# Presentation: 567916

## Turbulence & Transport in Burning Plasmas

- Acknowledgments:
- Plasma Microturbulence Project
- (LLNL, General Atomics, U. Maryland, PPPL, U. Colorado, UCLA, U. Texas)
- DOE Scientific Discovery Through Advanced Computing
- _[http://fusion.gat.com/theory/](http://fusion.gat.com/theory/pmp)__[pmp](http://fusion.gat.com/theory/pmp)_
- J. Candy, R. Waltz (General Atomics)
- W. Dorland (Maryland) W. Nevins (LLNL)
- R. Nazikian, D. Meade, E. Synakowski (PPPL)
- J. Ongena (JET)

- Candy, Waltz (General Atomics)

**Greg Hammett, Princeton Plasma Physics Lab (PPPL)**_[http://w3.pppl.gov/~hammett](http://w3.pppl.gov/~hammett)__               AAAS Meeting, Seattle, Feb. 2003_

- _[http://fire.](http://fire.pppl.gov/)__[pppl](http://fire.pppl.gov/)__[.](http://fire.pppl.gov/)__[gov](http://fire.pppl.gov/)_

## The Plasma Microturbulence Project

- A DOE, Office of Fusion Energy Sciences, SciDAC (Scientific Discovery Through Advanced Computing) Project
- devoted to studying plasma microturbulence through direct numerical sumulation
- National Team (& four codes):
- GA (Waltz, Candy)
- U. MD (Dorland)
- U. CO (Parker, Chen)
- UCLA (Lebeouf, Decyk)
- LLNL (Nevins P.I., Cohen, Dimits)
- PPPL (Lee, Lewandowski, Ethier, Rewoldt, Hammett, ...)
- UCI (Lin)
- They’ve done all the hard work ...

## Summary:  Turbulence & Transport in Burning Plasmas

- Simple physical pictures of tokamak plasma turbulence & how to reduce it  (reversed magnetic shear, sheared flows, plasma shaping...)
- Several good ideas for improvements in fusion reactor designs
- Impressive progress with comprehensive 5-dimensional computer simulations being developed to understand plasma turbulence & optimize performance

## Cut-away view of aTokamak

## Helical orbit of particle following magnetic field

- (Size of particle gyro-orbit enlarged for viewing)(This is just a hand sketch:  real orbits have very smooth helical trajectory.)

- Helical orbit of particle following magnetic field

## Magnetic fields twist, form nested tori

## R. Nazikian et al.

## 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

## 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)

## Comprehensive 5-D computer simulations of core plasma turbulence being developed by 

- Comprehensive 5-D computer simulations of core plasma turbulence being developed by
- Plasma Microturbulence Project.  Candy & Waltz (GA) movies shown: d3d.n16.2x_0.6_fly.mpg & supercyclone.mpg,  from _[http://fusion.gat.com/comp/parallel/gyro_gallery.html](http://fusion.gat.com/comp/parallel/gyro_gallery.html)_ (also at
- _[http://w3.pppl.gov/~hammett/refs/2004](http://w3.pppl.gov/~hammett/refs/2004)_).

## 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

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

## +

- Most Dangerous Eddies:
- Transport long distances
- In bad curvature direction

- Sheared Flows

- Sheared Eddies
- Less effective

- Eventually break up

- =

- Biglari, Diamond, Terry (Phys. Fluids1990), Carreras, Waltz, Hahm, Kolmogorov, et al.

**Sheared flows can suppress or reduce turbulence**

## Sheared ExB Flows can regulate or completely suppress turbulence (analogous to twisting honey on a fork)

- Waltz, Kerbel, Phys. Plasmas 1994 w/ Hammett, Beer, Dorland, Waltz Gyrofluid Eqs., Numerical Tokamak Project, DoE/HPCC Computational Grand Challenge

- Dominant nonlinear interaction between turbulent eddies and -directed zonal flows.

- Additional large scale sheared zonal
- flow (driven by beams, neoclassical)
-  can completely suppress turbulence

## R. Nazikian et al.

## All major tokamaks show turbulence can be suppressed w/ sheared flows & negative magnetic shear / Shafranov shift

- Internal transport barrier forms when the flow shearing rate dv/dr > ~  the max linear growth rate linmax of the instabilities that usually drive the turbulence.
- Shafranov shift ’ effects (self-induced negative magnetic shear at high plasma pressure) also help reduce the linear growth rate.
- Advanced Tokamak goal: Plasma pressure ~ x 2,   Pfusion  pressure2 ~ x 4

- Synakowski, Batha, Beer, et.al. Phys. Plasmas 1997

## R. Nazikian et al.

## Stronger plasma shaping improves performance

- JET data from G. Saibene, EPS 2001, J. Ongena, PPCF 2001.  Seen in other  tokamaks also.

- Confinement degrades if density too large relative to empirical Greenwald density limit nGr = Ip /( a2), but improves with higher triangularity.
- Compared to original 1996 ITER design, new ITER-FEAT 2001 and FIRE designs can operate at significantly lower density relative to Greenwald limit, in part because of higher triangularity and elongation.

## Improved new fusion designs ↓ uncertainties

- Empirical Greenwald density limit
- Pressure limit
- New ITER-FEAT design uses segmented central solenoid to increase shaping.
- FIRE pushes to even stronger shaping (feedback coils closer) & reduced size with high field cryogenic CuBe (achievable someday with high-Tc superconductors?)

**Improved new fusion designs ****↓**** uncertainties**

|  | R 
(m) | a 
(m) | B 
(T) | Ip (MA) | nGr1020/m3 | <ne>
/nGr | x | x | Pfusion
MW | P/2R |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| ITER-96 | 8.14 | 2.80 | 5.68 | 21.0 | 0.85 | 1.50 | 1.75 | 0.35 | 1500 | 5.9 |
| ITER-FEAT | 6.20 | 2.00 | 5.30 | 15.1 | 1.19 | 0.85 | 1.85 | 0.48 | 400 | 2.0 |
| FIRE | 2.14 | 0.60 | 10.0 | 7.7 | 6.92 | 0.66 | 2.00 | 0.70 | 150 | 2.2 |
| Aries-AT ~goal | 5.20 | 1.30 | 5.86 | 12.8 | 2.41 | 1.00 | 2.18 | 0.84 | 1760 | 9.0 |

- Caveats:  remaining uncertainties regarding confinement, edge pedestal scaling, ELMs, disruptions & heat loads, tritium retention, neoclassical beta limits, but also good ideas for fixing potential problems or further improving performance.

## Solving gyro-averaged kinetic equation to find time-evolution of particle distribution function              f( x, E, v||/v, t)  
Gyro-averaged Maxwell’s Eqs. (Integral equations) determine Electric and Magnetic fields
“typical” grid 96x32x32 spatial, 10x20 velocity, x 3 species for 104 time steps.
Various advanced numerical methods: implicit, semi-implicit, pseudo-spectral, high-order finite-differencing and integration, efficient field-aligned coordinates, Eulerian (continuum) & Lagrangian (particle-in-cell).

- Gyro-averaged Maxwell’s Eqs. (Integral equations) determine Electric and Magnetic fields
- “typical” grid 96x32x32 spatial, 10x20 velocity, x 3 species for 104 time steps.
- Various advanced numerical methods: implicit, semi-implicit, pseudo-spectral, high-order finite-differencing and integration, efficient field-aligned coordinates, Eulerian (continuum) & Lagrangian (particle-in-cell).

**Complex 5-dimensional Computer Simulations being developed**

## Gyro-averaged, non-adiabatic part of 5-D particle distribution function: fs=fs( x,,,t) determined by gyrokinetic Eq. (in deceptively compact form):

- Gyrokinetic Eq. Summary

- Generalized Nonlinear ExB Drift
- Incl. Magnetic fluctuations

- (**x**,t) is gyro-averaged, generalized potential. Electric and magnetic fields from gyro-averaged Maxwell’s Eqs.

## Bessel Functions represent averaging around particle gyro-orbit

- Gyroaveraging eliminates fast time scales of particle gyration (10 MHz- 10 GHz)Easy to evaluate in pseudo-spectral codes.  Fast multipoint Padé approx. in other codes.

## Comparison of GYRO Code & Experiment

- Gyrokinetic turbulence codes now including enough physics (realistic geometry, sheared flows, magnetic fluctuations, trapped electrons, fully electromagnetic fluctuations) to explain observed trends in thermal conductivity, in many regimes.
- Big improvement over 15 years ago, when there were x10 – x100 disagreements between various analytic estimates of turbulence & expts.
- Now within experimental error on temperature gradient.  Importance of critical gradient effects emphasized in 1995 gyrofluid-based IFS-PPPL transport model.
- Caveats:  Remaining challenges: quantitative predictions of internal transport barriers, test wider range of parameters, & more complicated edge turbulence.

- Candy & Waltz, Phys. Rev. Lett. 2003

## Turbulence & Transport Issues Particularly Important in Burning plasmas

- Performance of burning plasma & fusion power plant very sensitive to confinement:  potential significant improvements
- Uncertainties:  Maintain good H-mode pedestal in larger machine at high density?  ELM bursts not too big to avoid melting wall?  Can internal transport barriers be achieved in large machine, for long times self-consistently with beta limits on pressure profiles and desired bootstrap current?
- In present experiments, pressure profile can be controlled by external heating, currents primarily generated inductively.  In a reactor, pressure and current profiles determined self-consistently from fusion heating and bootstrap currents.  (Fortuitously, bootrap currents give naturally hollow profiles, which gives favorable reversed magnetic shear.)
- Proposed Burning Plasma devices will pin down uncertainties in extrapolations: help design final power plant.
- Comprehensive computer simulations being developed to understand & optimize performance

## Summary:  Turbulence & Transport in Burning Plasmas

- Simple physical pictures of tokamak plasma turbulence & how to reduce it  (reversed magnetic shear, sheared flows, plasma shaping...)
- Several good ideas for improvements in fusion reactor designs
- Impressive progress with comprehensive 5-dimensional computer simulations being developed to understand plasma turbulence & optimize performance

## Selected Further References

- This talk:  _[http://fire.pppl.gov](http://fire.pppl.gov/)_ & _[http://w3.](http://w3.pppl.gov/~hammett)__[pppl](http://w3.pppl.gov/~hammett)__[.](http://w3.pppl.gov/~hammett)__[gov](http://w3.pppl.gov/~hammett)__[/~](http://w3.pppl.gov/~hammett)__[hammett](http://w3.pppl.gov/~hammett)_
- Plasma Microturbulence Project  _[http://fusion.gat.com/theory/pmp](http://fusion.gat.com/theory/pmp)_
- GYRO code and movies _[http://fusion.gat.com/comp/parallel/gyro.html](http://fusion.gat.com/comp/parallel/gyro.html)_
- GS2 gyrokinetic code _[http://gs2.sourceforge.net](http://gs2.sourceforge.net/)_
- My gyrofluid & gyrokinetic plasma turbulence references: _[http://w3.](http://w3.pppl.gov/~hammett/papers/)__[pppl](http://w3.pppl.gov/~hammett/papers/)__[.](http://w3.pppl.gov/~hammett/papers/)__[gov](http://w3.pppl.gov/~hammett/papers/)__[/~](http://w3.pppl.gov/~hammett/papers/)__[hammett](http://w3.pppl.gov/~hammett/papers/)__[/papers/](http://w3.pppl.gov/~hammett/papers/)_
- “Anomalous Transport Scaling in the DIII-D Tokamak Matched by Supercomputer Simulation”, Candy & 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”, Dorland, Jenko et al. 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.

## Backup Slides

## R. Nazikian et al.

## R. Nazikian et al.

## Recent advances in computer simulations

- Computer simulations recently enhanced to include all key effects believed important in core plasma turbulence (solving for particle distribution functions f( x, v||, v,t) w/ full electron dynamics, electromagnetic fluctuations, sheared profiles).
- Challenges:
- Finish using to understand core turbulence, detailed experimental comparisons and benchmarking
- Extend to edge turbulence
- Edge region very complicated (incl. sources & sinks, atomic physics, plasma-wall interactions)
- Edge region very important (boundary conditions for near-marginal stability core, somewhat like the sun's convection zone).
- (3) Use to optimize fusion reactor designs.  Large sensitivity  both uncertainty and opportunity for signficant improvement

## Comparison of experiments with 1-D transport model

- Caveats: core turbulence simulations use observed or empirical boundary conditions near edge.  Need more complicated edge turbulence code to make fully predictive & sufficiently accurate.  Edge very challenging: wider range of time and space scales, atomic physics, plasma-wall interactions...

- GLF23 based on gyrofluid & gyrokinetic simulations

- Kinsey, Bateman, et al., Nucl. Fus. 2003