be essentially independent of the wall conductivity. [Preview Abstract] |
Tuesday, November 17, 2015 12:00PM - 12:30PM |
GI2.00006: The tokamak density limit: A thermo-resistive disruption mechanism Invited Speaker: David Gates A magnetic island growth mechanism based on radiative cooling of the internal island flux surfaces [1] is shown to produce the correct physical scaling [2] to explain one of the long standing mysteries of tokamak physics - the empirical Greenwald density limit [3]. In this presentation we will review the phenomenology of the density limit and the correlation between the Greenwald limit and the onset threshold for radiation-driven tearing modes. The behavior of magnetic islands with a 3D electron temperature distribution which is consistent with a large ratio of radial to parallel heat conductivity - and a corresponding 3D resistivity profile - is examined for islands with near-zero net heating in the island interior. The effect of varying impurity mix on the local island onset threshold is consistent with the established experimental scalings for tokamaks at the density limit. A simple analytic theory [4] is developed which reveals the effect of heating and cooling in the island interior as well as the effect of island asymmetry. It is shown that a new term accounting for the thermal effects of island asymmetry is a crucial addition to the Modified Rutherford Equation. The resultant model exhibits a robust onset of a rapidly growing tearing mode - consistent with the disruption mechanism observed at the density limit in tokamaks. Additionally, a fully non-linear 3D cylindrical calculation is performed that simulates the effect of net island heating / cooling by raising / suppressing the temperature in the core of the island. In both the analytic theory and the numerical simulation a sudden threshold for explosive growth is found to be due to the interaction between three distinct thermal non-linearities, which affect the island resistivity, thereby modifying the growth dynamics. Expanding on the model presented, we speculate that the mechanism described may be applicable to a much wider range of tokamak disruptions than just those near the Greenwald limit. \\[4pt] [1] P. H. Rebut and M. Hugon, \textit{Plasma Physics and Controlled Nuclear Fusion Research} 1984 (IAEA, Vienna, 1985), Vol. 2.\\[0pt] [2] D. A. Gates and L. Delgado-Aparicio, Phys. Rev. Letters \textbf{108} (2012) 165004\\[0pt] [3] M. Greenwald et al, Nucl. Fusion \textbf{28} (1988) 2199.\\[0pt] [4] R. B. White et al, Phys. Plasmas \textbf{22} (2015) 022514. [Preview Abstract] |
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