Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas
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Transcript of 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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
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 ionexcitation
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 ionexcitation
ITG turbulence CTEM turbulence RSAE Summary
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 turbulence CTEM turbulence RSAE Summary
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 turbulence CTEM turbulence RSAE Summary
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 turbulence CTEM turbulence RSAE Summary
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 turbulence CTEM turbulence RSAE Summary
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 turbulence CTEM turbulence RSAE Summary
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
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 ionexcitation
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
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 ionexcitation
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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
ITG turbulence CTEM turbulence RSAE Summary
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