june 3, 2004w.m. nevins1 the plasma microturbulence project w.m. nevins ( ) for the plasma...

June 3, 2004 W.M. Nevins 1

The Plasma Microturbulence Project

W.M. Nevins ( )For the

Plasma Microturbulence Project Team


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 we’ve 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 we’ve done)


Four GK “kernels” — a 2x2 Matrix ofPlasma Turbulence Simulation Codes

Continuum PIC

Flux Tube GS2 SUMMIT

Global GYRO GTC

• Why both Continuum and Particle-in-Cell (PIC)?– Cross-check on algorithms

– Continuum currently most developed (already has kinetic e’s , 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, e=c/pe) physics (ETG modes, etc.)

– Turbulence on multiple space scales (ITG+TEM, TEM+ETG, ITG+TEM+ETG, …)

– Efficient parameter scans


A PIC algorithm for kinetic e’s and B

Benchmarking GEM against GYRO and GTC

Linear Growth Rates

Turbulent Transport


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

http://gs2.sourceforge.net/



http://fusion.gat.com/comp/parallel/gyro.html


PMP Codes Scale to large numbers of processors:GYRO is a benchmark code for the ORNL Cray X-1GTC ported to both ORNL Cray X-1and Japanese Earth Simulator

16 32 64 128 256 512 1024processors

16

32

64

128

256

512

1024

For details on GYRO performance, see http://fusion.gat.com/comp/parallel/performance.html

GYROconstant problem size

GTC problem size with Nprocessors

For details on GTC performance, see http://gk.ps.uci.edu/zlin/parallel/index.html


SciDAC Computing ResourcesEnabled Studies of Plasma Micro-turbulence

NERSC (LBNL)• FY ‘01 usage: 1.36M node-hrs

• FY ‘02 usage: 2.63M 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 ‘04 allocation: 1 M node-hrs(but CCS doesn’t 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 PI’s, not that of our user-community)


Has the PMP produced good science?Judge for yourselves

Refereed publications:2004J. 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 .2003C. 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.Y. Chen and S.E. Parker, Journal of Computational Physics 189 (2), 463-475.Y. Chen, S.E. Parker, B.I. Cohen et al., Nucl. Fusion 43, 1-7.Y. Chen, S.E. Parker, B.I. Cohen et al., Nuclear Fusion 43, 1121.C. Holland, P.H. Diamond, S. Champeaux et al., Nuclear Fusion 43 (8), 761.W.W. Lee and H. Qin, Phys. Plasmas 10, 3196.J. L. V. Lewandowski, Phys. Plasmas 10, 3204.J. L. V. Lewandowski, Plasma Phys. Controlled Fusion 45, L39.T. S. Pedersen, A. H. Boozer, et al., J. Phys. B: At. Mol. Opt. Phys. 36, 1029.

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.



Talks at major meetings:2004Ron 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.

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.



More Talks at major meetings:

2002J. 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.

2001B.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.


Code Benchmarking RequiresError Bars on our “Measurements”

Is the difference between the red and black curves significant?


Uncertainty in the Estimate of the Mean (a short detour into statistics)

€

χ(t) ≡ χ + ˜ χ (t)

χ ≡1

Tdt

0

T

∫ χ (t)

δχ (t) ≡ χ (t) − χ

Cδχ τ( ) ≈δχ t( )δχ t + τ( )

δχ 2

τ int ≈ dτ Cδχ τ( )−∞

∞

∫

Definitions: Then:

€

χ− χ( )2

=1

T 2dt ˜ χ (t)

0

T

∫ d ′ t ˜ χ ( ′ t )0

T

∫

€

≈1

T 2dt d ′ t δχ (t)δχ ( ′ t )∫∫

= δχ2 τintT

Real data has “trends” which must be Removed from χ Added back to our error estimate

(and I’m still not completely satisfied …)

€

+ ˙ χ least−squares

T

2

⎛

⎝ ⎜

⎞

⎠ ⎟2


Code Comparisons (GYRO vs. GTC)Scaling of Heat Transport with Machine Size


χi(t) from GYRO & GTC differ due to long-lived transient


The Local Transport Conjectureand the role of flux-tube codes

In the limit a/ and at each radius, χi(r) from a global simulation approaches χi from a flux-tube simulation with the equilibrium parameters evaluated at that radius.

• Test conjecture using micro-turbulence simulation data

– Strong radial variation in χi(r) even at constant T/T

– GS2 simulations track χi(r) from GYRO (Candy, et al)

– PG3EQ simulations also track χi(r) from GYRO.


Can local conjecture & flux tube codes

resolve late-time behavior of χ for a/ ?



resolve late-time behavior of χ for a/ ?Lesson: We need to be “humble” about assigning error bars!


Why long-lived transients, and why does χi 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 i≈0 couples to “sideband” at finite kr i

to produce “zonal flow” and radial propagation of ITG turbulence:

Model exhibits long time-scales,intermittency, fixed-points, …


Is the ITG Turbulence the Same

(or similar) in PMP Codes?• Turbulence is stochastic

trying to reproduce time/space dependence is a fool’s errand

• Need realization-independent way to characterize turbulence– Correlation functions

– Spectral density

€

Cδφ (Δx,τ | x, t) =δφ(x + Δx, t + τ )δφ * (x, t)

δφ(x, t)δφ * (x, t)

€

Sδφ k,ω( ) = δφ2

dΔx dτ ∫∫ Cδφ (Δx,τ )e−ik⋅Δx−iωτ

QuickTime™ and aAnimation decompressorare needed to see this picture.

QuickTime™ and aAnimation decompressorare needed to see this picture.

GYRO

GTC


Perpendicular Spectral DensityEarly vs. Late-time Comparisons


The Radial Correlation Function

€

Cδφ (Δr | r ) =δφ(r + Δr ,θ = 0,ζ ,t)δφ * (r ,θ = 0,ζ ,t)

ζ , t

δφ(r ,θ = 0,ζ ,t)δφ * (r ,θ = 0,ζ ,t)ζ , t

GYROa/-scan

PMPCode-scan


The Transverse Correlation Function

€

Cδφ (Δy | r ) =δφ r ,θ = 0,ζ +

B

Bθ

ΔyR ,t( )δφ * r ,θ = 0,ζ ,t( )

ζ , t

δφ r ,θ = 0,ζ ,t( )δφ * r ,θ = 0,ζ ,t( )ζ , t

GYROa/-scan

PMPCode-scan


The Lagrangian Correlation Function

€

Cδφ (τ | r ) =δφ(r ,θ = 0,ζ + Δζ max(τ ),t +τ )δφ * (r ,θ = 0,ζ ,t)

ζ , t

δφ(r ,θ = 0,ζ ,t)δφ * (r ,θ = 0,ζ ,t)ζ , t

GYROa/-scan

PMPCode-scan


• Eddy Turn-over Time Tracks Eddy Life-time

ITG turbulence saturates due to onset of ExB trapping

5xτEddy

τEddy

τExB

Suggesting that:

If I could predict τEddy, then

I’d know τExB

If I knew τExB, I’d know

If I knew , thenmaybe I could estimate χi !

The Eddy Turnover Time

€

τExB ≈ πΔr

ρ s

⎛

⎝ ⎜

⎞

⎠ ⎟Δy

ρ s

⎛

⎝ ⎜

⎞

⎠ ⎟

a

ρ i

eδφ

T

2 1/ 2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥a

cs

⎛

⎝ ⎜

⎞

⎠ ⎟


Amazingly, this program actually succeeded, yielding (almost) everything you wanted to know about the

“Cyclone” T-Scan in 7 parameters

• Model assumes:– ITG turbulence saturates

by 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

Chi_i

0.0

1.0

2.0

3.0

4.0

5.0

6.0

4.0 6.0 8.0 10.0 12.0

R/L_T

model

Chi_I

Chi_i

0.0

1.0

2.0

3.0

4.0

5.0

6.0

4.0 6.0 8.0 10.0 12.0

R/L_T

Chi_I

Alt_model

model


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]


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 Ohm’s Law,”Phys. Plasmas 11 (2004) 2433. An invited talk at 2003 APS/DPP Meeting.


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 tokamak[Ross and Dorland, Phys. Plasmas 9, 5031 (2002) and “preview” talk at 2004 DDT meeting] 0

5

10

15

20

25

R/LT

Lower ne&n

i

Standardcollisionality

- -C Mod EDA H modermid

=0.56a

Fully kinetic electrons and ions

/Measured R LP

heat

4 5 6 7


Is χ decreasing with VEXB/max a viable paradigm?

g xamgxam

0

1.0

2.0

3.0

4.0

5.0

6.0

1.050.0050.0-1.0-0

2.0

4.0

6.0

8.0

1

2.1BxE 6.1=qBxE 4.2=q

)b(

v/ L ’V BxE itiT

χi Does not scale with VEXB/max

gxamg

xam

0

1.0

2.0

3.0

4.0

5.0

6.0

1.050.0050.0-1.0-

v/ L ’V )B/ B( rot itiTp

0

2.0

4.0

6.0

8.0

1

2.1BxE 6.1=qrot 6.1=qBxE 4.2=qrot 4.2=q

)b(

Toroidal flow-shear does not suppress transport

PG3EQ results presented by A. Dimits at 2001 APS/DPP Meeting


• Electrostatic ETG and ITG nearly homologous χETG~ √me/Mi χITG

(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

Electron Thermal Transport & the ‘ETG’ Mode

ETG

ITG

june 3, 2004w.m. nevins1 the plasma microturbulence project w.m. nevins ( ) for the plasma...

Documents

b kinetic electrons

kinetic es

codeshave b

b proponents of pic

gyro performance

user communities

gyrokinetic codes

itg tem etg