TORPEX: experiments and theory Ivo Furno Past and present: A. Burckel, A. Diallo (PPPL), L....

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


4

Simple magnetized torus: a paradigm for tokamak SOL

Parallel losses

B, curvature

Source (EC and UH resonance)

Plasma gradients Btor

Bz


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


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


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 ?


• Plasma flow/rotation ?



8



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


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


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


r

zz’r’

r

3D Global simulation, N=16

12

λz = Nlargest available scale) , k= ktoroidal = 0, k|| ≠ 0

r

z’z

r’

r


Turbulence phase space

N

Lp

R

Ideal Interchange

Resistive Interchange

Drift

k|| =0, λv =Lv/N

kφ =0, λv =LvInterchange drive notimportant


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


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)



From now on we will concentrate on ideal interchange modes (kII≈0)

What kind of modes are responsible for the turbulence ?








16



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



• 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)





How do blobs propagate?






19



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


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)


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)


23

Comparison with existing 2D scaling laws

Experimental data in normalized units Damping due toion-polarization currents

Damping due toparallel currents

He

H2Ar

Ne


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


25

Agreement with generalized 2D blob model


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











27



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


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



• 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)











31



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


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)~

~



• 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











35



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)


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




• 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











39



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


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)


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)


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)





• 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



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/


http://crpp.epfl.ch/torpex/



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


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Preliminary resultsAverage blob dynamics in H2 shows no significant difference for different

Problem with geometry (e.g. current closure on several plates)?


49

E.M. effects


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

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TORPEX: experiments and theory Ivo Furno Past and present: A. Burckel, A. Diallo (PPPL), L....

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