TORPEX: experiments and theory
Ivo Furno
Past and present: A. Burckel, A. Diallo (PPPL), L. Federspiel (TCV), A. Fasoli, E. Küng, D.Iraji, B.Labit (TCV), S.H.Müller (UCSD),
G. Plyushchev, M. Podestà (PPPL), F.M. Poli (Warwick),
P. Ricci, B.Rogers (Dartmouth), C. Theiler
Centre de Recherches en Physique des Plasmas (CRPP)
École Polytechnique Fédérale de Lausanne, Switzerland (EPFL)
The TORPEX device
A. Fasoli, et al., Phys. Plasmas 13, 055902 (2006)
Major radius 1 m
Minor radius 0.2 m
Magnetic field B 0.1 T
Pulse duration 1 s
Neutral gas pressure 10-4-10-5 mbar
Injected power @ 2.45GHz PRF < 20 kW
Plasma density n ~ 1016-1017 m-3
Electron temperature
Ion temperature
Te ~ 5-15 eV
Ti ≤ 1 eV
Gas
Ion sound Larmor radius
H, D, Ar, He, Ne
s/a ~ 0.02
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 20102
Flexible magnetic configuration• 28 water cooled toroidal coils |B|<0.1 T
• 4 poloidal field coils: |Bz|<5 mT
Tokamak-like (Vloop~3-10V, 50ms, Ip<5kA)
Cusp field + strong OH (Vloop~120V, 3ms) for magnetic reconnection studies
EC resonant surface @ 2.45 GHz
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 20103
4
Simple magnetized torus: a paradigm for tokamak SOL
Parallel losses
B, curvature
Source (EC and UH resonance)
Plasma gradients Btor
Bz
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Movable LP array
4x Movable sectors
Local 2-D LPs“Flux” probe
3mm
Collector 1mm
5mm
Ceramic tubes
Grid (Copper)
5mm
Ceramic tubes
Grid (Copper)
Gridded energyanalyzer
LP fixed arrays HEXTIP
Fast camera
Real-space analysis:
|n| > tot(n) Define structure
observables:
trajectory, speed, size,…
Spectral methods:
linear and non-linear:
frequency, wave number, energy cascade, …
Statistical methods:
PDFs, moments,…
Conditional sampling methods
TORPEX diagnostics
Movable LP array
4x Movable sectors
Local 2-D LPs“Flux” probe
3mm
Collector 1mm
5mm
Ceramic tubes
Grid (Copper)
5mm
Ceramic tubes
Grid (Copper)
Gridded energyanalyzer
LP fixed arrays HEXTIP
Fast camera
Real-space analysis:
|n| > tot(n) Define structure
observables:
trajectory, speed, size,…
Spectral methods:
linear and non-linear:
frequency, wave number, energy cascade, …
Statistical methods:
PDFs, moments,…
Conditional sampling methods
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Fast ion source
GEA
5
66
A turbulent plasma
• H2 plasma
• Pf = 400 W
• Btor=76mT on axis; Bz=2.1mT
• pgas= 6.0 x 10-5 mbar
Source-free regionMain plasma region
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Questions addressed on TORPEX
What kind of modes are responsible for turbulence and intermittency?
How are macroscopic structures (blobs) generated?
How do blobs propagate? Can their dynamics be influenced/controlled?
Do the observed fluctuations and structures have a universal character?
What are the consequences, in terms of
• Plasma flow/rotation?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
7 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for turbulence and intermittency?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
8
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Nature of instabilities: exp. dispersion relation
9
N 1/Bz
kzN2
kII ~ 0kII ≠ 0
N = number of field line turns = vertical distance between field line return points
ex. N = 2
Statistical analysis of 2-points correlations
0 10 20 30
f [kHz]
k II [
m-1]
-50
0
10
0
Ex. of kII spectrum
kz
kII
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Fluid model
ρi << L, << 1ω << Ωci
Braginskii model
Electrostatic Drift-reduced Bragiskii
equations
CollisionalPlasma
n
t ,n Dn
2n 2
RnTe
z Te
n
z n
z
|| (nV||e ) S
Parallel dynamicsMagnetic curvature SourceDiffusionConvection
+ similar equations for Te, Ω (vorticity = )
+ parallel momentum balance for V||e, V||I
source profile from measurements
2
10 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
3D Global simulation, N=2
r
zz’r’
r
11
λz = , k= ktoroidal ≠ 0, k|| = 0 (except sheath effects)
II
II
r
z’z
r’
r
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
r
zz’r’
r
3D Global simulation, N=16
12
λz = Nlargest available scale) , k= ktoroidal = 0, k|| ≠ 0
r
z’z
r’
r
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Turbulence phase space
N
Lp
R
Ideal Interchange
Resistive Interchange
Drift
k|| =0, λv =Lv/N
kφ =0, λv =LvInterchange drive notimportant
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 201013
P. Ricci and B.N. Rogers, accepted in PRL
Interpretation of measured dispersion relation
f
14
N 1/Bz
Ideal interchange Resistive interchange
z N
kzN2
k// ~ 0 k// ≠ 0
l z = D
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence?
• Ideal interchange, resistive interchange or drift waves, depending on
pressure gradient and vertical magnetic field
15
F. M. Poli, et al., PoP (2006); PoP (2007); PoP (2008); PhD Thesis
A. Diallo et al., PoP (2007)
L. Federspiel et al., PoP (2009); Master Thesis
P. Ricci et al., PoP (2009); Phys. Rev. Lett. (2008)
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
From now on we will concentrate on ideal interchange modes (kII≈0)
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
16
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
17
Dynamics of blob ejection
Time resolved 2D profiles of ne, Te, Vpl from
conditional sampling Ideal interchange mode
moves upwards with vExB
A radially elongated
structure forms from a
positive cell The ExB flow shear shears
the structure The structure breaks into
two parts in ~100 μs ⇒
formation of the blob
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
How are macroscopic structures (blobs) generated ?
• Strong ExB shear flow breaking interchange wave crest
• Energy is transferred from shear flow to blobs
18
S. H. Müller, et al., PoP (2007); PhD Thesis
I. Furno et al., Phys. Rev. Lett. (2008) ; PoP (2008)
C. Theiler et al., PoP (2008)
A. Diallo et al., Phys. Rev. Lett. (2008)
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
19
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
limiter
Study of filaments/blobs in simple geometry
20
Steel limiter on low-field side, defining region with
• Constant curvature along field lines
• Nearly constant connection length (~2R)
• Near-perpendicular incidence of
magnetic field lines
• No magnetic shear
r
z
Probe tips
Region where limiter intercepts both ends of field lines
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Vertical cut
21
Analysis of filament/blob motion
Blobs identified by pattern recognition
Automated evaluation of
• Radial velocity v
• Vertical size a
• Density n, n
r [m]
r [m]
z [m
]
S. H. Müller et al., POP (2006)
C. Theiler et al., PRL 103, 065001 (2009)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
22
Joint probability of blob velocity – size
Range of blob sizes below diagnostic resolution
• Similar sizes in all gases
• Similar values of n/n
• Mean velocity of blobs over
their entire trajectory
• Significant differences in the
typical velocity, ranging from
500 m/s (Ar) to 2000 m/s (He)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
23
Comparison with existing 2D scaling laws
Experimental data in normalized units Damping due toion-polarization currents
Damping due toparallel currents
He
H2Ar
Ne
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
velocity 2Ls
2
R3
1/ 5
cs
size 4L2
sR
1/ 5
s
Normalization:
L: connection lengthR: major radius
24
Generalization of 2D blob models and scaling laws
Vorticity equation
C. Theiler et al., Phys. Rev. Lett. 103, 065001 (2009)
||J
polJ
I
niJ
Fig. from Krasheninnikov et al.
n
n
aa
avblob
~~~21
~2~2/5
sign(Bz)2cs
2mi
RB
n
z
nmi
B2
D
Dt2 ne2cs
TeL˜ nmi
B2 in
2
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
25
Agreement with generalized 2D blob model
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Damping due toion-polarization currents
Damping due toparallel currents
How do blobs propagate?
• Agreement between data and a generalized 2D model for blob velocity Parallel currents to the limiter, cross-field ion polarization currents, and ion-
neutral collisions
26
C. Theiler et al., Phys. Rev. Lett. 2009; PhD Thesis
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
27
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
28
~10000 signals of Isat
H2, He, ArPressure scanBz scan
1% < ñ / n < 95%
In TORPEX
~30% of signals with S<0
In tokamaks SOL: S>0 S<0 when LCFS is crossed
Relation between moments of PDF
kurtosis
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
29
Universal statistical properties of fluctuations Unique relation Kurtosis vs. Skewness
Measured S vs. K curve and PDF are
described by the Beta distribution
~ 800 signals from TCV edge / SOL plasmas (L-mode)
give similar results: statistics associated with interchange OE Garcia et al., PPCF (2006)
holes
TCV: courtesy of J. Horacek
K = 1.5 S2 + 2.8
Sandberg, PRL 103, 165001 (2009) Process described by quadratic polynomial of Gaussians processes
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Do the observed fluctuations and structures have a universal character ?
• Unique S vs. K relationship, Beta PDFCommon to a variety of phenomena with convection
E.g. surface T fluctuations in ocean waves, x-ray fluctuations in accretion disks
• Similar scaling and PDF found in TCV edge data
30
B. Labit et al., Phys. Rev. Lett. (2007); PPCF (2007)
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
31
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
ne (m-3)
Bz > 0
Bz < 0blob detected
[s]
[s]
v(km/s)
Bz > 0
Bz < 0
32
Effect of blobs on plasma flow / rotationRef. probe
= 90°
v1
0
-1 (s)
[km/s
-200 0 200
Bz > 0
6
0
-6
z (c
m)
Measured with Mach probe along vertical chord in blob region When blob passes by probe, sudden change in toroidal rotation (not simply due to Te effect on Mach number through cS) is detected
2D profile shows positive and negative fluctuations of v
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Same trend for opposite Bz signs, though time averaged profiles are very different
Symmetry in fluctuations of v (skewness ~0)
33
Scaling of blob induced flow with blob amplitude
Bz > 0
Bz < 0
v,max (km/s)
v,min (km/s)~
~
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What are the consequences, in terms of
• Plasma flow/rotation ? Toroidal velocity blobs or holes are associated with density blobs The variations of toroidal rotation increase (nonlinearly?) with blob amplitude
34
B. Labit et al., RSI (2008); paper in preparation
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
35
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
36
Mode region: Fluctuation-induced particle flux
Time domain, 2D flux pattern from CAS consistent with Fourier analysis Heat is convected by particle flux (T, are in phase)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
37
Blob region: structure related particle flux
Instantaneous
structure related fluxFraction of
positive
structures
Time domain, 2D flux pattern from CAS inconsistent with Fourier analysis,
but consistent with structure analysis
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ? Two different mechanisms
Fluctuation-induced flux (quasi-coherent e.s. instabilities)
Blob-related flux (dominant in source-free region, depending on instantaneous ExB pattern)
38
M.Podestà et al., Phys. Rev. Lett. (2007); PhD Thesis
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What kind of modes are responsible for the turbulence ?
How are macroscopic structures (blobs) generated ?
How do blobs propagate? Can their dynamics be influenced/controlled ?
Do the observed fluctuations and structures have a universal character ?
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ?
39
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Fast ion source and detector
Collaboration CRPP - UCI
Miniaturized Li6+ ion emitter
Thermo-ionic effect (~1200o)
Ion energies: 100ev – 1keV
Alumino-silicate coatingTungsten body
1 c
m
40 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
First grid
Second gridCollector
6 m
m
BN casing
Ion emitter
Acc. grid
Screaning grid
4 cm2 cm
Heating wires (30W)
41
Efast= 300eV
Experimental fast ion current density profiles
Without plasma With plasma
r=1.5cmz=2.0cm
r=1.8cmz=3.2cm
Fast ion current density profiles are broadened (both radially and vertically) by the plasma
r (cm)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
r (cm)
z (c
m)
42
Simulated fast ion motion in turbulent E-field
Source with realistic spread in energies (10%) and in angular distribution (0.2rad)
Motion of tracer particles in turbulence
calculated by 2D fluid simulations
Periodic boundary conditions
k||=02D simulation
z(mm)
r (mm)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
43
Simulated fast ion current density profiles
With
out p
lasm
a W
ith p
lasm
a 300eV, blob region 300eV, mode region
Simulation qualitatively explains the shape of the experimental profiles• Elongated profiles can be explained by spread in velocity distribution
• Radial broadening, due to fluctuations and blobs, is consistent with experiments
z(cm)
z(cm)
z(cm)
z(cm)
r (cm)r (cm)
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
What are the consequences, in terms of
• Plasma flow/rotation ?
• Transport for thermal plasma ?
• Transport for non-thermal plasma particles (fast ions) ? First experiments reveal effects of plasma turbulence on fast ion profilesRadial spreading due to fluctuations and blobs in simulation and experiment
44
G. Plyushchev, RSI (2007); PhD Thesis; A.Burckel, Master
Thesis
Questions addressed on TORPEX
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Summary
The results obtained on the TORPEX simple toroidal plasma device enable a
quantitative model validation for building blocks the problem of intermittent
transport in edge plasma
• Nature of the underlying instabilities
• Turbulence local statistical properties
• Turbulence spatio-temporal structures (blobs)
• Transport of thermal and suprathermal particles, heat and momentum
More results and details at http://crpp.epfl.ch/torpex/
45 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Outlook Studies on blob physics
• Control of blob dynamics with various limiter configurations
• E.m. effects
Full code validation project
Change in magnetic topology, in particular for fast ion physics studies
• Ohmic discharges
Fast ions
• Development of a large source - collaboration with group in Stuttgart
• Energy resolved measurements
• Full 3D particle motion solver
Extensive use of non-perturbative optical diagnostics
• Laser Induced Fluorescence for ion velocity resolution
• Imaging with fast framing camera + intensifier, with and without GPI46 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
47
Idea: control of blob velocity via wall tilt
Design
• By pivoting the limiter around a
vertical axis, we can achieve ||~10o
Limiter à configuration
variableSchematic top view
Parallel electron current should depend on angle
between B-field lines and wall R. H. Cohen and D. D. Ryutov, PoP 1995; CPP 2006
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
48
Preliminary resultsAverage blob dynamics in H2 shows no significant difference for different
Problem with geometry (e.g. current closure on several plates)?
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
49
E.M. effects
I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 2010
Multi Bdot array
First current meas. inside a blob
50/50 I. Furno, Mini-Workshop Laboratory Plasma Research - Berlin, 12th March 20102.03.2010
First Ohmic experiments on TORPEXOhmic phase:
• Ip 1kA• Ip duration ~ 2ms• Vloop ~ 8V
Vloop duration ~ 4ms• Stable profiles for ~ 1.2ms• Plasma current is reproducible
within 20% from shot-to-shot
Ohmic transformerClosed field lines
50
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