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Gyrokinetic Simulation of Energetic Particle Turbulence and Transport
Zhihong LinUniversity of California, Irvine
&
UCI: L. Chen, W. Heidbrink, A. Bierwage, I. Holod, Y. Xiao, W. Zhang
GA: M. S. Chu, R. Waltz, E. Bass, M. Van Zeeland
ORNL: D. Spong, S. Klasky
UCSD: P. H. Diamond
LLNL: C. Kamath
Frascati: F. Zonca, S. Briguglio, G. Vlad
&
US DOE SciDAC GSEP Team
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I. Motivation
Kinetic Effects of Thermal Particles on EP Physics• In a burning plasma ITER, shear Alfven wave (SAW) instability
excited by fusion products (energetic α-particle) can be dangerous to energetic particle (EP) confinement
• SAW instability, e.g., toroidal Alfven eigenmode (TAE) and energetic particle mode (EPM), has thresholds that are imposed by damping from both thermal ions and trapped electrons
• Significant damping of meso-scale (EP gyroradius ρEP) SAW via resonant mode conversion to kinetic Alfven waves (KAW)
► Finite parallel electric field
► Radial wavelengths comparable to thermal ion gyroradius ρi (micro-scale)
• Wave-particle resonances of thermal particles are important in compressible Alfven-acoustic eigenmodes: BAE & AITG
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Nonlinear Mode Coupling, Turbulence & Transport
• Effects of collective SAW instabilities on EP confinement depend on self-consistent nonlinear evolution of SAW turbulence
► Complex nonlinear phase space dynamics of EP► Complex nonlinear mode-mode couplings among multiple SAW modes
• Both nonlinear effects, in turn, depend on global mode structures and wave-particle resonances
► Nonlinear mode coupling induced by micro-scale kinetic physics
• Physics of couplings between meso-scale SAW and micro-scale drift-Alfven wave (DAW) turbulence is even more challenging
• Current nonlinear paradigm of coherent SAW cannot fully explain EP transport level observed in experiments. Possible new physics:
► Parallel electric field can break EP constant of motion, thus leads to enhanced EP transport
► KAW can propagate/spread radially► Nonlinear mode coupling
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Gyrokinetic Turbulence Approach for EP Simulation• Fully self-consistent simulation of EP turbulence and transport must
incorporate three new physics elements► Kinetic effects of thermal particles► Nonlinear interactions of meso-scale SAW modes with micro-scale kinetic
effects and wave-particle resonances► Cross-scale couplings of meso-micro turbulence
• Large dynamical ranges of spatial-temporal processes require global simulation codes efficient in utilizing massively parallel computers at petascale level and beyond
• Therefore, studies of EP physics in ITER burning plasmas call for a new approach of global nonlinear gyrokinetic simulation
• US SciDAC GSEP (Gyrokinetic Simulation of Energetic Particle Turbulence and Transport): develop gyrokinetic EP simulation codes based on complementary PIC GTC & continuum GYRO
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II. Gyrokinetic Simulation Using GTC & GYRO
GTC Summary• Gyrokinetic Toroidal Code: global,
particle-in-cell, massively parallel
• GTC physics module developed for specific application► Perturbative (df) ions: momentum transport► Fluid-kinetic hybrid electron: electromagnetic turbulence with kinetic
electrons► Multiple ion species► Global field-aligned mesh► Guiding center Hamiltonian in magnetic coordinates► General geometry MHD equilibrium using spline fit► Fokker-Planck collision operators
• More than 40 journal publications. Many more GTC papers published by computational scientists
http://gk.ps.uci.edu/GTC
Lin et al, Science98
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Nishimura, Lin & Wang, PoP07; TTF08
GTC Simulation Found Generation of Toroidal Frequency Gap and Excitation of TAE by Energetic
Particle Pressure Gradients
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GYRO Summary• GYRO is a flexible and physically comprehensive df gyrokinetic code
• Pre-run data tools & post-run analysis graphics code VuGYRO
• New TGYRO driver code is a steady state gyrokinetic transport code for analyzing experiments or predicting ITER performance
• More than >10 regular users at >7 institutions and >30 publications (with >7 first authors); parameter scan transports database +400 runs.
• Documented (publications & manuals): http://fusion.gat.com/theory/Gyro
• nonlocal global (full or partial torus) or local flux-tube (cyclic or 0 BC)• equilibrium ExB and profile stabilization• transport at fixed profile gradients or fixed flow• electrostatic or electromagnetic• multi-species ion (impurities or fast particles) and electrons• covers all turbulent transport channels: energy(plus e-i exchange), plasma
& impurity, momentum, pol. rotation shift, current-voltage (small dynamos), ExB & magnetic flutter, ITG/TEM/ETG; also has neoclassical driver
• electron pitch angle collisions and ion-ion (all conserving) collisions• “s-a” circular or Miller shaped (real) geometry• reads experimental data (or selected) input profiles and transport flows
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TAE Simulations Using GYRO in Flux Tube Geometry Verifies Predictions from MHD Theories
• Dependence of ω and γ on equilibrium q and β values verified• Dependence of ω and γ on temperature and density gradient of α’s observed• Growth rate γ reduced when ω falls outside of gap indicating continuum
damping • Modes other than TAE’s found, could be due to parallel electric fields
D=
an
nr
41 2 3
cs
a
n=1
2 34
65
vA
2qR
Maxwellian Distribution
Chu & Waltz, TTF08
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III. GSEP Verification
Code Reference Capability Role in verification
GTC Lin et al, Science 281, 1835 (1998)
Global, gyrokinetic, turbulence
Production codes for EP simulations; Benchmark between GTC and GYRO
GYRO Candy and Waltz, J. Comput. Phys. 186, 545 (2003)
HMGC Briguglio et al, Phys. Plasmas 5, 301 (1998)
Global, hybrid MHD-gyrokinetic turbulence
Nonlinear benchmark with GTC & GYRO
NOVA-K
Cheng, Phys. Report 211, 1 (1992)
Global, linear eigenmode
Linear benchmark with GTC & GYRO
TAEFL/AE3D
Spong et al, Phys. Plasmas 10, 3217 (2003)
AWECS Bierwage and Chen, Comm. Comput. Phys.,2008
Local, linear gyrokinetic PIC
• First linear benchmark case using GTC, GYRO, HMGC & TAEFL• In initial simulations, all find gap modes; agree within 20%
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Benchmarking In Progress – Initial Comparisons Show Reasonable Agreement
Example of n = 3 mode comparison between GTC (green) and TAEFL (blue)
Typical TAE n=4 mode structures for
benchmark caseFrequency gap structures for
benchmark case
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Nonlinear Global Gyrokinetic/MHD Hybrid Code HMGC
• Established EP code HMGC deployed for linear/nonlinear benchmark and for initial physics studies
Vlad et al, IAEA08, TH/5-1
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Fundamental constituents Derived Observables
Primacy hierarchy
Linear SAW wave
Nonlinear saturation
Transport Scaling Trend Statistics
Observable Polarization, structure, frequency, threshold
Spectral intensity, bispectra, zonal flows/fields
EP PDF, transport
Similarity experiment
ITPA database
Agent/ mechanism
EP spatial gradient, velocity anisotropy
Wave-wave, wave-particle interaction
Cross-phase, relaxation
Dimensionless scaling
Inter-machine
IV. GSEP Validation• Validation targets DIII-D shot #122177 (2005, ITPA EP database) &
#132707 (2008, GSEP-dedicated experiment)• First step of validation is linear simulation using benchmark suite• Next step will be nonlinear simulation using GTC, GYRO & HMGC
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Validation Targets DIII-D Shot #122117 (2005): Well Diagnosed with Observed TAE and RSAE Activities
Heidbrink et al, PRL07; NF08
Anomalous Loss of Energetic Particles Observed
DIII-D
Shot #122117
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Simulations of DIII-D Shot #122117
Linear dispersion and frequency gap structure from TAEFL simulation of DIII-D shot #122117
• TAEFL simulations found 3 modes: EAE at 208 kHz, RSAE at 53 kHz, TAE at 90 kHz.
• RSAE and TAE are consistent with the frequency range of coherent modes that were observed experimentally.
• RSAE converts to a TAE for q=4.15 and 4.4 accompanied by large (~factor of 2) frequency upshifts as observed experimentally.
Spong et al, IAEA08, TH/3-4
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DIII-D Shot #132707 (2008) Dedicated to GSEP
TAE RSAE
BAAE
#132707 t=725 ms
• Circular (~1.15) version of 122117 created for ease of comparison to codes and theory
• Discharge has very similar AE activity to 122117
• Many diagnostic improvements have been made since shot #122117 (2005) including more Fast Ion D-alpha channels and a linear BES array
Van Zeeland et al, IAEA08, EX/6-2
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Simulations of DIII-D Shot #132707
HMGC simulations
Real frequency, growth rate, and frequency gap structure of n=3 mode from TAEFL simulation
Radial profile of TAE mode poloidal harmonics in GYRO simulation
Power spectrum P(w,r) shows mode activity near qmin (r=0.4) after nonlinear saturation. Two qmin values are used for ensitivity studies.
Radial fast ion density profile at the beginning of simulation and after nonlinear saturation.
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V. Energetic Particle Transport by Microturbulence• Recent tokamak experiments revive interest of fast ions transport induced by
microturbulence [Heidbrink & Sadler, NF94; Estrada-Mila et al, PoP06; Gunter et al, NF07]
• Radial excursion of test particles found to be diffusive in GTC global simulation of ion temperature gradient (ITG) turbulence
• Detailed studies of diffusivity in energy-pitch angle phase space► Diffusivity drops quickly at higher particle energy due to averaging effects of larger
Larmor radius/orbit width, and faster wave-particle decorrelation
Zhang, Lin & Chen, PRL 101, 095001 (2008)
Diffusivity driven by ITG turbulence for isotropic, mono-energetic particles.
Diffusivity as a function of particle energy & pitch angle.