Diagnostics. Electric probes. Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico Lisbon, Portugal

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Instituto de Plasmas e Fusão Nuclear Instituto Superior Técnico

Lisbon, Portugal

http://www.ipfn.ist.utl.pt

C. Silva| Lisboa, Jan. 2014 | IST

Diagnostics

 Electric probes

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C. Silva | Lisboa, Jan. 2014 | IST

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Langmuir probes

 Simplest diagnostic (1920) – conductor immerse into the plasma

 Data interpretation complicated as probes perturb the plasma

 Limited to the plasma region were the probes can survive or do not perturb plasma

 Allows the determination of a large variety of plasma parameters (some of them only possible with probes)

 The importance of edge effects resulted in the continued use of probes

 The most widely used diagnostic techniques for low temperature plasmas, T_e < 100 eV

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Plasma Parameters (JET)

Core

T < 20 keV n ~ 1x10

²⁰

m

^-3

Edge plasma

T < 100 eV n < 1x10

¹⁹

m

^-3

Industrial / Space plasmas T < 10 eV

n < 1x10

¹⁵

m

^-3

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 Physics of probes equivalent to that of plasma- wall interaction

 Electrostatic potentials are shielded within a

short distance. Sheath keeps the plasma neutral

 Sheath dimension 10 λ_D ~ 0.1 mm, thin layer (λ_D~ 10^-5m for T_e = 20 eV, n = 1 ×10¹⁹ m^-3).

 Thin:

λ_D << d (probe dimension, ~mm)

 Collisionless:

l (mean free path, cm - m) >> λ_D

Debye shielding

Not to scale

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Sheath

 As electrons are more mobile a electric field arises in the sheath so that Γ_i = Γ_e.

 Probe rapidly charges up

negatively, floating potential. Probe floats below the plasma potential

 Sheath has a positive charge

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Sheath analysis

 Relation density and potential follows Boltzmann factor (Maxwellian)

 Space divided quasi-neutral plasma and the sheath (n_i  n_e)

Sheath analyses: Simplest possible case (B = 0, Z = 1, T_i= 0, collisionless, plane probe, 1D), all particles absorbed by the probe

 Aim: estimate parameters at sheath edge (se)

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Sheath analysis

 Energy conservation in the sheath

 Combining particle and energy conservation

 n_i> n_e sheath: Solve the 1D Poisson’s equation

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y(x) is non-oscillatory if a > 0  |V_se|  kT_e/2e v_se²  kT_e/m_i or v_se  c_s with c_s = (kT_e/m_i)^1/2

Bohm criterion

This is called the Bohm sheath criterion (1949):

 Ions must stream into the sheath with c_s for a sheath to form (depends on T_e).

 How can the ions get such a large velocity?

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Pre-sheath

 There must be a small electric field in the plasma that accelerates ions to an energy ~ ½kT_e toward the sheath edge. This region is called the pre- sheath (E_sheath ≈ kT_e/λ_D ≈ 10⁵ E_pre-sheath).

 The pre-sheath field is weak enough that quasi-neutrality does not have to be

violated. The point where (n_i − n_e)/n_i becomes significant, corresponding to the plasma–sheath interface.

 The density at the sheath edge cannot be the same as the plasma density in the main plasma.

Sheath edge: v_se = c_s, V_se = - ½kT_e , therefore n_se = n₀e^{- ½}≈ 0.6n₀

 Total pressure constant

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Summary

 A plasma can coexist with a material boundary only if a thin sheath forms, isolating the

plasma from the boundary.

 In the sheath there is a potential drop (few times kT_e) which

repels electrons from and

accelerates ions toward the wall.

 The sheath drop adjusts itself so that the fluxes of ions and

electrons leaving the plasma are almost exactly equal, so that

quasi-neutrality is maintained.

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 T_i  0, weak dependence

 Probe geometry: Results generally applied provided the sheath is thin, probe considered locally planar – used with probes of any shape

 Exact numerical solution with B = 0, T_i  0 (Loframboise ,1966): approximate

analysis adequate, ~10%.

 Orbit-limited collection: λ_D > d

More general cases

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 Ion flux to a surface

_se = _w, no dependence on the sheath potential drop

 Potential drop between plasma and a floating surface ( _se^e = _seⁱ)

Probe parameters

 eV_f/kT_e ≈ 3 for T_e ≈ T_i, D plasma V_p = V_f + 3Te

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Single probe

 What if the surface is not floating, but electrically biased?

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Single probe, I – V characteristic

 B=0, Z=1, T_i=0, Maxwellian distribution, no secondary emission,

collisionless, no particle sources, d > λ_D Sheath: V_se= c_s, n_se=0.5 n₀

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Single probe, I - V characteristic

T_e, V_f and I_sat derived from the characteristic and then n from I_sat

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Effect of the magnetic field

 Particles collected over larger distances

 Collisionless assumption may not be valid as, l  L

 Typical case: ρ_e < d and ρ_i ≈ d ~ mm (magnetized / strong magnetized)

 Determination of the effective probe area can be complex

 Despite theoretical difficulties, Bohm formula is valid and information may be extracted assuming for the area A_, limiting the analysis to V_ap ~< V_f

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Double and triple probes

Valid only if no significant gradients exist Double probe

Triple probe

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References

 Principles of Plasma Diagnostics, Hutchinson, Cambridge

 The Plasma Boundary of Magnetic Fusion Devices,

Stangeby, IoP

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Typical circuit

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Typical I, V signals

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I - V characteristic

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Typical applications

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Fixed probes

 Graphite probes fixed in the plasma facing components (same material as PFCs) – do not perturb plasma

 Study plasma-wall interaction

 Materials: Graphite, Tungsten

 Γ_wall= I_sat/eA_p [m^-2s^-1]

 q_wall=γT_eΓ_wall [W/m²]

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JET divertor probes

 Essential for the characterization of the divertor particle and heat fluxes

 Array of embedded probes made of the target material (CFC / W). The probes have heat conduction capabilities that are similar to that of the target plates, and they will erode at a similar rate

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Divertor probes for ITER

 Successful operation of the divertor relies on achieving a ‘detached’ divertor regime. Probes give the most direct indication of detachment – I_sat drops

 Main problem: For heavily loaded PFCs (10 MWm⁻³), the design of the Langmuir probe becomes as difficult as that of the target

 Heat conduction capabilities and a erosion rate that are similar to that of the target plates (replaced in parallel with the exchange of the divertor ).

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Reciprocating probes

 Reduce the probe heat loads (few 100 ms)

 Pneumatic systems

 Typical velocity 1 m/s

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JET reciprocating probe head

 9 – pin probe head (C, BN)

 Allows determination of a large variety of parameters (some only possible with

probes) ( Isat, Vf, Te, M_//, E_θ, E_r, Γ_ExB…)

 Local measurements (only limited pin size)

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

 Ideal for turbulence studies

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Reciprocation at JET

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Reciprocation at JET

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ISTTOK probe arrays

Radial array

Poloidal array

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Gundestrup probe

Determination of the poloidal e toroidal plasma rotation

M

_//

= 0.4 ln(I

_sat^u

/I

_sat^d

)

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Retarding field energy analyzer

 Simple Langmuir probes can tell us nothing about T_i. (This require measuring the ion current at positive voltages at which the current to the Langmuir probe is dominated by highly mobile electrons.)

 RFA operation: The slit plate is biased negatively to repel electrons. The transmitted ions are retarded in the electric field created by a swept

positive voltage applied to grid 1. The collector measures the ion current.

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Space plasmas

 One of two Langmuir probes on board ESA's space vehicle Rosetta (intended to study the comet

67P/Churyumov-Gerasimenko).

 The probe is the spherical part, 50 mm in diameter and made from titanium with a surface coating of titanium nitride. This specific Langmuir 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 of Saturn

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Typical results

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Examples of application

 Heat loads (IR, thermocouples), particle flux, detachment monitor, …

 High temporal resolution, local measurement

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ELM studies

Filaments during ELMs

 ELMs have a complex internal structure (filaments) clearly seen in the far SOL density (also seen in other diagnostics as the fast visible camera)

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SOL profiles at JET

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Edge plasma studies with probes

 Determination of plasma parameters in different regimes

 Heat and particle loads

 Detailed ELM structure and propagation

 Characterization and control of turbulence

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Turbulence in tokamaks

 Turbulence is responsible for and increase in the radial transport (anomalous transport) limiting the tokamaks performance

 SOL transport occurs via intermittent convective bursts (composed of long filaments along B)

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Turbulent particle flux

B E n

B E

~



 ~



_

B v E

E_ _r ^

~ ~

~  

If local density and E_fluctuations are in phase then a net time-averaged radial transport exists

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 Temperature fluctuations are often ignored and therefore density and plasma potential fluctuations derived respectively from the ion

saturation current and floating potential fluctuations.

 I

_sat

 nT

^1/2

, V

_p

= V

_f

+ 3T

Fluctuations measurements

 Results from emissive and ball pen probes as well as numerical codes indicate that the fluctuation level in V_f is larger than in V_p and therefore standard Langmuir probes overestimate the turbulent transport

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Typical fluctuations analysis

    

 ( )  ² ( ) ²

) ( )

(

y t y x

t x

y t y x t

C_xy x



 



Fluctuations poloidal structure

Poloidal correlation