The Plasma Microturbulence Project

1
The Plasma Microturbulence Project
UCI

• W.M. Nevins ( )
• For the
• Plasma Microturbulence Project Team

UCLA
2
Summary of Progress on Achieving Scientific
Deliverables

• The (partially funded) PMP proposal promised
• A unified framework with
• Four GK kernels (which we have GS2, GYRO,
  Summit, and GTC)
• A common front end ? Morphed to two front ends
• GS2 and GYRO
• PG3EQ, UCAN, and GTC united under SUMMIT
  framework
• A common back end (which we have GKV)
• And users beyond the code development groups
  (which weve done)
• Kinetic electrons and (at least) ?B? in all four
  codes
• Have ?B , ?B? kinetic electrons in GS2
• Have ?B? kinetic electrons in GYRO
• PIC algorithms for ?B? kinetic electrons
  demonstrated in GEM(but not yet installed in
  SUMMIT framework )
• Kinetic electrons in GTC
• To do LOTS of good science with our codes (which
  weve done)

3
Four GK kernels a 2x2 Matrix ofPlasma
Turbulence Simulation Codes

• Why both Continuum and Particle-in-Cell (PIC)?
• Cross-check on algorithms
• Continuum currently most developed (already has
  kinetic es , ?B?, ?B )
• Proponents of PIC-codes believe they will
  ultimately be more efficient
• If we can do Global simulations, why bother with
  Flux Tubes?
• Electron-scale (?e, ?ec/?pe) physics (ETG modes,
  etc.)
• Turbulence on multiple space scales (ITGTEM,
  TEMETG, ITGTEMETG, )
• Efficient parameter scans

4
A PIC algorithm for kinetic es and
?B??Benchmarking GEM against GYRO and GTC
Turbulent Transport
Linear Growth Rates
5
The PMP Supports User Communities for both GS2
and GYRO Codes

• Strong user community trained and working to
  validate gyrokinetic codes against experimental
  data, including
• Bourdelle, Bravenec, Budny, Ernst, Hallatschek,
  Hill, Jenko, Mikkelsen, Redi, Ross, Yuh, and
  others
• Workshops to educate user community (December
  2002, )
• Websites for code distribution and documentation
• http//gs2.sourceforge.net/ and
  http//fusion.gat.com/comp/parallel/gyro.html
• Work by these Gyrokinetic code users has led to
  publications and talks at major meetings,
  including
• D. W. Ross, TTF 2004 B. N. Rogers, Sherwood
  2004
• D. Ernst, APS 2003 F. Jenko, IAEA 2002
• K. Hallatschek, APS 2002 H. Yuh, ICOPS 2002

6
PMP Codes Scale to large numbers of
processorsGYRO is a benchmark code for the ORNL
Cray X-1GTC ported to both ORNL Cray X-1and
Japanese Earth Simulator
GTC problem size ?with Nprocessors
GYRO constant problem size
For details on GYRO performance, see
http//fusion.gat.com/comp/parallel/performance.ht
ml
For details on GTC performance, see
http//gk.ps.uci.edu/zlin/parallel/index.html
7
SciDAC Computing ResourcesEnabled Studies of
Plasma Micro-turbulence

• NERSC (LBNL)
• FY 01 usage 1.36M node-hrs
• FY 02 usage 2.63M node-hrs
• FY 03 usage 4.78M node-hrs
• Accounting unit re-normalized (by a factor of
  2.5)
• FY 04 allocation 2M node-hrs(and we will
  certainly use it all)

• CCS (ORNL)
• FY 03 usage 3.5M node-hrs
• FY 04 allocation 1 M node-hrs(but CCS doesnt
  seem to mind if you exceed your allocation )

Plus substantial use of Linux Clusters at PPPL,
GA, MIT and U of MD ? The PMP is largest user of
computer time among OFES-funded activities(and
this counts only usage by our PIs, not that of
our user-community)
8
Has the PMP produced good science?Judge for
yourselves

• Refereed publications
• 2004
• J. Candy, R. E. Waltz, and W. Dorland, Phys.
  Plasmas 11.
• J. Candy, R.E. Waltz, and M.N. Rosenbluth, Phys.
  Plasmas 11, 1879.
• V. K. Decyk and Charles D. Norton, Scientific
  Programming 12, 45.
• D. R. Ernst, P. T. Bonoli, P. J. Catto et al.,
  Phys. Plasmas .
• S. Ethier and Z. Lin, Computer Physics
  Communications .
• T. S. Hahm, P.H. Diamond, Z. Lin et al.,
  Plasma Phys. Controlled Fusion .
• F.L. Hinton, R.E. Waltz, and J. Candy, Phys.
  Plasmas 11, 2433.
• W. W. Lee, Comput. Phys. Comm. .
• Z. Lin and T. S. Hahm, Phys. Plasmas 11, 1-99.
• S.E. Parker, Y. Chen, W. Wan et al., Phys.
  Plasmas 11, 2594.
• M. Romanelli, C. Bourdelle, and W. Dorland,
  Phys. Plasmas .
• R.E. Waltz, Fusion Science and Technology
• W.X. Wang, W.M. Tang, et al., Computational
  Physics Communication .
• 2003
• C. Bourdelle, W. Dorland, X. Garbet et al.,
  Phys. Plasmas 10, 2881.
• J. Candy and R.E. Waltz, Phys. Rev. Lett. 91,
  045001.
• J. Candy and R.E. Waltz, J. Comp. Phys. 186, 545.

•  
• 2002
• R. V. Budny, R. Andre, et al., Plasma Phys.
  Control. Fusion 44, 1215.
• Y. Chen, Samuel T. Jones, and Scott E. Parker,
  EEE Tran. Plasma Sci. 30, 74.
• B.I. Cohen, A.M. Dimits, W.M. Nevins et al.,
  Phys. Plasmas 9 (1), 251-262.
• Bruce I. Cohen, Andris M. Dimits, et al., Phys.
  Plasmas 9 (5), 1915-1924.
• T. S. Hahm, Plasma Phys. Controlled Fusion 44,
  A87.
• F. Jenko and W. Dorland, Phys. Rev. Lett. 89,
  225001.
• Z. Lin, S. Ethier, T. S. Hahm et al., Phys.
  Rev. Lett. 88, 195004.
• D. W. Ross, R. B. Bravenec, W. Dorland et al.,
  Phys. Plasmas 9, 177.
• D. W. Ross and W. Dorland, Phys. Plasmas 9, 5031.
• E. J. Synakowski, M. G. Bell, et al., Phys.
  Control. Fusion 44, A165.
• R. E. Waltz, J. Candy, and M.N. Rosenbluth, Phys.
  Plasmas 9, 1938.
• 2001
• A.M. Dimits, B.I. Cohen, W.M. Nevins et al.,
  Nuclear Fusion 41, 1725-1732.
• I. H. Hutchinson, R. Boivin, P. T. Bonoli et
  al., Nucl. Fusion 41, 1391.
• F. Jenko, W. Dorland, and G. W. Hammett, Phys.
  Plasmas 8, 4096.
• W. W. Lee, J. L. V. Lewandowski, T. S. Hahm et
  al., Phys. Plasmas 8, 4435.
• Z. Lin and L. Chen, Phys. Plasmas 8, 1447.

9
Has the PMP produced good science?Judge for
yourselves

• 2003
• Y. Chen, Electromagnetic gyrokinetic
  simulations, presented at the International
  Sherwood Fusion Theory Meeting.
• W. Dorland, Sheared flows and boundary layer
  physics in tokamak plasma, presented at the New
  Themes in Plasma and Fusion Turbulence, London.
• W. Dorland, Anomalous heating in a kinetic
  Alvfen wave cascade, presented at the 7th
  Workshop on the Interrelationship between Plasma
  Experiment in Laboratory and Space.
• W. Dorland, US Plasma Microturbulence Project,
  presented at the Eighth International Symposium
  on Simulation Science, Hayama, Japan.
• D.R. Ernst, Role of Trapped Electron Mode
  Turbulence in Internal Transport Barrier Control
  in Alcator C-Mod, presented at the 45th Annual
  Meeting of the Division of Plasma Physics,
  Albuquerque, NM.
• F.L. Hinton, Electromagnetic turbulence effects
  in the neoclassical Ohm's law, presented at the
  45th Annual meeting of the Division of Plasma
  Physics, Albuquerque, NM.
• S. Klasky, S. Ethier, Z. Lin et al.,
  Grid-Based Parallel Data Streaming implemented
  for the Gyrokinetic Toroidal Code, presented at
  the SC2003, Phoenix, AZ.
• W. W. Lee, Thermodynamic and numerical
  properties of a gyrokinetic plasma implications
  on transport scale simulation, presented at the
  18th International Conference on Numerical
  Simulation of Plasmas, Cape Cod, MA.
• Z Lin, presented at the 10th European Fusion
  Theory Conference, Helsinki, Finland.
• S.E. Parker, Electromagnetic Turbulence
  Simulations with Kinetic Electrons, presented at
  the 45th Annual Meeting of the Division of Plasma
  Physics, Albuquerque, NM.
• M. H. Redi, R. Bell, P. Bonoli et al.,
  Gyrokinetic Calculations of Microturbulence and
  Transport on NSTX and Alcator-CMOD H-modes,
  presented at the 30th European Physical Society
  Conference on Plasma Physics and Controlled
  Fusion, St. Petersburg, Russia.

• Talks at major meetings
• 2004
• Ron Bravenec, Synthetic Diagnostics, presented
  at the 15th Topical Conference on
  High-Temperature Plasma Diagnostics.
• V. K. Decyk, UCLA Parallel PIC Framework A
  Toolkit for new PIC Codes, presented at the SIAM
  Conference on Parallel Processing for Scientific
  Computing, San Francisco, CA.
• W. Dorland, Resonant Heating in the Alfven
  Cascade, presented at the Fields Institute.
• P.N. Guzdar, Pedestal Physics, to be presented
  at the 20th IAEA Fusion Energy Conference,
  Vilamoura, Portugal.
• T.S. Hahm, to be presented at the 20th IAEA
  Fusion Energy Conference, Vilamoura, Portugal.
• W. W. Lee, MFE Simulation Data Management,
  presented at the DoE Data Management Workshop,
  SLAC, Palo Alto, CA.
• Z. Lin, to be presented at the 20th IAEA Fusion
  Energy Conference, Vilamoura, Portugal.
• B.N. Rogers, Non-Curvature Driven Modes in the
  H-Mode Pedestal, presented at the Sherwood
  Conference, Missoula, MT.
• D.W. Ross, Experimental Comparisons with
  Gyrokinetic Codes (preview talk), presented at
  the Transport Task Force Meeting, Salt Lake, UT.
• R.E. Waltz, Advances in Comprehensive
  Gyrokinetic Simulations of Transport in
  Tokamaks", to be presented at the 20th IAEA
  Fusion Energy Conference, Vilamoura, Portugal.

10
Has the PMP produced good science?Judge for
yourselves

• More Talks at major meetings
• 2002
• J. Candy, Comprehensive Gyrokinetic Simulations
  of Turbulent Transport in DIII-D with the GYRO
  Code, presented at the 44th Meeting of the
  Division of Plasma Physics.
• J. Candy, GYRO Modeling of Anomalous Transport
  in Tokamaks, presented at the International
  Sherwood Fusion Theory Conference.
• W. Dorland, Secondary instabilities in ETG
  Turbulence, presented at the VII Easter Plasma
  Meeting, Turin.
• W. Dorland, Collisionless plasma turbulence,
  presented at the 29th Annual IoP Plasma Physics
  Group Conference.
• W. Dorland, Gyrokinetic Turbulence in
  Magnetically Confined Plasmas, presented at the
  European Physical Society, Montreux.
• F. Jenko, Simulations of finite-beta turbulence
  in tokamaks and stellarators, presented at the
  19th IAEA Fusion Energy Conference, Lyon, France.
• Z. Lin, S. Ethier, T. S. Hahm et al., Size
  Scaling of Turbulent Transport in Tokamak
  Plasmas, presented at the 19th IAEA Fusion
  Energy Conference, Lyon, France.
• W.M. Nevins, The Experiment/Theory Dialogue in
  the Age of Simulations, presented at the 2002
  Transport Task Force Meeting, Annapolis, MD.

• 2001
• B.I. Cohen, "Kinetic electron closures for
  electromagnetic simulation of drift and
  shear-Alfven waves" B.I. Cohen, et al., Phys.
  Plasmas 9, 1915 (2002)., presented at the 43rd
  Annual meeting of the Division of Plasma Physics,
  Long Beach, CA.
• W. Dorland, Numerical Simulations and Burning
  Plasma Concepts in 2004, presented at the Fourth
  Symposium on Current Trends in International
  Fusion Research, Washington, DC.
• T. S. Hahm, Gyrokinetic Simulation of Transport
  Scalings and Turbulent Structure, presented at
  the 43rd Annual Meeting of the Division of Plasma
  Physics, Long Beach, CA.
• R.E. Waltz, Gyrokinetic Turbulence Simulation of
  Profile Shear Stabilization and Broken GyroBohm
  Scaling, presented at the 43rd Annual Meeting of
  the Division of Plasma Physics, Long Beach, CA.

11
Code Benchmarking RequiresError Bars on our
Measurements
Is the difference between the red and black
curves significant?
12
Uncertainty in the Estimate of the Mean (a
short detour into statistics)
Definitions
Then
13
Code Comparisons (GYRO vs. GTC)Scaling of Heat
Transport with Machine Size
14
?i(t) from GYRO GTC differ due to long-lived
transient
15
?i(t) from GYRO GTC differ due to long-lived
transient
16
The Local Transport Conjectureand the role of
flux-tube codes

• In the limit a/??? and at each radius, ?i(r)
  from a global simulation approaches ?i from a
  flux-tube simulation with the equilibrium
  parameters evaluated at that radius.
• Test conjecture using micro-turbulence simulation
  data
• Strong radial variation in ?i(r) even at constant
  ?T/T
• GS2 simulations track ?i(r) from GYRO (Candy, et
  al)
• PG3EQ simulations also track ?i(r) from GYRO.

17
The Local Transport Conjectureand the role of
flux-tube codes

• In the limit a/??? and at each radius, ?i(r)
  from a global simulation approaches ?i from a
  flux-tube simulation with the equilibrium
  parameters evaluated at that radius.
• Test conjecture using micro-turbulence simulation
  data
• Strong radial variation in ?i(r) even at constant
  ?T/T
• GS2 simulations track ?i(r) from GYRO (Candy, et
  al)
• PG3EQ simulations also track ?i(r) from GYRO.

18
Can local conjecture flux tube codes resolve
late-time behavior of ??? for a/??? ?
19
Can local conjecture flux tube codes resolve
late-time behavior of ??? for a/??? ?
20
Can local conjecture flux tube codes resolve
late-time behavior of ??? for a/??? ?
21
Can local conjecture flux tube codes resolve
late-time behavior of ??? for a/??? ?
Lesson We need to be humble about assigning
error bars!
22
Why long-lived transients, and why does ?i depend
on a/??Turbulence Spreading and the 4-wave model

• PMP a/?-scan motivated series of papers on
  turbulence spreading
• Chen et al, Phys. Plasmas 7, 3129 (2000)
• Guzdar et al, Phys. Plasmas 8, 459 (2001)
• Chen et al, PRL 92, 075004 (2004)
• Zonca et al, Phys. Plasmas 11, 2488 (2004)
• Basic plot ITG pump at kr ?i0 couples to
  sideband at finite kr ?ito produce zonal
  flow and radial propagation of ITG turbulence

Model exhibits long time-scales, intermittency,
fixed-points,
23
Is the ITG Turbulence the Same (or similar) in
PMP Codes?
GTC

• Turbulence is stochastic
• trying to reproduce time/space dependence is a
  fools errand
• Need realization-independent way to characterize
  turbulence
• Correlation functions
• Spectral density

GYRO
24
Perpendicular Spectral DensityEarly vs.
Late-time Comparisons
25
The Radial Correlation Function
GYRO a/?-scan
PMP Code-scan
26
The Transverse Correlation Function
GYRO a/?-scan
PMP Code-scan
27
The Lagrangian Correlation Function
GYRO a/?-scan
PMP Code-scan
28
The Eddy Turnover Time

• Eddy Turn-over Time Tracks Eddy Life-time
• ITG turbulence saturates due to onset of ExB
  trapping

• Suggesting that
• If I could predict ?Eddy, thenId know ?ExB

• If I knew ?ExB, Id know ?????

• If I knew ?????, thenmaybe I could estimate ?i !

29
Amazingly, this program actually succeeded,
yielding (almost) everything you wanted to know
about the Cyclone ?T-Scan in 7 parameters

• Model assumes
• ITG turbulence saturatesby onset of ExB trapping
• Nonlinear rates scale ?Max
• Model successfully predicts
• Eddy life-time
• Eddy turn-over time
• ExB Shearing rate
• Correlation lengths
• Turbulent intensity
• ITG Transport
• Fails to predict Dimits shift
• Turbulence saturates before onset of ExB trapping

30
Validation of GYROagainst DIII-D Experiments

• GYRO simulations with
• Kinetic electrons
• ExB shear
• Collisions
• Plasma shape
• Reproduce magnitude, profile, and ?-dependence
  of DIII-D transport
• J.Candy, Invited Talk at 2002 APS/DPP Meeting
• Fixed-flux GYRO simulations
• Enhance comparisons with Experiment
• Key step toward transport time-scale and FSP
• R. Waltz, Invited Talk at 2003 APS/DPP Meeting

31
GYRO Simulations of Turbulent Dynamo in DIII-D
L-Mode Plasma
See Hinton, F.L., R.E. Waltz, J. Candy, Effects
of Electromagnetic Turbulence in the Neoclassical
Ohms Law, Phys. Plasmas 11 (2004) 2433. An
invited talk at 2003 APS/DPP Meeting.
32
Validation of GS2 against Experiments

• Comparisons to EDA H-mode in C-Mod tokamak
• Nonlinear upshift in critical ?T (i.e., R/LT)
• Importance of ?e in retaining this shift
  w/kinetic electrons
• D. Mikkelsen, Invited talk at 2002 IAEA Mtg.
• Comparisons with L-modein DIII-D tokamakRoss
  and Dorland, Phys. Plasmas 9, 5031 (2002)  and
  preview talk at 2004 DDT meeting

33
Is ? decreasing with V?EXB/?max a viable
paradigm?
Toroidal flow-shear does not suppress transport
?i Does not scale with V?EXB/?max
PG3EQ results presented by A. Dimits at 2001
APS/DPP Meeting
34
Electron Thermal Transport the ETG Mode

• Electrostatic ETG and ITG nearly homologous
• ?ETG vme/Mi ?ITG(so ETG not important?)
• Zonal flows are nearly absent in ETG
  turbulence(so ETG is important?)
• Absence of zonal flows
• Streamers, significant ETG transport
• Dorland et al, PRL 85, 5579 (2003)
• Streamers, but no significant ETG transport
• Lin et al, TTF04 oral talk at 2004 IAEA Mtg.
  
• This issue yet to be resolved