Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas

ITG turbulence CTEM turbulence RSAE Summary

Properties of electrostatic and electromagneticturbulence in reversed magnetic shear plasmas

Wenjun DengUniversity of California, Irvine, USA

Ihor Holod1, Yong Xiao1,Xin Wang1,2, Wenlu Zhang1,3 and Zhihong Lin1

1 University of California, Irvine, USA2 IFTS, Zhejiang University, China

3 University of Science and Technology of China, China

Supported by SciDAC GSEP & GPS-TTBP


Motivations

Reversed (magnetic) shear (RS) in tokamak: safety factor q-profilehas an off-axis minimum. This minimum value is called qmin.

1 Internal transport barrier (ITB) can form at the integerqmin flux surface and suppress turbulent transport. Someproposed mechanisms are based on electrostatic drift waveturbulence.

We use global gyrokinetic particle code GTC [Lin et al.,Science 1998] to study two modes of drift wave turbulence:the ion temperature gradient (ITG) and the collisionlesstrapped electron mode (CTEM) turbulence.

2 Reversed shear Alfven eigenmode (RSAE) at the qmin fluxsurface can be driven unstable by fast ions and can causefast ion loss.

We use electromagnetic GTC to study RSAE and fast ionphysics. The results using fast ions and antenna excitationwithout thermal particle kinetic effects are benchmarkedwith HMGC [Briguglio et al., PoP 1998] simulations.

1/16


Motivations

Reversed (magnetic) shear (RS) in tokamak: safety factor q-profilehas an off-axis minimum. This minimum value is called qmin.

1 Internal transport barrier (ITB) can form at the integerqmin flux surface and suppress turbulent transport. Someproposed mechanisms are based on electrostatic drift waveturbulence.

We use global gyrokinetic particle code GTC [Lin et al.,Science 1998] to study two modes of drift wave turbulence:the ion temperature gradient (ITG) and the collisionlesstrapped electron mode (CTEM) turbulence.

2 Reversed shear Alfven eigenmode (RSAE) at the qmin fluxsurface can be driven unstable by fast ions and can causefast ion loss.

We use electromagnetic GTC to study RSAE and fast ionphysics. The results using fast ions and antenna excitationwithout thermal particle kinetic effects are benchmarkedwith HMGC [Briguglio et al., PoP 1998] simulations.

1/16


Outline

1 ITG turbulence spreading in RS plasmas (no ITB)

2 CTEM turbulence spreading in RS plasmas (no ITB)

3 Linear simulations of RSAE by antenna and fast ionexcitation


Outline





ITG linear eigenmode: gap structures only for integer qmin

qmin = 1

10−9

10−8

10−7

10−6

10−5 ⟨φ2

⟩

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

Rarefaction of therational surfaces

causes a potential gap.

0.6

0.8

1

1.2

1.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

q

r/a

qmin = 1

mode rational surface:nq(r) = m

n: toroidal mode #m: poloidal mode #

nq(rblack) = mmin

nq(rred) = mmin + 1nq(rblue) = mmin + 2

etc.n ∈ [25, 95]

qmin = 0.9552

10−9

10−8

10−7

10−6

10−5 ⟨φ2

⟩

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

2/16


ITG linear eigenmode: gap structures only for integer qmin

qmin = 1

10−9

10−8

10−7

10−6

10−5 ⟨φ2

⟩

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

Rarefaction of therational surfaces

causes a potential gap.

0.6

0.8

1

1.2

1.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

q

r/a

qmin = 1

qmin = 0.9552

mode rational surface:nq(r) = m

n: toroidal mode #m: poloidal mode #

nq(rblack) = mmin

nq(rred) = mmin + 1nq(rblue) = mmin + 2

etc.n ∈ [25, 95]

qmin = 0.9552

10−9

10−8

10−7

10−6

10−5 ⟨φ2

⟩

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

2/16


ITG nonlinear evolution: potential gap filled up

10−9

10−8

10−7

10−6

10−5

0 50 100 150 200

t/(R0/cs)

⟨φ2

⟩V

III III

qmin = 2

φ2

snapshots

Three snapshots taken

10−9

10−8

10−7

10−6

10−5

10−4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

⟨φ2

⟩ III

III

Radial structures of I, II, & III

I II III

3/16


ITG nonlinear evolution: gap filled up by turbulence spreading

−1.5e− 16

−1e− 16

−5e− 17

0

5e− 17

1e− 16

1.5e− 16

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Inte

grat

edΦ

E(a

.u.

)

r/a

outward flow

inward flow

Approximated E-field intensityflux in the early nonlinear

phase integrated from SnapshotI to II.

ΦE(r) ≡⟨E2vEr

⟩Turbulence flows into the qmin

region from both sides.

10−9

10−8

10−7

10−6

10−5

0 50 100 150 200

t/(R0/cs)

⟨φ2

⟩V

III III

qmin = 2

φ2

snapshots

φ2 time history, just forreminding when the snapshots

are taken

4/16


ITG nonlinear evolution: gap filled up by turbulence spreading

−1.5e− 16

−1e− 16

−5e− 17

0

5e− 17

1e− 16

1.5e− 16

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Inte

grat

edΦ

E(a

.u.

)

r/a

outward flow

inward flow

Approximated E-field intensityflux in the early nonlinear

phase integrated from SnapshotI to II.

ΦE(r) ≡⟨E2vEr

⟩Turbulence flows into the qmin

region from both sides.

10−9

10−8

10−7

10−6

10−5

10−4

0 50 100 150 200

t/(R0/cs)

⟨φ2

⟩

r/a = 0.427r/a = 0.490r/a = 0.554

⟨φ2

⟩near qmin grows after

⟨φ2

⟩outside the qmin region

saturates, and it doesn’t growexponentially, indicating not a

linear effect.

No linear mechanism forITB formation.

4/16


ITG nonlinear evolution: no coherent structures influctuations near qmin

0.2 0.3 0.4 0.5 0.6 0.7 0.8

∇rδT

i(a

.u.

)

Er

(a.

u.)

r/a

∇rδTi

Er

III

0.2 0.3 0.4 0.5 0.6 0.7 0.8

χi

(a.

u.)

r/a

χi

III

No nonlinear mechanism for ITB formation.Conclusion: no linear or nonlinear mechanism for ITBformation near qmin in ITG turbulence.

5/16


Outline





CTEM linear eigenmode only in the positive-shear region

10−8

10−7

10−6

10−5

10−4

10−3

10−2

0 10 20 30 40 50 60

t/(R0/cs)

⟨φ2

⟩V

I

II

III

IVV VI

qmin = 2

φ2

snapshots

Six snapshots taken

10−5

10−4

10−3

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

⟨φ2

⟩I and II scaled tothe same level

III

Linear eigenmode in I & II

Collisionless trapped electron mode (CTEM):

drift wave driven by trapped electron

precessional drift resonance

II

Linear eigenmode structure only inpositive-shear side due to precessional

drift reversal in negative-shear side

6/16


CTEM turbulence spreading into negative-shear region

10−5

10−4

10−3

10−2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

r/a

⟨φ2

⟩ II*IIIIVV

VI

II*: scaled up

10−6

10−5

10−4

10−3

10−2

0 10 20 30 40 50 60

t/(R0/cs)

⟨φ2

⟩

r/a = 0.2r/a = 0.3r/a = 0.4r/a = 0.71

Turbulence spreading frompositive-shear side tonegative-shear side

VI

Final turbulence structure

Front propagation speed vts ' 0.43v∗e

close to various theoretical estimates

[Gurcan et al., PoP 2005; Guo et al.,

PRL 2009]

No linear mechanism for ITBformation 7/16


CTEM nonlinear evolution: no coherent structures influctuations near qmin

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

∇rδT

e(a

.u.

)

Er

(a.

u.)

r/a

∇rδTe

Er

VI

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

χ(a

.u.

)

r/a

χi

χe

VI

No nonlinear mechanism for ITB formation.Conclusion: no linear or nonlinear mechanism for ITBformation near qmin in CTEM turbulence.

8/16


Conclusions for electrostatic turbulence simulations

The electrostatic drift wave turbulence itself does notsupport either linear or nonlinear mechanism for theformation of ITB in the reversed shear plasmas with aninteger qmin.Other external mechanisms, such as sheared flowsgenerated by MHD activities, are worth pursuing aspossible agents to suppress the electrostatic drift waveturbulence and form the ITB when qmin crossing aninteger. [Shafer et al., PRL 2009]Our nonlocal results raise the issue of the validity ofprevious local simulations finding the transport reductiondue to the precessional drift reversal of trapped electronsor the rarefaction of mode rational surfaces.

W. Deng & Z. Lin, Phys. Plasmas 16, 102503 (2009)9/16


time

full-f ITG

intensitydf ITG intensity

full-f zonal flows

df zonal flows

• Non-perturbative (full-f) & perturbative (df) simulation

• General geometry using EFIT & TRANSP data

• Kinetic electrons & electromagnetic simulation

• Neoclassical effects using Fokker-Planck collision

operators conserving energy & momentum

• Equilibrium radial electric field, toroidal & poloidal

rotations; Multiple ion species

• Applications: microturbulence & MHD modes

• Parallelization >100,000 cores

Global field-aligned mesh

Parallel solver PETSc

Advanced I/O ADIOS

Global Gyrokinetic Toroidal Code (GTC)

incorporates all physics in a single version

GTC simulation of DIII-D

shot #101391 using EFIT data

[Lin et al, Science, 1998]

http://gk.ps.uci.edu/GTC/

10/16


Outline





RSAE physics

RSAE is a form of shear Alfvenwave in the toroidal geometryand is localized near the qmin fluxsurface.RSAE can be driven unstable byfast ions.RSAE exhibits a variety ofphenomena, an important onebeing the “grand cascade”[Sharapov et al., PLA 2001].The “grand cascade” is used forqmin temporal and spatialdiagnosis in experiments. Oneexample on the right [Sharapovet al., NF 2006].

ωRSAE ≈ vAR

∣∣∣ mqmin− n

∣∣∣

11/16


Benchmark of RSAE antenna excitation (GTC & HMGC)

1.61.71.81.9

22.12.22.32.42.52.62.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

q

r/a

q-profile

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ωA/(v A/R

0)

(w/o

coup

ling)

r/a

m = 6m = 7

Alfven continuum (n = 4)

φ spectrum from HMGC

0 20 40 60 80 100 120 140 160

φ(a

.u.

)

t/(R0/vA)

GTC,<e,m = 6HMGC,<e,m = 6

time history of φ

HMGC: Hybrid MHD-Gyrokinetic Code [Briguglio et al., PoP 1998]12/16


RSAE mode structure by antenna excitation

φ poloidal structure from GTC

φ poloidal structure from HMGC

0 0.2 0.4 0.6 0.8 1

|φ|(

a.u.

)

r/a

m = 5m = 6m = 7

m-harmonic decomposition from GTC

m-harmonic decomposition from HMGC13/16


RSAE fast ion excitation

0 50 100 150 200 250 300 350

φ(a

.u.

)

t/(R0/vA)

<e,m = 7

=m,m = 7

φ time history (GTC)

0 50 100 150 200 250 300 350

|φ|(

a.u.

,lo

gsc

ale)

t/(R0/vA)

GTC,m = 7

φ poloidal structure (GTC)

φ poloidal structure (HMGC)14/16


Summary

GTC gyrokinetic particle simulations of electrostatic ITGand CTEM turbulence: the turbulence itself does notsupport either linear or nonlinear mechanism for theformation of ITB in the reversed shear plasmas with aninteger qmin.GTC gyrokinetic particle simulations of electromagneticRSAE: the first time using gyrokinetic particle approach tosimulate RSAE; the mode can be excited either by antennaor by fast ion; for the antenna excitation, when kineticeffects of thermal particles are artificially suppressed, thefrequency and mode structure in the GTC & HMGCsimulations agree well with each other.

GTC simulations of toroidal Alfven eigenmode (TAE) andβ-induced Alfven eigenmode (BAE) will also be reported in thisconference. 15/16


Other GTC related presentations

This afternoon:

1P34, O. Luk and Z. Lin, Collisional Effects on Nonlinear Wave-ParticleTrapping in Mirror Instability and Landau Damping

2P17, X. Wang et al., Hybrid MHD-particle simulation of discrete kineticBAE in tokamaks

2P19, H. S. Zhang et al., Gyrokinetic particle simulation of linear andnonlinear properties of GAM and BAE in Tokamak plasmas

Tomorrow afternoon:

3P13, I. Holod, Kinetic electron effects in toroidal momentum transport

3P18, Z. Lin and GTC team, Nonperturbative (full-f) global gyrokineticparticle simulation

3P27, Y. Xiao et al., Verification and validation of gyrokinetic particlesimulation

3P35, G. Y. Sun et al., Gyrokinetic particle simulation of ideal and kineticballooning modes

3P48, Z. Wang and Z. Lin, GTC Simulation of Cylindrical Plasmas

Wednesday morning:

Talk, W. Zhang, Gyrokinetic Particle Simulations of Toroidal AlfvenEigenmode and Energetic Particle transport in Fusion Plasmas

16/16

Education

Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas