19th IAEA Fusion Energy Conference Tuesday, October 15, 2002 Paper: TH/P1-13 Electromagnetic Turbulence Simulations with Kinetic Electrons from the the Summit Framework Scott Parker and Yang Chen University of Colorado, Boulder Bruce Cohen, Andris Dimits, Bill Nevins and Dan Shumaker Lawrence Livermore National Laboratory Jean-Noel Leboeuf and Viktor Decyk University of California, Los Angeles Questions/comments welcome: sparker@colorado.edu
Summit Framework: open source software environment for gyrokinetic turbulence particle simulations Recent 3D toroidal electromagnetic (δb ) kinetic electron results reported Moderate β significantly reduces energy transport Outline 1) Electromagnetic kinetic electron results from the Summit Framework - Linear benchmarks - Nonlinear results - Collisional effects - Zonal flow dynamics - Wavelength spectra - How important is the mass ratio? - Convergence studies 2) Summit Framework - Basic idea - Why bother? - Current status - Quasi-ballooning coordinates
Growth Rate GS2 GYRO γ a / c s Summit Linear comparison between GS2, GYRO and Summit with kinetic electrons and δb ω a / c s β (%) Real Frequency - Kinetic electrons increase growth rate (trapped-electron drive) - Increasing β is stabilizing - Growth rate "goes through the roof" when kinetic balloon threshold is crossed β (%) GYRO/GS2 results from Candy&Waltz JCP (2002)
Summit shows a decrease in χ i for increasing β when below ballooning limit Puzzle: Why do turbulence simulations give transport levels that are greater than experimental values? e.g. D. Ross Sherwood 1C47 (2002) (possibly global effects, inaccuracies in profile measurements, sensitivity to critical gradients, etc.) Plausible solution: Experiments operate in this low transport region just below the kinetic ballooning threshold Growth Rate Summit Results: Three-Dimensional Toroidal Kinetic Electrons Electromagnetic e-i Collisions Energy Flux γ a / c s χ i / c s ρ s β=0.2% β=0.01% adiabatic e's m i / m e = 1836 ν ei L n /c s = 0.1 β (%) β = µ 0 n T e / B 2 = β exp / 4 t c s / L n
Collisonality reduces trapped electron drive and is stabilizing γ a / cs GYRO GS2 Summit ν ei a / cs GYRO/GS2 results from Candy&Waltz JCP (2002)
Critical gradient is lower with kinetic electrons, sub-critical region still exists. 2 χ i c s ρ s /L n γ kinetic e's γ L n /c s χ i kinetic e's R/L T χ i with adiabatic electrons
Residual level and damping of zonal flows are not changed significantly by kinetic electron physics Comparison with Rosenbluth-Hinton Zonal flow damping with and without kinetic electrons φ final / φ initial eφ/te h = (r/r) 1/2 / q 2 t v ti / qr Rosenbluth and Hinton PRL 80 724 (1998)
Kinetic vs. adiabtic e wavelength spectra are similar - Kinetic e spectra has larger amplitude (more unstable due to trapped e's) - Kinetic spectra and has larger k r S(kx) A. U. adiabatic e's Kinetic e's S(ky) kx ρi radial wave number ky ρi y - other perp. direction (zonal flows are removed for these diagnostics)
Scan of mass ratio dependence with kinetic electrons at very low-β Cyclone base case (typical H-mode parameters) Mass ratio dependence for these parameters is weak for m i /m e greater than 400 χ i / c s ρ s ( m i / m e ) 1/2
Results are well-converged with respect to particle number, timestep and grid size Box size convergence appears ok, doubling the box does not change results significantly Convergence with respect to particle number Bursty energy flux observed when approaching the zero collisionality limit Not unexpected from the entropy balance equation1 or the balance between dissipation and flux 1 Hu and Krommes PoP 1 3211 (1994) e-i collisionality scan of energy flux χ i / c s ρ s 8M, 64x64x32 16M, 128x128x32 32M, 128x128x32 (particles, grid) χ i / c s ρ s ν ei L n /c s = 0.0 ν ei L n /cs = 0.05 ν ei L n /c s = 0.5 t c s / L n t c s / L n
Summit: "Summit is an open-source framework for both local and global massively parallel gyrokinetic turbulence simulations with kinetic electrons and electromagnetic perturbations. Summit is part of the Plasma Microturbulence SciDAC Project." from: www.nersc.gov/scidac/summit SciDAC PMP Summit
Current work, features, physics Realistic magnetic equilibrium (Leboeuf, Dimits, Shumaker) Framework design, design of objects and methods (Decyk) Quasi-ballooning coordinates (Dimits) Electron fluid hybrid model with kinetic closure, electromagnetic, moderate beta (Cohen, Parker) Full electron dynamics, both electrostatic and electromagnetic (Chen, Parker, Cohen) e-i and i-i collisions (Chen) Future work Global effects (Leboeuf, Dimits, Shumaker) Compressional component to B (Chen, Parker, Cohen) Particle-continuum hybrid method (Vadlamani, Parker)
Why bother? GK simulators are really driven by solving unsolved problems. GK simulators are forced into a routine of continually adding physics to keep their code competitive. If there are 6 codes, that means 5/6 times the scientist is solving a problem with an already existing solution. Solution A software framework where the scientist can add his/her physics and tap existing features when/if needed. Pitfalls All gk simulators want to solve the same unsolved problem. (not an issue) Why should I share my code features? (not an issue) My existing code runs great, what is the (short term) payoff to install my features and get running within the framework? (big issue) One massive code, little inovation, no cross-checks. (not an issue)
Integration into framework is gradual, benchmarking at every step! LLNL/CU/UCLA Gyrokinetic Framework! All codes should use this main program! and call input.f at this time program main_program...!----------------------------------------------------! initilization call mpi_setup call timer_setup call initialize(runsteps,nt) if (start) then call loader_wrapper else call restart_wrapper endif!-------------------------------------------------------! main time loop ipush=1 do timestep=1,runsteps nt = nt + 1 t = (nt - 1)*dt call accumulate call poisson(timestep-1,ipush) call efield! predictor push ipush=0 call push_wrapper(timestep,ipush) call accumulate call poisson(timestep,ipush)...
T oroidal-poloidal dis cretization Quasiballooning Coordinates θ ζ B - almost field-aligned - avoids grid discontinuities in field line direction - fixed finite-difference stencil and particle shape in what can be a highly twisted, nonorthogonal computational domain - general geometry - global implementation (annular geometry) F ield-aligned-coordinate dis cretization z B grid is field-aligned, but grid discontinuity occurs at ends of the box along z (magnetic field line does not connect back on itself after going once around poloidally) y Quas iballooning dis cretization z' B grid is almost aligned and grid cells at the ends of the box along z' exactly match y'
The quasiballooning radial discretization uses points at the same physical toroidal angle as the reference point. - isotropic particle shapes - isotropic mesh-based smoothing ζ θ = θ 0 V t = 0 0 ζ θ θ 0 V t 0 0 field-aligned coordinates (β = const.) quasiballooning i-1 i i+1 r i-1 i i+1 r