Characteristics and classification of · PDF fileclassification of plasmas PlasTEP trainings...

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

126.07.2011

●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. +

226.07.2011Summer School, Warsaw

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


Artificial plasma


Various plasma sources

Different ways to generate plasma

● Corona discharge

●Dielectric barrier discharge

26.07.2011 5Summer School, Warsaw

● 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


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


●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

+

-

+

-

+

-

+

-

+

+

-

+

-

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


+

-

-

+

-

+

-+-

-

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


●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


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

++

-

-

-

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


-

+

+

-

+

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

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+-

+-

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


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


Debye length λD = ε0 kBTe

e02 ne

+

+-

+

+

+

++

+

+

+

+

-

-

-

--

-

- - --

+

+

+ +-

-

-

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


+

• 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


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

+

-

+-

+

-

+

-

+

-

+-

E


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


• 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


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


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


+

- +

-

+

+

-

+

-

+

-

+

-

-

+-

+-

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


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

+

+

+-

-

+

+

-

+

-

+-

+-

-

+

+

E

Electrons losses higher

Plasma sheaths


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

-

+

Diffusion to walls Charge extraction from walls

Attachment

-

-

Formation of plasma


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


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


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


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


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


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


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


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


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


16 orders of magnitude by plasma density

Environmental plasmas

Electron temperature 1-10 eV

Plasma density 1010-1014 cm-3

Characteristics and classification of · PDF fileclassification of plasmas PlasTEP trainings...

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