Carlos Silva Instituto de Plasmas e Fusão Nuclear...(theories of ion collection) → 10-20% uncertainty in n determination PIC codes 90’s gave significant contributionsignificant

DiagnosticsCentro de Fusão Nuclear

Electric andElectric and Magnetic probes

Carlos SilvaInstituto de Plasmas e Fusão Nuclear

Langmuir probes

Centro de Fusão Nuclear

Simplest diagnostic (1920) – conductor immerse into the plasma (I,V)Data interpretation very complicated as probes perturb the plasmaperturb the plasmaLimited to the plasma region were the probes can survive or do not perturb plasmaAllows the determination of a large variety of plasma parameters (some of them only possible with probes)with probes)

Plasma Parameters (JET)CCentro de Fusão

NuclearCore (Hottest possible)

T<20 keV20 3n~1x1020 m-3

Edge plasma (Coldest possible)T<200 eVT<200 eVn~1x1019 m-3

Industrial / Space plasmas Hei

ght (

m)

Industrial / Space plasmasT<10 eVn~1x1015 m-3

HMajor radius (m)Major radius (m)

Plasma-wall interaction


Physics of probes equivalent to that of plasma-wall interactionp

Plasma is quasi-neutral. Sheath shields the plasma from external applied voltagesexternal applied voltages. Sheath keeps the plasma neutral (ambipolar transport)

Sh th di i 10 λ 0 1Sheath dimension 10 λD ~0.1 mm, thin layer

As electrons are more mobile a electric field arises in the sheath so that Γi = Γe.

SheathCentro de Fusão Nuclear

Probe does not assume plasma potentialplasma potential

Probe floats at a potential ~3kTe/e below the plasma

t ti l fl ti t ti lpotential, floating potential: Vf = Vp - 3kTe/e

Sheath has a positive charge

Shielding not perfect: pre-sheath 0.5kTe/e accelerates ions to the sheath – Bohmions to the sheath Bohm criterion

Bohm criterion


Due to the large electron velocity a surface will collect initially a higher electron fluxThis generated an electric field that accelerates ionsPotentials are limited to 0.5kTe/e eotherwise ne≠ni

Sheath solution: Vse=Cs

B=0 Z=1 Ti=0 collisionlessB 0, Z 1, Ti 0, collisionless

Bohm criterion


Plasma parameters pacross the sheath

Single probe


Single probe, I - V characteristic


Sheath: Vse=Cs, nse=n/2Applied voltage: Vpr

B=0 Z=1 Ti=0 Maxwellian distribution no secondary emissionB 0, Z 1, Ti 0, Maxwellian distribution, no secondary emission, collisionless, no particle sources, d >λD

Single probe, I - V characteristic


Effect of the magnetic field


Probe theories


Probes perturb plasma: The interpretation is difficult as the non-perturb parameters have to be estimated.Discussed until now: planar probesCylindrical, spherical ?

(theories of ion collection) → 10-20% uncertainty in n determinationy

PIC codes 90’s gave significant contributionsignificant contribution

B. Orbital Motion Limit (OML) theory

C. Allen-Boyd-Reynolds (ABR) theory

Allen, Boyd, and Reynolds (ABR) simplified the problem by assumingab initio that Ti = 0, so that there are no orbital motions at all: the ions are all drawn radially into the probe.

Originally, the ABR theory was only for spherical probes, but it was later extended to cylindrical probes by Chen. Sheath, but no orbiting

ABR theory for cylindrical probes

Assume that the probe is centered at r = 0 and that the ions start at rest from r = ∞, where V = 0, Poisson’s equation in cylindrical coordinates is

For each assumed value of J (normalized probe current), this equation can be integrated from ξ =∞ to any arbitrarily small ξ. The point on the curve where ξ = ξp (the probe radius) gives the probe potential ηp for that value of J. By computing a family of curves for different J (Fig. 22), one can obtain a J-ηp curve for a probe of radius ξp by cross-plotting (Fig 23).

D. Bernstein-Rabinowitz-Laframboise (BRL) theory

The first probe theory which accounted for both sheath formation and orbital motions was published by Bernstein and Rabinowitz (BR), who assumed an isotropic distribution of ions of a single energy Ei. This was further refined by Laframboise (L), who extended the calculations to a Maxwellian ion distribution at temperature Ti.

The BRL treatment is considerably more complicated than the ABR theory. In ABR, all ions strike the probe, so the flux at any radius depends on the conditions at infinity, regardless of the probe radius. In BRL theory, however, the probe radius must be specified beforehand, since those ions that orbit the probe will contribute twice to the ion density at any given radius r, while those that are collected contribute only once. The ion density must be known before Poisson’s equation can be solved, and clearly this depends on the presence of the probe. There is an “absorption radius” (see the figure), depending on J, inside of which all ions are collected.

F. Tests of collisionless theories1. Fully ionized plasmas

The first test of the BRL theory was done in a Q-machine, a fully ionized potassium plasma at 2300K, by Chen et al.

Figure 29 shows that the slope of Isatagrees will with BRL theory.

Figure 30 shows that the agreement over two orders of magnitude was within 10%, as long as Isat was taken at η = 20.

Double and triple probes


Typical circuit


I - V characteristic


I - V characteristic


Reciprocating probes


Pneumatic systems

Typically 1 m/s

Fixed probes


Graphite probes fixed in the plasma facing components (same material as PFCs)M t i l G hit T tMaterials: Graphite, Tungsten

Γwall= Isat/eAp [p/m2]wall sat p [p ]

qwall=°γTe Γwall [W/m2]

JET probe headCentro de Fusão Nuclear

9 – pin probe head (C, BN)

Allows the simultaneous determination of: Isat, Vf, Te, M//, Eθ, Er, ∇Isat, ΓExB…(500 kHz)

Local measurements (only limited pin size)

High temporal resolution (limitedHigh temporal resolution (limited by the data acquisition system)

ISTTOK probe arrays


Gundestrup probe


1

2 8

3

4

5

6

7

Determination of the poloidal e toroidal plasma rotation

5

rotation

Space plasmas

Centro de Fusão Nuclear One of two Langmuir probes on board

ESA's space vehicle Rosetta. The probe is the spherical part, 50 mm in diameter and made from titanium with a surface coating of titanium nitride. This specific g pLangmuir probe is on a mission to study the space plasma around the comet.

Probes also used in the Cassini mission to measure the inner magnetosphere ofto measure the inner magnetosphere of Saturn

Edge plasma studies with probesCentro de Fusão Nuclear

Determination of plasma parameters in different regimesCharacterization and control of turbulence

-100

-50

0

50

Vf

(V)

Vbias=100 V 30

40

A)

11729-Positive bias

11752-Negative bias

-150

-100Vbias=100 VVbias=0 VVbias=-200 V

05

10

kV/m

)

0

10

20

Isat

(m

A)

/s)

-10-50

Er

(kV

2

4

06 s-1

)

0

2

4

6

8

ial v

eloc

ity

(km

/s)

-4

-2

0

2

ExB

she

ar (

x106

15.5 16.0 16.5 17.0Time (ms)

-2

0

Rad

ial

15.5 16.0 16.5 17.0Time (ms)

-15 -10 -5 0 5 10r-a (mm)

Ex

Typical fluctuations analysis


( ) [ ][ ])()( ytyxtxC

−−+=

ττ

Fluctuations poloidal structure Poloidal correlation

250LCFS(a)

0.5Edge plasmaLCFS

(c)

16573

0.8

1.0

( )[ ] [ ]22 )()( ytyxtx

Cxy−−

=τ

100

150

200

requ

ency

(kH

z)

LCFS(a)

0.2

0.3

0.4

S (k

θ) (

a.u.

)

LCFS

0.0

0.2

0.4

0.6

Cor

rela

tion

-6 -4 -2 0 2 4 6kθ (cm-1)

0

50

Fre

250

-6 -4 -2 0 2 4 6kθ (cm-1)

0.0

0.1S

1.000

-30 -20 -10 0 10 20 30Time (µs)

-0.4

-0.2

100

150

200

250

uenc

y (k

Hz)

Edge plasma

0.100

1.000

(w)

(a.u

.)

-6 -4 -2 0 2 4 6k (cm-1)

0

50

100

Fre

que

(b)

0 50 100 150 200Frequency (kHz)

0.001

0.010S(w

(d)

kθ (cm-1) Frequency (kHz)

TurbulenceCentro de Fusão Nuclear

Turbulence in tokamaksCentro de Fusão Nuclear

30

t (m

A)

r-a=6 mm

10

20

Ion

Sat.

Cur

rent

(

Turbulence is responsible for and increase in the radial transport ( l t t) li iti th t k k f

13.0 13.5 14.0 14.5 15.0 15.5Time (ms)

0

(anomalous transport) limiting the tokamaks performance Gradients originate instabilities that try to suppress the gradients

Turbulent particle transport


En θ~~

BEeff ×Γ

BBEθ=Γ ×

e

BEeffr n

v ×=

Large structures in tokamaksCentro de Fusão Nuclear

Turbulence originates large scale structureslarge scale structures (energy transfer between turbulence and large scales) (Jupiter bands, golf current, etc)Recently observed inRecently observed in tokamaks (difficult to study due to its large

l )scale)

Large structures in tokamaks140 (b) -60 -60


LCFS

HFS

Rake 60

80

100

120

140

requ

ency

(kH

z)

(b)

20

40

al (

V)

Poloidal arrayRadial array

a)

LCFS probe

Poloidalarray

020

40Fre

q

1.0 1.0 )

-40

-20

0

20

Flo

atin

g po

tent

ial

Edge plasma fluctuations h l b l b h i

21.6 21.8 22.0 22.2 22.4 22.6 22.8 23.0Time (ms)

-40

0.8

1.0Toroidal correlationRadial correlation

b)

have a global behaviour, contrary to the onserved on the scrape-off layer

-0.2

0.0

0.2

0.4

0.6

0.8

Cor

rela

tion

Radial correlation

-60 -40 -20 0 20 40 60Tau (µs)

-0.4-0.2

Magnetic probesCentro de Fusão Nuclear

Magnetic probes


Magnetic probes on ISTTOKCentro de Fusão Nuclear

MHD modes


MHD activityCentro de Fusão Nuclear

Carlos Silva Instituto de Plasmas e Fusão Nuclear...(theories of ion collection) → 10-20% uncertainty in n determination PIC codes 90’s gave significant contributionsignificant

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