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Debye Shielding
Plasma characterization
using Langmuir probes
• An ionized gas has a certain amount of free charges that can
move in presence of electric forces
Instituto de Plasmas e Fusão Nuclear
Instituto Superior Técnico
Lisbon, Portugal
http://www.i pfn.is t.utl.pt
Horácio Fernandes| Oeiras, July 2016 | IST
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Debye Shielding
Debye Shielding
• Shielding effect: the free charges move towards a perturbing charge
to produce, at a large enough distance D, (almost) a neutralization
of the electric field.
E
D
• The quantity
E~0
is called the (electron) Debye length of the plasma
• The Debye length is a measure of the effective shielding length
beyond which the electron motions are shielding charge density
fluctuations in the plasma
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Debye Shielding
Irving Langmuir
• Typical values of the Debye Length under different conditions:
Plasma
Electron
Magnetic
temperature field
T(K)
B(T)
10 7
-10 8
10
Debye
length
λD(m)
10 −11
10 −4
Solar core
Tokamak
Gas
discharge
10 32
10 20
10 16
10 4
--
10 −4
Ionosphere
10 12
10 3
10 −5
10 −3
7
−8
Magnetosphe
re
10
Solar w ind
10 6
10 5
10 −9
10
10 5
10 4
10 −10
10
1
10 6
--
10 5
Interstellar
medium
Intergalactic
medium
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Density
n e(m -3)
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10
10
 Coined the term plasma because it reminded him of
blood plasma (1927)
 Developed Langmuir probe for exploring properties of
plasmas
10 2
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Langmuir probe
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7/15/2016
Langmuir probes
Plasma Parameters (fusion)
 Simplest diagnostic (1920) – conductor immerse into the plasma
 Data interpretation complicated as probes perturb the plasma
 Limited to the plasma region w ere the probes can survive or do not
perturb plasma
 The importance of edge effects resulted in the continued use of probes
 Allow s the determination of a large variety of plasma parameters (some of
them only possible w ith probes)
 The most w idely used diagnostic techniques for low temperature
plasmas, Te < 100 eV
Core
T < 20 keV
n ~ 1x1020 m-3
Edge plasma
T < 100 eV
n < 1x1019 m-3
Industrial / Space plasmas
T < 10 eV
n < 1x1015 m-3
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Sheath
Debye shielding
 Physics of probes equivalent to that of plasma-wall
interaction
 As electrons are more mobile a electric
field arises in the sheath so that Γi = Γe.
 Electrostatic potentials are shielded w ithin a short
distance. Sheath keeps the plasma neutral
 Probe rapidly charges up negatively,
floating potential. Probe floats at a
~3kTe/e below the V p: V f = V p - 3kTe/e
 Shielding not complete, particles with thermal energy
can escape. Potential ~kTe leaks into the plasma.
 Sheath dimension 10 λ D ~ 0.1 mm, thin layer (λ D~
10-5 m for Te = 20 eV, n = 1 ×1019 m-3).
 Thin:
λD << d (probe dimension, ~mm)
 Collisionless:
l (mean free path, cm - m) >> λD
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– Bohm criterion
Not to scale
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Sheath analysis
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Sheath
 Space divided quasi-neutral plasma and the sheath (ni  ne)
Sheath analyses: Simplest possible case (B = 0, Z = 1, Ti = 0, collisionless,
plane probe, 1D), all particles absorbed by the probe
 Aim : estimate parameters
at sheath edge (se)
 Sheath has a positive charge
 Shielding not perfect: pre-sheath (V =
0.5kTe/e) accelerates ions to the sheath
 Relation density and potential follows
Boltzmann factor (Maxwellian)
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 kTe) w hich repels
electrons from and accelerates ions
tow ard the wall.
The sheath drop adjusts itself so
that the fluxes of ions and electrons
leaving the plasma are almost
exactly equal, so that quasineutrality is maintained.
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Probe parameters
Single probe
 Flux to a surface
  se =  w, no dependence on the sheath potential drop
 Potential drop between plasma and a floating surface (  see =  sei)
 eV f/kTe ≈ 3 for Te ≈ Ti , D plasma
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Single probe, I – V characteristic
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Single probe, I - V characteristic
 Sheath: Vse= c s , nse=0.5 n0
 Applied voltage: Vpr
 B=0, Z=1, Ti =0, Maxw ellian distribution, no secondary emission,
collisionless, no particle sources, d > λ D
Te, Vf and Isat derived from the characteristic
and then n from Isat
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Typical circuit
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Typical I, V signals
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I - V characteristic
Fixed probes
 Graphite probes fixed in the plasma
facing components (same material as
PFCs) – not flush w ith surface
 Study plasma-w all interaction
 Materials: Graphite, Tungsten
 Γ wall= Isat/eAp [m -2s -1]
 qwall=γTe Γ wall [W/m 2]
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Reciprocating probes
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Reciprocation at JET
 Reduce the probe heat loads
(few 100 ms)
 Pneumatic systems
 Typical velocity 1 m/s
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ISTTOK probe arrays
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Space plasmas
Poloidal array
 One of tw o 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 w ith 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
Radial array
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Turbulence in tokamaks
Further Reading
 Turbulence is responsible for and increase in the radial transport
(anomalous transport) limiting the tokamaks performance
P.C. Stangeby,
The Plasma Boundary of Magnetic
Fusion Devices, IoP (2000)
ISBN-13: 000-0750305592
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