Post on 03-Feb-2022
Suppressed Ion-Scale Turbulence and Critical Density Gradient in the C-2
Field-Reversed Configuration L. Schmitz (UCLA, TAE)
with C. Lau, D. Fulton, I. Holod, Z. Lin, (UCI), !
T. Tajima, M. Binderbauer, H. Gota, B. Deng, J. Douglass (TAE) and the TAE Team!
!
!!
Norman Rostoker !Memorial Symposium!August 24-25, 2015!
Irvine, CA!!
5
0
-5
f D (
MH
z)
0 1 2Time (ms)
2 L. Schmitz Norman Rostoker
Memorial Symposium
Goal of FRC Turbulence/Transport Studies:�Active Profile, Boundary, and Transport Control
Transport Models,
Dimensionless Scaling
Predictive Kinetic
Turbulence Modeling
Advanced Turbulence/
Profile Measurements
Active Profile,
Boundary, Transport Control
3 L. Schmitz Norman Rostoker
Memorial Symposium
Outline § Introduction
§ Experimental fluctuation/turbulence studies in the C-2 FRC
§ Gyrokinetic Modeling: FRC core and boundary fluctuations
§ Critical gradients, core/SOL transition and barrier effects
§ Summary
4 L. Schmitz Norman Rostoker
Memorial Symposium
FRC Geometry / C-2 Parameters
Solenoid coil (External B-Field)
B-Field Null (R)
Separatrix (Rs) Scrape-off layer
Core Plasma
Bez
Typical C-2 Parameters
FRC Core SOL Density (1019 m-‐3)
2-‐4 0.5-‐2
Ti (eV) 600-‐1000 ≤250 Te (eV) ≤ 150 30-‐80 Be (Gauss) ≤ 1200 Sep. Radius (cm)
35-‐45
Neutral Beam Power
≤ 4 MW
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Memorial Symposium
FRC Radial and Parallel Transport� Scrape-off layer (SOL):
Radial and parallel Transport (along z)
τ⊥−1 = 1
r∂∂r
rDr1n∂n∂r
⎛⎝⎜
⎞⎠⎟
Radial transport:
τ−1 = (τii lnRM )
−1
τ−1 = (τii lnRM )
−1
Radial Gradient scale length : If depends on , parallel and perpendicular transport are coupled
-10 -5 0 5 10
0.6
0.4
0.2
z (m)
r (
m)
From continuity (particle conservation:) ∇(nv i ) = −∇⊥ (nv i ) τ = τ⊥
Ln⊥
Ln⊥ = D⊥τ ii lnRM
D⊥
D⊥
Separatrix
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Memorial Symposium
Schematic and Principle of Doppler Backscattering Diagnostic (DBS)
ts=ti-kevExBks=ki-ke
b
c
ke
kIkS
tI,kI
ee .Be,ez
ñ/n: local density fluctuation level ñ(r)/n(r) vs. kθ - here kθ~ 0.5-12 cm-1 (kθρs~1-40)
ExB velocity from Doppler shift of back-scattered signal: ωDoppler = vturb kθ ~ vExBkθ
è vExB ~ ωDoppler / 2ki
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Memorial Symposium
Radial Density Profile and DBS Probing Radii
§ DBS: 6 remote-tunable channels (co-linear beams), probing the FRC core (outside field null) and the SOL
§ Beam path calculated via GENRAY ray/beam tracing, based on reconstructed (CO2) density profiles
ts=ti-kevExBks=ki-ke
b
c
ke
kIkS
tI,kI
ee .Be,ez
60
40
20
0
-20
-40
-60
-60 -40 -20 0 20 40 60
x (cm)
y (c
m)
750+s
MW Launch
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Memorial Symposium
Density Fluctuations Peak Outside Separatrix Very Low Fluctuations in FRC Core
n Fluctuation levels peak outside the separatrix n Very low fluctuation levels in the FRC core
-20 -10 0 10 20rFIR < r6\(cm)
0.0
0.1
0.2
0.3
0.4
0.5
bn
/n
Doppler Backscattering FIR Scattering
2 <kρs < 8 kρs < 4
rr rFIR –Rs (cm)
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Memorial Symposium
FRC Core Plasma: Unique Inverted Wavenumber Spectrum�
§ FRC Core: Decreased Fluctuations; Inverted Spectrum at low kρs
§ Spectrum extends to kρe > 0.3: Only unstable electron modes!
§ SOL: Ion and electron-scale modes
§ Broad exponential spectrum: (ñ/n)2 ~ exp (-0.32 kθρs)
10 L. Schmitz Norman Rostoker
Memorial Symposium
Outline § Introduction
§ Experimental fluctuation/turbulence studies in the C-2 FRC
§ Gyrokinetic Modeling: FRC core and boundary fluctuations
§ Critical gradients, core/SOL transition and barrier effects
§ Summary
11 L. Schmitz Norman Rostoker
Memorial Symposium
GTC (Gyrokinetic Toroidal Code) Simulations
First-principles, integrated microturbulence simulations; adapted for FRC geometry (Boozer coordinates): Useful for predictive modeling and reduced transport models Input: Experimental (measured) or calculated FRC equilibria Gyrokinetic or kinetic ions, kinetic electrons Local/global simulations, electromagnetic effects Fokker-Planck-collisions Presented here: Results from linear, electrostatic flux-tube simulations, separate calculations for the FRC core and SOL Future work: Coupled SOL/core, kinetic ions, nonlinear runs
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Memorial Symposium
Simulation Geometry, Parameters
Core and SOL local simulation: Realistic C-2 Equilibrium Periodic boundary conditions in z and θ Gyrokinetic ions (D) and electrons, νe,i*=ν/νtransit <<1
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Memorial Symposium
FRC-Core: Ion Modes Suppressed via FLR Effects, only Electron Modes Unstable
Calculated Linear Growth Rate from GTC
Measured Saturated Spectrum
• Spectrum extends to kθρe > 0.3: matches linearly unstable k-range Dominant electron modes; ion modes weak/absent due to FLR* effects:
*Rosenbluth, Krall and Rostoker, NF Suppl. pt1, 143 (1962)
kѡ��ѩe
0.8
0.4
�������
aR/c
s 0.24 0.28 �������
d=1
Core
R/LTe=5.25
no collisions
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Memorial Symposium
Ballooning Structure with/without Collisions
collisionless (ballooning) with collisions (ballooning, virtually no change in mode structure) θ
ζ
ζ
ζ
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Memorial Symposium
Local Gyrokinetic SOL Simulations
i-‐i e-‐i e-‐e 0.0058 0.172 0.082
𝜈*
Gyrokinetic D Ions Drift-kinetic electrons Ti = 5Te, Zeff =1.5 Fokker-Planck Collisions Flux-tube, local �simulation at r/Rs=1.2; periodic boundary in z
⇒ 𝜈*e-‐e=𝜈e-‐e/(vth-‐e/L) (moderate electron collisionality )
SOL
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Memorial Symposium
SOL: Exponential Wavenumber Spectrum;Unstable Ion Modes
#29587-29610, #29750-29802
ρs=[(kTe+kTi)/mi]1/2/ωci
Measured Saturated Spectrum Calculated Linear Growth Rate from GTC (w/collisions)
17 L. Schmitz Norman Rostoker
Memorial Symposium
Driving Gradients Differ in FRC Core and SOL aR
/cs
3.0
2.0
1.0
00.75 0.8 0.85 0.9 0.95 1.0
de
Core di=1
R/LTi=R/Ln= 6
no collisions
kѡ� ѩe=0.3
∇Te ∇n
No instability below ηe <0.75
Electron drift/Interchange Core modes driven by and curvature
Instability to 1/ηi =0
Density gradient-driven SOL ion drift modes
aR/c
s
0.3
0.2
0.1
00 0.2 0.4 0.6 0.8 1.0
� di
R/LTe= R/LTi
= 6
SOL�de=1
kels= 0.85
w/collisions
SOL Modes are Driven by Core Modes are Driven by
∇Te
18 L. Schmitz Norman Rostoker
Memorial Symposium
Outline § Introduction
§ Experimental fluctuation/turbulence studies in the C-2 FRC
§ Gyrokinetic Modeling: FRC core and boundary fluctuations
§ Critical gradients, core/SOL transition and barrier effects
§ Summary
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Memorial Symposium
E×B Shear Increases the SOL Critical Gradient
§ Radial density gradient increases after ~0.5 ms (SOL is depleted) § SOL fluctuation increase once critical density gradient is exceeded § Fluctuation decrease once ExB shearing rate increases exceeds the turbulence decorrelation rate: ωΕ×Β>ΔωD (Biglari, Diamond, Terry, Phys. Fluids B1,1989) § The radial correlation length decreases with increasing ExB shear
Density profile time history
6
4
2
0
R/L n
0.14
0.07
0
0 0.5 1.0 1.5 2.0 2.5
1.0
0.5
0
-0.5
Time (ms)
t E�B
, tD (
106 ra
d/s)
ñ/n (a
u)1.5
1.0
0.5
0
h r (c
m)
R/Ln crit
0.6
0.4
0.2
0
0.2
0.4
0.6
r (m
)
2.3
1.9
1.5
1.1
0.7
0.4
0
ne (1019 m-3)
r/Rs=1.1
r/Rs=1.1
r/Rs=0.9
r/Rs=0.9
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Memorial Symposium
Measured Critical Gradient and Calculated Core Linear Threshold from GTC
a R/
c s
2.0
1.5
1.0
0.5
0
R/LTe, R/Ln4.8 5.2 5.6
r/Rs=0.97 Corekele = 0.27kele = 0.30
de= di= 1
2 3 4R/Ln
0.16
0.08
0
ñ/n
(au)
r/Rs ~ 1.15r/Rs = 0.95r/Rs ~ 0.85
kele ~ 0.07-0.28
R/Ln critR/Ln crit
(SOL)(Core)
Measured R/ Ln crit (FRC core/SOL)
FRC core growth rate vs. R/LTe from linear GTC simulation
21 L. Schmitz Norman Rostoker
Memorial Symposium
2 3 4R/Ln
0.16
0.08
0
ñ/n
(au)
r/Rs ~ 1.15r/Rs = 0.95r/Rs ~ 0.85
kele ~ 0.07-0.28
R/Ln critR/Ln crit
(SOL)(Core)
R/Ln
kels = 0.85kels = 1.70
3 4 5 6
0.4
0.3
0.2
0.1
0a R
/cs
R/Ln
r/Rs=1.2 SOL
kels = 0.85kels = 1.70
3 4 5 6
Measured SOL Critical Density Gradient Similar to Predicted Linear Instability Threshold
Measured R/ Ln crit (FRC core/SOL)
FRC core growth rate vs. R/Ln from linear GTC simulation
22 L. Schmitz Norman Rostoker
Memorial Symposium
Core-SOL Coupling: Evidence �for Radial Transport Barrier
§ Radial turbulence correlation
length λr ≤ ρi § No evidence of sustained extended radial structures or streamers λr reduced just outside Rs: Evidence of radial transport barrier. § Shear decorrelation just outside the separatrix: ωΕ×Β>ΔωD (Biglari, Diamond, Terry,
Phys. Fluids B1,1989)
-10 0 10
tE
xB, 6
tD
(1
05 r
ad/s
)
r-Rs (cm)
6
4
2
0
>
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Memorial Symposium
Summary • C-2 FRC core: Ion modes stable due to FLR effect; only
electron modes unstable (driven by electron temperature gradient and curvature)
• Moderate, larger-scale ion-mode SOL turbulence observed/predicted; driven by the radial density gradient.
• Strong evidence of radial transport barrier in the SOL. No experimental evidence of sustained large-scale radial structures/streamers (radial correlation length λr < ρi)
• Observed critical SOL density gradient compares well
with predicted linear instability threshold; compatible with required reactor SOL width