TORPEX is a device for studying turbulence and transport, in which toroidal plasmas (n~1017m-3, Te~10eV) are produced by microwaves at f=2.45GHz in the electron cyclotron (EC) range. The mechanisms for the EC wave absorption and sustainment of plasmas with differentprofiles are investigated as a function of the B-field configuration, gas pressure and injected power. In addition to the broad ionization from bulk electrons, a localized source is provided by electrons accelerated at the upper hybrid resonant layer, where most of the microwave power is absorbed. Different plasma profiles correspond to different fluctuation characteristics, measured by Langmuir probes. Argon plasmas are usually characterized by coherent peaks with f~10kHz and by large-scale structures that move in the ExB direction, while Hydrogen plasmas appear more turbulent and show no evidence of coherent structures. Experiments on the link between the plasma production scenarios, determining the plasma profiles, and the characteristics of the fluctuations are discussed.

Abstract

TORPEX – Machine, parameters

GOALS: Isolate basic plasma physics phenomena in ‘simple’, flexible magnetic configurations:

- Study of turbulent phenomena/instabilities in currentless toroidal plasmas- Study of plasma production and heating by means of radiofrequency waves

in the Electron Cyclotron range of frequencies

Diagnostics

HFSLFS

low

hor

upp

‘High frequency’Langmuir probes

Fixed Langmuir probes

Gridded Energy AnalyserSpectrometer, Camera,Photodiodes (Optics)

Power measurements

Movable Langmuir probe4x movable sectors:Install/remove easily sectors dedicated to particular experiments, e.g. :

Hextip (2D probe)

Local 2-D LP

Hextip

Diagnostics, outlook

4-tips Langmuir probe for the measurements of fluxes and correlation between density and potential fluctuations

Set of 3 photodiodes installed at different toroidal/poloidal locations

âCharacterize fluctuations by means of non-intrusive optical diagnostics

Quantitative link between optical signals and plasma parameters?

B

∇B

vv∇∇B,eB,e

vv∇∇B,iB,i

EE∇B-drifts lead to charge separation

F = F = --eEeE||||

Particles accelerated along the field lines â‘short circuiting’ of electric field

Friction (electron-ion collisions) inhibits parallel motion âelectric field

Basic confinement mechanism: Btor + Bvert

θ B

Sheath parallel lossE ExB loss

Two basic loss channels:

Confinement time: Theory Vs measurement

S. H. Müller et al., Phys. Rev. Lett. 93, 16 (2004)

• Dependence of τ on Bvert seems to be correctly predicted by basic (simplistic) model• Theoretical values of τ are generally too high by about a factor of 3

Typical plasm

a profilesH

ydrogenA

rgon

LFS

HF

S

-Magnetron source

-Up to 50kW of pulsed microwave (MW) power at 2.45GHz during 100ms

-Can be modulated at frequencies fmod

Plasma production by EC waves

- Resonant wave-particle interaction at frf=fec- ‘Primary’ electrons accelerated at energies E>W i- Primaries ionize neutral gas by electron-impact ionization â thermal plasma- Wave absorption at EC and UH resonances- Small ionization from thermal population

fuh=(fec2+fp2)1/2 â fuh(n)

(M.Podestà et al., ‘Plasma production by low-field side injection of Electron Cyclotron waves in a simple magnetized torus’, submitted to Physics of Plasmas)

Geometry of the UH resonant layer changes dynamically with absorbed power:

• Interaction between waves and particles depends on density profile• Expansion of UH layer limited by the walls

R0

ruh

h

RRec

A

A’

∆r

Btor

BBv

δres

cut A-A’

1

r

n

a

∆r1 ∆r2 ∆r3

r1 r2 r3

2

3

walls

Absorbed power increases â n increases â fuh shifts toward the walls:

Absorption at UH resonance

Density and resonance frequencies in Hydrogen on the equatorial plane h=0mm as a function of the absorbed microwave power Pabs.

Note the dependence of density gradient length Ln on the absorbed power:

Pabs can be used to ‘control’ Ln

LFS

overdense plasma

Understanding the ionization process: simple Monte-Carlo code

Propagation/Absorption mechanisms

- Recover the spatial dependence of the ionization profile: source term required in most of the codes

- Compare with experiments: quantitative information on particle source

Assumptions:

- Stationary background profiles (from experiments)

- Electron dynamics dominated by advection along field lines â 1-D along B

- Electrons gain energy at fec, fuh- Possible interactions: scattering on neutrals, ionization, Coulomb collisions

Inputs:

- Starting energy, starting location

- Background profiles and machine configuration (Btor, Bvert, pgas, …)

Outputs:

- Spatial ionization profile

- Ionization efficiency

- Characteristic time-scales

Comparison with experimental dataParticle source term S(r)

Numerical

codes

Studies of background

profiles

Exploitation of modulation techniques for transport

studies

Global particle balance/ ionization rate

where

Contribution of the thermal population:

{

Exp. Results: power modulation, role of UH and EC resonances

EC

UH

EC

UH

Argon: ionization at the EC resonance Hydrogen: ionization at the UH resonance

EC power modulated at 500Hz with square pulses, Duty cycle 20%, between Pabs=0.5kW and Pabs=1.8kW

Measured fractional density variation ∆n=(nhigh-nlow)/nlow

Positions of resonant layers extrapolated to the whole poloidal section â good agreement between theory and measurements â indirect ‘calibration’ of Langmuir probes!

HFS LFS LFSHFS

Exp. Results: global particle balance

EC

EC

UH

UH

UH+EC

UH+EC

Assumption: particle confinement time τp does not change substantially with powerâ expression for Riz can be used to fit the experimental data Ntot=Ntot(Pabs)=Riz·τp

• Max. energy of primaries E

Reconstruction of ionization profile

Modeling the particle source term:• Relative contributions Rec, Ruh from EC and UH resonances deduced from experiments with modulated microwave power• Simple model with input profiles from experiments to evaluate the spatial profile of the particle source r(R,h) at EC and UH layers• Analytical expression for

Fractional density variation for modulated microwave power (Pabs=0.4-1.8kW) in Hydrogen plasma.

Estimation of the spatial profile of the particle source in Hydrogen by means of a numerical code.

Reconstruction of the spatial profile, analytical formula with ∆h=1cm, ∆frf=±20MHz

Coupling between Density and Power

Density and power signals sometimes exhibit strong coupling leading to large-

amplitude oscillations

• Signature of ionization processes at fuh?

• Relation with other instabilities?

Density/power signals:

Power Spectral Density from the reflected power signal. Note the harmonics âsignature of non-linear coupling?

Instabilities, spectral analysis/1

LFS

A B

⊗B

e-

66 LPs in saturation current mode at the same toroidal position

U

H

L

r = (16.35±0.25) cmδx = 1.3mm (A-B), ∆x = 10mm (pairs)L = 12cm

Rxx (τ ) =ττ 0

α

cos(ω0τ )

Ex.: Linear analysis/auto-correlation functions:

Argon: Rxx (τ )∝ e−t

τ0

f (kHz)

P xx

(f)

f (kHz)

P xx

(f)

τ (ms) τ (ms)

Hydrogen:

ex. Measured values in Argon: kpar~0.01cm-1, kθ~0.5cm-1, kR~3cm-1vde~1.3km/s , vθ~1km/s∆φ(n, Vfl)=0

Instabilities, discussion/open questions

A linear dispersion relation can be evaluated in both cases- Directly from the phase shift- By means of statistical estimates

The observed instabilities could be identified as drift waves

Coherent modes and turbulent spectra are observed depending on the experimental conditions:

Other processes could explain the measurements (e.g. ‘global’ density oscillations due to coupling with RF power)

Doppler shift corrections?

Statistical dispersion relation

Dispersion relation (slab, kinetic) for the experimental values is compatible with unstable

drift mode:

Turbulence imaging: Conditional Average Sampling (CAS) technique

LFSMovable probe array scans the poloidal section on a shot-to-shot basis

Reference signal:• Signal from a fixed probe

(Isat, Vfloat)• Reflected power• Optical signals• …

Extract information on coherent correlations between signals at different time-scales, rejecting incoherent ‘noise’

Turbulence imaging: CAS, exp. Results/1

reconstruction of electron diamagnetic wave

Hydrogen plasma, Prf~500W

(τc: auto-correlation time of the reference signal)

Turbulence imaging: CAS, exp. Results/2

visualization of coherent structures

Argon plasma, Prf=4kW

Signal: Isat

Reference signal: Isat

Structures rotating in the ExB direction, confirmed by experiments with reversed Btor:

ExB

vstruct~300ms-1 (in Argon)

Under way: fluctuations study with optical diagnostics

Optical signals from PhotoMultiplier Tube (PMT) show well defined trends for different plasma parameters â good candidates for further investigations of turbulence/instabilities

Moments of the Probability Density Function of the raw signals from PMT

(scan of vertical magnetic field).

The PMT is looking along a line covering the entire poloidal section

‘Local’ measurements are also possible:Ex. Comparison between PMT signal and ion saturation current signal from a Langmuir probe (radial scan).

fiber to feedthrough

light collection region

focusing lens mirrorholder(teflon or macor) 1cm

Future work: modulation studies/1

Possibilities:- Time-of-flight measurements (on-off of the source), or- Evolution after a perturbation of the stationary state, measure time evolution of plasma parameters (density, temperature, ...)- System Response Analysis: compare spatial/temporal behavior of plasma parameters with a selected transport model- Fourier transform, time-domain modeling, …

Identify transport matrix coefficients?

Modulation/Perturbative techniques

Good control of the source term amplitude of the perturbation, frequency, duty cycle, ...

Response of density/temperature profiles can be decoupled ?

Can take into account off-diagonal terms in the transport matrix ?

Small perturbations linearized equations?

Good spatial/temporal resolution

Local measurements over the whole poloidal section

No absolute calibration(not required for modulation methods!)

Modulation of EC power in TORPEX: TORPEX diagnostics:

(Moret J.M. et équipe TORE SUPRA, Nucl. Fusion 32 (1992) 1241)

Future work: modulation studies/2

Steady-state Vs modulation techniques

q

ne∇Te

χpb

χinc

N.J.Lopes Cardoso, Plasma Phys. Control. Fusion 37 (1995) 799

- Steady-state techniques only allow to evaluate χpb from ‘stationary’ power balance:

χpb ≠ χinc when χ is nonlinear, or affected by an offset

Comparison between results obtained with the two techniques gives crucial information on transport coefficients and their dependence on

plasma parameters

example: qe= - χe ne ∇Te+ qoffset

χpb = - qe/(ne∇Te)

χinc = - δqe/(ne δ∇Te)

χpb ≠ χinc