Vienna, Austria - Nucleus · Vienna, Austria IAEA Scientific Secretary Ms. Sehila Maria Gonzalez de Vicente International Atomic Energy Agency Vienna International Centre, Wagramer

Vienna, Austria 12 – 14 June 2017

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8th

IAEA Technical Meeting on

Theory of Plasma Instabilities

12 -14 June, 2017

Vienna, Austria

IAEA Scientific Secretary

Ms. Sehila Maria

Gonzalez de Vicente

International Atomic Energy Agency

Vienna International Centre, Wagramer

Straße 5

PO Box 100, A-1400 Vienna, Austria

NAPC Physics Section

Tel: +43-1-2600-21753, Fax: +43-1-26007

E-mail: [email protected]

International Programme Advisory Committee

Chair: T.S. Hahm (Republic of Korea)

H. Wilson (UK), B. Breizman (USA), C. Hegna (USA), Y. I. Kolesnichenko

(Ukraine), A. G. Peeters (Germany), M. Yagi (Japan), F. Zonca (Italy)

Meeting Website:

https://nucleus.iaea.org/sites/fusionportal/Pages/List-of-TMs-on-Theory-of-Plasma-

Instabilities.aspx

Second Joint ITER-IAEA Technical Meeting

Analysis of ITER Materials and Technologies

11-13 December 2012

The Gateway Hotel Ummed Ahmedabad

Ahmedabad, India

mailto:[email protected]

https://nucleus.iaea.org/sites/fusionportal/Pages/List-of-TMs-on-Theory-of-Plasma-Instabilities.aspx

https://nucleus.iaea.org/sites/fusionportal/Pages/List-of-TMs-on-Theory-of-Plasma-Instabilities.aspx

Topics

I. Overview: State of the art and importance of multi-scale

physics for understanding burning plasmas;

II. Linear and nonlinear instabilities and their

theoretical/computational methodologies including critical

gradient problem and comparison with experiments;

III. Core/edge turbulent transport including momentum

transport, turbulence-profile interaction, barrier formation,

core-edge coupling, and isotopic dependence;

IV. Magneto-hydrodynamic (MHD) instabilities including

energetic particle physics and their interaction with

microturbulence in burning plasmas;

V. Physics and modelling of multi-scale interactions and their

impact on plasma performance and control.

1

Monday, 12 June, 2017

9:00-9:30 Registration

9:30-9:45 Welcome and Opening Address

S. Gonzalez- De-Vicente, T.S. Hahm

Session 1: MHD 1

Chair: V. Pastukhov

9:45-10:20 I-1: Del Sarto D.

Fast secondary reconnection in the sawtooth crash

10:20-10:55 I-2: Imada K.

Finite orbit width effects on NTM threshold

10:55-11:25 Coffee Break

Session 2: MHD 2

Chair: V. Pastukhov

11:25-12:00 I-3: Brunetti D.

Analytic characterisation of ideal infernal type instabilities in tokamaks with

large edge pressure gradients

12:00-12:25 O-1: Ferrari H.E.

Effect of ideal kink instabilities on particle redistribution

12:25-13:30 Lunch Break

Session 3: Basic tokamak physics

Chair: D. Del Sarto

13:30-13:55 O-2: Nicolas T.

Self-collition algorithms for Fokker - Planck operator simulation in full - f PIC

codes and direct verification of classical transport

13:55-14:20 O-3: Qi L.

Bounce-averages gyrokinetik simulation of trapped electron turbulence in

elongated tokamak

14:20-14:45 O-4: Grosshauser S.R.

Role of linear dynamics in saturated gyro-kinetic turbulence

14:45-15:10 O-5: Elfimov A.G.

Excitation of Geodesic modes by plasma fluxes during neutral beam injection in

tokamaks

2


Session 4: Transport Barrier

Chair: S. Mahajan

15:40-16:15 I-4: Galassi D.

Impact of diverted geometry on turbulence and transport barrier formation in

3D global simulations of tokamak edge plasma

16:15-16:40 O-6: Pastukhov V.P.

Simulations of self-sustained turbulent convection and formation of ITB in

tokamak core plasmas

16:40-17:05 O-7: Klaywittaphat P.

Plasma instability during ITBs formation with pellet injection in tokamak

17:05-17:35 Discussion on Sessions 1-4

S. Mahajan

Tuesday, 13 June, 2017


Session 5: Particle Transport 1

Chair: W. Wang

9:30-10:05 I-5: Nakata M.

Gyrokinetic simulations on turbulent transport of D-T ions and He-ash in ITER

plasmas

10:05-10:40 I-6: Falessi M.

Gyrokinetic theory for particle transport in fusion plasmas


Session 6: Particle Transport 2

Chair: W. Hornsby

11:10-11:45 I-7: Nunami M.

Kinetic simulation studies for impurity transport in stellarator plasmas

11:45-12:20 I-8: Raghunathan M.

Tungsten heavy-impurity behaviour in internally kinked JET-like hybrid

scenarios with toroidal flow

3

12:20-13:20 Lunch Break

Session 7: Flows and Momentum Transport

Chair: M. Nunami

13:20-13:55 I-9: Hahm T.S.

Collisionless zonal flow decay due to resonant magnetic perturbations in

tokamak plasmas

13:55-14:30 I-10: Wang W.

Non-inductive electron current generation in toroidal plasmas

14:30-15:05 I-11: Hornsby W.

Core intrinsic toroidal rotation mechanisms tested against ASDEX Upgrade

observations


Session 8: Edge Turbulence

Chair: T. Hahm

15:35-16:10 I-12: Lin Z.

GTC simulations of effects of resonant magnetic perturbations on DIII-D edge

transport

16:10-16:45 I-13: Mahajan S. M.

Gyro kinetic investigations of Instabilities and transport in tokamak pedestals

16:45-17:10 O-8: Jhang H.

A mechanism for the strong excitation of zonal modes during an edge pedestal

collapse


T. Hahm

4

Wednesday, 14 June, 2017


Session 9: Energetic partcle physics 1

Chair: H. Jhang

9:30-10:05 I-14: Lu Z.X.

Local and global analysis of symmetry breaking for ITG and BAE modes

10:05-10:30 O-9: Ryu C.M.

Destabilization of TAEs in KSTAR Plasmas

10:30-10:55 O-10: Zhou D.

Stabilization of RSAEs by barely trapped energetic electrons in tokamak

plasmas


Session 10: Energetic particle physics 2

Chair: Z. Lin

11:20-11:45 O-11: Marchenko V.S.

Excitation of beta-induced Alfven eigenmode by a plasma flow around magnetic

island

11:45-12:10 O-12: Xiang N.

Heat flux transported by fast electrons in front of lower hybrid wave antenna on

EAST tokamak


Z. Lin

12:25 Closing

5

Abstracts

List of Invited Orals:

I-1: Del Sarto D., Fast secondary reconnection in the sawtooth crash

I-2: Imada K., Finite orbit width effects on NTM threshold

I-3: Brunetti D., Analytic characterisation of ideal infernal type instabilities in tokamaks with

large edge pressure gradients

I-4: Galassi D., Impact of diverted geometry on turbulence and transport barrier formation in

3D global simulations of tokamak edge plasma

I-5: Nakata M., Gyrokinetic simulations on turbulent transport of D-T ions and He-ash in ITER

plasmas

I-6: Falessi M., Gyrokinetic theory for particle transport in fusion plasmas

I-7: Nunami M., Kinetic simulation studies for impurity transport in stellarator plasmas

I-8: Raghunathan M., Tungsten heavy-impurity behaviour in internally kinked JET-like hybrid

scenarios with toroidal flow

I-9: Hahm T.S., Collisionless zonal flow decay due to resonant magnetic perturbations in

tokamak plasmas

I-10: Wang W., Non-inductive electron current generation in toroidal plasmas

I-11: Hornsby W., Core intrinsic toroidal rotation mechanisms tested against ASDEX Upgrade

observations

I-12: Lin Z., GTC simulations of effects of resonant magnetic perturbations on DIII-D edge

transport

I-13: Mahajan S. M., Gyro kinetic investigations of Instabilities and transport in tokamak

pedestals

I-14: Lu Z.X., Local and global analysis of symmetry breaking for ITG and BAE modes

6

I-1: Fast secondary reconnection in the sawtooth crash

Daniele Del Sarto1, Maurizio Ottaviani

2

1

IJL UMR 7198 CNRS, Université de Lorraine, F-54506, Vandoeuvre-les-Nancy, France 2

CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France

E-mails of Corresponding Author: [email protected], [email protected]

The sawtooth cycle is

an almost periodic oscillation of temperature in a tokamak plasma,

characterized by a slow growth and a fast collapse [1]. The internal kink mode instability is

typically considered an ingredient in this cycle, although in the resistive MHD regime its growth

rate is considered too slow to account for the observed fast sawtooth collapse, especially in

weakly collisional plasmas. For these reasons, non-collisional effects are usually called in to

explain experimental observations [2].

Here we approach this problem from a different point of view, by performing an analysis of

secondary reconnecting instabilities in thin current sheets with both resistive and electron inertia

effects. We show that when the current sheet is generated by a primary instability of the internal

kink type (large ∆’ regime), reconnection proceeds thanks to a secondary tearing-mode

developing on a time scale much shorter than the primary instability characteristic time. By

applying these results in the purely resistive reconnection regime we obtain estimates in

agreement with the numerical results obtained by Yu et al. [3] for the nonlinear dynamics of the

internal kink instability in a cylindrical tokamak. When a transition to an inertia-driven

reconnection regime is allowed, we also find that non-collisional physics becomes important for

the sawtooth crash above a value of the Lundquist number which scales like S ∼ (R/de)12/5

in

terms of the tokamak major radius R and of the electron skin depth de. This value is commonly

achieved in present day devices. As collisionality is further reduced, the characteristic rate

increases, approaching Alfvénic values when the primary instability approaches the collisionless

regime. These results have been recently discussed in Ref.[4].

References [1] S. Von Goeler, W. Stodiek, N. Sauthoff, Phys. Rev. Lett. 33, 1201 (1974).

[2] A.W. Edwards, D.J. Campbell, W.W. Engelhardt et al., Phys. Rev. Lett. 57, 210 (1986).

[3] Q. Yu, S. Gunter, K. Lackner, Nucl. Fusion 54, 072005 (2014).

[4] D. Del Sarto, M. Ottaviani, Phys. Plasmas 24, 012102 (2017).



7

I-2: Finite Orbit Width Effects on NTM Threshold

K. Imada1, J.W. Connor

2, A. Dudkovskaia

1, P. Hill

1, H.R. Wilson

1

1York Plasma Institute, Department of Physics, University of York, Heslington, York,

YO10 5DD, U.K. 2CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB, U.K.

E-mail of Corresponding Author: [email protected]

The control and stabilisation of neoclassical tearing modes (NTMs) is essential to the successful

operation of future tokamaks, such as ITER. An NTM control system requires knowledge of the

magnetic island threshold physics, whereby a sufficiently small seed island tends to heal itself.

Theory and experiments indicate that the threshold island width is typically O(1cm), which is

comparable to the banana orbit width of trapped ions, ρb. In toroidal geometry, the finite banana

width effect gives rise to the neoclassical polarisation current, which is induced when the

magnetic island chain is in relative motion with the plasma [1]. This in turn generates a parallel

return current, which contributes to the magnetic island evolution via the modified Rutherford

equation. Whether stabilising or destabilising, it will influence the threshold for w ~ ρb.

By expanding in the small ratio of w/r, where r is the minor radius where the island is located,

but retaining the ordering w ~ ρb, we have developed a new drift kinetic theory for the ion

response to the magnetic island. This results in a 4D particle orbit-averaged kinetic equation in

toroidal geometry, where the solution depends on the toroidal canonical momentum, pϕ,

(representing poloidal flux, ψ), the helical angle ξ (labelling the field lines at the rational

surface), pitch angle λ and kinetic energy v2. Our new code solves the above equation for the

perturbed ion distribution function, taking into account the momentum conservation and

quasineutrality, both of which are crucial for determining bootstrap and neoclassical polarisation

current perturbations.

In this paper, we present our new results on the ion response to the magnetic island perturbation.

When collisions are neglected, the ion distribution

function is flattened across the drift-island structure;

the same as the island geometry, but shifted radially

by an amount proportional to ρθ (ρθ is the poloidal

Larmor radius; ρb = ε1/2

ρθ, and ε is the inverse aspect

ratio). Our numerical calculations show that, even

for a moderately small ratio of ρθ/w, the finite orbit

width effects are significant, particularly around the

island separatrix layer. Not only is the density

flattening across the island incomplete (with

consequences for the bootstrap current perturbation),

but there exists a sub-stantially wider ion parallel

flow layer than predicted by the analytic theory.

There is also a substantial flow within the island,

which had not been considered in earlier works.

This is likely to have a significant contribution to

the modified Rutherford equation, and hence to the

island threshold physics.

Fig.1: The radial profile of perturbed ion

parallel flow across the island O-point.

Blue is the analytic result in for ρθ << w,

while red is the numerical result with

ρθ/w = 0.2 (|w| = 0.1 on the plot).


8

References: [1] H.R. Wilson et al., Phys. Plasmas 3, 248 (1996)

This project is funded by EPSRC grand number EP/N009363/1. Computational time is provided

by Plasma Physics HEC Consortia (grant number EP/L000237/1, UK), Marconi-Fusion (Italy)

and IFERC-CSC (Japan).

9

I-3: Analytic characterisation of ideal infernal type instabilities in tokamaks with large

edge pressure gradients

D. Brunetti1, W. A. Cooper

2, J. P. Graves

2, E. Lazzaro

1, A. Mariani

2, S. Nowak

1 and

C. Wahlberg3

1Istituto di Fisica del Plasma IFP-CNR, Via R. Cozzi 53, 20125 Milano, Italy

2École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), 1015

Lausanne, Switzerland 3Department of Astronomy and Space Physics, EURATOM/VR Fusion Association, P.O. Box

515, Uppsala University, SE-751 20 Uppsala, Sweden


The quiescent high confinement mode (QH-mode) tokamak regimes share with the H-mode a

large edge pressure gradient and a high energy confinement time. Experimental observations in

QH-mode conditions showed the appearance of low-n magnetohydrodynamic oscillations which

replace the ELM activity (ELMs have n>>1). The associated energy loads on the plasma facing

components are much lower compared to regimes where ELMs are present. The appearance of

these benign low-n oscillations has been linked with kink/peeling modes.

The steep edge pressure gradient in the low collisionality regime is associated with a significant

bootstrap current contribution which reduces locally the magneti shear. When the magnetic

shear is allowed to become small, infernal modes can be driven unstable by an increase of the

pressure gradient. These instabilities are characterised by toroidicity induced coupling between a

main Fourier mode and its neighbouring sidebands. Numerical studies of low-n MHD

instabilities in the QH-mode regime with a plateau in the safety factor near the edge found

infernal-like features.

Hence in this work we focus our attention on the analytic description of low-n edge localised

infernal-type instabilities with the inclusion of the equilibrium toroidal rotation and a vacuum

region that separates plasma and the metallic wall (ideal or resistive). Instability conditions for

such type of perturbation are derived and discussed in connection with experimental findings.


10

I-4: Impact of diverted geometry on turbulence and transport barrier formation in 3D

global simulations of tokamak edge plasma

D. Galassi1, P. Tamain

2, C. Baudoin

2, H. Bufferand

2, G. Ciraolo

2, N. Fedorczak

2, Ph. Ghendrih

2,

N. Nace2 and E. Serre

1

1 Aix-Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France

2 CEA, IRFM, 13108 Saint-Paul-lez-Durance, France


Electrostatic turbulent transport in tokamak edge plasma is widely recognised to impact the

Scrape-Off Layer (SOL) width and the quality of the confinement through the development of

transport barriers. The multi-scale nature of the problem demands a simulation tool able to avoid

time and space scale separations. This first-principle approach is adopted by the flux driven,

fluid turbulence code TOKAM3X [1]. While the effort of edge turbulence modelling is usually

focused on simplified limited plasma configurations, it seems mandatory to move towards more

realistic magnetic equilibria. In this framework, TOKAM3X simulations have been run with

COMPASS-like and JET-like diverted magnetic configurations, in order to highlight the

influence on turbulent transport of specific features of the divertor geometry, as the presence of

the X-point and a strong shaping of the flux surfaces [2].

Turbulence resulting from simulations is ballooned around the outboard midplane, consistently

with the interchange nature of the instability. Through the action of the parallel transport,

turbulent structures acquire a flux-tube shape, although keeping a non-zero parallel wave

number, and extend in the parallel direction towards the divertor region. At the divertor

entrance, filaments become strongly elongated in the radial direction, under the effect of the flux

expansion, as observed in experiments. Fluctuations are strongly damped in the X-point

proximity, both in closed flux surfaces and in few Larmor radii outside the separatrix.

Nevertheless, further away in the SOL, an elevated level of fluctuations is registered, leading to

an effective radial transport, whose amplitude depends on the specific geometry.

Unlike the case with limiter configuration, a spontaneous formation of a steady transport barrier

is observed in diverted geometry in the vicinity of the Last Closed Flux Surface, leading to a

reduction up to ≈ 70% in radial turbulent transport. By consequence, the radial pressure gradient

is locally enhanced. The efficiency of the transport barrier is characterized as a function of the

parameters of the model, such as the particle source driving the radial pressure gradient and the

ion temperature. The shaping of the flux surfaces is found to impact significantly the ExB shear,

and so, ultimately, the quenching of turbulent structures.

References: [1] P. Tamain et al. , J. Comp. Phys. 321 (2016) 606 [2] D. Galassi et al. , Nucl. Fusion 57 (2017) 036029


11

I-5: Gyrokinetic simulations on turbulent transport of D-T ions and He-ash in ITER

plasmas

Motoki Nakata1, Mitsuru Honda

2, and Masanori Nunami

1

1National Institute for Fusion Science / National Institutes of Natural Sciences, Toki, Japan 2National Institutes for Quantum and Radiological Science and Technology, Naka, Japan


Understanding of turbulent transport processes and accurate predictions of the resultant

transport levels are crucially important issues towards future

burning plasma experiments in ITER and DEMO reactors.

Since the burning plasmas are always composed of multiple

particle species such as fuel ions (D and T), He-ash, and the

other impurities, the systematic studies on the particle and

heat transport are indispensable to realize the sustained

burning state with optimized impurity exhausts and D/T

fueling. In earlier works [e.g., Ref. 1], the D-T and He-ash

(or impurity) transport has separately been investigated for

the ITG-turbulence in circular tokamak approximations, and

an imbalance of the D-T particle fluxes has been found in a

relatively higher collisionality.

In this study, the ITG-TEM driven turbulent heat and particle transport in the ITER D-T-He

plasmas is explored with a gyrokinetic Vlasov simulation GKV [2], where simultaneous

treatments of multiple ions and real-mass kinetic electrons including their inter-species

collisions are incorporated [3, 4], and a good prediction capability has been confirmed against

the actual JT-60U tokamak experiment [5]. In particular, we explore an optimal profile

condition which satisfies the steady burning plasma

condition [6] with He-ash exhaust (outward) and fuel-pinch

(inward), i.e., ΓHe > 0 ; ΓD,T < 0 ; 𝜂𝑖𝑇𝑖Γ𝐻𝑒 > 𝑄𝑖/𝛼∗ and

Γ𝑒~0 (or equivalently 𝜏𝐻𝑒 < 𝛼∗𝜏𝐸 ), where 𝛼∗~7 - 15 is a

constant. The GKV simulations reveal the different

nonlinear saturation levels and spatial structures in D-T ions

and He-ash fluctuations [Fig. 1]. It is found that the

imbalance of the D-T particle fluxes becomes more

pronounced in proportion to the He-ash accumulation.

Furthermore, the density-gradient scans of turbulent particle

and energy fluxes at 𝜌 =0:5 clarify that there exists an

optimal profile regime (Rax/Ln ≤ 1.27) in which the above

steady burning condition is satisfied [Fig. 2]. Effects of the

plasma shape on turbulent transport properties will also be discussed.

References: [1] C. Estrada-Mila, J. Candy et al., Phys. Plasmas 12 022305 (2005)

[2] T. -H. Watanabe and H. Sugama, Nucl. Fusion 46 24 (2006)

[3] M. Nakata, M. Nunami et al., Comput. Phys. Commun. 197 61 (2015)

[4] M. Nunami, M. Nakata et al., Plasma Fusion Res. 10 1403058 (2015)

[5] M. Nakata, M. Honda et al., Nucl. Fusion 56 086010 (2016)

[6] D. Reiter, G. H. Wolf et al., Nucl. Fusion 30 2141 (1990)

Fig. 1: Fluctuations of D (in blue), T

(in yellow), and He(in red) in multi-

species ITG-TEM turbulence.

Fig. 2: Density-gradient scan of

particle and energy fluxes, where the

steady burning condition is satisfied

in Rax/Ln ≤ 1:27(dashed-line).


12

I-6: Gyrokinetic theory for particle transport in fusion plasmas

M. Falessi1,2

, F. Zonca3

1

Department of Physics, "Roma Tre" University, Via della Vasca Navale, 84 (00146) Roma,

Italy. 2 Istituto nazionale di fisica nucleare, Sezione di “Roma 3”, Via della Vasca Navale, 84 (00146)

Roma, Italy. 3ENEA - C.R. Frascati UTFUS-MAG, Via E. Fermi, 45 (00044) Frascati (Roma), Italy

Predicting the dynamics of a thermonuclear plasma during a magnetic confinement experiment

is fundamental in order to make nuclear fusion a reliable source of energy. The development of

a set of equations describing the plasma evolution on a given time scale is the main requirement

to reach this goal. A limited amount of works have studied in a self-consistent way collisional

transport and fluctuation induced transport. The motivation of this work stems from the

fundamental importance of the self-consistency of the adopted description in order to understand

transport processes on the energy confinement (transport) time scale because of the mutual

interaction between collisions and turbulence. In turn, this is crucial in order to predict fluxes of

particle and energy and, ultimately, the overall plasma evolution. Using flux coordinates and the

drift ordering we derive a set of evolutions equations for the number of particles and the energy

density on the transport time scale. These equations show the interplay between collisions and

fluctuations and, in particular, show that fluctuations may enhance collisional transport while

the collisions can damp long lived structures formed by saturated instabilities, i.e zonal

structures. Fluctuation induced fluxes are described using gyrokinetic field theory, which makes

a comparison with the theory of phase space zonal structures possible, revealing that the

fluctuations induced part of the transport equations can be obtained by taking the proper

moment of the long length scale limit of the equation governing the evolution of phase space

zonal structures. Finally, we show that plasma nonlinear evolution can yield to structures

formation that are characterized by mesoscales, intermediate between the typical ones of plasma

turbulence and those of the reference plasma equilibrium.

13

I-7: Kinetic simulation studies for impurity transport in stellarator plasmas

Masanori Nunami1,2

, Motoki Nakata1,2

, Masahiko Sato1

1National Institute for Fusion Science / National Institutes of Natural Sciences, Toki, Japan

2Graduate University for Advanced Studies, Toki, Japan


Understanding of transport phenomena of plasma heat and particles is one of the most important

issues to design the fusion reactors. Especially, the studies

on the transport of the mixed plasma consists of multi-ion-

species are strongly demanded for burning plasma studies

in the ITER, future fusion reactors, and also stellarator

systems such as the Large Helical Device (LHD) [1]. In the

LHD experiments, high ion temperature plasmas often have

the extremely hollow impurity density profiles, namely

impurity hole, which is also a critical issue for high

performance in magnetically confined plasmas. In the

plasmas, the particle fluxes of each species should be

quantitatively evaluated with kinetic simulation approaches,

where the neoclassical particle fluxes should be balanced

with the turbulent particle fluxes if the system in the steady

state with negligible auxiliary particle sources. In this work,

in order to clarify above issues, gyrokinetic simulations by

using GKV [2] and drift kinetic simulations by using

PENTA [3] are carried out to investigate anomalous and neoclassical transport of particles

including impurity ion in the stellarator plasmas. In the

LHD plasmas, the gyrokinetic simulations indicate that

the anomalous particle flux of the impurity carbon

would be outward directed [4]. On the other hand, the

external momentum torque by the neutral beam

injection affects the neoclassical particle flux of carbon

through the radial electric field generation. If there

exists co-injected external torque, there can be not only

ion-root radial electric field but also electron-root

electric field. Therefore, in the case of the electron-root

electric field, the neoclassical carbon flux can be

inward directed which is consistent with the fact that

the positive neoclassical particle fluxes and the negative

turbulent fluxes should be balanced in a steady state.

References: [1] A. Komori, et al., Fusion Sci. Technol. 58, 1 (2010). [2] T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006).

[3] D. A. Spong, Phys. Plasmas 12, 056114 (2005). [4] M. Nunami, et al., 26th IAEA Fusion Energy Conference, TH/P2-3 (2016).

0.5 1 1.5-15

-10

-5

0

LTe / LTe0

Γs

e

H

He

C

Fig. 1: Anomalous particle fluxes of each species for changing electron temperature gradients in the LHD plasma.

-10 0 10 20

0

5

10

[×10+19

]

Σi Zi Γi

Γe

Er [kV/m]

Γ [m

2/s

]

F|| = 0

F|| = F||exp

F|| = 5 x F||exp

Fig. 2: Dependences of neoclassical particle fluxes of electron (red curves) and total ions (blue curves) to radial electric field with external momentum torques.


14

I-8: Tungsten heavy-impurity behaviour in internally kinked JET-like hybrid scenarios

with toroidal flow

M. Raghunathan1, J. P. Graves

1, T. Nicholas

1, W. A. Cooper

1, X. Garbet

2, and

D. Pfefferlé3

1École Polytechnique Federale de Lausanne (EPFL), Centre de Recherches en Physique des

plasmas (CRPP), CH-1015 Lausanne, Switzerland 2CEA, IRFM, F-13108 Saint Paul-lez-Durance, France

3Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA

In tokamaks like ITER with a tungsten wall, or JET with an ITER-like wall (ILW), it is

imperative to control tungsten accumulation in the core of operational plasmas, especially since

tungsten accumulation can lead to radiative collapse and disruption [1]. We investigate the

behaviour of tungsten trace impurities in a JET-like hybrid-scenario with both axisymmetric and

saturated 1/1 ideal helical-core in the presence of strong plasma rotation. For this purpose, we

develop particle orbits in a saturated internally kinked plasma using VENUS-LEVIS [3],

modified to include plasma rotation [4] and parallel transport to simulate the behaviour of the

tungsten particles with neoclassical effects [5]. We find there to be a competition between the

centrifugal force causing outward diffusion and the neoclassical friction force which produces

an inward pinch. We find that the presence of the 1/1 saturated ideal continuous mode augments

the friction force and leads to a strong inward pinch of impurities towards the magnetic axis

despite the strong outward diffusion provided by the centrifugal force, as frequently observed in

experiments.

References: [1] J. P. Graves et al, Plasma Phys. Control Fus. 57 014033 (2015).

[2] D. Pfefferlé et al, Comput. Phys. Commun. 185, 3127 (2014).

[3] Brizard, A.J., Phys. Plasmas 2, 459 (1995).

[4] Nakajima, N. and Okamoto, Journal of the Physical Society of Japan 61, 833 (1992).

[5] K. G. McClements and R. .J. McKay, Plasma Phys. Control Fus. 51 115009 (2009).

15

I-9: Collisionless Zonal Flow Decay due to Resonant Magnetic Perturbations in Tokamak

Plasmas

T.S. Hahma,b

and G.J. Choia

aSeoul National University, Seoul, Korea

bNational Fusion Research Institute, Daejeon, Korea


Externally imposed non-axisymmetric resonant magnetic perturbations (RMPs) can mitigate or

suppress large edge localized modes (ELMs) in tokamak H-mode plasmas [1,2]. However, this

results in an increase of the L-H transition power threshold [3-5]. Motivated from this

observation, we perform a theoretical study of the 3D magnetic field effect on zonal flows in

tokamak plasmas using gyrokinetic equations, extending the previous works on axisymmetric

tokamak [6,7] and LHD-like stellarator [8]. We find that tangential component of the 3D

magnetic field (parallel to the original tokamak magnetic field) induces a slow secular radial

drifts of toroidally trapped particles. Velocity-dependence of these drifts causes a long term

phase-mixing of zonal flows. Consequently, the zonal flows asymptote to the Rosenbluth-

Hinton residual level in a short time scale, but further decay algebraically in time afterwards.

This long term decay rate is comparable to the collisional decay rate for the present day

tokamaks for 𝑞𝑟𝜌𝑖 ~1, but can be faster in the future machines with higher edge temperature. As

zonal flows play a key role triggering the L-H transition by regulating drift wave turbulence [9],

our result indicates a lower zonal flow level and thus a higher L-H transition power threshold in

the presence of stronger 3D field in tokamak plasmas.

References: [1] T.E. Evans et al, Physical Review Letters 92, 235003 (2004).

[2] Y.M. Jeon et al, Physical Review Letters 109, 035004 (2012).

[3] P. Gohil et al, Nuclear Fusion 51, 103020 (2011).

[4] S.M. Kaye et al, Nuclear Fusion 51, 113019 (2011).

[5] W.-H. Ko et al, 58th Annual Meeting of the APS Division of Plasma Physics (San Jose, California,

2016) JO9.00004.

[6] M.N. Rosenbluth and F.L. Hinton, Physical Review Letters 80, 724 (1998).

[7] L. Wang and T.S. Hahm, Physics of Plasmas 16, 062309 (2009)

[8] H. Sugama and T.-H. Watanabe, Physics of Plasmas 13, 012501 (2006).

[9] P.H. Diamond, S.-I. Itoh, K. Itoh and T.S. Hahm, Plasma Physics and Controlled Fusion 47, R35

(2005).


16

I-10: Non-inductive electron current generation in toroidal plasmas

Weixing Wang

Princeton Plasma Physics Laboratory


Gyrokinetic simulations including self-consistent neoclassical and turbulent dynamics are used

to investigate non-inductive current generation in fusion plasmas. We focus our study on

electron current. Two phases in electron current generation are illustrated in the initial value

simulation. In the early phase before turbulence develops, the electron bootstrap current is

established in a time scale of a few electron collision times, which closely agrees with the

neoclassical prediction. The second phase follows when turbulence begins to saturate, during

which turbulent fluctuations are found to strongly affect electron current. The profile structure,

amplitude and phase space structure of electron current density are all significantly modified

relative to the neoclassical bootstrap current by the presence of turbulence. The current profile is

modified in a way that correlates with the fluctuation intensity gradient, which may suggest its

connection with the electron parallel Reynolds stress associated with turbulence intensity

gradient. Relative to the neoclassical bootstrap current, the reduction of total electron current

increases as collisionality decreases. The implication of this result to the fully non-inductive

current operation in burning plasma regime should be investigated. Finally, significant non-

inductive current is observed in flat pressure region, which is nonlocal and results from the

effect of turbulence spreading.


17

I-11: Core intrinsic toroidal rotation mechanisms tested against ASDEX Upgrade

observations

W A Hornsby1, C Angioni

1, E Fable

1, P Manas

1, R M McDermott

1, Z X Lu

1, A G Peeters

2

and the ASDEX Upgrade Team

1Max-Planck-Institut für Plasmaphysik, Boltzmannstr 2, D-85748 Garching, Germany

2Theoretical Physics V, Dept. of Physics, Universität Bayreuth, Bayreuth, D-95447, Germany

The quantitative prediction of intrinsic toroidal rotation caused by turbulent momentum

transport presents one of the major current challenges in the theoretical understanding of

tokamak plasmas. A combined theoretical and experimental effort of addressing a

comprehensive and systematic comparison of the predictions of many intrinsic momentum

generation mechanisms is made against dedicated ASDEX Upgrade experiments, will be

presented. The database comprises of ~ 190 observations of Ohmic L-mode plasmas [1]. These

observations are compared with gyrokinetic turbulence simulations, utilising the nonlinear

gyrokinetic turbulence code GKW [2] which has been increasingly upgraded to include the

symmetry breaking mechanisms that are most important for describing the turbulent momentum

flux.

Radially global gradient-driven turbulence simulations with kinetic electrons reproduce hollow

intrinsic flow profiles seen in the majority of experiments and their corresponding large flow

gradients at mid-radius. It is shown that the dominant intrinsic mechanism is profile shearing

[3], and its dependence on the equilibrium profiles is discussed. The scaling of the turbulent

flow with the ion gyroradius is shown to be weak.

In addition, quasilinear and nonlinear local simulations are used to study further symmetry

breaking mechanisms that are well described in the flux tube model. These include neoclassical

background flow effects, up-down magnetic equilibrium asymmetry, higher order poloidal

derivatives and Coriolis effects which are not included in the global model. The sum of these

symmetry breaking mechanisms predict mostly hollow rotation profiles, as observed, but sustain

smaller gradients than those in the global simulations [4]. However, when added to the global

results, the total predicted rotation gradients result in improved agreement with experimentally

measured values.

References: [1] R.M. McDermott et al 2014 Nucl. Fusion 54 043009

[2] A.G. Peeters et al 2009, Computer Physics Communications 180 2650

[3] Y. Camenen et al 2011 Nucl. Fusion 51 073039

[4] W.A. Hornsby et al 2017 Nucl. Fusion 57 046008

18

I-12: GTC simulations of effects of resonant magnetic perturbations on DIII-D edge

transport

Zhihong Lin

Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA


Vacuum resonant magnetic perturbations (RMP) applied to otherwise axisymmetric tokamak

plasmas produce in general a combination of non-resonant effects that preserve closed flux

surfaces (kink response) and resonant effects that introduce magnetic islands and/or stochasticity

(tearing response). The effect of the plasma kink response on the linear stability and nonlinear

transport of edge turbulence is first studied using the gyrokinetic toroidal code (GTC) for a DIII-

D plasma with applied n = 2 vacuum RMP. GTC simulations use the 3D equilibrium of DIII-D

discharge 158103, which is provided by nonlinear ideal MHD VMEC equilibrium solver in

order to include the effect of the plasma kink response to the external field but to exclude island

formation at rational surfaces. Analysis using the simulation results reveal no increase of growth

rates for the electrostatic drift wave instability and for the electromagnetic kinetic-ballooning

mode in the presence of the plasma kink response to the RMP. Furthermore, nonlinear

electrostatic simulations show that the effect of the 3D equilibrium on zonal flow damping is

very weak and found to be insufficient to modify turbulent transport in the electrostatic

turbulence (Holod et al 2017 Nucl. Fusion 57 016005).

Full plasma responses to RMPs, including both kink and tearing parts as provided by the

resistive MHD code M3D-C1, have been implemented into GTC to study the effect of magnetic

islands and stochastic field regions on microturbulence. Preliminary GTC simulations show that

full plasma responses to RMP have little effects on electrostatic turbulence when electron

responses are assumed to be adiabatic. In the next step, the more interesting physics of kinetic

election responses is now being studied. Electron response to zonal flow in stochastic fields can

be adiabatic and zonal flow dielectric constant can increase significantly for long wavelength

fluctuations. Zonal flow generation is then reduced and the microturbulence can be enhanced

greatly.

Finally, a link between the increased pedestal top turbulence level and the shift in radial electric

field profile has been identified and demonstrated in GTC simulations using the axisymmetric

magnetic field. When ELM is suppressed by RMP, the radial electric field shear is significantly

reduced due to changes of toroidal rotation, which allows enhanced microturbulence in the outer

edge region. A nonlinear outward turbulence spreading of the turbulence is observed, which

may contribute to the measured increase of transport at the pedestal top. Moreover, GTC

simulations find that the RMP magnetic fields with closed flux surfaces have little effects on

neoclassical particle flux, heat flux, and bootstrap current. Nontheless, the 3D RMP fields may

drive non-ambipolar particles, which may induce changes of the radial electric fields.

Preliminary simulations of non-ambipolar fluxes in the magnetic islands and stochastic regions

will be reported.

In Collaboration with I. Holod, L. Shi, S. Taimourzadeh, J. Y. Fu, N. Farrero, R. Nazikian,

D. Spong, and A. Wingen. Work supported by General Atomics and DOE.


19

I-13: Gyro kinetic investigations of Instabilities and transport in tokamak pedestals

Swadesh M Mahajan, Mike Kotschenreuther, David Hatch, X.Liu

I will present the first ever detailed gyrokinetic investigations of linear and nonlinear

instabilities in the tokamak H-mode pedestals. The results, both in the linear and nonlinear

regimes, are qualitatively different from what was learnt in the gyro kinetic analysis of the

plasma core. It is found that the linear pedestal modes tend to show quite different two-

dimensional structures, for instance, several modes interest may peek at the top or bottom and

not at the mid plane leading to unexpected nonlinear consequences and associated transport.

Interestingly we find that drift class of modes (such as Electron and IonTemperature Gradient

(ETG and ITG) and Micro Tearing Modes (MTM)) produce outward transport almost entirely in

the energy channel. Combined with the experimental inference that pedestals, without ELMs,

are observed to have much smaller particle transport than energy transport, one can immediately

conclude that 1) MHD-like modes cannot be, wholly, responsible for pedestal energy transport

(otherwise particle transport would be excessively high compared to this inference) 2) They

could be responsible for the relatively smaller particle transport, sometimes determining the

density profile, but then energy transport must be dominated by some combination of the drift

modes above. I will also present a new picture of the pedestal characteristics (distance from the

conventional EPED model) derived on the basis of the instability analysis. The very strong

gradients in the pedestal allow the construction of a simple semi analytical kinetic model

(SKIM) that can help in understanding the simulation results. Naturally, this new investigation

will guide us as to the best fusion worthy scenarios for tokamaks.

20

I-14: Local and global analysis of symmetry breaking for ITG and BAE modes

Z.X. Lu

Max-Planck-Institut für Plasmaphysik, Boltzmannstr 2, 85748 Garching, Germany


The mode structure symmetry breaking such as flux surface averaged parallel wavenumber ⟨ k||⟩

and poloidal angle ⟨ 𝜃⟩ is important for estimating the momentum transport due to its connection

to the off-diagonal transport [1]. It is also a key concept to demonstrate the non-perturbative

effect of energetic particles on Alfven eigenmodes and to study the interaction between low

frequency Alfven eigenmodes and thermal/energetic particles [2]. In this work, the symmetry

breaking of the 2D structure of the Ion Temperature Gradient (ITG) mode and Beta-induced

Alfven Eigenmode (BAE) is studied based on local and global analysis. The Mode Structure

Decomposition (MSD) approach [3] is developed with the complex envelope phase variation

(θ𝑘) [4] and global effects taken into account. The results are compared to ORB5, GKW for ITG

and XHMGC for BAE.

For the ITG problem, a novel theoretical method for the calculation of parallel mode structure

has been developed [4,5,6]. It is shown that the radial symmetry breaking is intimately coupled

to the parallel symmetry breaking [6]. For local simulations, in addition to the ``tilting angle''

( Re{𝜃𝑘} ), the intensity gradient described by Im{𝜃𝑘} affects the local eigenvalue and the

symmetry breaking. ``Global-oriented local simulations'' are suggested where global corrections

are taken into account in the local model and its importance for the study of turbulent

momentum transport is discussed.

For the BAE problem, the wave-packet calculation technique for weakly coupled poloidal

harmonics is proposed to demonstrate the BAE mode structure symmetry breaking, with the

non-perturbative effect of the energetic particles (EPs) included. The theoretical global analysis

identifies the essence of ``boomerang'' structures with/without asymmetric tails in poloidal plane

as well as the radial and parallel symmetry breaking. The agreement between the wave-packet

calculation and XHMGC is achieved. The global effect and non-perturbative EP effect are

important ingredients for the symmetry breaking and their effects on EP transport as well as the

implications to experimental observations are discussed.

References: [1] C. Angioni, Y. Camenen, F.J. Casson, E. Fable, R.M. McDermott, A.G. Peeters, and J.E. Rice. Off-

diagonal particle and toroidal momentum transport: a survey of experimental, theoretical and modelling

aspects. Nucl. Fusion, 52(11):114003, 2012.

[2] Z. Lin, Y. Q. Liu, H. S. Zhang, and W. L. Zhang. Nonlinear interactions of low frequency Alfven

eigenmodes. In Proceedings of the 25th International Conference on Plasma Physics and Controlled

Nuclear Fusion Research. IAEA, 2016.

[3] Z. X. Lu, F. Zonca, and A. Cardinali. Theoretical and numerical studies of wave-packet propagation

in tokamak plasmas. Phys. Plasmas, 19(4):042104, 2012.

[4] Z. X. Lu. The complex mixed WKB-full-wave approach and its application to the two dimensional

mode structure analysis of ITG/CTEM drift waves. Phys. Plasmas, 22(5): 052118, 2015

[5] Z. X. Lu, W. X. Wang, P. H. Diamond, G. Tynan, S. Ethier, J. Chen, C. Gao, J. E. Rice, Effects of q-

profile structures on intrinsic torque reversals. Nucl. Fusion, 55 (9), 2015

[6] Z.X. Lu, E. Fable, W. Hornsby, C. Angioni, A. Bottino, Ph. Lauber, and F. Zonca. Symmetry

breaking of ion temperature gradient mode structure: from local to global analysis. Phys. Plasmas,

accepted, 2017.


21

List of Regular Orals:

O-1: Ferrari H.E., Effect of ideal kink instabilities on particle redistribution

O-2: Nicolas T., Self-collition algorithms for Fokker - Planck operator simulation in full - f PIC

codes and direct verification of classical transport

O-3: Qi L., Bounce-averages gyrokinetik simulation of trapped electron turbulence in elongated

tokamak

O-4: Grosshauser S.R., Role of linear dynamics in saturated gyro-kinetic turbulence

O-5: Elfimov A.G., Excitation of Geodesic modes by plasma fluxes during neutral beam

injection in tokamaks

O-6: Pastukhov V.P., Simulations of self-sustained turbulent convection and formation of ITB in

tokamak core plasmas

O-7: Klaywittaphat P., Plasma instability during ITBs formation with pellet injection in

tokamak

O-8: Jhang H., A mechanism for the strong excitation of zonal modes during an edge pedestal

collapse

O-9: Ryu C.M., Destabilization of TAEs in KSTAR Plasmas

O-10: Zhou D., Stabilization of RSAEs by barely trapped energetic electrons in tokamak

plasmas

O-11: Marchenko V.S., Excitation of beta-induced Alfven eigenmode by a plasma flow around

magnetic island

O-12: Xiang N., Heat flux transported by fast electrons in front of lower hybrid wave antenna

on EAST tokamak

22

O-1: Effect of ideal kink instabilities on particle redistribution

H. E. Ferrari1,2

,R. Farengo1, P. L. Garcia-Martinez2, M.-C. Firpo3, A. F. Lifschitz4

1Comisión Nacional de Energía Atómica, Centro Atomico Bariloche, Bariloche, Argentina

2CONICET, Centro Atómico Bariloche, Bariloche, Argentina

3LPP, CNRS - Ecole Polytechnique, 91128 Palaiseau cedex, France 4LOA, ENSTA, CNRS, Ecole Polytechnique, 91761 Palaiseau, France


We studied the effect of kink like instabilities on the redistribution of impurities. We used the

ideal kink as a model for the sawtooth. The kink was modeled as in [1], where the total fields

are the sum of a simple analytical equilibrium (large aspect ratio, circular cross section) plus the

perturbation produced by the ideal kink mode. The code was implemented in CUDA C and runs

on a GPU, allowing us to do simulations with a large number of particles with modest resources.

For Ni impurities, we studied the effect of stochasticity in the sawtooth collapse, in a

configuration similar to the classical experiment of Wesson et al [2]. Stochasticity only appears

when modes with different helicities are present. We found that the combined effect of

stochasticity of the magnetic field and the time dependent electric field associated to the rotation

of the mode could explain the fast migration of Ni to the core when the crash occurs [3].

For W impurities, we are trying to explain the results of a series of discharges in ASDEX U with

W plasma facing components. It has been reported in [4] that, in a typical H-mode discharge

with central ECRH a saturated (1,1) mode is present in between crashes. When the sawtooth

crash is produced the W profile is flattened as it is expected. However, when a saturated kink

(1,1) is present after the crash, the W profile shows a hollow profile before the next crash.

Preliminary results show that a resonance between the rotation frequency of the mode and the

transit frequency of the W particles is needed to explain the expulsion of W particles from the

magnetic axis. The mode frequency ω correspond to the plasma rotation velocity vR. The

resonance is possible because the thermal velocity of the W particles is vthW << vR,, and most of

the W particles have a passing rotation frequency close to ω. When we considered D particles,

there are no such resonances due to the fact that vthD >> vR, and the distribution of passing

rotation frequency is too wide to see any resonance. This effect could have implications for ash

removal.

References: [1] Farengo et al, Phys. Plasmas. 21, 082512 (2014).

[2] Wesson J. A et al, Phys. Rev. Lett., 79:5028-5021, Dec 1997.

[3] Firpo et al, Plasma. Phys. Control. Fusion 59 (2017) 034005.

[4] Sertoli M. et al, Nucl. Fusion 55 (2015) 113029.


23

O-2: Self-collision algorithms for Fokker-Planck operator simulation in full-f PIC codes

and direct verification of classical transport

T. Nicolas1, J.-F. Luciani

2, H. Lütjens

2, and J. P. Graves

1

1École Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des

Plasmas (CRPP), 1015 Lausanne, Switzerland 2Centre de Physique Théorique, École Polytechnique, CNRS, F-91128 Palaiseau Cedex, France

In this contribution, we summarize the features of a new algorithm for computing self-collisions

between macroparticles in full-f Particle-In-Cell codes, applied to hybrid kinetic/MHD models.

The method, detailed in Ref. [1], relies on Langevin kicks of test particles on a well-chosen

Maxwellian distribution. By construction, the method conserves energy and momentum in a

statistical sense. Comparison with binary collisions, which exactly reproduce the Landau

integral operator in the limit of a large number of markers, show good agreement in the

momentum and energy transfer rates between the different parts of the distribution function in

physically relevant cases (small density supersonic beam, slowing-down of energetic particles,

and mixing between slowly moving large density bulks with different temperatures).

However, the algorithm shows a significant difference with Braginskii classical transport.

Comparison with the Braginskii formula for the heat flux, 𝑞 = 𝜅⊥∇𝑇 , with

𝜅⊥ = 2𝑛𝑖𝑇𝑖/(𝑚𝑖𝜔𝑐𝑖2 𝜏𝑖), shows that the 𝜅⊥ coefficient obtained with the new algorithm is larger

than the Braginskii value by approximately a factor 1.5. This discrepancy, which shows the

limits of the algorithm, can be attributed to the fact that the latter relies on an uncontrolled

approximation. More interestingly, comparison is done with the binary collision algorithm. A

significant discrepancy with the Braginskii formula is also found: the 𝜅⊥ obtained with binary

collisions is lower than Braginskii by a factor of approximately 1.5. This discrepancy is

unexplained so far. It is noted that direct numerical verification of Braginskii classical transport

is virtually non-existent in the literature, although such a study is found in Ref. [2]. The latter

concludes that binary collisions do agree with the Braginskii formula, which is in contradiction

with our findings. We believe it is because one dependency of the Braginskii diffusion

coefficient had been neglected.

References: [1] T. Nicolas, et al. Plasma Phys. Contr. F. 59(5), 054005 (2017).

[2] S. Ma, et al. Comput. Phys. Commun. 77(2), 190 (1993).

24

O-3: Bounce-averaged gyrokinetic simulation of trapped electron turbulence in elongated

tokamak plasmas

L. Qia, J. M. Kwon

a, T. S. Hahm

a,b and Sumin Yi

a

aNational Fusion Research Institute, Daejeon, Korea

bSeoul National University, Seoul, Korea


Plasma elongation effects on turbulence and zonal flow are explicitly investigated for the first

time with global bounce-averaged gyrokinetic simulations for Collisionless Trapped Electron

Mode (CTEM). Being the most efficient steady state turbulence simulation scheme, bounce-

averaged gyrokinetic simulation provides deeper insights into nonlinear physics separated from

linear effects in the investigation. Results show that shorter radial scale zonal flows which are

more prominent for CTEM compared to ITG, are more enhanced with higher elongation leading

to reduced transport. Radial correlation of density fluctuation exhibits two characteristic scales

similar to previous gyrokinetic simulation [Y. Xiao and Z. Lin, PRL 2009] and experimental

measurements [Hennequin, EPS 2015]. With a higher elongation, a dual mode with

propagations in both electron and ion diamagnetic direction is observed along with more

strongly sheared zonal flow.


25

O-4: Role of linear dynamics in saturated gyro-kinetic turbulence

S.R. Grosshauser, S. Schröder, W.A. Hornsby, R. Buchholz, A. Weikl, A.G. Peeters, D. Strintzi

University of Bayreuth, Physics department, Universitätsstrasse 30 Bayreuth, Germany

To assess the importance of the linear drive in non-linear gyro-kinetic turbulence, the relative

strength of linear drive and non-linear coupling is measured using gyrokinetic simulations. It is

found that the modes with the largest amplitude in the non-linear state are also those for which

the linear drive dominates. The maximum in the spectrum of mode amplitude versus wave

vector, which is shifted towards smaller wave vectors when compared with the linear growth

rate spectrum, is found not to be a consequence of inverse cascade physics. At very small wave

vectors, as well as for wave vectors in the tail of the spectrum, the non-linear energy transfer

(nonlinear mode coupling) dominates over the linear drive. The results obtained here give some

support to the assumptions made in quasi-linear transport models.

PACS numbers: 52.25.Fi, 52.25.Xz, 52.30.Gz, 52.35.Qz, 52.55.Fa

26

O-5: Excitation of Geodesic modes by plasma fluxes during neutral beam injection in

tokamaks

A.G. Elfimov, F. Camilo de Souza, R. M. O. Galvão

Institute of Physics, University of São Paulo, São Paulo, 05508-090, Brazil


Geodesic Acoustic Modes (GAM) are M=0, =±1, ±2 poloidal and N=0 axisymmetric toroidal

modes initially found in MHD approach [1]

with dispersion defined by the electron and

anisotropic ion pressure with frequency ieiG mRTT 2

0

2 /227 in kinetic model [2]

. These

modes may be important for plasma transport, as well, useful as a diagnostic tool to indicate L-

H confinement transition in tokamaks. GAMs are observed at the plasma border in ohm heating [3]

and easily excited by ICR or by neutral beam (NB) injection [4]

in the plasma core. Typically,

the injected beam velocity is less than electron thermal velocity, but it is higher than the phase

velocity of GAM sidebands vTe>> VNB >>Rq. Thus, the beam do not interact directly with

GAMs, but their velocity is slowing down to the critical velocity nbeef mTZV 31

0 5.5 without

pitch angle changing due to electron collisions forming some “bump on tail” distribution for fast

ions 22

0|| 2)(exp TbvVv driven by NB or 22

0 2)(exp TbvVv affecting trapped ions

during ICR heating. Here, we study the effect of the minor concentration nb of the energetic

bump particles on GAM spectrum and taking into the account the electron current and ion fluxes

in large aspect ratio tokamaks with circular surfaces. Using gyro kinetic theory, it is shown that

may be reduced to the equation for 0VRq 0 )1(11026

5 22

34

where

10

V

Rq , )i1(1

2

0

2

V

G , Ti

G

Gv

Rq ,

3

0

2

2/3

0

5

2

Vnq

Tn

b

b ,

2exp

82

23

2/3

32

GG

b

b

bqT

Vqn .

We found that the standard GAM is split into two modes, first one is lower frequency GAM and

unstable higher frequency energetic mode at the phase resonance with the bump velocity

Rq≈V0. This solution may be presented in the simplified form

)( minminmin where )801(725.0812min .

References: [1] N. Winsor, J.L. Jonson, J.M.Dowson, Phys. Fluids, 11, 2448 (1968).

[2] F. Zonca and L.Chen, R.A. Santoro Plas. Phys. & Contr. Fusion 38, 2011 (1996).

[3] A.V. Melnikov et al, Plasma Phys. & Control. Fusion, 48 (2006) S87.

[4] H. L. Berk et al, Nuclear Fusion 46, S888 (2006).


27

O-6: Simulations of self-sustained turbulent convection and formation of ITB in tokamak

core plasmas

V.P. Pastukhov, N.V. Chudin, A.Yu. Dnestrovskij, D.V. Smirnov

National Research Center "Kurchatov Institute", Moscow, Russian Federation


Internal transport barrier (ITB) is one of the challenging problems for improved plasma

confinement in tokamaks. It is known that linearly unstable low-frequency (LF) fluctuations of

plasma potential, density and temperatures are typically localized near rational magnetic

surfaces. Due to partial overlapping and toroidal or nonlinear coupling such fluctuations can

form radially extended turbulent convective cells which sustain anomalous particle and heat

transport. Rather reasonable concept of ITB formation [1] is based on the idea that radial

distribution of rational magnetic surfaces with sufficiently low m and n numbers is non-uniform,

in particular, there are “gaps” between such surfaces in the vicinity of main rational surfaces

with very low (m, n) numbers. According to the concept, such “gaps” prevent overlapping of

plasma fluctuations that can result in radial breaking of turbulent convective cells which have

sufficiently low dominant (m, n) numbers.

To verify this concept we perform simulations of temporal evolution of self-sustained turbulent

convection and the resulting anomalous transport in tokamak core plasmas under conditions

which can trigger the convective cell breaking. The simulations are based on a relatively simple

adiabatically-reduced MHD-like model of LF-turbulence [2] which results in the anomalous

cross-field transport. Turbulent convection in our simulations is described by a set of coupled

nonlinear equations for toroidal harmonics of velocity, pressure and density. To imitate the

effects of partial decoupling mentioned above we introduce additional boundary conditions for

fluctuations of plasma potential and pressure with toroidal numbers n < nmax . These boundary

conditions are localized near the main rational surfaces, such as: q = 1; 1.5; 2. Simulations

demonstrate changes in structures of dominant convective cells under such boundary conditions

which result in reduction of anomalous fluxes and formation of jumps in pressure profiles in the

vicinity of the main rational surfaces. The pressure jumps are similar to those in ITBs. The jump

heights depend on values of nmax , effective width of the “gaps” in the vicinity of the main

rational surfaces, heating power and its radial distribution, etc.

References: [1] K.A. Razumova, V.F. Andreev, L.G. Eliseev, et al., Nucl. Fusion, 51, 083024(2011)

[2] V.P. Pastukhov, N.V.Chudin and D.V. Smirnov, PPCF, 53, 054015(2011)


28

O-7: Plasma instability during ITBs formation with pellet injection in tokamak

P. Klaywittaphat1, B. Chatthong

2, T. Onjun. R. Picha

3, J. Promping

3

1Faculty of Engineering, Thaksin University, Phatthalung, Thailand,

2Department of Physics, Faculty of Science, Prince of Songkla University, Songkla, Thailand

3Thailand Institute of Nuclear Technology, Bangkok

Simulations of a standard H-mode International Thermonuclear Experimental Reactor (ITER)

scenario in the presence of an internal transport barrier (ITB) are carried out using the 1.5D

BALDUR integrated predictive modelling code. The plasma instability during ITB formation

triggered by pellet injection in tokamak is investigated. In these simulations, a combination of a

neoclassical transport model NCLASS and an anomalous transport model (MMM and Mixed

Bohm/gyro- Bohm core transport model) is used. The boundary condition is described at the top

of the pedestal, which is calculated theoretically based on a combination of magnetic and flow

shear stabilization pedestal width scaling and an infinite-n ballooning pressure gradient model.

The toroidal flow calculation is based on NTV (neoclassical toroidal viscosity) toroidal velocity

model. It was found that the deep penetration of the pellet was confirmed to be effective for

suppressing anomalous transport and for forming the internal transport barrier, locating mostly

between r/a = 0.6 and 0.8 and having a strong impact on the plasma performance in ITER.

Results of plasma instabilities during ITB formation with pellet injection are also reported.

29

O-8: A mechanism for the strong excitation of zonal modes during an edge pedestal

collapse

Hogun Jhang, R. Singh and S. S. Kim

National Fusion Research Institute, Daejeon 305-333, Republic of Korea


A recent nonlinear reduced magnetohydrodynamic (MHD) simulation shows that dynamics of

geodesic acoustic modes (GAM) may play an important role in edge pedestal collapse, in

particular, when the critical alpha (=normalized pressure gradient) is reduced near/below the

ideal threshold value [H Jhang et. al, Nucl. Fusion 57 (2017) 022006]. A strong burst of GAM

activity is observed near the end of the crash and leads to secondary crashes. This phenomenon

was attributed to the onset of a tertiary instability driven by the excitation of strong zonal flows.

This raises a question of a dynamical mechanism which could generate such a strong zonal flow

during the pedestal collapse. To address this question, we perform an analytic study of coupled

zonal flow-ballooning modes. In this study, we assume that Reynolds and Maxwell stress

drivers for the zonal mode are exactly cancelled (in line with observations in the simulation) and

consider only the contribution from the geodesic curvature coupling drive. A simple analysis

shows a possible onset of a new nonlinear instability which can induce a strong growth of zonal

flows. This mechanism is akin to the poloidal spin-up process due to asymmetric sources

[Hassam and Antonsen Jr., Phys. Plasmas 1 (1994) 337].


30

O-9: Destabilization of TAEs in KSTAR Plasmas

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

POSTECH, South Korea

E-mail of Corresponding Author: ryu201@postech,ac.kr

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

studied by using the gyrokinetic code GENE. The GENE code is an Eulerican code which can

run fast to calculate the eigenmodes. For KSTAR discharges, TAEs of low toroidal mode

number are shown to be excited by energetic particles (EPs) during the neutral beam injection

[1]. The dependence of the real frequency, growth rate and mode structures of TAEs on the EP

density gradients at different mode locations are studied, to understand the characteristics of

TAEs in KSTAR plasmas. The equilibrium magnetic geometry and profiles are loaded from the

experimental data constructed using the GENE internal interface module TRACER-EFIT, and

all three species, electron, ion, fast particles with a realistic mass ratio (assuming deuterium

plasma, mi/me = 3672) are treated gyrokinetically.

The numerical simulations indicate that a TAE excited near the core region has a rather broad

mode structure, and the mode excited outside has a small radial extent. TAEs with smaller radial

extents is more stable [2]. Thus, in KSTAR, TAEs can be more easily excited in the core region

of a tokamak than the outside for a given EP density gradient.

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).

mailto:ryu201@postech,ac.kr

31

O-10: Stabilization of RSAEs by barely trapped energetic electrons in tokamak plasmas

Deng Zhou

Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, 230031, China

E-mail of Corresponding Authors: [email protected]

In recent experiments on DIII-D, the reversed shear Alfenic eignemodes (RSAEs), driven

unstable by energetic ions, were stabilized when electron cyclotron resonance heating (ECRH)

was applied and the heating location was just inside the minimum of the safety factor (qmin).

Although in normal situation toroidal precessional frequencies of energetic electrons are much

lower than the frequencies of RSAEs, in the DIII-D experiments the toroidal precessional

frequencies of barely trapped energetic electrons (BTEEs) were comparable to those of RSAEs

because of the high local pressure gradient and high qmin at the mode location. The toroidal

precessional direction is in the ion diamagnetic drift direction along which the mode can be

driven unstable by negative pressure gradients of energetic ions. In this work, the perturbation

method is adopted to investigate the resonance interaction between RSAEs and barely trapped

energetic electrons produced by ECRH. The kinetic contribution of potential functional from

BTEEs is derived and evaluated using the DIII-D experimental parameters. The damping rate

contributed by BTEEs is proportional to the beta of BTEEs and depends on the length of their

pressure gradient. It is typically comparable or larger than the Landau damping contributed from

background ions and electrons.

References: [1] M. A.Van Zeeland et al., “Reversed shear Alfv´en eigenmode stabilization by localized electron

cyclotron heating”, Plasma Phys. Control. Fusion 50, 035009 (2008).

[2] F. L. Betti and J. P. Freidberg, “Stability of Alfven gap modes in burning plasmas”, Phys. Fluids B 4 ,

1465 (1992).


32

O-11: Excitation of beta-induced Alfven eigenmode by a plasma flow around magnetic

island

V.S. Marchenko1, А.Panwar

2, S.N. Reznik

1, C.M. Ryu

2

1

Institute for Nuclear Research, Kyiv, Ukraine 2

University of Science and Technology, Pohang, South Korea

Alfven eigenmodes (AE) in fusion experiments are usually associated with presence of

significant population of energetic particles. However, there are few cases of AE excitation in

Ohmic discharges, i.e. without energetic species [1-3]. In all such cases, the modes belong to the

family of the so called beta-induced Alfven eigenmodes (BAE), and are driven unstable by

magnetic islands, which interact with resistive wall and/or resonant error field, i.e. they are

almost locked in the lab frame. The last observation implies that the source of free energy for

BAE is a relative motion between magnetic island and ambient plasma.

In Ref.[4] it was shown that island motion in the frame of plasma confined by curved and non-

uniform magnetic field generates the parallel electron current, which is dominantly localized at

the island separatrix. In the present work [5] it is shown that electron drift speed in this current

sheet can easily exceed the BAE phase velocity, resulting in BAE excitation via inversed

electron Landau damping. The excited mode has identical with magnetic island mode numbers

and forms a standing wave in the island frame, consistent with experiments. Secondary

generation of a geodesic acoustic mode as a beat wave between primary BAE and magnetic

island will be also described.

References: [1] Buratti P. et al. 2005 Nucl. Fusion 45 1446.

[2] Chen W. et al. 2010 J. Phys. Soc. Japan 79 044501.

[3] Liu L. et al. 2015 Plasma Phys. Control. Fusion 57 065007.

[4] Smolyakov A.I. et al. 2007 Phys. Rev. Lett. 99 055002.

[5] Marchenko V.S. et al. 2016 Nucl. Fusion 56 106021.

33

O-12: Heat flux transported by fast electrons in front of lower hybrid wave antenna on

EAST tokamak

Nong Xiang1, 2

, Zhongzheng Men1, 2

, Xueyi Wang3, Jing Ou

1, 2

1

Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, Chin 2 Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei 230031, China 3Physics Department, 206 Allison Laboratory, Auburn University, AL 36849-5311, USA


Lower hybrid current drive has been proved to be an effective approach to achieve long-pulse,

high performance plasma on EAST tokamak. Hotspots near the guard limiters of lower hybrid

antenna were often observed in recent lower hybrid current drive experiments on EAST

tokamak as the input power is over 2MW. The hotspots not only caused serious damages to the

guard limiters, but strongly degraded the plasma performance due to enhanced impurity

productions [1]. It is believed that the fast electrons produced due to the interactions of electrons

and lower hybrid modes with a high parallel refractive index n// in front of the antenna are

responsible to the observed hotspots [2,3]. In published studies, the heat flux to the limiters is

calculated by assuming that the energy absorbed by electron Landau damping is carried by the

fast electrons to the limiters, and by ignoring the sheath structure formed in front of the limiter

surface. In this work, a particle-in-cell simulation code GCPIC is developed to investigate the

interactions between plasma containing fast electron component and the guard limiters. The heat

flux to the guard limiters is obtained via one-dimensional simulations and the sheath effects on

the heat flux to the guard limiters are discussed. It is found that the sheath dynamics is strongly

affected by fast electrons. The sheath potential is significantly increased and sensitive to the fast

electron concentrations. As a result the ion heat flux is enhanced to be comparable to the

electron’s. It is shown that the enhanced heat flux due to the presence of fast electron component

is responsible for the appearance of hotspots. The effects of the secondary electron emission

which strongly depends on the wall materials are also discussed.

References

[1] Y. L. Li, G.S.Xu, et al. , Phys. Plasma, 22, 022510 (2015).

[2] K.M. Rantamaki, T.J.H. Pattikangas, et al., Nucl. Fusion, 40, 1477 (2000).

[3] J.P.Gunn, V.Fuchs, et al., Nucl. Fusion, 56, 1 (2016).


Notes

Notes

Notes

Vienna, Austria - Nucleus · Vienna, Austria IAEA Scientific Secretary Ms. Sehila Maria Gonzalez de Vicente International Atomic Energy Agency Vienna International Centre, Wagramer

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