The document summarizes simulations of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas. It describes simulations of (1) ion temperature gradient turbulence and collisionless trapped electron mode turbulence, finding no linear or nonlinear mechanisms for internal transport barrier formation, and (2) reversed shear Alfvén eigenmodes driven by fast ions. It concludes that external mechanisms like sheared flows may be needed to suppress drift wave turbulence and form internal transport barriers.

1. ITG turbulence CTEM turbulence RSAE Summary
Properties of electrostatic and electromagnetic
turbulence in reversed magnetic shear plasmas
Wenjun Deng
University of California, Irvine, USA
Ihor Holod1 , Yong Xiao1 ,
Xin Wang1,2 , Wenlu Zhang1,3 and Zhihong Lin1
1
University of California, Irvine, USA
2
IFTS, Zhejiang University, China
3
University of Science and Technology of China, China
Supported by SciDAC GSEP & GPS-TTBP

2. ITG turbulence CTEM turbulence RSAE Summary
Motivations
Reversed (magnetic) shear (RS) in tokamak: safety factor q-profile
has an off-axis minimum. This minimum value is called qmin .
1 Internal transport barrier (ITB) can form at the integer
qmin flux surface and suppress turbulent transport. Some
proposed mechanisms are based on electrostatic drift wave
turbulence.
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 collisionless
trapped electron mode (CTEM) turbulence.
1/16

3. ITG turbulence CTEM turbulence RSAE Summary
Motivations
Reversed (magnetic) shear (RS) in tokamak: safety factor q-profile
has an off-axis minimum. This minimum value is called qmin .
1 Internal transport barrier (ITB) can form at the integer
qmin flux surface and suppress turbulent transport. Some
proposed mechanisms are based on electrostatic drift wave
turbulence.
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 collisionless
trapped electron mode (CTEM) turbulence.
2 Reversed shear Alfv´n eigenmode (RSAE) at the qmin flux
e
surface can be driven unstable by fast ions and can cause
fast ion loss.
We use electromagnetic GTC to study RSAE and fast ion
physics. The results using fast ions and antenna excitation
without thermal particle kinetic effects are benchmarked
with HMGC [Briguglio et al., PoP 1998] simulations.
1/16

4. ITG turbulence CTEM turbulence RSAE Summary
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 ion
excitation

5. ITG turbulence CTEM turbulence RSAE Summary
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 ion
excitation

6. ITG turbulence CTEM turbulence RSAE Summary
ITG linear eigenmode: gap structures only for integer qmin
Rarefaction of the
rational surfaces
causes a potential gap.
1.4
qmin = 1
1.2
1
q
0.8
0.6
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/a
mode rational surface:
nq(r) = m
qmin = 1 n: toroidal mode #
10−5
φ2 m: poloidal mode #
10−6
10−7 nq(rblack ) = mmin
10−8
r/a
nq(rred ) = mmin + 1
10−9 nq(rblue ) = mmin + 2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 etc.
n ∈ [25, 95] 2/16

7. ITG turbulence CTEM turbulence RSAE Summary
ITG linear eigenmode: gap structures only for integer qmin
Rarefaction of the
rational surfaces
causes a potential gap.
1.4
qmin = 1
1.2
1
q
0.8
qmin = 0.9552
0.6
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/a
mode rational surface:
nq(r) = m
qmin = 1 n: toroidal mode # qmin = 0.9552
10−5 10−5
φ2 m: poloidal mode # φ2
10−6 10−6
10−7 nq(rblack ) = mmin 10−7
10−8
r/a
nq(rred ) = mmin + 1 10−8
r/a
10−9 nq(rblue ) = mmin + 2 10−9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 etc. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
n ∈ [25, 95] 2/16

8. ITG turbulence CTEM turbulence RSAE Summary
ITG nonlinear evolution: potential gap filled up
10−5 10−4
II III I
φ2 I φ2 II
V 10−5 III
10−6
10−6
10−7
qmin = 2 10−7
10−8
φ2 10−8
t/(R0 /cs ) snapshots r/a
10 −9 10−9
0 50 100 150 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Three snapshots taken Radial structures of I, II, & III
I II III
3/16

9. ITG turbulence CTEM turbulence RSAE Summary
ITG nonlinear evolution: gap filled up by turbulence spreading
1.5e − 16
1e − 16
Integrated ΦE (a. u.)
outward flow
5e − 17
0 10−5
II III
−5e − 17
φ2 I
−6 V
inward flow 10
−1e − 16
r/a
−1.5e − 16
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
10−7
qmin = 2
Approximated E-field intensity −8
10
φ2
flux in the early nonlinear t/(R0 /cs ) snapshots
−9
phase integrated from Snapshot 10
0 50 100 150 200
I to II. φ2
time history, just for
reminding when the snapshots
ΦE (r) ≡ E 2 vEr
are taken
Turbulence flows into the qmin
region from both sides.
4/16

10. ITG turbulence CTEM turbulence RSAE Summary
ITG nonlinear evolution: gap filled up by turbulence spreading
1.5e − 16 10−4
1e − 16
Integrated ΦE (a. u.)
10−5 φ2
outward flow
5e − 17
0
10−6
−5e − 17 10−7 r/a = 0.427
inward flow r/a = 0.490
−1e − 16
10−8 r/a = 0.554
r/a
−1.5e − 16
t/(R0 /cs )
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
10−9
Approximated E-field intensity 0 50 100 150 200
flux in the early nonlinear φ2 near qmin grows after φ2
phase integrated from Snapshot outside the qmin region
I to II. saturates, and it doesn’t grow
exponentially, indicating not a
ΦE (r) ≡ E 2 vEr linear effect.
Turbulence flows into the qmin No linear mechanism for
region from both sides. ITB formation.
4/16

11. ITG turbulence CTEM turbulence RSAE Summary
ITG nonlinear evolution: no coherent structures in
fluctuations near qmin
III III
(a. u.)
Er (a. u.)
χi (a. u.)
χi
r δTi
r δTi
Er
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8
r/a r/a
No nonlinear mechanism for ITB formation.
Conclusion: no linear or nonlinear mechanism for ITB
formation near qmin in ITG turbulence.
5/16

12. ITG turbulence CTEM turbulence RSAE Summary
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 ion
excitation

13. ITG turbulence CTEM turbulence RSAE Summary
CTEM linear eigenmode only in the positive-shear region
10−2 Collisionless trapped electron mode (CTEM):
IV
10−3 φ2 V V VI drift wave driven by trapped electron
10−4 III
precessional drift resonance
10−5
qmin = 2
10−6 II
II
10−7 φ2
I t/(R0 /cs ) snapshots
10−8
0 10 20 30 40 50 60
Six snapshots taken
10−3
φ2
I and II scaled to
the same level
10−4
I
10−5
II r/a Linear eigenmode structure only in
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 positive-shear side due to precessional
Linear eigenmode in I & II drift reversal in negative-shear side
6/16

14. ITG turbulence CTEM turbulence RSAE Summary
CTEM turbulence spreading into negative-shear region
10−2
II*
φ2 III VI
IV
10−3 V
VI
10−4
r/a
10−5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
II*: scaled up
10−2
φ2
10−3
10−4 r/a = 0.2
Final turbulence structure
r/a = 0.3
10−5
r/a = 0.4 Front propagation speed vts 0.43v∗e
r/a = 0.71
t/(R0 /cs ) close to various theoretical estimates
10−6
0 10 20 30 40 50 60 [G¨rcan et al., PoP 2005; Guo et al.,
u
Turbulence spreading from PRL 2009]
positive-shear side to No linear mechanism for ITB
negative-shear side formation 7/16

15. ITG turbulence CTEM turbulence RSAE Summary
CTEM nonlinear evolution: no coherent structures in
fluctuations near qmin
VI VI
(a. u.)
Er (a. u.)
χ (a. u.)
r δTe
r δTe χi
Er χe
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
r/a r/a
No nonlinear mechanism for ITB formation.
Conclusion: no linear or nonlinear mechanism for ITB
formation near qmin in CTEM turbulence.
8/16

16. ITG turbulence CTEM turbulence RSAE Summary
Conclusions for electrostatic turbulence simulations
The electrostatic drift wave turbulence itself does not
support either linear or nonlinear mechanism for the
formation of ITB in the reversed shear plasmas with an
integer qmin .
Other external mechanisms, such as sheared flows
generated by MHD activities, are worth pursuing as
possible agents to suppress the electrostatic drift wave
turbulence and form the ITB when qmin crossing an
integer. [Shafer et al., PRL 2009]
Our nonlocal results raise the issue of the validity of
previous local simulations finding the transport reduction
due to the precessional drift reversal of trapped electrons
or the rarefaction of mode rational surfaces.
W. Deng & Z. Lin, Phys. Plasmas 16, 102503 (2009)
9/16

17. ITG turbulence CTEM turbulence RSAE Summary
Global Gyrokinetic Toroidal Code (GTC)
incorporates all physics in a single version
• 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 GTC simulation of DIII-D
shot #101391 using EFIT data
• Applications: microturbulence & MHD modes
full-f ITG
• Parallelization >100,000 cores intensity
df ITG intensity
Global field-aligned mesh
Parallel solver PETSc
Advanced I/O ADIOS full-f zonal flows
[Lin et al, Science, 1998] df zonal flows
http://gk.ps.uci.edu/GTC/ time
10/16

18. ITG turbulence CTEM turbulence RSAE Summary
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 ion
excitation

19. ITG turbulence CTEM turbulence RSAE Summary
RSAE physics
vA m
RSAE is a form of shear Alfv´ne ωRSAE ≈ R qmin −n
wave in the toroidal geometry
and is localized near the qmin flux
surface.
RSAE can be driven unstable by
fast ions.
RSAE exhibits a variety of
phenomena, an important one
being the “grand cascade”
[Sharapov et al., PLA 2001].
The “grand cascade” is used for
qmin temporal and spatial
diagnosis in experiments. One
example on the right [Sharapov
et al., NF 2006]. 11/16

20. ITG turbulence CTEM turbulence RSAE Summary
Benchmark of RSAE antenna excitation (GTC & HMGC)
2.7
2.6
2.5
2.4
2.3
2.2
q
2.1
2
1.9
1.8
1.7
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
r/a
q-profile
φ spectrum from HMGC
1
(w/o coupling)
m=6
m=7 GTC, e, m = 6
0.8
HMGC, e, m = 6
0.6
φ (a. u.)
0.4
ωA /(vA /R0 )
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 20 40 60 80 100 120 140 160
r/a t/(R0 /vA )
Alfv´n continuum (n = 4)
e time history of φ
HMGC: Hybrid MHD-Gyrokinetic Code [Briguglio et al., PoP 1998]
12/16

21. ITG turbulence CTEM turbulence RSAE Summary
RSAE mode structure by antenna excitation
m=5
m=6
m=7
|φ| (a. u.)
0 0.2 0.4 0.6 0.8 1
r/a
φ poloidal structure from GTC m-harmonic decomposition from GTC
φ poloidal structure from HMGC m-harmonic decomposition from HMGC 13/16

22. ITG turbulence CTEM turbulence RSAE Summary
RSAE fast ion excitation
e, m = 7
m, m = 7
φ (a. u.)
0 50 100 150 200 250 300 350
t/(R0 /vA ) φ poloidal structure (GTC)
φ time history (GTC)
|φ| (a. u., log scale)
GTC, m = 7
0 50 100 150 200 250 300 350
t/(R0 /vA ) φ poloidal structure (HMGC)
14/16

23. ITG turbulence CTEM turbulence RSAE Summary
Summary
GTC gyrokinetic particle simulations of electrostatic ITG
and CTEM turbulence: the turbulence itself does not
support either linear or nonlinear mechanism for the
formation of ITB in the reversed shear plasmas with an
integer qmin .
GTC gyrokinetic particle simulations of electromagnetic
RSAE: the first time using gyrokinetic particle approach to
simulate RSAE; the mode can be excited either by antenna
or by fast ion; for the antenna excitation, when kinetic
effects of thermal particles are artificially suppressed, the
frequency and mode structure in the GTC & HMGC
simulations agree well with each other.
GTC simulations of toroidal Alfv´n eigenmode (TAE) and
e
β-induced Alfv´n eigenmode (BAE) will also be reported in this
e
conference. 15/16

24. ITG turbulence CTEM turbulence RSAE Summary
Other GTC related presentations
This afternoon:
1P34, O. Luk and Z. Lin, Collisional Effects on Nonlinear Wave-Particle
Trapping in Mirror Instability and Landau Damping
2P17, X. Wang et al., Hybrid MHD-particle simulation of discrete kinetic
BAE in tokamaks
2P19, H. S. Zhang et al., Gyrokinetic particle simulation of linear and
nonlinear 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 gyrokinetic
particle simulation
3P27, Y. Xiao et al., Verification and validation of gyrokinetic particle
simulation
3P35, G. Y. Sun et al., Gyrokinetic particle simulation of ideal and kinetic
ballooning modes
3P48, Z. Wang and Z. Lin, GTC Simulation of Cylindrical Plasmas
Wednesday morning:
Talk, W. Zhang, Gyrokinetic Particle Simulations of Toroidal Alfven
Eigenmode and Energetic Particle transport in Fusion Plasmas
16/16