Plasma Characterisation Using Combined Mach/Triple Probe Techniques

Plasma Characterisation Plasma Characterisation Using Combined Mach/Triple Using Combined Mach/Triple

Probe TechniquesProbe Techniques

W. M. Solomon, M. G. ShatsW. M. Solomon, M. G. Shats

Plasma Research LaboratoryPlasma Research Laboratory

Research School of Physical Sciences and EngineeringResearch School of Physical Sciences and Engineering

Australian National UniversityAustralian National University

Canberra ACT 0200Canberra ACT 0200

W. M. Solomon, M. G. Shats 2

What Is A Mach Probe?What Is A Mach Probe?

Two identical collectors separated by a Two identical collectors separated by a ceramic insulatorceramic insulator

The insulator makes the Mach probe The insulator makes the Mach probe sensitive to plasma drifts. Generally,sensitive to plasma drifts. Generally,

s

I

sI

sI

F low, V d

DownstreamUpstream

ssd IIV /


Evidence That Mach Probes Are Evidence That Mach Probes Are Sensitive to FluctuationsSensitive to Fluctuations

Probes often used Probes often used to study density to study density fluctuations, .fluctuations, .

ObserveObserve

If probe was If probe was primarily primarily sensitive to , sensitive to , then would not then would not expect this.expect this.

s

s

s

s

I

I

I

I~

RMS

~RMS

en~

en~


Far from the probe Far from the probe sheath, the ions have sheath, the ions have an average velocity an average velocity dependent on their dependent on their thermal velocity and thermal velocity and their drift.their drift.

Bohm Theory Revised: Mach Bohm Theory Revised: Mach Probe Saturation Currents And Probe Saturation Currents And Drift VelocityDrift Velocity Ions arrive at the probe sheath with the Ions arrive at the probe sheath with the

ion acoustic velocityion acoustic velocity

422

dti

tix

VVVu

iies mTTqc /

sI

sI

xu

xuc

s

sI

sI

I

Vd

cs

xu

xu

Sheath


Bohm Theory Revised: Mach Bohm Theory Revised: Mach Probe Saturation Currents And Probe Saturation Currents And Drift VelocityDrift Velocity

Using conservation of energyUsing conservation of energy

……and assuming a Boltzmann distribution and assuming a Boltzmann distribution for the densityfor the density

The saturation current takes the formThe saturation current takes the form We can then determine drift velocity by We can then determine drift velocity by

taking the ratio of the taking the ratio of the upstream/downstream currentsupstream/downstream currents

wherewhere

ssx qmcum 22

2

1

2

1

ess Tnn /exp

ss IIR /ti

ed mV

RqTV

4

)ln(

sss nqAcI


Enter the TMT ProbeEnter the TMT Probe

Since the plasma is Since the plasma is unmagnetised for ions, unmagnetised for ions, we may align the Mach we may align the Mach probe so that it is probe so that it is sensitive to radial sensitive to radial motions.motions.

Two triple probes Two triple probes surround the radial Mach surround the radial Mach probe – all are aligned to probe – all are aligned to the same flux surface by the same flux surface by electron gun.electron gun.


Likewise for Likewise for and (Row 4)and (Row 4)

TMT Solution Algorithm TMT Solution Algorithm DescribedDescribed Row 2 shows signals readily Row 2 shows signals readily

determined from the probes.determined from the probes.

Is (in) Is (out) +1 f1 +2 f2

T e1 p1 T e2 p2

M in im ised

| - |?i e~ ~G uessT i

V rin =ni e

E p

~T e V re

~

M ach Trip le 1 Trip le 2

YesN o

E q 6

M odifyT i

Solved

T =T +TV =V +Vn=n+n

i i i

r r r

~_

~_

~_

efpf

e TT

,2ln

xE ppp /~~

BEV pre /~~

TTee and and pp (Row 3) readily (Row 3) readily determined by the triple determined by the triple probeprobe


TMT Solution Algorithm TMT Solution Algorithm DescribedDescribed

Then, with some arbitrary Then, with some arbitrary initial choice of initial choice of TTi i , compute, compute

Is (in) Is (out) +1 f1 +2 f2

T e1 p1 T e2 p2

M in im ised


V rin =ni e

E p

~T e V re

~


YesN o

E q 6

M odifyT i

Solved

T =T +TV =V +Vn=n+n

i i i

r r r

~_

~_

~_

ti

eri mV

RqTV

4

)ln(

~

~~

~~

VnVn

VVnn

nV

Compute Compute nnee and then the and then the fluxflux


Practically, minimisePractically, minimise by modifying by modifying TTii

TMT Solution Algorithm TMT Solution Algorithm DescribedDescribed

Invoke the condition of Invoke the condition of ambipolarity of the ambipolarity of the fluctuation driven fluxesfluctuation driven fluxes Is (in) Is (out) +1 f1 +2 f2

T e1 p1 T e2 p2

M in im ised


V rin =ni e

E p

~T e V re

~


YesN o

E q 6

M odifyT i

Solved

T =T +TV =V +Vn=n+n

i i i

r r r

~_

~_

~_

ei ~~

ei ~~

Output of algorithm is Output of algorithm is then time-resolved then time-resolved measurements of measurements of TTi i , , nne e , , and and VVri ri , with fluctuations , with fluctuations properly accounted for.properly accounted for.


Why Do Ion Temperature Why Do Ion Temperature Fluctuations Appear High?Fluctuations Appear High?

As large (or larger) As large (or larger)

than than ! ! ObserveObserve If have high levels If have high levels

for then is also for then is also higher fromhigher from

But is it real???But is it real???

rire VV~~

%30~/~

ii TT

ee nn /~

ti

eri mV

RqTV

4

)ln(

iT~

riV~


More Probe Measurements! More Probe Measurements! Testing The Condition Of Testing The Condition Of Ambipolarity…Ambipolarity… What if ?What if ?

TotalTotal fluxes must be still be equal in fluxes must be still be equal in steady state, but fluctuations may drive steady state, but fluctuations may drive non-ambipolar fluxes.non-ambipolar fluxes.

From Poisson’s equation…From Poisson’s equation…

… … time-resolved measurements of time-resolved measurements of EErr will will help answer this question.help answer this question.

ei ~~

rireer VVn

dt

dE

q

0


Ahhhh! More Probes: Fork Probe Ahhhh! More Probes: Fork Probe Measures Radial Electric FieldMeasures Radial Electric Field

A fork probe, consisting A fork probe, consisting of two more triple of two more triple probes radially probes radially separated (slight separated (slight toroidal displacement) toroidal displacement) is added to the probe is added to the probe set, also aligned by set, also aligned by electron gun.electron gun.

MeasureMeasure yE prr


Combining Measurable Signals Combining Measurable Signals And Solving For The RestAnd Solving For The Rest

Summarising our unknowns as functions of Summarising our unknowns as functions of TTi i ..

Combining them into Poisson’s equationCombining them into Poisson’s equation

In the above equation, the remaining In the above equation, the remaining unknown is . Then solutions take the formunknown is . Then solutions take the form

We can “choose” We can “choose” so as to satisfyso as to satisfy

eiis

si TTTqAc

ITn

/exp

iti

ieiri TmV

TRqTTV

4

ln

irirerei TVVVTndt

dE

q

~ 0

rei VfT

totrere VnVn ~~reV

reV


Estimating The Total FluxEstimating The Total Flux

To proceed, we need an estimate of the To proceed, we need an estimate of the total flux, total flux,

Use Use IonisationIonisation rate and rate andapproximate profiles forapproximate profiles fornnee and and nnnn (neutral (neutraldensity) to estimatedensity) to estimateflux. In steady stateflux. In steady state

tot

Vnndr

dne


The ResultsThe Results

0

500

1000

1500

2000

0 2 4 6 8 10

r (cm)

vre0

(m

/s)

0

2000

4000

6000

8000

10000

vref

(m

/s)

vre0 vref

0

500

1000

1500

2000

2500

0 2 4 6 8 10

r (cm)

vri0

(m

/s)

0200400600800100012001400

vrif

(m/s

)

vri0 vrif

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10

r (cm)

ne

0 (

x10

18 m

-3)

0

0.02

0.04

0.06

0.08

ne

f (x

10

18 m

-3)

ne0 nef

240

260

280

300

320

340

360

0 2 4 6 8 10

r (cm)

To

t. f

lux

(x1

01

8m

-2s-1

)

-50050100150200250300

Flu

ct.

Flu

x

(x1

01

8m

-2s-1

)

flux_tot fluxef fluxif


The ResultsThe Results

0

500

1000

1500

2000

0 2 4 6 8 10

r (cm)

vre0

(m

/s)

0

2000

4000

6000

8000

10000

vref

(m

/s)

vre0 vref

0

500

1000

1500

2000

2500

0 2 4 6 8 10

r (cm)

vri0

(m

/s)

0200400600800100012001400

vrif

(m/s

)

vri0 vrif

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10

r (cm)

ne

0 (

x10

18 m

-3)

0

0.02

0.04

0.06

0.08

ne

f (x

10

18 m

-3)

ne0 nef

240

260

280

300

320

340

360

0 2 4 6 8 10

r (cm)

To

t. f

lux

(x1

01

8m

-2s-1

)

-50050100150200250300

Flu

ct.

Flu

x

(x1

01

8m

-2s-1

)

flux_tot fluxef fluxif


Conclusion: Fluctuations Can Conclusion: Fluctuations Can Drive Non-Ambipolar FluxesDrive Non-Ambipolar Fluxes The complex of probes allows local time-The complex of probes allows local time-

resolved measurements of key plasma resolved measurements of key plasma parametersparameters Electron densityElectron density Electron and Ion TemperatureElectron and Ion Temperature Electron and Ion particle FluxesElectron and Ion particle Fluxes

Fluctuations fluxes in H-1 are indeed non-Fluctuations fluxes in H-1 are indeed non-ambipolar in L-mode.ambipolar in L-mode.

In fact, fluctuations seem to drive In fact, fluctuations seem to drive onlyonly electron transport, as in the electron transport, as in the regions of maximum fluctuations.regions of maximum fluctuations.

ei ~~

Plasma Characterisation Using Combined Mach/Triple Probe Techniques

Documents

mach probe sensitive

probe sheath

radial mach probe

probe set

mach probe saturation

mach probes

shatsmore probe measurements

triple probes