Electromagnetic Turbulence Simulations withKinetic Electrons from the the Summit Framework

Scott Parker and Yang ChenUniversity of Colorado, Boulder

Bruce Cohen, Andris Dimits, Bill Nevins and Dan Shumaker Lawrence Livermore National Laboratory

Jean-Noel Leboeuf and Viktor DecykUniversity of California, Los Angeles

19th IAEA Fusion Energy Conference Tuesday, October 15, 2002Paper: TH/P1-13

Questions/comments welcome: sparker@colorado.edu

Summit Framework: open source software environment for gyrokinetic turbulence particle simulations

Recent 3D toroidal electromagnetic (δB⊥) kinetic electron results reported

Moderate β significantly reduces energy transport

Outline

1) Electromagnetic kinetic electron results from the Summit Framework - Linear benchmarks - Nonlinear results - Collisional effects - Zonal flow dynamics - Wavelength spectra - How important is the mass ratio? - Convergence studies2) Summit Framework - Basic idea - Why bother? - Current status - Quasi-ballooning coordinates

β (%)

γ a

/ c s

GYROGS2

Summit

Growth Rateω

a /

c s

β (%)

Real Frequency

GYRO/GS2 results from Candy&Waltz JCP (2002)

Linear comparison betweenGS2, GYRO and Summit withkinetic electrons and δB

- Kinetic electrons increase growth rate (trapped-electron drive)

- Increasing β is stabilizing

- Growth rate "goes through the roof" when kinetic balloon threshold is crossed

β (%)

γ a

/ c s

Growth Rate

Summit Results: Three-Dimensional Toroidal Kinetic Electrons Electromagnetic e-i Collisions

β=0.2%

Energy Flux

χ i /

c s ρ

s

t cs / Ln

β=0.01%adiabatic e's

mi / me = 1836νei Ln/cs = 0.1

Summit shows a decrease in χi for increasingβ when below ballooning limit

Puzzle: Why do turbulence simulations give transportlevels that are greater than experimental values?e.g. D. Ross Sherwood 1C47 (2002)

(possibly global effects, inaccuracies in profile measurements, sensitivity to critical gradients, etc.)

Plausible solution: Experiments operate in this low transport region just below the kinetic ballooning threshold

β = µ0 n Te / B2 = βexp / 4

GYRO/GS2 results from Candy&Waltz JCP (2002)

γ a

/ c s

νei a / cs

GS2GYRO

Summit

Collisonality reduces trapped electron drive and is stabilizing

γ Ln/csχi csρs/Ln

R/LT

2

Critical gradient is lower with kinetic electrons, sub-criticalregion still exists.

χi with adiabatic electrons

γ kinetic e's

χi kinetic e's

t vti / qR

eφ/Te

Zonal flow damping with and without kinetic electrons

φ fin

al /

φ ini

tial

h = (r/R)1/2 / q2

Comparison with Rosenbluth-Hinton

Rosenbluth and Hinton PRL 80 724 (1998)

Residual level and damping of zonal flows are not changed significantly by kinetic electron physics

S(k x

)

A. U

.

S(k y

)

kx ρi

radial wave number

ky ρiy - other perp. direction

adiabatic e'sKinetic e's

Kinetic vs. adiabtic e wavelength spectra are similar - Kinetic e spectra has larger amplitude (more unstable due to trapped e's) - Kinetic spectra and has larger kr

(zonal flows are removed for these diagnostics)

χ i /

c s ρ

s

( mi / me )1/2

Scan of mass ratio dependence with kinetic electrons at very low-βCyclone base case (typical H-mode parameters)

Mass ratio dependence for these parameters is weak for mi/me greater than 400

χ i /

c s ρ

s

t cs / Ln

χ i /

c s ρ

s

t cs / Ln

8M, 64x64x3216M, 128x128x3232M, 128x128x32(particles, grid)

νei Ln/cs = 0.0νei Ln/cs = 0.05νei Ln/cs = 0.5

Convergence with respect to particle number

Results are well-converged withrespect to particle number, timestepand grid size

Box size convergence appears ok,doubling the box does not changeresults significantly

Bursty energy flux observed when approachingthe zero collisionality limit

Not unexpected from the entropy balance equation1 or the balance between dissipation and flux

1Hu and Krommes PoP 1 3211 (1994)

e-i collisionality scan of energy flux

Summit:

"Summit is an open-source framework for both local and global massively parallel gyrokinetic turbulence simulations with kinetic electrons and electromagnetic perturbations. Summit is part of the Plasma Microturbulence SciDAC Project."

from: www.nersc.gov/scidac/summit

SciDAC

PMP

Summit

Current work, features, physics

Realistic magnetic equilibrium (Leboeuf, Dimits, Shumaker)

Framework design, design of objects and methods (Decyk)

Quasi-ballooning coordinates (Dimits)

Electron fluid hybrid model with kinetic closure, electromagnetic, moderate beta (Cohen, Parker)

Full electron dynamics, both electrostatic and electromagnetic(Chen, Parker, Cohen)

e-i and i-i collisions (Chen)

Future work

Global effects (Leboeuf, Dimits, Shumaker)

Compressional component to B (Chen, Parker, Cohen)

Particle-continuum hybrid method (Vadlamani, Parker)

Why bother?

GK simulators are really driven by solving unsolved problems.

GK simulators are forced into a routine of continually adding physics to keep theircode competitive. If there are 6 codes, that means 5/6 times the scientist is solvinga problem with an already existing solution.

Solution

A software framework where the scientist can add his/her physics and tap existing features when/if needed.

Pitfalls

All gk simulators want to solve the same unsolved problem. (not an issue)

Why should I share my code features? (not an issue)

My existing code runs great, what is the (short term) payoff to install my features and get running within the framework? (big issue)

One massive code, little inovation, no cross-checks. (not an issue)

! LLNL/CU/UCLA Gyrokinetic Framework

! All codes should use this main program ! and call input.F at this time

program main_program . . .

!----------------------------------------------------! initilization

call mpi_setup call timer_setup

call initialize(runsteps,nt)

if (start) then call loader_wrapper else call restart_wrapper endif

!-------------------------------------------------------! main time loop

ipush=1 do timestep=1,runsteps

nt = nt + 1 t = (nt - 1)*dt

call accumulate

call poisson(timestep-1,ipush)

call efield

! predictor push ipush=0

call push_wrapper(timestep,ipush)

call accumulate

call poisson(timestep,ipush) . . .

Integration into framework is gradual, benchmarking at every step

B�

T oroidal-poloidal discretization

B

�

�

F ield-aligned-coordinatediscretization

B

�

�

Quas iballooning discretization

ζ

θ

grid is field-aligned, but grid discontinuityoccurs at ends of the box along z(magnetic field line does not connect back on itself after going once around poloidally)

z

y

z'

y'

grid is almost aligned and grid cells at the ends ofthe box along z' exactly match

Quasiballooning Coordinates

- almost field-aligned- avoids grid discontinuities in field line direction- fixed finite-difference stencil and particle shape in what can be a highly twisted, nonorthogonal computational domain

- general geometry- global implementation (annular geometry)

ζ

ri-1 i i+1

θ = θ0V’t = 0

0

The quasiballooning radial discretization uses pointsat the same physical toroidal angle as the reference point.

- ∼isotropic ⊥ particle shapes - ∼isotropic mesh-based smoothing

ζ

ri-1 i i+1

θ ≠ θ0V’t ≠ 0

0

field-alignedcoordinates(β = const.)

quasiballooning