Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of nondiffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations. Published by AIP Publishing.This work was supported by U.S. DOE under Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICT (Direccion General de Investigaciones Cientıficas y Tecnologicas) of Spain under Project No. ENE2015-68265

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. II. Characterization of transport by means of passive scalars

From theoretical and modeling points of view, following Lagrangian trajectories is the most straightforward way to characterize the transport dynamics. In real plasmas, following Lagrangian trajectories is difficult or impossible. Using a blob of passive scalar (a tracer blob) allows a quasi-Lagrangian view of the dynamics. Using a simple two-dimensional electrostatic plasma turbulence model, this work demonstrates that the evolution of the tracers and the passive scalar field is equivalent between these two fluid transport viewpoints. When both the tracers and the passive scalar evolve in tandem and closely resemble stable distributions, namely, Gaussian distributions, the underlying turbulent transport character can be recovered from the temporal scaling of the second moments of both. This local transport approach corroborates the use of passive scalar as a turbulent transport measurement. The correspondence between the local transport character and the underlying transport is quantified for different transport regimes ranging from subdiffusive to superdiffusive. This correspondence is limited to the initial time periods of the spread of both the tracers and the passive scalar in the given transport regimes.This work was supported by U.S. DOE Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265

Transport dynamics of self-consistent, near-marginal drift-wave turbulence. I. Investigation of the ability of external flows to tune the non-diffusive dynamics

The reduction of turbulent transport across sheared flow regions has been known for a long time in magnetically confined toroidal plasmas. However, details of the dynamics are still unclear, in particular, in what refers to the changes caused by the flow on the nature of radial transport itself. In Paper II, we have shown in a simplified model of drift wave turbulence that, when the background profile is allowed to evolve self-consistently with fluctuations, a variety of transport regimes ranging from superdiffusive to subdiffusive open up depending on the properties of the underlying turbulence [D. Ogata et al., Phys. Plasmas 24, 052307 (2017)]. In this paper, we show that externally applied sheared flows can, under the proper conditions, cause the transport dynamics to be diffusive or subdiffusive.This work was supported by U.S. DOE Contract No. DE-FG02-04ER54741 with the University of Alaska Fairbanks and in part by a grant of HPC resources from the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. This research was also sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2015-68265

A positioning algorithm for SPH ghost particles in smoothly curved geometries

An algorithm to place ghost particles across the domain boundary in the context of Smoothed Particle Hydrodynamics (SPH) is derived from basic principles, and constructed for several simple, three-dimensional, geometries. The performance of the algorithm is compared against the more commonly used ‘‘mirrored with respect to the local tangent plane" approach and shown to converge to it whenever the distance of the particles to the reflecting boundary is much smaller than a local measure of the surface’s curvature. The algorithm is demonstrated, tested and compared against the usual approach via simulations of a compressible flow around a cylinder, and the numerical cost of implementing it is addressed. We conclude that use of ghost particles to enforce boundary conditions is not only viable in the presence of smoothly curved boundaries, but more robust than the usual method for low-resolution scenarios.This research was sponsored in part by the DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under National Project No. ENE2015-68265. Research was also funded in part by the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC, Spain

Tracer particle transport dynamics in the diffusive sandpile cellular automaton

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.This research has been sponsored in part by Ministerio de Economía y Competitividad of Spain under Projects No. ENE2015- 68265-P and No. ENE2015-66444-R. Research also supported in part by DOE-OFES Grant No. DE-FG02-04ER5741 at University of Alaska. Sandpile simulations have been run in Uranus, a supercomputer cluster at Universidad Carlos III de Madrid (Spain) that has been funded by the Spanish Government via the national projects UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219 and ENE2012-31753

Three-dimensional linear peeling-ballooning theory in magnetic fusion devices

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions that minimize the perturbed energy and that can be solved to find the growth rate of the perturbations. This theory allows of the evaluation of 3D effects on edge plasma stability in tokamaks such as those associated with the toroidal ripple due to the finite number of toroidal field coils, the application of external 3D fields for elm control, local modification of the magnetic field in the vicinity of ferromagnetic components such as the test blanket modules in ITER, etc.This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2012-38620-C02-02 and also in part by Comunidad de Madrid Project No. S2009/ENE-1679.Publicad

Magneto-hydrodynamical nonlinear simulations of magnetically confined plasmas using smooth particle hydrodynamics (SPH)

The successful application of techniques inspired in Smoothed Particle Hydrodynamics (SPH) to magnetohydrodynamical (MHD) nonlinear simulations of magnetically confined plasmas requires the previous solution to a number of challenging issues that are still not fully resolved, namely, the construction of precise, arbitrary initial conditions in complicated geometries, the formulation of adequate boundary conditions for the magnetic field, and the correct treatment of three-dimensional toroidal boundaries of the arbitrary shape. In this paper, we present an SPH implementation of the nonlinear MHD equations that include our proposed solution to these issues and test its performance on a broad selection of nonlinear MHD problems: (1) the propagation of circularly polarized Alfven waves, (2) the occurrence of magnetic reconnection for a Harris current-sheet, and (3) the nonlinear MHD stability properties of various cylindrical pinches.This research was sponsored by DGICYT (Dirección General de Investigación Científica y Técnica) under Project No. ENE2015-68265, MINECO (Ministerio de Economía y Competitividad) under Project No. UNC313-4E-2361, and the Erasmus Mundus Program: International Doctoral College in Fusion Science and Engineering FUSION-DC

Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

The massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.This work was supported in part in the USA by Grant No. DE-FG02-04ER54741 to the University of Alaska, Fairbanks, AK, from the Office of Fusion Energy Sciences, Office of Science, United States Department of Energy. It was also supported in part at Universidad Carlos III, Madrid, Spain, by Spanish National Project No. ENE2009-12213-C03-03. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. It also took advantage of resources at the Barcelona Supercomputing Center (BSC), Centro Nacional de Supercomputación, Barcelona, Spain. One of us (Leboeuf) would particularly like to thank David Vicente from BSC and Zhengji Zhao from NERSC for their help in the porting, debugging, and optimization of UCAN2 on the mainframes at their respective centers

BCYCLIC: A parallel block tridiagonal matrix cyclic solver

13 pages, 6 figures.A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.This research has been sponsored by the US Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC. This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract DE-AC05-00OR22725.Publicad

Fourier signature of filamentary vorticity structures in two-dimensional turbulence

It is shown that coherent regions of isotropic two-dimensional (2D) turbulence can be clearly identified in the phase part of the Fourier spectrum. Certain spectral phase events are particularly prominent, and are much stronger in the range of wave numbers corresponding to the dissipation range. It is shown that these events are associated with spatially localized filamentary structures in the 2D vorticity field that historically have been related to the intermittency of dissipation. The identified phase signature provides a particularly transparent diagnostic of the temporal evolution of the coherent coupling of disparate scales in anisostropic intermittent dissipative events. These results open the possibility of using the phase of the Fourier transform as a new turbulence diagnostic that identifies and quantitatively characterizes details pertaining to dissipative events.Research supported in part by the Spanish national projects No. ENE2009-12213-C03-03, ENE2012-33219, UNC313-4E-2361 and ENE2012-31753 and the US DOE Office of Science Grants No. DE-FG02-04ER54741 and DE-FG02-89ER53291. Simulations run at the Uranus supercomputer cluster at Universidad Carlos III de Madrid