LIGKA: a new gyrokinetic code in realistic tokamak geometry with full orbits

S. Günter, P. Lauber, A. Könies, S. PinchesMax-Planck-Institut für Plasmaphysik, Garching/Greifswald, Germany

D. Testa, A. FasoliCRPP Lausanne, Switzerland

and comparison with experiment

• LIGKA– Linear gyrokinetic non-perturbative tokamak model– [Ph. Lauber, Ph.D. Thesis, T.U. München 2003]

• CAS3D-K– Linear perturbative drift-kinetic approach for

stellarators– [A. Könies, Phys. Plasmas 7 1139 (2000)]

• HAGIS– Initial value nonlinear drift-kinetic f model– [S. D. Pinches et al., Comput. Phys. Commun. 111, 131 (1998)]

Codes developed at IPP

• Linear shear Alfven perturbations– Calculates mode frequency, growth rate and mode

structure, including FLR effects

• Non-perturbative– Allows change from MHD eigenmode structure– Nonlinear eigenvalue problem (Nyquist solver)

H. Qin, W. M. Tang, G. Rewoldt, Phys. Plas. 6 2544 (1999)Based on model by

LIGKA: Linear GyroKinetic shear Alfven physics

In addition:

• Accurate treatment of unperturbed particle orbits– Numerical integration of full

drift orbit effects (HAGIS)

• General tokamak geometry– From numerical equilibrium

code (e.g. HELENA)

H. Qin, W. M. Tang, G. Rewoldt, Phys. Plas. 6 2544 (1999)Based on model by

LIGKA: Linear GyroKinetic shear Alfven physics

LIGKA: Linear GyroKinetic shear Alfven physics

qRvA

2

JET #42979, t = 10.121s

LIGKACASTO

R

Benchmark for TAE mode with open gap: global mode, ballooning structure

[D. Borba and W. Kerner, J. Comp. Phys. 153 101 (1999)]

• Global modes• Anti-ballooning character• Formed at top of TAE gap• Stronger damping than TAE

1 ik 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Radius

Elec

trost

atic

Pote

ntia

l,

p=0

p=1

p=2

p=3

Freq

uenc

y [

/A]

Radius0.66 0.840.45

0.75JET #42979, t = 10.121s

Shear Alfvén

Continuum

p=0

p=1

p=2

p=3

Incr

easin

gly

dam

ped

LIGKA: Benchmark for KTAE modes

• Modeled via change in LIGKA code boundary conditions– No vacuum region

• Systematically find all stable modes– Including damping rates

• Analogous to TAE antenna experiments

– [Fasoli et al., PRL 76 1067 (1996)]

Frequency [/A]

Plas

ma

resp

onse

JET #42979, t = 10.121sTAE

KTAE

p=0p=1p=2

p=3p=4

10

12

14

16

18

20

0.35 0.4 0.45 0.5 0.55 0.6

[Conner et al, Proc. 21st EPS Conf., Montpellier, 18B 616 (1996)]

LIGKA: External antenna drive

Comparison with JET damping rate experiments

• so far: often large discrepancies between measured and calculated damping rates for TAE modes (except for PENN model)

• Wrong isotope scaling for fluid model reported

Fasoli, Jaun

ii

iiieff nmnA /

CAS3D-K (passing particles only) Asymptotic expansion in Aeff

Local approximation for passing particles

LIGKA (passing particles only)

0.5 1 1.5 2 2.5 3 3.5Aeff ~ mi/mp

0

0.1

0.2

0.3

0.4A. Könies

[%]

JET #42979, t = 10.121s

Isotope mass scaling ok in hybrid code

• Local fluid approximation: Aeff-1/2

• Kinetic model agrees with hybrid model: LIGKA and CAS3D-K

Comparison with JET experiments

PENN: - significant radiative damping in the plasma centre

- mode structure not TAE-like

Testa (2004): experimental mode structure (JET, similar discharge)

Comparison with PENN results

open TAE gap for experimental density profile

TAE gap closes for modified density profile (within exp. error bars!)

vA= B/ 0experimental density profilemodified density profile

Comparison with PENN results

Kinetic effects important if TAE gap closed

Damping rates increase up to 0.6 % (experiment ~2 %, open gap ~0.25 %)

# 52206, t=62.9s

ω/ωA0

ωTAE

=0.340

10 normalised radius

1

2e19

normalised radius0

0.70.8

temperature: ion / electron [keV]

2e19

q - profile

density / experimental density profile

1

4

2

3

0 1normalised radius0

Comparison with JET experiments

Z

R

ω/ωTAE = 0.98, γ/ω = 0.92%

3 4Radius [m]

arbi

trary

uni

ts

total perturbation(outward midplane)

0

0 1normalised radius

m=1m=2

m=30

Comparison with JET experiments

ω/ωTAE = 0.98, γ/ω = 0.92%

3 3.2 3.4 3.6 3.8 4

Radius [m]

arbi

trary

uni

ts

total perturbation(outward midplane)

0

Comparison with JET experiments

γ/ω = 1.5%

Summary and Conclusion

LIGKA: - linear gyrokinetic code with realistic tokamak geometry and fast particle orbits

• Agreement between calculated and measured damping rates strongly depends on density profile at the plasma edge (TAE gap open or closed)

• Is there a difference between (limiter) discharges with qa being a rational value and not?

Outlook:

• Code can deal with energetic particle modes as well (non-perturbative)

• Coupling to non-linear HAGIS code

• Further comparison with experiments

• ITER predictions