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Characteristics and classification of plasmas
PlasTEP trainings course and Summer school 2011 Warsaw/Szczecin
Part-financed by the European Union (European Regional Development Fund
Warsaw/Szczecin
Indrek Jõgi, University of Tartu
●Introduction
●Characterization
●classification
Outline of the talk
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●classification
Summer School, Warsaw
Plasma and environment
Environmental plasma
Ionized gas with low temperatures but high electron energies
Large amount of active species are produced
phenolradicals: O, OH, N etc. +
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radicals: O, OH, N etc. +
CO2 and H2O
Other organic and inorganic species are neutralised similarly
At some cost of energy
Everything was plasma at the beginning of the Universe
95 or 99 %
Plasma in the Universe
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Artificial plasma
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Various plasma sources
Different ways to generate plasma
● Corona discharge
●Dielectric barrier discharge
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● Plasma torches
●Microwave plasmas
●Hollow cathode discharge
● Electron beams
Solid Liquid
120 K
1200 K0,1 eV
0,01 eV
104 K
105 K
1 eV
10 eV
EnergyTempe-
rature
Plasma: 4th state of the matter
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GasPlasma
1200 K
12000 K
0,1 eV
1-10 eV
102K
103 K 0.1 eV
0.01 eV
E = TkB
e0
E = T/11600
- FL = e0 ( E+v×××× B )
●Occurrence of electrical conductivity
●Screening of electric fields
Plasma: role of charge carriers
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●Screening of electric fields
●Occurence of a multitude of oscillation and waves (Langmuir
oscillations, ion acoustic oscillations, cyclotron oscillations, drift
waves, surface waves etc.)
● Interaction with magnetic fields
●Formation of characteristic boundary sheaths due to the contact
of plasmas with solid surfaces
+
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Quasi-neutral gas of charged particles that
exhibits collective behaviour
How many charges do we need?
Neutral particles in gas interact only during collisions while charged particles in
plasma interact through long-range forces
Plasma: definition
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+
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-+-
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How many charges do we need?
Main criterias:
● Charged particles are close enough to affect large number of other particles
●Debye screening length is short compared to the dimensions of plasma itself. Plasmas
are quasi-neutral
● Electron plasma frequency (plasma oscillations) is large compared to electron neutral
collision frequency
Plasma: characteristics
●Neutrality and ionization degree
●Debye length, plasma frequency and plasma parameter
●Larmor radius and cyclotron frequency
●Conductivity
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●Conductivity
●Cross-sections and mean free path
●Electron energy distribution
Ideal gas
For ideal gas in thermal equilibrium the probability that velocity lays in the range
dv around velocity v is proportional to
Maxwellian distribution:
e0 = 1.60·10-19 C
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Pressure is a measure of the density in thermal energy associated with the number
of gas atoms per unit volume
Average kinetic energy per particle
Rms. speed
e0 = 1.60·10 C
me = 9.11·10-31 kg
mp = 1.67·10-27 kg
kB = 1.38·10-23 J/K
ε0 = 8.85·10-12 F/m
c = 3.00·108 m/s
electron at 300K: 105 m/s
nitrogen at 300K: 500 m/s
0.04 eV at 300K while 1.3 eV at 104 K
++
-
-
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All neutrals in a volume do not have to be ionized to obtain plasma
Ionization degree – the relative amount of charged particles in the total gas
i = ne
n0+ne
In atmosphere n ∼ 1019 cm-3 n ∼ 1-10 cm-3
Ionization degree
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+
+
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+
In atmosphere n0 ∼ 1019 cm-3 ni ∼ 1-10 cm-3
i ∼10-18
In environmental plasmas ni ∼1010 to 1015 cm-3
Collisions with neutrals vs. the collective charge effects
Environmental plasmas – collisions dominate
plasma density ne
i ∼10-9 -10-4
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In most cases, the number of positive and negative
charges will be roughly equal
These charged particles will strongly intract with
each other in plasmaNeutral
Quasi-neutral
Plasma neutrality
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each other in plasma
+
Neutral
particle
Charged
particle
Q Q/r
Collective motions
Non-neutral plasmas:
E-beams, some magnetized plasmas
-
Sphere of
influence
When there is charge imbalance in the plasma, it’s
influence will be neutralised in short distance
∇ E = e0 (ni-ne)
In plasma the influence decays faster than in neutral gas
1/r exp(-r/λλλλD)vs. r/λD1 32
V m
2
4
6
8
0
CoulombDebye
Space charge
Debye length
109
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Debye length λD = ε0 kBTe
e02 ne
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++
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--
-
- - --
+
+
+ +-
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electron
density
electron
temperature
λD = 740 cm kBTe
ne
In practical units:
kBTe [eV], ne [cm-3]
1/r exp(-r/λλλλD)vs. r/λD1 32
-1Space charge
Debye length
+
Inside the sphere defined by Debye length, one can observe charge imbalance
while in larger sphere the charges are neutral
λD = 740 cm kBTe
ne
Debye length
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+
• Debye screening length is short compared to the dimensions of plasma itself.
Plasmas are quasi-neutral
kBTe =4 eV ne =1012 cm-3 λD =14.8 µm
kBTe =10 eV ne =1015 cm-3 λD =0.74 µm
Electric field does not penetrate the plasma
Plasma parameter – inverse value of the number of charged particles inside the Debye sphere
• Charged particles are close enough to affect large number of other particles
λ ∝kBTe
Plasma parameter
g = 1/ND
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ND = n πλD34
g < 1
3ND ∝ n
T 3
λD ∝kBTe
ne
- ideal plasma
g > 1 - non-ideal plasma
Plasma frequency
When charges with opposite signs are slightly moved in plasma,
there will be restoring force moving it back and the charges will
oscillate with a certain frequency
Plasma frequency
e 2 ncharge density
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E
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fp = 1/2π e02 n
ε0 mmass of charges
fp = 8980 Hzne
Electron mass smaller and thus they respond faster defining the plasma
frequency
fp ∼ 0.1-100 GHzfp = 1/2π e02 ne
ε0 me
+-
+
-+-
-
Responsible for longitudinal electrical oscillations
These oscillations are collisionless differently from acoustic waves where collisions
between particles are necessary
Determines one condition for the ideal plasma to occur
Determines the cut off frequency for electric fields to penetrate the plasma
Plasma frequency
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• Electron plasma frequency (plasma oscillations) is large compared to electron
neutral collision frequency
fp>>>>>>>> fc
Determines one condition for the ideal plasma to occur
When fc is the collision frequency
fp ∼ 0.1-100 GHz fc ∼ MHz to 100 GHz
Moving charge will experience Lorentz force in magnetic induction
FL = e0 v×××× B B - v⊥⊥⊥⊥
It will start to move in circular motion
perpenticularly to magnetic field
Larmor radius and cyclotron frequency
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ωL = e0Bm
FL
perpenticularly to magnetic field
Moving in parallel to magnetic field is not
affected
Cyclotron frequency rL = mv⊥⊥⊥⊥Larmor radiuse0B
Composite motion is a helical spiral motion along the lines of magnetic induction
ωL = e0Bm
Oppositely charged particles move along opposite direction
- v⊥⊥⊥⊥ rL = mv⊥⊥⊥⊥e0B
+ B v⊥⊥⊥⊥
Radius is smaller for electrons
Larmor radius and cyclotron frequency
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Magnetic field penertates the plasma
Radius is smaller for electrons
Cyclotron frequency is larger for electrons
E×××× B Drift velocity vE =B2
Cyclotron frequency has to be larger than collision frequency for plasma to be
magnetized
j = e0 ( neve–ni vi )= e0 ( neµµµµe–niµµµµi ) E
Action of electrical field E forces free electrons and ions of the plasma to gain drift
velocities and generate an electric current
E
+
+
-- +
-Usually electrons determine the currents
Electrical conductivity
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- +
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Usually electrons determine the currents
µµµµe>>>>>>>> µµµµi ne≈≈≈≈ niand
Electrical conductivity σσσσ = e0neµµµµe
σσσσ = e0neττττe/me
Weakly ionized plasmas is independent on σσσσ ∝ neττττe ne
Fully ionized plasmas is not a function of σσσσττττe∝ 1/ne ne
ττττe — mean free time of flight
Diffusion will result in the expandsion of plasma
Diffusion of electrons faster due to higher speed and
smaller mass
n
electronsions
E E
ΓΓΓΓe = –nµeE – De∇∇∇∇n
ΓΓΓΓi = +nµiE – Di∇∇∇∇n
- electron flux
- ion flux
Ambipolar diffusion
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There will be slightly more electrons at the boundary of plasma and more positive
ions in the bulk of the plasma
xElectric field due to different flux will counteract electron diffusion
E
The diffusion will be controlled by the inertia of ion collisions but increased by
electron temperature
µiDe + µeDe
µi+ µe∇∇∇∇nDa = - ambipolar diffusion
Larger loss of charges at the boundaries with
electrodes or other surfaces
Positive charge in sheath
+
+
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+
E
Electrons losses higher
Plasma sheaths
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Electric field will prevent electrons to escape the plasma and
will accelerate the ions
+
Surface obtains negative potential in respect to
plasma
Sheath thickness will be roughly 4λD without applied voltage and potential
drop in the range of kTe/e0
Applying external voltage will change the thickness of plasma sheath
V
Ionization-
+
Recombination
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+
Diffusion to walls Charge extraction from walls
Attachment
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Formation of plasma
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Ionization
ionization has to balance the loss mechanisms
• Collisions by electrons, ions and neutrals
• photoionization
There is certain threshold energy for ionization:
e- on O2
-Ui
Ionization at high temperatures
Thermal energy of heavy particles becomes large enough
for ionization
Saha equation
-
+exp( )≈ 3×1027
ni
nn
T3/2
ni T-Ui
Formation of plasma
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Ionization by electric fields
Electric field accelerates charges and when they gain
sufficient energy they will ionize the neutrals
Most of environmental plasmas produced in this way
Electrons mostly doing the work
-
-
+
-
n i T
Momentum is redistributed
total kinetic energy is conserved
Light particles, electrons, can not loose much of the energy
Elastic collisions
2mM
Redistributed
energy <<<<
m
M
Collisions
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Energy is lost for ionization, dissocitiation or excitation
Inelastic collisions
Momentum is redistributed
Total kinetic energy transferred to
internal energy M
m
Penning effect: excited atom or molecule has enough energy to ionize or dissociate
another atom or molecule
e- + A A+ + 2e-
e- + A A* + e-
e- + AB A+ B + e-
By the simplest approach the particles are treated
as hard spheres without charge
Each atom presents a cross section obscuring
electrons path
Number of target atoms is
x
y
y
z
-
xyzvolume
σσσσ=ππππr2
n·xyz
Collision cross-sections
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In reality the particles not simple spheres and one has to take into account charge effects
and the energy of the particles
Number of target atoms is
Viewed from the side of xy there is a distance λλλλ where the face xy is totally blocked by
other particles: mean free path
Collision frequency
x
yn·xyz
λλλλ = 1/nσσσσ
ννννc = vnσσσσ around 1011 Hz at v ~ 105 m/s and atmospheric pressures
around 0 .1 µm at
atmospheric pressures
The probability for collisions depends on electron energy
Inelastic collisions have certain thershold
• ionization (above 10 eV)
• excitation (about 0.1-10 eV)
• dissociation (about 1-10 eV)
Collision cross-sections
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Cross sections decrease at higher
energies
At high speed of electrons the time for interactions decreases
The rate of ionizations, dissociations and excitations by electrons depend on electron
energy which has a distribution
Ar
These processes depend strongly on electron energy distribution
In environmental plasmas, electrons are carrying most of the energy and are main
agents in the ionization, dissociation and exitation processes
Maxwellian and Druyvesteyn Calculated
Electron energy-distribution
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Electron energy distribution becomes in equilibrium in timescales of 10-9 s
Electron energy and average speed much higher than ions and neutrals
Average electron energy 1 eV and average speed 106 m/s
Average energy of surrounding gas 0.025 eV and average speed 1000 m/s
Ionization, excitation and dissociation frequency can be obtained by integrating over
energy distribution and cross sections
Non-equilibrium plasma
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Electron
energy Cross-section
eV
Gas
energy
energy distribution and cross sections
Energy not used in reactions is eventually lost
rate is additionally proportional to ne
Optimization of both the electron density and
energy
The species with high energy have higher activity and shorter lifetime
Plasma chemistryPlasma physics
10-6 10-5 10-4 10-3 10-2 10-1 100 101 Time, s10-710-810-910-1010-12
Plasma-chemistry
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10-6 10-5 10-4 10-3 10-2 10-1 100 101 Time, s10-710-810-910-1010-12
Electron energy
distribution
Ionization
Dissociation
Excitation
Attachmenty
Ion reactions
Reactions of active
species
Radical reactions
Diffusion
Usually radical reactions in timescales of 10-6 to 10 s are most important in respect to
removal of hazardous gases
Temperature• low temperature plasmas (less than 2000K)
•high temperature plasmas (above 2000K)
Thermodynamic equilibrium• non-thermal or non-equilibrium plasmas Te>>Ti≈Tg
• thermal or equilibrium plasmas Te≈Ti≈Tg
Frequency• DC discharge
• pulsed DC (kHz)
• RF discharge (MHz)
•Microwave discharge (GHz)
Neutrality
Plasma: Classification
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Pressure• low-pressure plasmas <1 Pa
• moderate pressure plasmas ≈100 Pa
• atmospheric pressure plasmas
Ionization degree• weakly ionized plasmas 10-6 – 10-1
• fully ionized plasmas ≈ 1
Magnetization• magnetic plasmas
• non-magnetic plasmas
Neutrality• neutral
• non-neutral
Dusty plasmas
Most often classified by electron temperature
and plasma density
7 orders of magnitude by electron
temperature
16 orders of magnitude by plasma density
Plasma: Classification
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16 orders of magnitude by plasma density
Environmental plasmas
Electron temperature 1-10 eV
Plasma density 1010-1014 cm-3