Experimental studies of particle transport in the TORPEX toroidal plasma
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Transcript of Experimental studies of particle transport in the TORPEX toroidal plasma
Experimental studies of particle transport in the TORPEX toroidal plasma
TORPEX is a toroidal device where plasmas produced by microwaves are embedded in a helical magnetic field. It is mainly dedicated to basic plasma physics studies on instabilities and transport. In this type of devices, the plasma is primarily lost along the open field lines. Nevertheless, particle fluxes across the magnetic field are clearly measurable using different, complementary techniques. The local particle flux can be estimated over most of the cross-section from the plasma response to a modulation of the injected microwave power, and quantified on the basis of a diffusive-convective model. The fraction of the total particle flux caused by plasma instabilities, identified as drift-interchange modes, is also measured and related to the observed spectral features. The results are compared with the transport associated with macroscopic fluctuation structures, reconstructed from a 2D imaging of the spatio-temporal behavior of the density fluctuations.
B
The TORPEX Experiment Minimum ingredients for turbulence drive relevant to magnetic fusion
• Toroidal geometry: pressure gradients and magnetic field curvature
Plasma production by EC waves Diagnostic access, flexible control parameters
Major, minor radius 1 m, 0.2m
Magnetic field BT 0.1T,Bz 0.01T
Pulse duration up to CW, Prf<5kW
Neutral gas pressure 10-4-10-5 mbar
Injected [email protected] PRF < 50 kW
Plasma density n ~ 1016-1017 m-3
Electron, ion temperature Te~5 eV, Ti <<1 eV
Gas H, Ar, He, Ne, ..
Ion sound Larmor radius s/a ~ 0.02
TORPEX: a simple magnetized toroidal plasma
(A. Fasoli et al., PoP 2006)
TORPEX EC system
Transmission line:
Magnetron head
Power supply and control
Power up to 50kW (100ms), 5kW - CW Modulation frequency <120kHz (sinusoidal) Arbitrary waveform (sine, square, linear ramp, ...)
TORPEX diagnostics
Movable LP array
4x Movable sectors
Local 2-D LPs“Flux” probe
3mm
Collector 1mm
5mm
Ceramic tubes
Grid (Copper)
Gridded energyanalyzer
LP fixed arrays HEXTIP
-20 0 20-20
-10
0
10
20
z
[cm
]
Density [1016 m-3]
1
1.5
2
-20 0 20-20
-10
0
10
20Electron temperature [eV]
2
3
4
-20 0 20-20
-10
0
10
20
r [cm]
z
[cm
]
Plasma potential [V] Vf l+3.15 T
e
4
6
8
10
-20 0 20-20
-10
0
10
20
r [cm]
Particle source [a.u.]
2
4
6
Time-averaged profiles
Steep gradients in n, Te, Vpl
Non-local particle
source
vExB
(M. Podesta’ et al., PPCF 2006)
vde
Btor
-20 -15 -10 -5 0 5 10 15 20-20
-15
-10
-5
0
5
10
15
20
R-R0 [cm]
z [c
m]
0
0.5
1
1.5
2
2.5
3
3.5
4
background profile power pulse ON Measure density response to w power
modulation Reconstruct source profile, help from simple
MonteCarlo code Dependence on experimental parameters: pgas,
Bz, Prf, ...
Applications:
• Local particle balance/transport studies
• Implement in numerical codes for
turbulence simulation
(M. Podesta’ et al., PPCF 2006)
Reconstruction of the particle source
Electron distribution function
0 10 20 30 40 50 60 70 80 90 10010
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
UH layer
EC layer
eE
DF [
a.u
.]
E [eV]
TIV 3.3eV
Ttherm
2.5eV
Tfast
10.9eV,mawellian
nsup
/nth 5.6%
EC driven plasma: presence of suprathermal electrons
• Resulting eEDF?
• Impact on instabilities?
• Effects on measurements ?
(M. Podesta’ et al., submitted to PPCF)
Ø3mm
Gridded energy analyzer
Energetic electrons only from
UH layer No impact on (fluid)
instabilities Confirm measurements from
standard Langmuir Probes
maxwellian
-10 -5 0 5 100
1
2
3
4
5
Te [
eV
], n
[a.u
.]
-10 -5 0 5 100
0.2
0.4
0.6
0.8
Te/<
T e>
, n
/<n
>
r [cm]
(Te)
Te
n
Large level of density
fluctuations Coherent modes
detected, f < 15kHz
Drive ? Nature of instabilities ? Related transport ?
Fluctuation levelsFluctuation levels
Radial scan at midplane, triple probe + Isat
~~
LFSHFS
Characterization of instabilities Tools:
• Spectral methods, linear and non-linear: Frequency, wave number, energy cascade, …
• Real-space analysis: Visualization of macroscopic ‘structures’
• Statistical methods
Take advantage of machine flexibility:
measurements over whole cross-section,
including source/loss regions
n
Vfloat,1
Vfloat,2
6mm
Additional checks:
• Role of suprathermal electrons none
• Te fluctuations relevant for cross-phase measurements
Characterization of instabilities
0 5 10 15-1.5
-1
-0.5
0
0.5
1
1.5
f (kHz)
k // (m
-1)
1
2
3
4
5
6
7
8
9x 10
-3
0 5 10 15-50
0
50
100
150
200
f (kHz)
k z (m
-1)
1
2
3
4
5
x 10-3
Measured statistical dispersion relation Local conditional spectrum S(k,f):
Perpendicular phase velocities compatible with vExB + vde vExB at
LFS
k|| / k <<1, with k|| finite
M
j
jjK fSfkkI
MfkS
1
)()(],0[ )()(
1),(
I[0,K ](x)1 K /2 x K /2
0 otherwise
vde=Ten/(neB)
S(kz,f)
Mid-plane
S(k||,f) toroidal ~parallel
Measured statistical dispersion relation
f (kHz)
Mid-plane
f (kHz) F.M. Poli et al., PoP 2006
T( l ,m ) lm
l m
Far from the region of generation:• Non-local interactions between f0, 2f0 and f>f0
• Transfer of energy from coherent mode to
smaller scales (through -k mapping)
x
Non-linear spectral analysisbispectrum
Real-space analysis: ‘structures’
“Structures”: regions where signal
exceeds a threshold value
• |n| > tot(n)
Follow structures dynamics within
same discharge:
• Trajectory, speed, carried
density, birth/death region, ...
Approach
• Define structure observables
• Characterize all structures no averaging at this stage
• Statistical analysis
Structures closed by zerofluctuations assumed at the wall
Measurementpoints
(S.H. Müller et al., Letter to PoP 2006)
Example: structures trajectories Bin trajectory occurrences in
spatial grid (60x60)
Data
• 0.59 s discharge or
147501 time frames
• Select structures lasting
longer than 50 frames =
200s
Arrows: average velocity field
Contours: time-average
‘trajectory density’
Transport
Focus on particle flux Flux derived from:
• Fluctuations: n, vExB
• Macroscopic structures studies
• Modulation experiments
Goals:
• Identify basic mechanisms: diffusion? convection? turbulence?
• Link ‘macroscopic’ to ’microscopic’ flux
• Establish an ordering: Global Vs Local? Radial Vs Parallel? Time-scales?
~ ~
Transport - basic mechanisms?
2.5 2.6 2.70
0.5
1
1.5
2
2.5
t [ms]
I sat
[a.u
.]
Isat,i
ni
11.4 11.45 11.5 11.55
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
t [ms]
tip1tip2tip3tip4
Isat,e
ne
Clear drifts of ions/electrons in
opposite directions dominant role of ‘fluid’ drifts
vdrift,e >> vdrift,I
Open field lines: dominant parallel
losses
vExBvde vdi
Down-up
Up-down
tip#8......
tip#1
-10 -5 0 5 10
-10
-5
0
5
10
vExB
[rad/s]
-10 -5 0 5 10
-10
-5
0
5
10
r [cm]
z [c
m]
Amplitude [1016 m-3]
-10 -5 0 5 10
-10
-5
0
5
10
r [cm]
phase [rad/s]
0.5
1
1.5
2
400
600
800
1000
1200
1400
1600
1800
-10 -5 0 5 10
-10
-5
0
5
10
z [c
m]
Density [1016 m-3]
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1
2
3
4
5
EC modulation technique/1 Measure total transport
Unfold underlying
convection: low modulation
frequency
Measurements: clear role
of parallel dynamics
Analysis:
• Fourier analysis
• Combine response from
multiple frequencies
0 1 20.8
1
1.2
1.4
1.6
1.8
n [
101
6m
-3]
Measurements
1 1.2 1.4-0.2
0
0.2
0.4
0.6Laplace analysis
0 1 20
2
4
6
8
10
Te [
eV
]
1 1.2 1.4-0.5
0
0.5
1
0 1 20
5
10
15
20
25
Vpla
sma [
V]
t-t0 [ms]
1 1.2 1.4-0.5
0
0.5
1
t-t0 [ms]
1=320s
2=9.3s
1=64.3s
2=1.6s
1=52.3s
2=0.4s
EC modulation technique/2 Physical model: density continuity eq. +
convection:
Boxcar averaging: measure behavior of n, Te, Vpl simultaneously
Te increase (mainly) caused by
suprathermals v1 from perturbed ExB
n1 from enhanced ionization
Response to square EC power modulation
Preliminary results
-2 0 2 4 6
-10
-5
0
5
10
r [cm]
y [c
m]
0.5
1
1.5
2x 10
16
3 modulation frequencies: 120, 360, 720Hz << ffluct, p-1
Reconstruct 2-D, total convective
flux
• Flow radially inward from
source region
Caveat:
• Analysis does not converge in
the whole cross-section
• Need lower mod. frequencies
+ longer pulses
• Need 3-D model ?
-0.2 -0.1 0 0.1 0.2 0.3-4
-3
-2
-1
0
1
2
3
4
5
6
t-t0 [ms]
n,
Vpl
[a.u
.]
Vpl,1
n1
r=3cm, z=0
Radial flux at mid-plane Account for finite Te
Flux dominated by coherent modes Measured flux compatible with
profiles and global particle balance Linear dependence on fluctuation
amplitudes
radial,f (1015 m-2)
UH layer
~
Fluctuation induced particle flux
Under way: comparison with other
real-space analysis techniques, e.g.
conditional average sampling
Structure-induced transport “Transport events” across ad-hoc
surfaces
• Color code: average structure-
induced transport across
surface (+: outward/cntclockw.)
• Vectors: average structure
induced particle flux
• Contours: time-series skewness
Asymmetry between +/- structures
necessary for net transport Time delay: repetitive pattern,
corresponds to strong spectral
activityTime delay
‘Ohmic’ experiments Goal:
• Progressively increase fraction of closed flux surfaces
• Study transition open to closed field lines
First experiments under way• Induce 3–10 V during 50 ms• Use power supply of cusp field
system to operate Ohmic coils• Start and sustain the plasma with
EC waves Expected:
• Ip 3 kA• Te 60 eV• n 1018 m-3
Obtained so far• Ip 1000 A• Te 10 eV• n 5 1017 m-3
Magnetic diagnostics
Movable 3D Mirnov coils
Fixed Rogowski coil
Movable Rogowski coil
Scan over 40 shots
Total ne increases by ~30 times during Ohmic phase (up to 2x1018m-3)
Stationary phase of ~1.2ms achieved so far
‘Ohmic’ experiments - results/1z
[cm
]z
[cm
]
‘Ohmic’ experiments - results/2
Magnetic probe positions
csd coherence
Magnetic probe signals show two dominant frequencies (f0, f1)
during the Ohmic pulse
No magnetic oscillations observed before the Ohmic
Signals have high coherence at f0, f1 with a reference Isat signal
electromagnetic character of the mode
ref. Electrostatic probepsd
Ma
gn
eticE
lectrostatic
f0
f1
Summary Basic experiments can contribute to investigation of instabilities and transport
• Well diagnosed scenarios
• Flexibility of experimental conditions (gas type, profiles, magnetic field
configuration, ...)
Instabilities in TORPEX:
• Drift-interchange modes, k|| / k <<1 (k|| finite)
Transport dominated by drifts (parallel) and coherent modes (across B) Complementary analysis in real-space and Fourier-space:
• Spatio-temporal patterns, time statistics, …
• Wave-number and frequency spectra, non-linear interactions, ...
Relevance of TORPEX for Fusion
• Structure formation and propagation mechanisms
• Structure Vs. Micro-turbulence induced transport
• Development of quantitative analysis methods for 2D imaging data