Plasma turbulence in the tokamak scrape-off layer · Introduction Global model for SOL turbulence...
Transcript of Plasma turbulence in the tokamak scrape-off layer · Introduction Global model for SOL turbulence...
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Plasma turbulence in the tokamak scrape-off layer
F.D. Halpern1, S. Jolliet1, B. LaBombard2, J. Loizu1,A. Mosetto1, M. Podesta3, P. Ricci1, F. Riva1, J. Terry2,
C. Wersal1, S. Zweben3
1École Polytecnique Fédérale de LausanneCentre de Recherches en Physique des Plasmas, CH-1015 Lausanne, Suisse
2Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA3Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540, USA
Theory and Modelling SeminarInstitute for Plasmas and Nuclear Fusion
Instituto Superior Técnico20th Oct 2014, Lisbon, Portugal
F.D. Halpern 1 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Scrape-off layer physics crucial for magnetic fusionHeat load to PFCs, rotation, impurities, L-H transition...
How do we develop 1st principles understanding of SOL dynamics?
F.D. Halpern 2 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Simple problem: inner wall limited (pol. ×-section)
Toroidal limiter (inner-wall limited)
Plasma inflowing from closed field
line region
F.D. Halpern 3 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Ballooning turbulence with kθρs ≈ 0.1 ∼ 1cm−1
δφ/σφ
δn/σ
n−4 −2 0 2 4
−4
−2
0
2
4
−1 −0.5 0 0.5 110−2
10−1
100
Phase(φ,n) / π
k θρ s
10−3 10−2 10−1 100
10−6
10−4
kθρs
fluc.
pow
er (r
el)
F.D. Halpern 4 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Gaussian in near SOL, intermittent in far SOL
−1 −0.5 0 0.5 10
0.5
1
1.5
δn/n
P(δ
n/n)
Near SOL
−1 −0.5 0 0.5 10
0.5
1
1.5
δn/nP
(δn/
n)
Far SOL
F.D. Halpern 5 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Fluctuation level O(1), skewed PDF
0.10.20.30.40.40.5
δn/n
−0.5
0
0.5
1
1.5
Ske
wne
ss
0 0.5 1 1.5 2
0
1
2
3
Kur
tosi
s
r−r0
[cm]
F.D. Halpern 6 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Power balance → exponentially decaying profiles
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
r−r0
[cm]
p/p 0
SimulationExponential fit
Turbulence Sonic flows towards PFCs
F.D. Halpern 7 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Some of the topics we have studied...
X What mechanism sets the turbulence levels?
X What instability drives the perpendicular transport?
X How does the SOL width change with parameters?
X Can we reconcile theory, simulations, and experiments?
X Poloidal limiter geometry → ISTTOK [Rogerio’s MSc work]
X What are the effects of neutrals?
X How is toroidal rotation generated in the SOL? [Loizu, PoP 2014]
× Is SOL transport related to the density limit? [LaBombard, NF 2005/08]
× How is the SOL coupled with the closed flux surface region?[Tamain et al.]
F.D. Halpern 8 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
A tool to simulate SOL turbulence
Global Braginskii Solver (GBS) [Ricci, PPCF (2012)]
I Drift-reduced Braginskii equationsd/dt � ωci , k2⊥ � k2‖
I Evolves n, φ, V||e , V||i , Te , Ti in 3D
I Global, flux-driven, no separation be-tween equilibrium and fluctuations
I Power balance between plasma outflowfrom the core, turbulent transport, andparallel losses
I Scalable ρ? up to medium size tokamak(e.g. TCV, C-Mod)
F.D. Halpern 9 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Drift-reduced Braginskii equations to describe the SOL
∂n
∂t=−
ρ−1?B
[φ, n] +2
B[nC(Te ) + Te C(n)− nC(φ)]− n∇‖v‖e − v‖e∇‖n
∂ω̃
∂t=−
ρ−1?B
[φ, ω̃]− v‖i∇‖ω̃ +B2
n∇‖j‖ +
2B
nC(p) +
B
3nC(Gi ), ω̃ = ∇
2⊥(φ + τTi )
∂
∂t
(v‖e +
mi
me
βe
2ψ
)=−
ρ−1?B
[φ, v‖e ]− v‖e∇‖v‖e +mi
me
[νj‖/n +∇‖φ−
∇‖pen− 0.71∇‖Te −
2
3n∇‖Ge
]∂v‖i
∂t=−
ρ−1?B
[φ, v‖i ]− v‖i∇‖v‖i −2
3∇‖Gi −
1
n∇‖p
∂Te
∂t=−
ρ−1?B
[φ,Te ]− v‖e∇‖Te +4
3
Te
B
[7
2C(Te ) +
Te
nC(n)− C(φ)
]+
+2
3
{Te
[0.71∇‖v‖i − 1.71∇‖v‖e
]+ 0.71Te (v‖i − v‖e )
∇‖n
n
}+D‖
Te(Te )
∂Ti
∂t=−
ρ−1?B
[φ,Ti ]− v‖i∇‖Ti +4
3
Ti
B
[C(Te ) +
Te
nC(n)− C(φ)
]+
+2
3Ti
(v‖i − v‖e
) ∇‖nn−
2
3Ti∇‖v‖e −
10
3
Ti
BC(Ti ) +D
‖Ti
(Ti )
+Sheath BCs consistent with PIC simulations [Loizu, PoP (2012)]
F.D. Halpern 10 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Parameters, normalizations, coordinates
I Coordinate system: (θ, r , ϕ)→ (poloidal , radial , toroidal)
I Equations expressed in normalized units:
I L⊥ → ρsI L‖ → R
I v → csI t ∼ γ−1 → R/cs
I The dimensionless code parameters are as follows:
I ρ? = ρs/R
I ν = e2nR/(miσ‖cs)
I βe = 2µ0pe/B2
I q ≈ (r/R)Bϕ/BθI Simplified notation in analytical expressions:
I p0 = 〈p〉t , t � γ−1 I Lp = −〈p/∂rp〉t
F.D. Halpern 11 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Poloidal cross sections showing SOL turbulence
F.D. Halpern 12 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Modes saturate due to pressure non-linearity
We observe in simulations [Ricci, PoP (2013)]:
I Mode saturation caused by local pressure non-linearity
∂rp1 ∼ ∂rp0 → p1p0 ∼σrLp
I Radial eddy length σr is mesoscopic [Ricci, PRL (2008)]
σr ≈√Lp/kθ
I Turbulent flux Γ1 dominated by radial E× B convection
Γ1 = ρ−1?
〈p1
∂φ1∂θ
〉
F.D. Halpern 13 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Saturation model yields E× B turbulent flux
Gradient removal hypothesis
F.D. Halpern 14 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Self-consistent prediction of pressure gradient length
In steady state, ∇ · Γ1 balances parallel losses ∼ ∇‖ · (pv‖e), hence
Lp ≈q
cs
(γ
kθ
)max
I Results in iterative scheme to predict Lp self-consistently:
I Compute γ = f ( Lp︸︷︷︸vary
, kθ︸︷︷︸scan
, ρ?, q, ν, ŝ,mi/me︸ ︷︷ ︸plasma parameters
)
I Vary Lp until LHS = RHS using secant method
F.D. Halpern 15 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Excellent agreement between theory and simulations
Lp predicted using self-consistent procedure [Halpern, NF (2014)]
0 30 60 90 120 150 1800
30
60
90
120
150
180
Lp (gradient removal)
Lp(sim
ulation)
GBS sims.: ρ−1? = 500–2000, q = 3–6, ν = 0.01–1, β = 0–3× 10−3
F.D. Halpern 16 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Dominant instability depends principally on q, ν, ŝ, Ti/TeI Build instability parameter space using reduced models→ gradient removal theory, linear dispersion relations
I Verify results using GBS non-linear simulations [Mosetto, PoP (2013)]
−2 0 2−3
−2.5
−2
−1.5
−1
−0.5
0
ŝ
log10(ν)
IBMIDW
RDW
RBM
I Which instability drives ⊥ transport?I Inertial/Resistive Ballooning modes/Drift Waves?foobar
F.D. Halpern 17 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Dominant instability depends principally on q, ν, ŝ, Ti/TeI Build instability parameter space using reduced models→ gradient removal theory, linear dispersion relations
I Verify results using GBS non-linear simulations [Mosetto, PoP (2013)]
−2 0 2−3
−2.5
−2
−1.5
−1
−0.5
0
ŝ
log10(ν)
IBMIDW
RDW
RBM
I Which instability drives ⊥ transport?I Inertial/Resistive Ballooning modes/Drift Waves?
F.D. Halpern 17 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Presence of RBMs verified in TCV SOL sims
I (ñ, φ̃) phase difference, joint (ñ, φ̃) pdf [Halpern, NF (2014)]
0.01
0.1
1
kθ
−4
−2
0
2
4
(p1−〈p
1〉)/σp 1
0.01
0.1
1
kθ
−4
−2
0
2
4
(p1−〈p
1〉)/σp 1
−1 −0.5 0 0.5 10.01
0.1
1
P(φ1, p1)/π
kθ
−4 −2 0 2 4−4
−2
0
2
4
(φ1 − 〈φ1〉)/σφ1
(p1−〈p
1〉)/σp 1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
−3
ŝ = 0 ŝ = 0
ŝ = 1 ŝ = 1
ŝ = 2 ŝ = 2
Curvature-driven, non-adiabatic mode → RBMs
F.D. Halpern 18 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Addition of finite Ti weakens adiabatic coupling
I Analysis extended to include Ti effects [Mosetto, PoP (submitted)]
I Joint (ñ, φ̃) pdf in GBS sims with τ = 1, τ = 4
RBM component is enhanced by finite Ti
F.D. Halpern 19 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
SOL width in RBM regime scales with ρ?, q
I SOL width obtained analytically with RBMs [Halpern, NF 2013/14]:
I Our simple model leads to a dimensionless scaling:
Machine size
Electromagnetic effectsCollisionality vs
connection length
F.D. Halpern 20 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Parallel dynamics physics in agreement with simulations
I Verify saturated RBM theory with GBS EM simulations
I ρ−1? = 500, βe = 0–3× 10−3, ν = 0.01–1, q = 3, 4, 6
αd/q
α
10−3
10−2
10−1
100
0
0.2
0.4
0.6
0.8
1
20
40
60
80
100
(Contours of Lp given by theory, symbols are GBS simulations)
F.D. Halpern 21 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
GBS simulations confirm size-scaling up to TCV sizeCASTOR
TCV
F.D. Halpern 22 / 40 Plasma turbulence in the tokamak scrape-off layer
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IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Dimensionless scaling follows GBS simulation data
Comparison carried out over wide range of parameters (ρ?, q, β, ν)
0 30 60 90 120 150 1800
30
60
90
120
150
180
F.D. Halpern 23 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Good agreement with SOL width measurements
Lp ≈ 7.2× 10−8q8/7R5/7B−4/7φ T−2/7e0 n
2/7e0 (1 + Ti/Te)
1/7 [ m ]
0 0.03 0.06 0.09 0.120
0.03
0.06
0.09
0.12Alcator C-MODCOMPASSJ ETTCVTore Supra
Exp. data:G. Arnoux
I. Furno
J.P. Gunn
J. Horacek
M. Kočan
B. Labit
B. LaBombard
C. Silva
F.D. Halpern 24 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Good agreement with SOL width measurements
Lp ≈ 7.2× 10−8q8/7R5/7B−4/7φ T−2/7e0 n
2/7e0 (1 + Ti/Te)
1/7 [ m ]
0 0.03 0.06 0.09 0.120
0.03
0.06
0.09
0.12
ITER start-up prediction
Alcator C-MODCOMPASSJ ETTCVTore Supra
Exp. data:G. Arnoux
I. Furno
J.P. Gunn
J. Horacek
M. Kočan
B. Labit
B. LaBombard
C. Silva
F.D. Halpern 24 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Turbulence levelsDominant instabilitiesScrape-off layer width scaling
Not so fast...Recent measurements (e.g. JET, C-Mod) show 2 different ∇ scales
Figure : Data: G.Arnoux [NF’12] (left), B.LaBombard (right)
I Carry out detailed simulation/theory/experiment comparison
I Alcator C-Mod, TCV, RFX (in tokamak mode)
F.D. Halpern 25 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
An ideal testbed for simulation-experiment comparisonI Inner-wall limited Ohmic C-Mod
discharges [Zweben, PoP (2009)]
I R = 0.67m, a = 0.20m,B = 2.7, 3.8T, κ = 1.2
I Density scan at each value of B
I Characterize C-Mod SOL turbulence using GPI diagnostic,and compare with GBS results
I Low β, no Ti or B̃ diagnostics → simple electrostatic,cold ion model
I δDαDα, pdf moments ,τauto , Lr , Lθ, vr , vθ, P(kθ), P(ω)
Very stringent test!
F.D. Halpern 26 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Simulated pressure profiles show double scale length
I Two-scale fit for pe yields Lp,near ≈ 5mm, Lp,far ≈ 2cm
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
r−r0 [cm]
p/p 0
I Probe measurements from 2009 campaign not precise enough
I From now on, concentrate on characterizing turbulence
F.D. Halpern 27 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Simulated pressure profiles show double scale length
I Two-scale fit for pe yields Lp,near ≈ 5mm, Lp,far ≈ 2cm
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
r−r0 [cm]
p/p 0
I Probe measurements from 2009 campaign not precise enough
I From now on, concentrate on characterizing turbulence
F.D. Halpern 27 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Simulated pressure profiles show double scale length
I Two-scale fit for pe yields Lp,near ≈ 5mm, Lp,far ≈ 2cm
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
r−r0 [cm]
p/p 0
I Probe measurements from 2009 campaign not precise enough
I From now on, concentrate on characterizing turbulence
F.D. Halpern 27 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Simulated pressure profiles show double scale length
I Two-scale fit for pe yields Lp,near ≈ 5mm, Lp,far ≈ 2cm
0 0.5 1 1.5 20
0.2
0.4
0.6
0.8
1
r−r0 [cm]
p/p 0
I Probe measurements from 2009 campaign not precise enough
I From now on, concentrate on characterizing turbulence
F.D. Halpern 27 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Turbulent modes in the near SOLUse joint-pdf and phase between φ, p fluctuations to understandnature of turbulent modes
I φ1, n1 well correlated → almost adiabatic modeI Small phase shift → curvature drive not important
−4 −2 0 2 4−4
−2
0
2
4
(φ−)/σφ
(p−
<p>
)/σ p
−1 −0.5 0 0.5 110
−3
10−2
10−1
100
P(φ,pe)/π
k yρ s
0
F.D. Halpern 28 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Turbulent modes in the far SOLUse joint-pdf and phase between φ, p fluctuations to understandnature of turbulent modes
I Weak correlation between φ1, n1 → non-adiabaticI Phase shift ∼ π/2 → curvature driven ballooning mode
−4 −2 0 2 4−4
−2
0
2
4
(φ−)/σφ
(p−
<p>
)/σ p
−1 −0.5 0 0.5 110
−3
10−2
10−1
100
P(φ,pe)/π
k yρ s
0
F.D. Halpern 29 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Gas-puff imaging of C-Mod SOL
Phantom 710 high-speed camera at 400’000fps [S.Zweben, J.Terry]
F.D. Halpern 30 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
δDα/Dα diagnostic for GBSUsing DEGAS modeling of GPI emissivity, model Dα fluctuations
I Emissivity locally parametrized as E ∝ Tαe nβe , use H656 line
I Fluctuations modelled as δDα/Dα ≈ α(Te , ne)T̃e +β(Te , ne)ñ
−0.3
−0.3
−0.2
−0.2
−0.1
−0.1
−0.1
00
0
0.2
0.2
0.2
0.4
0.4
0.4
0.8
0.8
0.8
1
1
1
22
2
55
5
10
10
10
20
20
20
log Te [ eV ]
log n
e [ m
−3 ]
−1 0 1 2 3 4
17
18
19
20
21
22
0
5
10
15
200.1 0.1
0.2
0.2
0.20.3
0.3
0.30.4
0.4
0.40.5
0.5
0.5
0.6
0.6 0.6
0.6
0.7
0.7
0.7
0.7
0.8 0.8
0.8
0.8
0.8
0.9
0.9
0.9
0.9
11
1
1
1.1
log Te [ eV ]
log n
e [ m
−3 ]
−1 0 1 2 3 4
17
18
19
20
21
22
0.2
0.4
0.6
0.8
1
I Simulate finite GPI resolution (3× 3mm + 2.5µs smoothing),B-field tilt respect to sensors (8mm poloidal smoothing)
F.D. Halpern 31 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
δDα/Dα synthetic diagnostic results
I Left to right: ñ, δDα/Dα, δDα/Dα (diode), δDα/Dα (full)
θ/π
r−r0 [m]
0 0.01 0.02−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
r−r0 [m]
0 0.01 0.02−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
r−r0 [m]
0 0.01 0.02−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
r−r0 [m]
0 0.01 0.02−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
High kθ modes strongly damped by smoothing
F.D. Halpern 32 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Large δDα/Dα fluctuations, skewed PDF
I δDα/Dα level increases withSOL, ∼ 30% in far SOL
I Skewness ∼ 1→ blobs (?)
I Moment profiles robust withplasma parameters
0
0.1
0.2
0.3
0.4
δDα/
Dα
−1
−0.5
0
0.5
1
1.5
Ske
wne
ss0 0.005 0.01 0.015 0.02 0.025 0.03
−1
0
1
2
3
Kur
tosi
sr−r
0[m]
B=2.7T low nB=2.7T high nB=3.8T low nB=3.8T high n
Quantitative comparison using shaded area (GPI sensors)
F.D. Halpern 33 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Large δDα/Dα fluctuations, skewed PDF
I δDα/Dα level increases withSOL, ∼ 30% in far SOL
I Skewness ∼ 1→ blobs (?)
I Moment profiles robust withplasma parameters
0
0.1
0.2
0.3
0.4
δDα/
Dα
−1
−0.5
0
0.5
1
1.5
Ske
wne
ss0 0.005 0.01 0.015 0.02 0.025 0.03
−1
0
1
2
3
Kur
tosi
sr−r
0[m]
B=2.7T low nB=2.7T high nB=3.8T low nB=3.8T high n
GPI
Quantitative comparison using shaded area (GPI sensors)
F.D. Halpern 33 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
GBS agrees with [Zweben PoP 2009] within error bars
I Compare GBS radial/poloidalaverage against GPI data
I Shot-to-shot variation indicatedwith error bars
I GBS gives good match forδDα/Dα and higher moments
I Previous gyrofluid simulationsgave δDα/Dα ≈ 5–10%
0
0.2
0.4
0.6
0.8
δ D
α/D
α
0
0.5
1
1.5
2
Skew
ness
2 2.5 3 3.5 4 4.50
1
2
3
4
Kurt
osis
B [T]
GBS low n
GBS high n
GPI
F.D. Halpern 34 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Typical spatial, temporal turbulent scales give reasonableagreement
I Compute τauto , Lrad , Lpol using2 point correlations functions Cij
Cii (τauto) =1
2
L = 1.66δx√
− lnCij (t = 0)
I Good match for L ∼ 1.5cm,τauto underpredicted by ∼2
0
10
20
30
40
τauto
[µ
s]
0
0.5
1
1.5
2
Lra
d [cm
]
2 2.5 3 3.5 4 4.50
1
2
3
Lpol [
cm
]
B [T]
GBS low n
GBS high n
GPI low n
GPI high n
F.D. Halpern 35 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Propagation velocities
I Obtain vrad , vpol from time lag that maximizes correlationbetween two neighboring points separated by δx → v = δx/τ
I Good agreement in vrad → poloidal mode structureI Large mismatch in vpol → resolution smoothing in GBS data?
2 2.5 3 3.5 4 4.50
0.5
1
1.5
2
2.5
3
vp
ol [
km
/s]
B [T]2 2.5 3 3.5 4 4.5
0
0.5
1
1.5
2
vra
d [km
/s]
B [T]
GBS low n
GBS high n
GPI
F.D. Halpern 36 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Spectral power vs wavenumber of δDα/Dα
I From FFT of δDα/Dα in θ, then average over r , t
I Significant drop at kpol = 125m−1 high k due to smoothing
I Unsmoothed δDα/Dα has same power law scaling as GPI
101
102
103
10−4
10−3
10−2
10−1
100
kpol
[m−1
]
flu
c.
po
we
r (r
el)
GPI
GBSGBS(no sm.)
B=2.7T, low n
Renormalized
101
102
103
10−4
10−3
10−2
10−1
100
kpol
[m−1
]
flu
c.
po
we
r (r
el)
GPI
GBSGBS(no sm.)
B=3.8T, high n
Renormalized
F.D. Halpern 37 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Alcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Spectral power vs frequency of δDα/Dα
I From FFT of δDα/Dα in t, then average over t, r = 2±0.2cmI GPI measurements and GBS show same asymptotic behavior
100
101
102
103
10−6
10−4
10−2
100
f [kHz]
fluc. pow
er
(rel)
GPI +k
GPI −k
GBS +k
GBS −k
B=2.7TB=2.7T, low n
Renormalized
100
101
102
103
10−6
10−4
10−2
100
f [kHz]
fluc. pow
er
(rel)
GPI +k
GPI −k
GBS +k
GBS −k
B=3.8T, high n
Renormalized
F.D. Halpern 38 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Summary and outlook
I Towards first principles understanding of SOL width:
X Non-linearly saturated drift/ballooning turbulence
X SOL width scales with ρ?, q, collisionality
X Simple analytical scaling agrees with experimental data
I Detailed comparison between GBS and C-Mod discharges
X Lp, δDα/Dα pdf moments, Lrad , Lpol , vrad , P(ω), P(kpol )× τauto , vpol → under/overpredicted by factor ∼ 2
I Next: 2 Lp’s profile structure using 2014 C-Mod discharges
I More advanced simulation model → Ti , shapingI Mirror langmuir probe → high res. profiles, (n, φ) phase
F.D. Halpern 39 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Thank you for your attention!
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Properties of the SOL
I Lfluc ∼ 〈L〉tI nfluc ∼ 〈n〉tI Collisional magnetized plasma
I Low frequency modes ω � ωciI Open field lines
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Sheath BCs from kinetic approach [Loizu, PoP (2012)]I COLLISIONAL PRESHEATH (CP)
I Quasi-neutral, IDA holds
I Potential drop ∼ 0.5Te over ∼ LI Ions accelerated to vs = cs sinα
I MAGNETIC PRESHEATH (MP)
I Quasi-neutral, IDA breaks
I Potential drop ∼ 0.5Te over ∼ ρsI Ions accelerated to vs = cs
I DEBYE SHEATH (DS)
I Non-neutral, IDA breaks
I Potential drop ∼ 3Te over ∼ 10λDI Ions accelerated to vs > cs
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Extra slides: Summary of the BC
v||i = cs
(1 + θn −
1
2θTe −
2φ
Teθφ
)v||e = cs
(exp (Λ− ηm)−
2φ
Teθφ + 2(θn + θTe )
)∂φ
∂s= −cs
(1 + θn +
1
2θTe
)∂v||i∂s
∂n
∂s= − n
cs
(1 + θn +
1
2θTe
)∂v||i∂s
∂Te∂s' 0
ω = − cos2 α[
(1 + θTe )
(∂v||i∂s
)2+ cs (1 + θn + θTe/2)
∂2v||i∂s2
]
where θA =ρs
2 tanα∂x A
A, and ηm = e(φmpe − φwall )/Te . [Loizu et al PoP 2012]
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
-
IntroductionGlobal model for SOL turbulence
Simulation/Experiment ComparisonConclusions
Resistive ballooning modes destabilized by EM effects
I Starting from reduced MHD, obtain simple dispersion relation
γ2(ν +
βe02
γ
k2⊥
)= 2
R
Lp
(ν +
βe02
γ
k2⊥
)−
k2‖
k2⊥γ
I Neglecting ideal ballooning mode, the resistive branch gives
(γ2 − γ2b
)k2⊥ = −γ
(1− αq2ν
)and we identify γ ∼ γb =
√2R/Lp and kb ∼
√(1− α)/(νγb)/q
F.D. Halpern 40 / 40 Plasma turbulence in the tokamak scrape-off layer
IntroductionGlobal model for SOL turbulenceTurbulence levelsDominant instabilitiesScrape-off layer width scaling
Simulation/Experiment ComparisonAlcator C-Mod tokamakGPI diagnosticSimulation/experiment comparison
Conclusions