# Presentation: 944471

## Physical Mechanisms Driving Gyrokinetic Turbulence

**Physical Mechanisms Driving Gyrokinetic Turbulence**

**G. W. Hammett**
**Princeton Plasma Physics Lab (PPPL)**
- _[http://w3.pppl.gov/~hammett](http://w3.pppl.gov/~hammett)_
**Pauli Institute, Vienna**
**Gyrokinetic Workshop**
**15-19 Sept. 2008**
**(based on APS  talk**
**Orlando, 11/12/2007)**

- Candy, Waltz (General Atomics)

## Physical Mechanisms Driving Gyrokinetic Turbulence

- Intuitive pictures of gyrokinetic turbulence, & how to reduce it:
- analogy with inverted pendulum / Rayleigh-Taylor instability
- reducing turbulence with sheared flows, magnetic shear, plasma shaping   advanced tokamak & advanced stellarator designs

## Motivation & Summary

## Fusion performance depends sensitively on confinement

- Normalized Confinement Time HH = E/Empirical

**Fusion performance depends sensitively on confinement**

- Sensitive dependence on turbulent confinement causes some uncertainties, but also gives opportunities for significant improvements, if methods of reducing turbulence extrapolate to larger reactor scales.

- Caveats:  best if MHD pressure limits also improve with improved confinement.  Other limits also:  power load on divertor & wall, ...

- Q = Fusion Power / Heating Power

## Intuitive pictures of gyrokinetic turbulence, & how to reduce it
analogy w/ inverted pendulum / Rayleigh-Taylor instability
reduce turbulence with sheared flows, magnetic shear, ...

- Intuitive pictures of gyrokinetic turbulence, & how to reduce it
- analogy w/ inverted pendulum / Rayleigh-Taylor instability
- reduce turbulence with sheared flows, magnetic shear, ...

- effective
- gravity

-     _**Inverted-density fluid**_
- Rayleigh-Taylor Instability

## (many of these insights developed with gyrofluid simulations in 1990’s, but gyrokinetics provides higher accuracy.)

**Intuitive pictures of gyrokinetic turbulence, & how to reduce it**

## Unstable Inverted Pendulum

_**Unstable Inverted Pendulum**_

- = (-g/|L|)1/2 = i(g/|L|)1/2 = i

- (rigid rod)

_**Density-stratified Fluid**_

- stable=(g/L)1/2

- =exp(-y/L)

- Max growth rate=(g/L)1/2

- =exp(y/L)

-     _**Inverted-density fluid**_
- Rayleigh-Taylor Instability

- Instability

## “Bad Curvature” instability in plasmas  Inverted Pendulum / Rayleigh-Taylor Instability

- Top view of toroidal plasma:

- plasma = heavy fluid

***B*** = “light fluid”

- geff =      centrifugal force

*R*

- Growth rate:

- Similar instability mechanism
- in MHD & drift/microinstabilities

- 1/L = p/p in MHD,
-   combination of n & T
- in microinstabilities.

## The Secret for Stabilizing Bad-Curvature Instabilities

- Twist in ***B*** carries plasma from bad curvature region
- to good curvature region:

- Unstable

- Stable

- Similar to how twirling a honey dipper can prevent honey from dripping.

## Spherical Torus has improved confinement and pressure limits (but less room in center for coils)

## These physical mechanisms can be seen

- in gyrokinetic simulations and movies

- Unstable bad-curvature
- side, eddies point out, direction of effective gravity

- particles quickly move along field lines, so density perturbations are very extended along fields lines, which twist to connect unstable to stable side

- Stable
- side, smaller eddies

## Sheared

- flows

## Slide 13

## Slide 14

## Rosenbluth-Longmire picture

## Rosenbluth-Longmire picture

- Can repeat this analysis on the good
- curvature side & find it is stable.
- (Leave as exercise.)

## Simple picture of reducing turbulence by negative magnetic shear

- Particles that produce an eddy tend to follow field lines.
- Reversed magnetic shear twists eddy in a short distance to point in the ``good curvature direction''.
- Locally reversed magnetic shear naturally produced by squeezing magnetic fields at high plasma pressure: ``Second stability'' Advanced Tokamak or Spherical Torus.
- Shaping the plasma (elongation and triangularity) can also change local shear

- Fig. from Antonsen, Drake, Guzdar et al. Phys. Plasmas 96
- Kessel, Manickam, Rewoldt, Tang Phys. Rev. Lett. 94

- (in std tokamaks)

- “Normal” in stellarators

- Advanced Tokamaks

## Selected Gyrokinetic References

- This talk available at  w3.pppl.gov/~hammett/talks
- 3 GYRO movies shown (d3d.n16.2x_06_fly, n32o6d0.8, & ETG-ki) from http://fusion.gat.com/theory/Gyromovies
- Web sites for 4 main gyrokinetic codes discussed here (incl. refs., documentation):
- GYRO (Waltz & Candy, GA):  _[fusion.gat.com](http://fusion.gat.com/theory/Gyro)__[/theory/Gyro](http://fusion.gat.com/theory/Gyro)_
- GS2 (Dorland & Kotschenreuther, U. Maryland/Texas): _[gs2.sourceforge.net](http://gs2.sourceforge.net/)_
- GENE (Jenko, Garching):  www.ipp.mpg.de/~fsj
- GEM (Parker & Chen, U. Colorado):  _[cips.colorado.edu/simulation/gem.htm](http://cips.colorado.edu/simulation/gem.htm)_
- “Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation”, J. Candy & R. E. Waltz, Phys. Rev. Lett. 2003
- “Burning plasma projections using drift-wave transport models and scalings for the H-mode pedestal”, Kinsey et al., Nucl. Fusion 2003
- “Electron Temperature Gradient Turbulence”, W. Dorland, F. Jenko, M. Kotschenreuther, B.N. Rogers,  Phys. Rev. Lett. 2000
- “Generation & Stability of Zonal Flows in Ion-Temperature-Gradient Mode Turbulence”, Rogers, Dorland, Kotschenreuther, Phys. Rev. Lett. 2000
- "Comparisons and Physics Basis of Tokamak Transport Models and Turbulence Simulations",  Dimits et al., Phys. Plasmas 2000.
- “Simulations of turbulent transport with kinetic electrons and electromagnetic effects”,** **Y. Chen, S.E. Parker, B.I. Cohen, A.M. Dimits et al., Nucl. Fus. 43, 1121 (2003)

## Selected Gyrokinetic References (cont.)

- Brizard & Hahm, Reviews of  Modern Physics 2007
*“**A Short Introduction to General Gyrokinetic Theory”*, H. Qin,  in Fields Institute Communications **46**, Topics in Kinetic Theory, American Mathematical Society, 171 (2005).  see also http://www.pppl.gov/~hongqin/QinPapers.php
*“**Geometric Gyrokinetic Theory for Edge Plasmas”*, H. Qin, R. H. Cohen, W. M. Nevins, and X. Q. Xu, Physics of Plasmas **14**, 056110 (2007)
- “Theory and Computation in Full-F Gyrokinetics” B. D. Scott, Princeton PPL Theory seminar, June 2005, and other useful presentations at http://www.ipp.mpg.de/~bds/
- E. A. Frieman and L. Chen, Phys. Fluids **25**, 502 1982
- T. M. Antonsen and B. Lane, Phys. Fluids **23**, 1205 1980
- P. J. Catto, W. M. Tang, and D. E. Baldwin, Plasma Phys. **23**, 639 (1981)
- D. H. E. Dubin, J. A. Krommes, C. Oberman, & W. W. Lee, Phys. Fluids **26**, 3524 (1983)
- T. S. Hahm, Phys. Fluids **31**, 2670 (1988)
- A. Brizard, J. Plasma Phys. **41**, 541  (1989)
- A. M. Dimits, L. L. Lodestro, and D. H. E. Dubin, Phys. Fluids B **4**, 274 (1992)
- W.W. Lee, Phys. Fluids 26, 556 (1983)
- "Astrophysical Gyrokinetics: Basic Equations and Linear Theory," Gregory G. Howes, Steven C. Cowley, William Dorland, Gregory W. Hammett, Eliot Quataert, Alexander A. Schekochihin, Ap.J 651, 590 (2006), astro-ph/0511812

## Acknowledgements:

- J. Candy & R. E. Waltz (GA)  (GYRO results & movies)
- W. Dorland (Univ. Maryland), M. Kotschenreuther (U. Texas)
- F. Jenko (Garching)
- S. Cowley (UCLA)
- W. Nevins, B.I. Cohen, A.M. Dimits, R. Cohen (LLNL)
- S.E. Parker and Y. Chen (U. Colorado)
- B. D. Scott (Garching)
- Hong Qin (PPPL)
- T.S. Hahm, A. Brizard, W.W. Lee, W. Tang, J. Krommes, T. Stoltzfus-Dueck
- Chris Holland, Anne White, Jon Kinsey, Gary Staebler
- D. Ernst, D. Mikkelsen, R. Budny
- Center for Multiscale Plasma Dynamics
- DOE Scientific Discovery Through Advanced Computing (SciDAC)
- Center for the Study of Plasma Microturbulence
- Edge Simulation Laboratory
- Earlier DOE SciDAC & Computational Grand Challenge projects, including Plasma Microturbulence Project & Numerical Tokamak Project
- DOE National Energy Research Supercomputing Center (NERSC)
- Many others...