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 /
W. M. Solomon, M. G. Shats 3
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~
W. M. Solomon, M. G. Shats 4
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
W. M. Solomon, M. G. Shats 5
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
W. M. Solomon, M. G. Shats 6
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.
W. M. Solomon, M. G. Shats 7
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
W. M. Solomon, M. G. Shats 8
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
| - |?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
~_
~_
~_
ti
eri mV
RqTV
4
)ln(
~
~~
~~
VnVn
VVnn
nV
Compute Compute nnee and then the and then the fluxflux
W. M. Solomon, M. G. Shats 9
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
| - |?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
~_
~_
~_
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.
W. M. Solomon, M. G. Shats 10
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~
W. M. Solomon, M. G. Shats 11
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
W. M. Solomon, M. G. Shats 12
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
W. M. Solomon, M. G. Shats 13
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
W. M. Solomon, M. G. Shats 14
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
W. M. Solomon, M. G. Shats 15
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
W. M. Solomon, M. G. Shats 16
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
W. M. Solomon, M. G. Shats 17
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 ~~
Top Related