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  1. MPI allows applications to treat processes as a logical collection of integer ranks for each MPI communicator, while internally translating these logical ranks into actual network addresses. In current MPI implementations the management and lookup of such network addresses use memory sizes that are proportional to the number of processes in each communicator. In this paper, we propose a new mechanism, called AV-Rankmap, for managing such translation. AV-Rankmap takes advantage of logical patterns in rank-address mapping that most applications naturally tend to have, and it exploits the fact that some parts of network address structures are naturally more performance criticalmore » than others. It uses this information to compress the memory used for network address management. We demonstrate that AV-Rankmap can achieve performance similar to or better than that of other MPI implementations while using significantly less memory.« less
  2. This project funding supported approximately 74 percent of a Ph.D. graduate student, not including costs of travel and supplies. We had a highly successful research project including the development of a second-order implicit electromagnetic kinetic ion hybrid model [Cheng 2013, Sturdevant 2016], direct comparisons with the extended MHD NIMROD code and kinetic simulation [Schnack 2013], modeling of slab tearing modes using the fully kinetic ion hybrid model and finally, modeling global tearing modes in cylindrical geometry using gyrokinetic simulation [Chen 2015, Chen 2016]. We developed an electromagnetic second-order implicit kinetic ion fluid electron hybrid model [Cheng 2013]. As a firstmore » step, we assumed isothermal electrons, but have included drift-kinetic electrons in similar models [Chen 2011]. We used this simulation to study the nonlinear evolution of the tearing mode in slab geometry, including nonlinear evolution and saturation [Cheng 2013]. Later, we compared this model directly to extended MHD calculations using the NIMROD code [Schnack 2013]. In this study, we investigated the ion-temperature-gradient instability with an extended MHD code for the first time and got reasonable agreement with the kinetic calculation in terms of linear frequency, growth rate and mode structure. We then extended this model to include orbit averaging and sub-cycling of the ions and compared directly to gyrokinetic theory [Sturdevant 2016]. This work was highlighted in an Invited Talk at the International Conference on the Numerical Simulation of Plasmas in 2015. The orbit averaging sub-cycling multi-scale algorithm is amenable to hybrid architectures with GPUS or math co-processors. Additionally, our participation in the Center for Extend Magnetohydrodynamics motivated our research on developing the capability for gyrokinetic simulation to model a global tearing mode. We did this in cylindrical geometry where the results could be benchmarked with existing eigenmode calculations. First, we developed a gyrokinetic code capable of simulating long wavelengths using a fluid electron model [Chen 2015]. We benchmarked this code with an eigenmode calculation. Besides having to rewrite the field solver due to the breakdown in the gyrokinetic ordering for long wavelengths, very high radial resolution was required. We developed a technique where we used the solution from the eigenmode solver to specify radial boundary conditions allowing for a very high radial resolution of the inner solution. Using this technique enabled us to use our direct algorithm with gyrokinetic ions and drift kinetic electrons [Chen 2016]. This work was highlighted in an Invited Talk at the American Physical Society - Division of Plasma Physics in 2015.« less
  3. Final Technical Report: Center for Plasma Edge Simulation (CPES) Principal Investigator: Scott Parker, University of Colorado, Boulder Description/Abstract First-principle simulations of edge pedestal micro-turbulence are performed with the global gyrokinetic turbulence code GEM for both low and high confinement tokamak plasmas. The high confinement plasmas show a larger growth rate, but nonlinearly a lower particle and heat flux. Numerical profiles are obtained from the XGC0 neoclassical code. XGC0/GEM code coupling is implemented under the EFFIS (“End-to-end Framework for Fusion Integrated Simulation”) framework. Investigations are underway to clearly identify the micro-instabilities in the edge pedestal using global and flux-tube gyrokinetic simulationmore » with realistic experimental high confinement profiles. We use both experimental profiles and those obtained using the EFFIS XGC0/GEM coupled code framework. We find there are three types of instabilities at the edge: a low-n, high frequency electron mode, a high-n, low frequency ion mode, and possibly an ion mode like kinetic ballooning mode (KBM). Investigations are under way for the effects of the radial electric field. Finally, we have been investigating how plasmas dominated by ion-temperature gradient (ITG) driven turbulence, how cold Deuterium and Tritium ions near the edge will naturally pinch radially inward towards the core. We call this mechanism “natural fueling.” It is due to the quasi-neutral heat flux dominated nature of the turbulence and still applies when trapped and passing kinetic electron effects are included. To understand this mechanism, examine the situation where the electrons are adiabatic, and there is an ion heat flux. In such a case, lower energy particles move inward and higher energy particles move outward. If a trace amount of cold particles are added, they will move inward.« less
  4. Cited by 2
  5. We have discovered a possible "natural fueling" mechanism in tokamak fusion reactors using large scale gyrokinetic turbulence simulation. In the presence of a heat flux dominated tokamak plasma, cold ions naturally pinch radially inward. If cold DT fuel is introduced near the edge using shallow pellet injection, the cold fuel will pinch inward, at the expense of hot helium ash going radially outward. By adjusting the cold DT fuel concentration, the core DT density profiles can be maintained. We have also shown that cold source ions from edge recycling of cold neutrals are pinched radially inward. This mechanism may bemore » important for fully understanding the edge pedestal buildup after an ELM crash. Work includes benchmarking the gyrokinetic turbulence codes in the electromagnetic regime. This includes cyclone base case parameters with an increasing plasma beta. The code comparisons include GEM, GYRO and GENE. There is good linear agreement between the codes using the Cyclone base case, but including electromagnetics and scanning the plasma beta. All the codes have difficulty achieving nonlinear saturation as the kinetic ballooning limit is approached. GEM does not saturate well when beta gets above about 1/2 of the ideal ballooning limit. We find that the lack of saturation is due to the long wavelength k{sub y} modes being nonlinearly pumped to high levels. If the fundamental k{sub y} mode is zeroed out, higher values of beta nonlinearly saturate well. Additionally, there have been studies to better understand CTEM nonlinear saturation and the importance of zonal flows. We have continued our investigation of trapped electron mode (TEM) turbulence. More recently, we have focused on the nonlinear saturation of TEM turbulence. An important feature of TEM is that in many parameter regimes, the zonal flow is unimportant. We find that when zonal flows are unimportant, zonal density is the dominant saturation mechanism. We developed a simple theory that agrees with the simulation and predicts zonal density generation and feedback stabilization of the most unstable mode even in the absence of zonal flow. We are using GEM to simulate NSTX discharges. We have also done verification and validation on DIII-D. Good agreement with GYRO and DIII-D flux levels were reported in the core region.« less
  6. This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electronmore » modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of parallel shear flows, which can be quite strong in NSTX. Recent long-time simulations of electron temperature gradient driven turbulence, show that zonal flows slowly grow algebraically via the Rosenbluth-Hinton random walk mechanism. Eventually, the zonal flow gets to a level where it shear suppresses the turbulence. We have demonstrated this behavior with Cyclone base-case parameters, except with a 30% lower temperature gradient. We can demonstrate the same phenomena at higher gradients, but so far, have been unable to get a converged result at the higher temperature gradient. We find that electron ion collisions cause the zonal flows to grow at a slower rate and results in a higher heat flux. So, far all ETG simulations that come to a quasi-steady state show continued build up of zonal flow, see it appears to be a universal phenomena (for ETG). Linear and nonlinear simulations of Collisional and Collisionless trapped electron modes are underway. We find that zonal flow is typically important. We can, however, reproduce the Tannert and Jenko result (that zonal flow is unimportant) using their parameters with the electron temperature three times the ion temperature. For a typical weak gradient core value of density gradient and no temperature gradient, the CTEM is dominant. However, for a steeper density gradient (and still no temperature gradient), representative of the edge, higher k drift-waves are dominant. For the weaker density gradient core case, nonlinear simulations using GEM are routine. For the steeper gradient edge case, the nonlinear fluctuations are very high and a stationary state has not been obtained. This provides motivation for the particle-continuum algorithm. We also note that more physics, e.g. profile variation and equilibrium ExB shear flow should be significantly stabilizing, making such simulations feasible using standard delta-f techniques. This research is ongoing.« less
  7. The linear stability properties of the microtearing mode are investigated in the edge and core regimes of the National Spherical Torus Experiment (NSTX) using the particle-in-cell method based gyrokinetic code GEM. The dependence of the mode on various equilibrium quantities in both regions is compared. While the microtearing mode in the core depends upon the electron-ion collisions, in the edge region, it is found to be weakly dependent on the collisions and exists even when the collision frequency is zero. The electrostatic potential is non-negligible in each of the cases. It plays opposite roles in the core and edge ofmore » NSTX. While the microtearing mode is partially stabilized by the electrostatic potential in the core, it has substantial destabilizing effect in the edge. In addition to the spherical tokamak, we also study the microtearing mode for parameters relevant to the core of a standard tokamak. The fundamental characteristics of the mode remain the same; however, the electrostatic potential in this case is destabilizing as opposed to the core of NSTX. The velocity dependence of the collision frequency, which is crucial for the mode to grow in slab calculations, is not required to destabilize the mode in toroidal devices.« less
  8. This paper introduces a technique for analyzing time integration methods used with the particle weight equations in δf method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes [1,2]. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for δf simulations using our weight equation analysis and for full-f simulations usingmore » the method of Langdon. It is found that the δf method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the δf method, as well as understanding differences between δf and full-f approaches to plasma simulation.« less
  9. The general geometry of the experimental tokamak magnetic equilibrium is implemented in the global gyrokinetic simulation code GEM. Compared to the general geometry, the well used Miller parameterization of the magnetic equilibrium is a good approximation in the core region and up to the top of the pedestal. Linear simulations indicate that results with the two geometries agree for r/a ≤ 0.9. However, in the edge region, the instabilities are sensitive to the magnetic equilibrium in both the L-mode and the H-mode plasmas. A small variation of the plasma shaping parameters leads to large changes to the edge instability.

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