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 power@2.45GHz 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