Jeff Candy

An Eulerian gyrokinetic-Maxwell solver

In this report we present a time-explicit, Eulerian numerical scheme for the solution of the nonlinear gyrokinetic-Maxwell equations. The treatment of electrons is fully drift-kinetic, transverse electromagnetic fluctuations are included, and profile variation is allowed over an arbitrary radial annulus. The code, gyro, is benchmarked against analytic theory, linear eigenmode codes, and nonlinear electrostatic gyrokinetic particle-in-cell codes. We have attempted preliminary finite-β calculations in the range β/βcrit= [0.0, 0.5] for a reference discharge. Detailed diagnostic data is presented for these simulations, along with a number of caveats which reflect the uncharted nature of the parameter regime.

Tokamak profile prediction using direct gyrokinetic and neoclassical simulation

Tokamak transport modeling scenarios, including ITER [ITER Physics Basis Editors, Nucl. Fusion 39, 2137 (1999)] performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes (local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles). Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (200...

A correlation electron cyclotron emission diagnostic and the importance of multifield fluctuation measurements for testing nonlinear gyrokinetic turbulence simulations

A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w(o) approximately 1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k(theta) < or = 1.8 cm(-1) and k(r) < or = 4 cm(-1), relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5 < r/a < 0.9, increase with radius from approximately 0.5% to approximately 2%, similar to density fluctuations that are measured simultaneously with beam emission spectroscopy. After incorporating synthetic diagnostics to effectively filter the code output, the simulations reproduce the characteristics of the turbulence and transport at one radial location r/a = 0.5, but not at a second location, r/a = 0.75. These results illustrate that measurements of the profiles of multiple fluctuating fields can provide a significant constraint on the turbulence models employed by the code.

GYRO: A 5-D Gyrokinetic-Maxwell Solver

GYRO solves the 5-dimensional gyrokinetic-Maxwell equations in shaped plasma geometry, using either a local (fluxtube) or global radial domain. It has been ported to a variety of modern MPP platforms including a number of commodity clusters, IBM SPs and the Cray X1. We have been able to quickly design and analyze new physics scenarios in record time using the Cray X1: (i) transport barrier studies (Phys. Plasmas 11 (2004) 1879), (ii) the local limit of global simulations (Phys. Plasmas 11 (2004) L25), (iii) kinetic electron and finite-beta generalizations of a community-wide benchmark case, and (iv) impurity transport with application to fuel separation in burning D-T plasmas (to be submitted to Nuclear Fusion). We report on recent physics progress and studies. Further, we discuss GYRO performance across several architectures.

Isotope mass and charge effects in tokamak plasmas

The effect of primary ion species of differing charge and mass - specifically, deuterium, hydrogen, and helium - on instabilities and transport is studied in DIII-D plasmas through gyrokinetic simulations with GYRO [J. Candy and E. Belli, General Atomics Technical Report No. GA-A26818, 2010]. In linear simulations under imposed similarity of the profiles, there is an isomorphism between the linear growth rates of hydrogen isotopes, but the growth rates are higher for Z > 1 main ions due to the appearance of the charge in the Poisson equation. On ion scales the most significant effect of the different electron-to-ion mass ratio appears through collisions stabilizing trapped electron modes. In nonlinear simulations, significant favorable deviations from pure gyro-Bohm scaling are found due to electron-to-ion mass ratio effects and collisions. The presence of any non-trace impurity species cannot be neglected in a comprehensive simulation of the transport; including carbon impurity in the simulations caused a dramatic reduction of energy fluxes. The transport in the analyzed deuterium and helium discharges could be well reproduced in gyrokinetic and gyrofluid simulations while the significant hydrogen discrepancy is the subject of ongoing investigation.

Influence of magnetic shear on impurity transport

The magnetic shear dependence of impurity transport in tokamaks is studied using a quasilinear fluid model for ion temperature gradient (ITG) and trapped electron (TE) mode driven turbulence in the collisionless limit and the results are compared with nonlinear gyrokinetic results using GYRO [J. Candy and R. E. Waltz, J. Comput. Phys 186, 545 (2003)]. It is shown that the impurity transport is sensitive to the magnetic shear, in particular for weak, negative, and large positive shear where a strong reduction of the effective impurity diffusivity is obtained. The fluid and gyrokinetic results are in qualitative agreement, with the gyrokinetic diffusivities typically a factor 2 larger than the fluid diffusivities. The steady state impurity profiles in source-free plasmas are found to be considerably less peaked than the electron density profiles for moderate shear. Comparisons between anomalous and neoclassical transport predictions are performed for ITER-like profiles [R. Aymar, P. Barabaschi, and Y. Shimo...

A high-accuracy Eulerian gyrokinetic solver for collisional plasmas

We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker-Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order conservative upwind scheme is used to permit high-accuracy electromagnetic simulation even in the limit of very high plasma β and vanishingly small perpendicular wavenumber, k ź ź 0 . To our knowledge, this is the first pseudospectral implementation of the collision operator in a gyrokinetic code. We show that the new solver agrees closely with GYRO in the limit of weak Lorentz collisions, but gives a significantly more realistic description of collisions at high collision frequency. The numerical methods are also designed to be efficient and scalable for multiscale simulations that treat ion-scale and electron-scale turbulence simultaneously.

Concurrent, parallel, multiphysics coupling in the FACETS project

FACETS (Framework Application for Core-Edge Transport Simulations), is now in its third year. The FACETS team has developed a framework for concurrent coupling of parallel computational physics for use on Leadership Class Facilities (LCFs). In the course of the last year, FACETS has tackled many of the difficult problems of moving to parallel, integrated modeling by developing algorithms for coupled systems, extracting legacy applications as components, modifying them to run on LCFs, and improving the performance of all components. The development of FACETS abides by rigorous engineering standards, including cross platform build and test systems, with the latter covering regression, performance, and visualization. In addition, FACETS has demonstrated the ability to incorporate full turbulence computations for the highest fidelity transport computations. Early indications are that the framework, using such computations, scales to multiple tens of thousands of processors. These accomplishments were a result of an interdisciplinary collaboration among computational physics, computer scientists and applied mathematicians on the team.

First results from core-edge parallel composition in the FACETS project

FACETS (Framework Application for Core-Edge Transport Simulations), now in its second year, has achieved its first coupled core-edge transport simulations. In the process, a number of accompanying accomplishments were achieved. These include a new parallel core component, a new wall component, improvements in edge and source components, and the framework for coupling all of this together. These accomplishments were a result of an interdisciplinary collaboration among computational physics, computer scientists, and applied mathematicians on the team.

Turbulent momentum transport due to neoclassical flows

Intrinsic toroidal rotation in a tokamak can be driven by turbulent momentum transport due to neoclassical flow effects breaking a symmetry of turbulence. In this paper we categorize the contributions due to neoclassical effects to the turbulent momentum transport, and evaluate each contribution using gyrokinetic simulations. We find that the relative importance of each contribution changes with collisionality. For low collisionality, the dominant contributions come from neoclassical particle and parallel flows. For moderate collisionality, there are non- negligible contributions due to neoclassical poloidal electric field and poloidal gradients of density and temperature, which are not important for low collisionality.