GTC Simulation of Turbulence and Transport in Tokamak Plasmas

Transcription

1 GTC Simulation of Turbulence and Transport in Tokamak Plasmas Z. Lin University it of California, i Irvine, CA 92697, USA and GPS-TTBP Team Supported by SciDAC GPS-TTBP, GSEP & CPES

2 Motivation First-principles simulations progress from code development & verification, to fundamental physics discovery & validation However, when directly comparing to experiments, first-principles simulations often short of a complete description of a complex system, e.g., radial variations of turbulence and transport, or nonlinear bifurcations for ITB and L-H transition in tokamak plasma How realistic is it to validate first-principles simulations by comparing with experiments? Validating transport models faces its own difficulty: model qualification [Terry et al, 2008] Alternate: First-principles simulations for validating transport models Validity of quasilinear (QLT) Treatment of nonlocality in turbulence and transport

3 GTC Simulation of Physics Basis for Transport Modeling Comprehensive e statistical s analysis a s of spatial a and temporal scales in GTC simulation of microturbulence to test validity of quasilinear theory (QLT) underlying existing transport models [Lin et al, PRL99, (2007)] QLT verified for electron transport in electron temperature gradient (ETG) turbulence and ion transport in ion temperature gradient (ITG) turbulence Instability driven by resonant particles; Overlap of phase space islands leads to diffusive radial scattering of resonant particles Nonlinear wave-particle decorrelation regulates transport; ITG saturates via zonal flow shearing; ETG via spectral cascade by nonlinear toroidal coupling QLT not verified for electron transport in ITG and ion transport in CTEM Validity of QLT for collisionless i l trapped electron (CTEM) turbulence? Zonal flow regulates saturation and transport in CTEM with Cyclone-like parameters Detuning of toroidal o precessional resonance weak; Ballistic propagation o of fluctuations and electron transport observed in simulation [Xiao & Lin, this meeting]

4 GTC Physics Modules UCI Perturbative (δf) method for ions Fluid-kinetic hybrid electron model for electrons Collisionless trapped electron mode (CTEM) turbulence Electromagnetic turbulence with kinetic electrons Shear Alfven wave (SAW) excited by energetic particle Multi-species via OO Fortran Energetic particle diffusion by microturbulence Guiding center Hamiltonian in magnetic coordinates Global field-aligned mesh: truly global geometry General geometry MHD equilibrium using spline fit Fokker-Planck collision operators via Monte-Carlo method

5 GTC Computational Methods UCI Finite difference & finite element elliptic solvers Iterative method for electrostatic simulation Sparse matrix solver (PETSc) )for direct solver Pade approximation & integral gyrokinetic Poisson equation Multi-level l l parallelism li Particle-field domain-decomposition: uni-directional MPI MPI-based particle decomposition Loop-level parallelization using OpenMP: multi-core PIC optimization: electron sub-cycling, vectorization Statistical analysis of fluctuations/particles, and noise control [Holod & Lin, PoP2007] Visualization of 3D fluid and 5D particle data

6 Fluid-kinetic Hybrid Electron Model in GTC UCI Electron response expanded using δ=(m δ 1/2 e /m i ) [Lin & Chen, PoP2001] Lowest order response adiabatic: massless fluid electron Remove collisionless tearing mode and its well-known numerical difficulties Recover MHD equations when all kinetic effects suppressed; allow δe Higher order response treats kinetic effects Retain wave-electron resonance & magnetically trapped electrons Reduce electron noise and relax Courant condition Penalty: no inductive δe (k =0), i.e., ie nocollisionless tearing mode Model treats rigorously all other k =0 modes: electrostatic δe, magnetic δb, zonal flows/fields, all ideal & resistive MHD modes Model optimal for drift & Alfvenic turbulence on ρ i scales Electrostatic ITG/CTEM simulation: linear [Rewoldt, Lin & Idomura, CPC2007], nonlinear [Lin et al, PPCF2007] Toroidal electromagnetic formulation & simulation of drift & Alfven waves [Nishimura, Lin & Wang, PoP2007]

7 Transport Driven by Local Fluctuation Intensity GTC comparative studies of ITG, ETG & CTEM turbulence Transport proportional to intensity ITG & ETG transport diffusive CTEM? Is QLT valid? Experimental test? ITG ETG CTEM

8 Transport of passive species is non-resonant Passing electrons adiabatic in ITG mode; Trapped electrons enhance ITG instability by NOT responding to ITG mode [Lin et al, PPCF2007] CTEM di driven by precessional resonance of ftrapped electrons; saturated by zonal flows for parameters used in simulation Electron transport by ITG & Ion transport by CTEM: non-resonant χ / (δφ) 2 ITG CTEM ion electron

9 Eddy Mixing or Wave-particle Decorrelation? GTC simulations: while saturation can be understood in the context of fluid processes, kinetic processes related to instability drive often regulate the transport of active species [Lin et al, PoP2005] Instability Drive Electron temperature gradient (ETG) Electron parallel resonance Ion temperature gradient (ITG) Ion parallel resonance Collisionless trapped electron mode (CTEM) Trapped electron precessional resonance Saturation Nonlinear toroidal Zonal flows Zonal flows coupling Turbulence structure Active species heat transport Radial streamers Isotropic Isotropic Wave-particle decorrelation Wave-particle decorrelation Precessional resonance de-tuning? Eddy mixing?

10 Relevant Time Scales in ITG/ETG/CTEM Turbulence 4χ e 2 δ v r τ wp = 3 1 τ = Δkv τ τ τ = rb eddy τ auto e s θ k θ e 2 4Lr = 3χ e Lr = δ v r χ Effective wave-particle decorrelation time Parallel decorrelation time (particle streaming across wave fields; independence of amplitude) Radial turbulence scattering time (Diffusion across radial width of m-harmonics) Resonant broadening time (Diffusion across radial streamer length) Eddy turnover time (Streamer rotation) Auto-correlation time (Fluid terminology) 1/τ s = rr v ZF Inverse of zonal flow shearing rate 1/ γ Linear growth time

11 Analysis of Turbulence Time Scales: Key to QLT Validity Condition for validity of quasilinear theory y(q (QLT) Wave-particle decorrelation time shorter than fluid auto-correlation time Overlap of phase space islands leads to diffusive process QLT verified for electron transport in ETG turbulence and ion transport in ITG turbulence QLT not verified for transport of electron in ITG and ion in CTEM Weak detuning of CTEM precessional resonance; Validity of QLT?

12 GTC Simulation of Nonlocality in Turbulent Transport ITG fluctuations: ti isotropic i eddies due to zonal flow shearing ITG transport proportional to local fluctuation intensity ITG transport scaling: gradual transition from Bohm to gyro-bohm Transport diffusive & driven locally [Lin et al, PRL2002] Turbulence spreading controls intensity it nonlocally ll [Lin & Hahm, PoP2004] P2004] Validating turbulence spreading in transport models?

13 CTEM Nonlinear Bursting & Spreading Burst originates at maximal drive, spreading both inward & outward Inward spreading ballistic with a speed close to drift velocity How to incorporate non-diffusive i process in transport t models? Ion transport Electron transport χ i χ e r/ρ i r/ρ i time (1/γ) time (1/γ)