TH/7-2 Radial Localization of Alfven Eigenmodes and Zonal Field Generation Z. Lin University of California, Irvine Fusion Simulation Center, Peking University
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Radial Localization of Alfven Eigenmodes and Zonal Field Generation Z. Lin University of California, Irvine Fusion Simulation Center, Peking University Z. X. Wang, W. W. Heidbrink, I. Holod, J. McClenaghan, UCI H. S. Zhang, Peking University W. J. Deng, B. Tobias, Princeton Plasma Physics Laboratory M. A. Van Zeeland, General Atomics M. E. Austin, University of Texas, Austin Y. Xiao, Zhejiang University W. L. Zhang, CAS Institute of Physics US DOE SciDAC GSEP Center, ITER-CN Simulation
Z. X. Wang, W. W. Heidbrink, I. Holod, J. McClenaghan, UCIH. S. Zhang, Peking University
W. J. Deng, B. Tobias, Princeton Plasma Physics LaboratoryM. A. Van Zeeland, General Atomics
M. E. Austin, University of Texas, AustinY. Xiao, Zhejiang University
W. L. Zhang, CAS Institute of Physics
US DOE SciDAC GSEP Center, ITER-CN Simulation Initiative
Zhihong Lin
Thank you. In this talk, I will discuss results from large scale simulations carried out by several graduate students at University of california, Irvine and Peking University
Outlines
• Motivation
• Linear AE physics
• Nonlinear AE physics
• Discussions & Summary
Energetic particle (EP) transport by Alfven eigenmode (AE) can degrade confinement of burning plasmas
This paper reports gyrokinetic particle simulation of AE excited by EP in DIII-D tokamak
Zhihong Lin
As highlighted in this session, energetic particle (EP) transport by Alfven eigenmode (AE) can degrade confinement of burning plasmas.This paper reports gyrokinetic particle simulation of AE excited by EP in DIII-D tokamak. After a brief introduction, I will discuss linear and nonlinear AE physics from simulation results.
Gyrokinetic Turbulence Simulation of EP Transport
• Fully self-consistent simulation of energetic particle (EP) turbulence and transport must► Incorporate kinetic effects of thermal particles at micro-scale► Treat EP and thermal plasmas on the same footing (non-perturbative)
• Large dynamical ranges of spatial-temporal processes require simulation codes efficient in utilizing peta-scale computers
• Therefore, studies of EP physics in ITER burning plasmas call for a new approach of global nonlinear gyrokinetic simulation
• US DOE SciDAC GSEP (Gyrokinetic Simulation of Energetic Particle Turbulence and Transport)
• Verification & Validation: RSAE frequency up-sweeping and mode structures from gyrokinetic simulations agree well with DIII-D experiments (shot # 142111) [D. A. Spong et al, PoP2012]
Zhihong Lin
The motivation of this work is that fully self-consistent simulation of EP turbulence and transport must incorporate kinetic effects of thermal particles at micro-scale and treat EP and thermal plasmas on the same footing (that is, non-perturbative approach).The resuting large dynamical ranges of spatial-temporal processes then require simulation codes efficient in utilizing peta-scale computers and beyond.Therefore, studies of EP physics in ITER burning plasmas call for a new approach of global nonlinear gyrokinetic simulation.This approach has been taken by the US DOE SciDAC GSEP (Gyrokinetic Simulation of Energetic Particle Turbulence and Transport).Rigorous verification & validation have been performed for gyrokinetic simulation of AE. For example, the reverse shear Alfven eigenmode (RSAE) frequency up-sweeping and mode structures from gyrokinetic simulations agree well with DIII-D experiments
Outlines
• Motivation
• Linear AE physics
• Nonlinear AE physics
• Discussions & Summary
Linear physics: What is EP effects on AE dispersion relation and mode structure?
Gyrokinetic simulations with kinetic effects of thermal plasmas and non-perturbative EP effects recover experimental results of toroidal Alfven eigenmode (TAE) in DIII-D
Non-perturbative EP effects induce TAE radial localization
Zhihong Lin
With this verification and validation, we now apply gyrokinetic simulation to study linear AE physics: that is, what is EP effects on AE dispersion relation and mode structure?We will show that gyrokinetic simulations with kinetic effects of thermal plasmas and non-perturbative EP effects recover experimental results of toroidal Alfven eigenmode (TAE) in DIII-D tokamak.An interesting new physics from simulation is that non-perturbative EP effects induce TAE radial localization.
Measurement Shows Fast Radial Drift of TAE in DIII-D• TAE moves rapidly while thermal plasma profiles barely change
• Cannot be explained by perturbative theory: thermal plasma profiles set MHD mode structure, EP only drives growth rate
TAE in DIII-D shot # 142111 around 525ms
Zhihong Lin
After the simulation finding TAE localization, we looked for experimental evidences. Indeed, measurement of the same DIII-D experiment shows fast radial drift of TAE. Plotted here are variations of TAE frequency and radial mode width from 510ms to 528ms. During this 18ms period, the thermal plasma profiles barely change, but the TAE with toroidal mode number n equal to 4 moves from inside to outside with respect to the flux surface of q equal to 4.5.This fast radial drift cannot be explained by the conventional perturbative theory, in which thermal plasma profiles set MHD mode structure, and EP only drives growth rate. A possible explaination to the fast radial drift of TAE is that as EP being convected outward by TAE, TAE is locally excited at the radial location with maximal EP gradient. We now show how simulations of TAE in this experiment find this localization before we knew this experimental data.
GTC Simulations Find TAE Radial Localization• Simulations scan EP profiles within experimental uncertainty • Unstable TAE radial structures move with EP density gradient• In contrast, stable TAE excited by antenna has larger radial width• EP non-perturbative contribution induces TAE radial localization
TAE in DIII-D shot # 142111 at 525ms
Zhihong Lin
Showing here is the n equal to 4 TAE frequency and radial mode structure in terms of electron density perturbation. The solid lines are experimental frequency and mode structure. These are Alfven continuum and the toroidal frequency gap extend from magnetic axis to plasma edge. To test the sensitivity of TAE mode structure on EP density gradients, gyrokinetic particle code GTC simulations scan EP density gradient profiles within experimental uncertainty. For these three EP density gradients represented by dashed lines, correspondng unstable TAE radial structures, represented by these three solid lines, move with EP density gradient. The frequency of these three cases are all very close to the experimental value. Case 2 radial mode structure agrees well with experimental measurement.In contrast, stable TAE excited by antenna in simulation, which represents the MHD mode structure as predicted by perturbative theory, has larger radial width. Therefore, EP non-perturbative contribution induces TAE radial localization, that is TAE mode structure peaks at and moves with the maximal EP pressure gradients.
Comparison of TAE Mode Structures between Simulation & Experiment
GTC
• EP non-perturbative contribution breaks radial symmetry of TAE eigenmode
TAE in DIII-D shot # 142111 at 525ms
DIII-DGTC
[Z. X. Wang et al, PRL2013]
Zhihong Lin
EP non-perturbative contribution also breaks radial symmetry of TAE eigenmode. Plotted here is the poloidal mode structure from GTC simulation, which shows radially sheared structure. In contrast, MHD mode structure would have radial symmetry when EP is removed from simulation. If we zoom in to this area where mode structure is measured by ECEI in DIII-D experiment, GTC simulation and DIII-D measurement have very similar mode structure, both show radial symmetry breaking.
Comparison of TAE Frequency between Simulation & Experiment
• EP non-perturbative contribution and trapped electron effects induce TAE frequency dependence on toroidal mode number n
TAE in DIII-D shot # 142111 at 525ms
Zhihong Lin
Finally, EP non-perturbative contribution and trapped electron effects induce TAE frequency dependence on toroidal mode number n. GTC simulations in the MHD limit find mode frequency independent of n, consistent with perturbative theory. On the other hand, GTC simulation with trapped electron effects show a modest dependence of frequency on n. Including EP effects leads to an even stronger frequency dependence on n, which is consistent with experimental trend. Moreover, both simulation and measurement show weak time variations of TAE frequency, that is, no frequency sweeping. In summary, linear GTC simulations find that EP non-perturbative contribution induces TAE radial localization, radial symmetry breaking, and frequency dependence on toroidal mode number n.
Outlines
• Motivation
• Linear AE physics
• Nonlinear AE physics
• Discussions & Summary
Nonlinear physics: How does AE saturate? What is NL dynamics
Conventional model: Perturbative theory and reduction of dimensionality from 3D to 1D, i.e., single toroidal mode, radially local
• Fast frequency chirping induced by radial variations of AE mode amplitude & guiding center dynamics
Zhihong Lin
Building on the success of linear simulation, we now move on to nonlinear AE physics, that is, how does AE saturate? What is AE nonlinear dynamics. These are important nonlinear physics that determines EP transport level.Of course, nonlinear physics is challenging. Conventional model often utilizes the perturbative theory and reduces dimensionality from 3D to 1D by treating a single toroidal mode and assuming radially local problem. Despite its simplicity, the 1D model has provided many useful insights and improved understandling of AE NL dynamics.Our interest is to use non-pertubative simulation to study nonlinear physics beyond 1D model. In this work, nonlinear gyrokinetic simulations find that zonal fields (zonal flow & zonal current) are generated by AE nonlinear mode coupling, and that fast frequency chirping is induced by radial variations of AE mode amplitude & guiding center dynamics.
• Removing thermal particle nonlinearity: even higher TAE amplitude and relaxation of EP profiles
• TAE saturates by zonal flow without relaxation of EP profiles
• Zonal current has little effects on TAE saturation
• gZF~1.9gTAE: zonal fields generated by TAE nonlinear mode coupling, not modulational instability
Nonlinear simulation of TAE in DIII-D shot # 142111 at 525ms
[Z. X. Wang, PhD Thesis, 2014]
Zhihong Lin
First, we study nonlinear mode coupling by allowing n equal to zero modes, or zonal fields, and extending the linear simulation to nonlinear regime. GTC nonlinear simulations find that zonal flow and zonal current are generated by TAE mode couping. Showing here are time history of TAE amplitude in solid red line and zonal flow amplitude in dotted-dashed red line. Suppressing zonal flow leads to higher TAE saturation amplitude in solid green line. Removing thermal particle nonlinearity leads to even higher TAE amplitude and relaxation of EP profiles in solid blue line.Our simulations thus find that TAE saturates by zonal flow without relaxation of EP profiles. On the other hand, zonal current has little effects on TAE saturation. Simulation further find that the growth rate of zonal flieds is almost twice of TAE growth rate and is independent of TAE amplitude. This indicates that zonal flields are generated by nonlinear mode coupling, not through modulational instability as in the driftwave turbulence.
Generation of Zonal Flow by Alfven Eigenmode
• Zonal flow generation by driftwave vs. Alfven eigenmode• Driftwave: modulational instability
• AE: nonlinear mode coupling
• Electrostatic vs. Electromagnetic turbulence• Electromagnetic: Stochastic magnetic fields could suppress zonal flow
generation because of increase of zonal flow dielectric constant due to electron adiabatic responses, i.e., electron shielding effects
• No similar effects in electrostatic turbulence
• Conjecture: Stochastic magnetic fields of RMP (resonant magnetic perturbation) could suppress zonal flow generation, and lead to enhanced driftwave turbulence in H-mode pedestal; Need to be tested by gyrokinetic simulation with 3D RMP fields
Zhihong Lin
Since zonal flow has long been recognized to regulate driftwave turbulence, it is of interest to compare the generation of zonal flow by driftwave turbulence and by Alfven eigenmode. As we have alread mentioned, zonal flow is generated by modulational instability in driftwave turbulence, but by nonlinear mode coupling in Alfven eigenmode. There is also interesting difference between electrostatic and electromagnetic turbulence in the generation of zonal flow. In electromagnetic turbulence, stochastic magnetic fields, if exist, could suppress zonal flow generation because of the increase of zonal flow dielectric constant due to electron adiabatic response, that is, electron shielding effects. In contrast, there is no similar effects in electrotatic turbulence even if electron EXB drift is stochastic. This observation could lead to the following conjecture, that is, stochastic magnetic fields of RMP (resonant magnetic perturbation) could suppress zonal flow generation, and lead to enhanced driftwave turbulence in H-mode pedestal; This needs to be tested by gyrokinetic simulation with 3D RMP fields.
GTC Nonlinear Simulations of BAE Find Fast Chirping
• Fast, repetitive, mostly downward chirping
• 90o phase shift between intensity and frequency oscillations
• Simulation consistent with recent NSTX TAE, ASDEX BAE
• Chirping mechanisms: nonlinear formation vs. destruction of phase space island due to radial variations of mode structure & guiding center dynamics (intrinsically 2D dynamics)
[H. S. Zhang et al, PRL2012]
[M. Podesta et al, NF2011; PPPL-4719]
Zhihong Lin
We now move on to discuss the 2nd exmaple of nonlinear physics beyond the 1D model, that is the role of radial variations in the fast chirping of Alfven eigenmode. Fast frequency chirping of Alfven eigenmode has been observed in many tokamak experiments and has been coorelated with enahnced fast ion loss. Showing here is the time history of frequency and intensity of TAE in NSTX experiments. We can see the fast and repetitive oscillations of both frequency and intensity, the mostly downward frequency chirping, and the 90o phase shift between intensity and frequency oscillations. These key experimental features have not previsouly been explained by first-principles toroidal simulation.Our nonlinear simulation of beta-induced Alfven eigenmode has, for the first time, recovered all these key features. Showing here is the time history of BAE frequency and intensity from GTC simulation. These oscillations are fast and repetive, and there is a 90o phase shift between intensity and frequency oscillations. The frequency oscillation is mostly downward chirping as can be seen from this intensity weighted frequency time history. Detailed analysis of wave and particle dynamics in the simulation has identified the chirping mechanisms through nonlinear formation vs. destruction of phase space island due to radial variations of mode structure & guiding center dynamics. All these key features have been explained by the intrinsically 2D dynamics.
Outlines
• Motivation
• Linear AE physics
• Nonlinear AE physics
• Discussions & Summary
AE is an example of MHD modes with kinetic effects in fusion plasma excited by pressure gradients or equilibrium currents
Gyrokinetic simulation of kinetic-MHD processes:
• MHD mode frequency < ion cyclotron frequency
• kinetic effects important in MHD modes
Zhihong Lin
We now come to the discussion and summmary. As we have discussed, applicatioms of gyrokinetic simulation has been successfully expanded from microturbulence to mesoscale Alfven eigenmode and energetic particles. AE is an example of many MHD modes with kinetic effects in fusion plasma excited by pressure gradients or equilibrium currents. Interactions of multiple kinetic and MHD proccesses are offten important. Such interactions can be treated effeciently in gyrokinetic simulation of kinetic-MHD processes, characterized by the mode frequency < ion cyclotron frequency, and kinetic effects at microscale and mesoscale.
and threaten fusion device integrity: NTM, RWM, sawtooth etc
• Kinetic effects at microscopic (thermal particles) & meso-scales (EP) and coupling of multiple processes play a crucial role in excitation and evolution macroscopic MHD modes
• Neoclassical tearing modes (NTM): set principal performance limit in both ITER baseline and hybrid scenarios
• Predictive NTM simulation needs to incorporate kinetic physics at multiple spatial and temporal scales:
microturbulence
neoclassical bootstrap current
magnetic island dynamics (current driven MHD instability)
• Gyrokinetic toroidal code (GTC) simulation of kinetic-MHD: first-principles, integrated simulation of nonlinear interaction between microturbulence, EP, MHD, & neoclassical transport
Zhihong Lin
Beyond microturbulence, mesoscale Alfven mode, and energetic particles, we now advocate gyrokinetic simulation of macroscopic MHD modes. Macroscopic MHD modes limit burning plasma performance and threaten fusion device integrity: NTM, RWM, sawtooth etc.Kinetic effects at microscopic (thermal particles) & meso-scales (EP) and coupling of multiple processes play a crucial role in excitation and evolution macroscopic MHD modes.For example, neoclassical tearing modes (NTM) set principal performance limit in both ITER baseline and hybrid scenarios.Predictive NTM simulation needs to incorporate kinetic physics at multiple spatial and temporal scales: including microturbulence, neoclassical bootstrap current, and magnetic island dynamics (current driven MHD instability). Such first-principles, integrated code does not exist for NTM simulation. This motivates the developmment of GTC as a computationl framework to provide first-principles, integrated simulation of nonlinear interaction between microturbulence, EP, MHD, & neoclassical transport.
Gyrokinetic Toroidal Code (GTC)
• GTC current capability for kinetic-MHD simulation:► General 3D toroidal geometry & experimental profiles► Microturbulence & EP: Kinetic electrons & electromagnetic fluctuations► MHD: Equilibrium current, resistive and collisionless tearing modes► Neoclassical transport► RF: fully kinetic ions► Ported to GPU (titan) & MIC (tianhe-2)
• Other GTC papers at this meeting: Microturbulence: TH/P2-44, Y. Xiao, Gyrokinetic Simulation of
Microturbulence in EAST Tokamak and DIII-D Tokamak EP: TH/P7-29, W. L. Zhang, Verification and Validation of Gyrokinetic
Particle Simulation of Fast Electron Driven Beta-Induced Alfven Eigenmode on HL-2A Tokamak
MHD: TH/P4-11, I. Holod, Global Gyrokinetic Simulations of Electromagnetic Instabilities in Tokamak Plasmas
RF: TH/P2-10, A. Kuley, Nonlinear Particle Simulation of Radio Frequency Waves in Fusion Plasmas
[Z. Lin et al, Science1998]
http://phoenix.ps.uci.edu/GTC
Zhihong Lin
These capabilities for kinetic-MHD simulation inclde general 3D toroidal geometry & experimental profiles. kinetic electrons & electromagnetic fluctuations for simulation of microturbulence and EP-driven Alfven eigenmode,Equilibrium current, resistive and collisionless tearing modes for MHD simulation, and Neoclassical transport. The verification and application in the area of microturbulence, EP, and MHD have been reported earlier this week in these GTC posters.Finally, we have extended gyrokinetic ion to fully kinetic ion to provide the first nonlinear totoidal simulation for radio frequency (RF) interaction with fusion plasmas, including lower-hybrid wave and ion Bernstein wave, ion cyclotron wave, fast wave etc. The verification of RF capability was reported Tuesday in this poster.These kinetic-MHD simulation and RF smulation requires efficient utilization of the petascale computer. GTC has been ported to the world two most powerful computers: GPU (titan) & MIC (tianhe-2).
Summary
• Linear physics: Gyrokinetic particle simulations find radial localization of toroidal Alfven eigenmodes in DIII-D tokamak due to non-perturbative contribution by energetic particles
Linear physics: Gyrokinetic particle simulations find radial localization of toroidal Alfven eigenmodes in DIII-D tokamak due to non-perturbative contribution by energetic particlesNonlinear physics: Gyrokinetic particle simulations findNonlinear saturation of toroidal Alfven eigenmodes by zonal flow, which is generated by TAE mode couplingNonlinear chirping of beta-induced Alfven eigenmode due to radial variations of mode amplitude and guiding center dynamicsFuture work: EP transport, coupling to MHD modes
