Destabilization of TAEs in KSTAR Plasmas

C. M. Ryu, M. Shahzad, H. Rizvi, A. Panwar

POSTECHKorea

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Layout

I. Overview

II. Verification and Validation of GENE code forAEs

III. TAEs observations in KSTAR plasmas

IV. Simulations of TAEs in KSTAR plasmas

V. Summary

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Overview Destabilization of toroidal Alfven eigenmodes (TAEs) in KSTAR tokamak plasmas has been

studied by using the gyrokinetic code GENE. The GENE code is an Eulerian code which canrun fast to calculate the eigenmodes. For the KSTAR discharge, TAEs with low toroidal modenumber are shown to be excited by energetic particles (EPs) during the neutral beaminjection [1].

The dependence of the real frequencies, growth rates and mode structures of TAEs on the EPdensity gradients at different radial locations are studied, to understand the characteristics ofTAEs in KSTAR plasmas.

The equilibrium magnetic geometry and profiles are loaded from the experimental dataconstructed by using the internal interface module TRACER-EFIT, and all the three specieselectron, ion, fast particle with the realistic mass ratio (assuming deuterium plasma,mi/me=3672) are treated gyrokinetically.

The numerical simulations shows that a TAE excited near the core region has a rather broadmode structure, and the mode excited outside has a smaller extent. TAE with a smaller radialextent is more stable [2]. Thus, in KSTAR, TAEs can be rather easily excited in the core regionof a tokamak than the outside for a given EP density gradient, agreeing with observations.

References:-

[1]. H. Rizvi, C. M. Ryu and Z. lin, Nuclear Fusion 56, 112016 (2016).

[2]. M. Shahzad, H. Rizvi and C. M. Ryu Phys. Plasmas 23, 122511 (2016).

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Layout

I. Overview

II. Verification and Validation of GENE code forAEs

III. TAEs observations in KSTAR plasmas

IV. Simulations of TAEs in KSTAR plasmas

V. Summary

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GENE: nonlinear gyrokinetic Vlasov code

GENE stands for “Gyrokinetic Electromagnetic Numerical Experiment”.

Eulerian approach: solving the 5D (δf) distribution function on a fixed grid in (X,

vıı, μ).

Supports local (flux-tube) and global (full-torus) simulations.

Two options to use: 1. Initial value (IV) solver for both linear and nonlinear

simulations 2. Eigenvalue solver (EV) only for linear simulations.

Option 1 of linear simulation is used.

Allows fully gyrokinetic electrons and ions, electromagnetic fluctuations, collisions

and external E×B shear flows.

Realistic tokamak geometry and experimental profiles can be used.

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ITPA benchmark case The Plasma equilibrium for the simulations is chosen from the ITPA benchmark

case Ref. [4] and Ref. [3].

The safety factor profile, with, q0=1.71, qa=0.16

n=6, (m, m+1)=(10, 11), qTAE=1.75

Mode radial location r/a=0.5

Poloidal harmonics (m=9-13) for shear Alfven continuum spectrum, using another

spectral code.

The existence of

TAEs from the

KAES code

References:-[3]. A. Mishchenko, et.al. ,Phys. Plasmas, 16, 082105 (2009).[4]. A. Koenies, et.al. , “Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particlesdriven TAE dynamics”, IAEA-FEC, ITR/PI-34 (2012).

Simulation setup for GENE code

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Large aspect ratio circular tokamak, R0=10 m, a=1 m. On-axis B0 = 3.0 T.

Background plasma consists of electrons and hydrogen ions. EPs consist of

deuterium ions. The unperturbed particle distribution is Maxwellian.

Flat background plasma profiles, ne=2.0*1019 m-3, Te=Ti=1keV, βe=0.0009,

vA=1.46*107 m/s, fTAE≈ 66 kHz.

EP density profile,

Flat EP temperature profile,

Plasma is quasi-neutral in the zeroth order,

Convergence test

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Grid resolution scans show good convergences for the real frequency (circle) and

the growth rate (square) of a TAE mode.

Nominal resolution for simulation, grid points along

direction.

Benchmarking of GENE code for AEs

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The poloidal mode structures of Φ obtained from GENE code (lower

panels) in comparison with the radial mode structures from

GYGLES code (upper panels) [3].

Comparison of the dependence

of the growth rates (a) and

frequencies (b) on 1/LnEP for

GYGLES [3] and GENE.

Φ Φ

1/LnEP=2.5

1/LnEP=2.5

1/LnEP=5.0

1/LnEP=5.0

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(TEP scan for ITPA benchmark)

Comparison of the dependence of

the growth rates (c) and frequencies

(d) on TEP by keeping nEP fixed, for

GYGLES and GENE.

TAE Frequency remains within the

TAE gap.

Growth rate increases to maximum

and slightly decreases at higher TEP.

Comparison of the dependence of

the growth rates (c) and frequencies

(d) on TEP by keeping βEP fixed, for

GYGLES and GENE.

At low TEP TAE Frequency is

outside the TAE gap, and it remains

within the TAE gap for higher TEP.

Growth rate increases to maximum

at TEP≈230 KeV (vthEP=vA/3) and

decreases at higher TEP due to FOW

stabilization.

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Φ

Φ

TEP=50 KeV

The poloidal mode structures of

electrostatic potential (Φ) and parallel

vector potential (Apar) obtained from

GENE code in comparison with the radial

mode structures from GYGLES code at

TEP=50 keV and TEP=600 keV by keeping

fixed βEP.

At low TEP≈50 keV, EPM type mode

radially shifted inward (r/a ≈ 0.35), with

single dominated poloidal harmonic

(m=10), and frequency of mode lying in

the continuum.

At high TEP≈600 keV, TAE mode radially

localized at r/a=0.5, with coupling of two

poloidal harmonics (m, m+1=10, 11), and

frequency of mode in the TAE gap.

The results of frequency, growth rateand mode structures, obtained fromthe gyrokinetic Eulerian code (GENE)have a very good agreement with theresults from the gyrokinetic particle-in-cell code (GYGLES).

TEP=600 KeV

Φ

Layout

I. Overview

II. Verification and Validation of GENE code forAEs

III. TAEs observations in KSTAR plasmas

IV. Simulations of TAEs in KSTAR plasmas

V. Summary

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TAEs in KSTAR plasmasIn KSTAR tokamak plasmas, interesting types of Alfvenic instabilities are observed.

o TAEs during plasma current ramp-up stage, excited by NBI.

o Excitation of multiple TAEs corresponding to different m and same n.

o Steady state TAE observation.

Unlike other tokamaks, TAEs in KSTAR plasmas have rather low toroidal modes

(i.e., n ≈ 1, 2).

o For discharge # 13522,

o Frequency range from 250-530 kHz

o TAE lasts longer time (up to 2.3Sec), just before theH-mode.

o Good agreement with theoretical estimation(squares), with constant plasma rotation.

𝑓𝑇𝐴𝐸 ~1

𝑞0 < 𝑛𝑒>

o For discharge # 13752,

o TAE frequency ≈ 375 kHz

o Red squares are for fTAE (without proper rotation

effect) considering q0.

o Black stars are corresponding to (constant/ 𝑛𝑒) time

variation without q0.

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o For discharge # 10574.

o NBI beams with energies 90, 80 and 80 KeV.

o B=2.7 T

o Multiple signals of TAEs, frequency ranges

≈ 130-180 KHz.

o Toroidal mode number analysis shows the

low ‘n’ TAEs.

TAE excitation using GTC [1]TAE observation in KSTAR

Layout

I. Overview

II. Verification and Validation of GENE code forAEs

III. TAEs observations in KSTAR plasmas

IV. Simulations of TAEs in KSTAR plasmas

V. Summary

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Simulation setup: KSTAR plasmas

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KSTAR discharge 10574 at t = 1658 ms, at the time of the plasma current ramp-up phase with

the neutral beam injection (NBI). TAEs with n=2 have been found.

Background plasma consist of electrons and deuterium ions and EPs by NBI are also

deuterium ions. Their unperturbed distribution are Maxwellian.

On axis parameters, ne0=2.4*1019 m-3, Te0=Ti0=4 keV, βe0=0.0054, vA0=8.46*106 m/s, R=1.8

m, q0=2.35, fTAE ≈ 160 kHz,

On axis parameters for EPs, nEP0 ≈ 0.087*1019 m-3, TEP0/Te ≈ 20, vthEP ≈ 2.8*106 m/s, βEP0 ≈

0.0043.

The equilibrium profiles are loaded from the experimental data constructed using the GENE

internal interface module TRACER-EFIT.

EP density profile,

Plasma is quasi-neutral in the zeroth order,

Simulation domain

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Plasma profiles of electron

density (a) electron

temperature (b) and safety

factor q (c).

Shear Alfven frequency

continuum spectrum of KSTAR

discharge (10574) for toroidal

mode number n = 2 as a

function of the normalized

radius, shows a coupling of

poloidal harmonics m=2-14.

Convergence test using KSTAR plasma equilibrium

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Same parameters and profiles, except maximal value of the EP density gradient

at ρ=0.335.

Grid resolution scan shows good convergence for the real frequency (circle) and the

growth rate (square) of the TAE mode.

Nominal resolution for simulation, grid points along

EP temperature effects (keeping βEP constant)

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For EP temperature scan, same parameters and profiles, except the maximal value of

the EP density gradient at ρ=0.335 shown in left panels.

EP temperature is increased by keeping EP pressure constant.

The growth rate is maximum at the TEP/Te≈20, where the parallel resonant velocity

vpar=vA/3 [5] is close to vthEP

At a very high value of TEP, the mode growth rate decreases due to the finite orbit

width effect (FOW) [6].

FOW stabilizing effects

(vthEP=vA/3 ) resonance

References:-[5]. L. Chen, Phys. Plasmas, 1, 1519 (1994).[6]. N. N. Gorelenkov, et. al., Phys. Plasmas, 6, 2802 (1999).

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EP density gradient effect on TAEs

(Right) For TAEs at the first TAE gap, the EP density

profiles are shown in Fig. (a). Fig. (b) shows the EP

density gradients (κnEP) profiles.

The TAE frequency remain almost constant while growth

rate increases to maximum with increase of κnEP .

Poloidal mode structures of electrostatic potential (Φ)

and parallel vector potential (Apar) of the adjoining

poloidal harmonics m=5, 6 corresponding to the κnEP

value for the maximum EP drive.

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(Right) For TAEs at the 2nd TAE gap, the EP density

profiles are shown in Fig. (a). Fig. (b) shows the EP

density gradients profiles.

The TAE growth rate increases to maximum with

κnEP, and maximum at κnEP=25.

Poloidal mode structures of electrostatic potential (Φ)

and parallel vector potential (Apar) of the adjoining

poloidal harmonics m=6, 7 corresponding to the

κnEP=25.

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(Right) For TAEs at the third TAE gap, the EP

density profiles are shown in Fig. (a). Fig. (b) shows

the EP density gradients (κnEP) profiles.

The TAE growth rate increases to maximum with

κnEP, maximum at κnEP=22.5 and then stabilizing due

to decrease in radial extent of the mode.

Poloidal mode structures of electrostatic potential (Φ)

and parallel vector potential (Apar) of the adjoining

poloidal harmonics m=7, 8 corresponding to the κnEP

value for the maximum EP drive.

stabilization

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Threshold value of EP density

gradient increases with a higher

poloidal mode coupling.

Growth rate of a TAE with higher

poloidal mode numbers are smaller

than that with lower poloidal mode

numbers.

Efficiency(where the growth rate

maximum kappa) of the EP drive for

the TAE decreases for a higher

poloidal mode coupling.

At higher EP density gradient, TAEs

with higher poloidal harmonics are

more stable. –growth rate smaller

Mode frequencies calculated from simulations overplotted on

the ideal MHD Alfven continuum; red lines are frequencies

corresponding to the κnEP,th, black lines are frequencies

corresponding to the κnEP values for the maximum EP drive.

Summary We have presented the first linear global gyrokinetic Eulerian simulation of the

excitation of Alfven eigenmodes (AEs) by fast particles in a tokamak plasmasusing the GENE code.

The GENE code has been verified and validated for AEs destabilized by the EPs.

For KSTAR discharge (10574), TAEs with poloidal harmonics (5, 6), (6, 7) and (7, 8)for a toroidal mode number n=2 are found to be excited at the first three radialmode locations.

The threshold value of κnEP,th to excite the TAE mode increases with the radiallocation.

The growth rate of a TAE with higher poloidal mode numbers is smaller than thatwith lower poloidal mode numbers. This indicates that perpendicularwavenumber kϴ may play an important role in finite orbit stabilization.

The EP drive efficiency for TAEs decreases for a higher mode radial position.

At a higher EP density gradient, TAEs with higher poloidal harmonics are lessunstable due to the decrease in the radial extents of the modes.

The core region of a tokamak is more favorable for TAE excitation, but if the EPdensity gradient becomes small enough, it can be stabilized.

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Thank you for your attention

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