工业等离子体原理（英文ppt）：工业等离子体原理

Principles and
Applications
of Industrial Plasma
Contents
1 Introduction
1.1 The social role of industrial plasma engineering
1.2 Important definitions
1.3 Plasma physics regimes and issues
2 Kinetic Theory of Gases
2.1 measurement of high vacuum
2.2 particle distribution functions
2.3 particle collisions
3 Motion of Charges in Electric and Magnetic
Fields
3.1 Charged particle motion in electric fields
3.2 Charged particle motion in magnetic fields
3.3 Charged particle motion in steady electric and
magnetic fields
4 Characteristics of Plasma
4.1 Bulk properties of plasma
4.2 Quasi-neutrality of plasma
4.3 Electrostatic Boltzmann equation
4.4 Simple electrostatic plasma sheaths
4.5 Plasma frequency
5 Electron Sources and Beams
5.1Thermionic emission sources
5.2 Photoelectric emission sources
5.3 Field emission sources
5.4 Hollow cathode sources
5.5 Secondary electron emission sources
5.6 Sources and beams characteristics
5.7 Charged particle beam transport
6 Ion Sources and Beams
7 Dark Electrical Discharges in
Gases
7.1 Background ionization
7.2 Saturation regime
7.3 Townsend discharge
7.4 Corona discharges
7.5 Corona sources
7.6 Electrical breakdown
8 DC Electrical Arc Discharges in Gases
8.1 Arc regime
8.1.1 Voltage-Current Characteristic
8.2Phenomenology of electrical arcs
8.2.1 Classical Arc Nomenclature
8.3 Physical processes in electrical
8.3.1 Body forces on arcs
8.3.2 Electrode Jet Formation
9 Inductive RF Electrical Discharges
in Gases
9.1 Introduction
9.2 Phenomenology of RF-plasma
Interactions
9.3 Skin depth of plasma
9.4 Inductive plasma torch
9.5 Other methods of generating
inductive plasmas
Chapter 1 Introduction
1.1 The social role of industrial plasma engineering
The plasma engineering have an important role to
promote the society development and increase the
living standard of the human beings due to it:
May resolve the problem of the energy sources for
the society development
May have very high efficiency and effectiveness of
energy consumposition
May accomplish industrial processing without
unwanted byproducts or waste materials
Discussed in details:
First,Plasmas offer two primary
characteristics of industrial interest,(1)
higher temperatures and energy densities
than that achieved by chemical or other
means;(2) energetic actives species,
ultraviolet or visible photons; charged
particles,including electrons,ions,and free
radicals; and highly reactive neutral species,
such as reactive atoms (O,F,etc),excited
atomic states,and reactive molecular
fragments such as monomers.
and as a result,Plasmas offer benefits
over other industrial processing method,
such more efficiently and cheaply,without
producing large volumes of unwanted
byproducts or waste materials,with
minimal pollution or production of toxic
wastes,
Some applications listed below:
1,More efficient energy utilization
a) Plasma lighting devices
b) Plasma chemistry
c) Materials processing with thermal plasma
2,Accomplishing unique results
a) Electron,ion,and plasma sources
b) New materials from plasma chemistry
c) Plasma etching and deposition for
microelectronics
d) Materials processing with thermal plasma
e) Communications using geophysical plasmas
f) Space propulsion systems
g) surface modification of materials
3,Production with minimum waste
materials
a) Plasma chemistry
b)Plasma etching and deposition for microelectronics
c) Materials processing with thermal plasma
d) Surface treatment of materials
e) Ion implantation of materials
4,Production with minimum toxic
waste
a) Plasma chemistry
b) Plasma etching and deposition for
microelectronics
c) Surface treatment of materials
d) Ion implantation of materials
1.2 Important definitions
The history of plasma may be recalled to 17th
century and the term plasma was introduced by
Irving Langmuir in 1928.
Now plasma research including three branches:
Plasma physics,concerned with the basic laws and
physic processes which govern the behavior of plasma,
magnetohydrodynamics(MHD)
Electrohydrodynamics(EHD)
Plasma chemistry,concerned with chemical reactions
which occur in the presence of a plasma
Plasma science and plasma engineering,concerned with
the application of plasma to devices or processes
1.3 Plasma physics regimes and issues
1 Density and temperature regimes
Temperature:1-20eV,1eV=11,605K
Density:1012-1025electron/m3
2 Heterogenous interactions of plasma
Plasma can interact with other states of matter individually,or with
combinatios of solids,liquids,and gases.
Interacting with neutral gases,will result in dissociation,ionization
and plasma chemical reaction,
Interacting directly with solid surface,usually associated with the
etching processing or sputtering
3 Approaches to the study of plasmas:
In the continuum approach,a plasma is treated as if it were a
continuous fluid.
A second major theoretical approach is to regard the plasma as a
collection of individual particles,and its collective behavior as the
result of their motion.
A third major approach is to regard the plasma as a black box with
inputs and outputs.
The challenges of plasma physics:
Multi-body problem;
Another difficulty is that the differential equations
which describe the conservation of particles,
momentum,and energy in plasmas are often
nonlinear.
Plasma experiments are usually difficult to set up and
interpret,Boundary condition;Multivariable
problem,
Difficult to diagnose because of its high kinetic
temperature and high energy density,two probe
methods,perturbing probe such as Langmuir probe
and non-perturbing prob such spectrum analysis
Homework:
1.Please review the social role of the
industrial plasma engineering.
It is not possible to fully understand the physical
processes which occur in the industrial applications
of plasma without a knowledge of the behavior of
gases on a microscopic scale,i.e,at the level of
individual atoms,molecules,and charged particles.
The behavior of gases on the microscopic scale is
described by a branch of physics called the kinetic
theory of gases,and the implications of this
behavior in the macroscopic world are treated by
the subjected of statistical mechanics.
2 Kinetic Theory of Gases
2.1 measurement of high vacuum
In the 19th century
when the first quantitative measurements were
made in vacuum system,the degree of vacuum
was measured with mercury manometers which
referred the pressure in the vacuum system to
that of the atmosphere,Thus,the common unit
of pressure was the millimeter of mercury (mm
Hg),in which one standard atmosphere (atm),
at 0℃,was equal to 760 mm Hg.
In the mid 20th century
An international standards committees
decided to change the name of the unit
pressure from millimeters of mercury to the
Torr,which is,at this time,the unit most
frequently found in the North America
literature of plasma science,The torr was
named in honor of Evangelista Torricelli
(1608-1647),an Italian physical known for
his work on barometers,
The usual applied situations of the units
Atmosphere,in industrial applications such as
thermal plasma processing and
magnetohydrodynamic power generation,for
these applications,the pressures are usually at or
slightly above 1 atm
Millitorr or micron,10-3 Torr or 10-6 Torr,which is
widely used in materials science and
microelectronic plasma processing,because the
used pressures in these applications are usually
between 10-3 Torr and 10 Torr.
SI system
After the introduction of the Torr,the same
international standards committee decided that
the official unit of pressure in the SI system of
units would henceforward be the pascal
(symbol Pa),defined as 1 Newton per square
meter (N/m2),In the field of industrial plasma
engineering,it is still common practice to
quote the vacuum pressure in Torr,with an
increasing tendency to cite the neutral particle
densities,rather than background pressures.
The relationship of each units
The conversion between the Pascal and the Torr is via
the standard atmosphere which is defined as exactly equal
to both 760 Torr and 1.01325× 105 Pa,given by
The pressure can be related to the number density in
particles per cubic meter by the perfect gas law,
where k is Boltzmann’s constant.
)(100 1 3 3.1 7 6 0)(' 5 PapT o r rp
nk Tp?
The conversion factor between the neutral number
density and the background pressure:
Here,the temperature is evaluated as 300K.
)('102 2 0.3)('7 6 0 100 1 3 3.1)/( 22
5
3 T o r rpT o r rp
kTmp a r t i c l e sn

2.2 Particle distribution functions
If the particles are allowed to interact and equilibrate,
their velocities and energies become distributed over a
range of values described by the Maxswell-Boltzmann
distribution function.
2.2.1 Velocity distribution functions
velocity distribution function means the proportion of the
number of particles in a unit velocity space volume to the
total particles.
if we define dnx,the number of particles in the velocity
interval between vx and vx+dvx
]
2
e x p[)
2
()(
2
2
1
2
1 kT
mv
kT
mn
dv
dnvf x
x
x
x
The number of particles in a unit cubical
volume in velocity space:
e x p)
2
( 2
3
2
3
3
kT
mn
dvdvdv
nd
zyx
x y z
]2[
2
kT
mv
2222
zyx vvvv
]
2
e xp[)
2
(4)(
2
22/3
2
1 kT
mvv
kT
mn
dv
dnvf v
The figure shows schematically the distribution of
speed f(v) as a function of the speed v for three
kinetic temperatures,T1<T2<T3
The three moments of the velocity distribution function
have physical significance:
The zeroth moment,equal to the area under the
distribution function,is the gas number density n:
The first moment is the arithmetic mean speed; This
speed is relevant with the mean free path
While the second moment is related to the root
mean square speed of the particles,This speed is
relevant with the kinetic energy of the particles.
0 )( ndvvf
21
0
)8()(1
mkTdvvvfnv?
21
0
21 )3())((1
m
kTdvvvf
nv r m s
Another
characteristic speed
is the most
probable speed:
2
1
)2(
m
kTv
m?
2.2.2 Energy distribution functions
When the gases is in
kinetic or
thermodynamic
equilibrium,the
energy of individual
particle also obeys a
Maxswell-Boltzmann
distribution,
2
2
1 mvw?
The distribution function of energies
between w and w+dw:
]e xp[
)(
2)(
2
3
2
1
2
1 kT
w
kT
wn
dw
dn
wf w
0 )(1 dwwwfnw
kTdwkTwkTww 23
0
23 ]e x p [)(2
0
)(
3
2 dwwwf
kn
T e ff
2.3 Particle collisions
Principal kinds of collision
Electrons
e+A→A ++2e Ionization
e+A→A *→e +A+h ν Excitation
e+ A* →2e + A + Penning ionization
e+A→e + A Elastic scattering
e+AB→e+ A+B Dissociation
e+AB→2e + A ++B Dissociative ionization
e+AB→A -+B Dissociative attachment
e+ A+ +B→A+B Recombination
Ions
A+ +B→A+B + Charge exchange
A+ +B→A + +B Elastic scattering
A+ +B→A ++B++e Ionization
A+ +B→A + +B* → A ++B+hν Excitation
A+ +e+B→A+B Recombination
A+ +BC→A + +B+C Dissociation
A +BC→C+AB Chemical reaction
2.3.1 Elastic binary collisions
Binary collisions:collisions involving only
two particles in gas or plasma
Elastic binary collisions:the total kinetic
energy of the two particles is conserved.
Inelastic binary collisions:the initial kinetic
energy of the two colliding particles is
greater than the kinetic energy after the
collision
Binary collisions between charged
particles,i.e,between two electrons,two
positive ions,or ions and electrons are
irrelevant in the industrial applications of
plasma because:
In most industrial plasmas the degree of
ionizations is generally quite low,the
dominant collisional process is between
charged particles and the neutral
background gas----------Lorentzian gas
2.3.2 Inelastic binary collisions
When two particles undergo an inelastic
binary collision,their kinetic energy is less
after the collision than it was prior to it.
One such process is the excitation of a
neutral atom by the energetic charged
particles.
If the neutral gas consists of molecules,
dissociation can occur,in which collisions
with energetic ion or electron will break up a
molecule into one or more of its constituent
parts.
Ionizing collision,in which one or more electron
is stripped away from the atom or molecule.
A charged-exchange collision results in
exchanging an electron between a cold neutral
atom or molecule and an energetic ion in plasma.
Finally,if a partially ionized plasma is of
atmospheric or greater density,significant
recombination can occur,Recombination must
be a three-body process,
2.3.3 Heterogeneous interactions at surfaces
Heterogeneous interactions are those which occur
between different states of matter,Most of these
heterogeneous interactions involve wall bombardment by
energetic free radicals,ions,or electrons,which can
result in knocking electrons (secondary electron emission)
or neutral atoms (sputtering or erosion) from the material
of the wall.
Recombination of ions and electrons when they reach a
surface from plasma;
Promoting catalysis
Deposition and coating of thin films because of a build up
of particles or induced chemical reactions or
polymerization on surface.
2.3.4 Plasma collisionality regimes
Lorentzian approach,electrons are assumed not
to interact with each other,and the positive ions
are considered to remain at rest.
Krook model,a refinement of Lorentzian gas,in
which the effective collision time is independent of
the particle momentum and energy.
Boltzman-Vlasov model,suitable for the fusion regime,a
high temperature plasma for which the collisional mean
free path is much larger than all of the characteristic
lengths of the system.
Fokker-Planck model,in which the motion of a colliding
particle in the velocity space of a fully ionized,highly
turbulent,or electric field dominated plasma is
determined by cumulative effect of weak deflections
resulting from distant encounters,or fluctuating electric
fields.
Homework:
1 Please give physical significances on these
functions listed below:
2 Please classify the heterogeneous interactions
at surfaces.
)( xvf?
0 )( dvvvf
3 Motion of Charges in Electric and
Magnetic Fields
An important difference between plasma and
ordinary neutral gases is that plasma responds
strongly to imposed electric and magnetic fields,
while neutral gases do not,This behavior of
plasma is important in many industrial
applications.
In order to better understand the behavior of
plasma,it is necessary to review the interaction
of individual charged particles and space charge
of one polarity with electric and magnetic fields,
3.1 Charged particle motion in
electric fields
A uniform
electrostatic field
can be generated
by two plane,
parallel electrically
conducting plates
The force on a charged particle by an
electric field is:
The force is a function of position and
conservative.
The electric field defined in terms of the
electrostatic potential V:
EqF?
)/( mVVE
The work done on the particle during a small displacement
dx in an electric field E is:
A definite work is:
Using Newton’s law,the work may be written as:
vdvmxd
dt
vd
mxdFdW
)( 21
2
1
2
1 VV
qdx
dx
dVqsdF
vv mm
v d vmdx
dt
dv
msdF
2
1
2
2
2
1
2
1
2
1
2
1
2
1


From above equations one obtains:
The constant W is the total energy of the motion,a
conserved quantity,The constant total energy is
In figure 3.1,an electron emitted with zero velocity from
cathode has a potential energy qVa,the electron
acquires kinetic energy at the expense of its potential
energy,as it finally hits the anode.
tc o n sWmqmq vVvV t a n
2
1
2
1 2
22
2
11
qVmW v 221
3.2 Charged particle motion in Magnetic Fields
The magnetic field is a field of force surrounding a current
flowing through a conductor,Magnetic field strength,H,
measured in amperes per meter in the SI system of units.
Magnetic induction,or magnetic flux density,B,measured
in tesla(T)
The relationship between the magnetic induction B and
magnetic field strength H is:
B=μH
where μis the magnetic permeability.
Plasma has a permeability equal to that of free space,μ0,
and thus B and H are related by a fixed constant in
plasma.
3.2.1 Magnetic particle dynamics
The force of a charged particle
moved in a magnetic field is
determined by equation:
This force is perpendicular to
both B and to the velocity v of
the particle,so this force
cannot change the kinetic
energy of the particle,only the
direction of its motion.
)( BvqF
Discussion:
The inability of a static magnetic field to do work
on a charged particle,or on a plasma,has an
important implications,
Magnetic containment of a plasma represents a
state of thermodynamic disequilibrium because
the entropy of the plasma can always increase
by expansion,
Only by applying electric fields or time-varying
magnetic fields can do work on plasma,and
resist this expansion across a magnetic field.
The character of the motion:
Supposing a charged particle
entering a uniform magnetic
field B with velocity v at right
angles,the force is:
The radius of gyration,R,is:
The angular velocity,or
gyrofrequency,is:
R
mqv BF v 2
qB
mvR?
)/( sr a d
m
qB
R
v
3.2.2 Particle trajectories in magnetic fields
The effects of a constant
magnetic field and of a
magnetic field gradient on
charged particles of opposite
sign are indicated in right figure.
Positive and negative charged
particles drift in opposite
directions when a plasma is
subject to a magnetic field
gradient,thus leading to
plasma polarization because
the particles have a smaller
radius of gyration in the
stronger field than they do in
the weaker field.
3.3 Charged particle motion in steady
electric and magnetic fields
If a particle is in a region where steady,
uniform electric and magnetic fields coexist,
the force on such particle is determined by
Lorentz equation:
)]([ BvEqF
3.3.1 Crossed-Field Particle Dynamics
An important case is,
electric field dominating
the plasma and the
electric and magnetic
fields being at right
angle,named
magnetron or crossed
fields shown in right
figure,
The components of Lorentz equation for
the crossed-field case are:
and
this equation states that vz is constant,so the
particle dynamics is confined to x-y plane.
BqvBvq
dt
d
m yxxv )(
BqvqEBvEq
dt
d
m xyyv )]([
0?
dt
dvm z
Using the angular frequency,
the equation listed above
can be written as:
This differential equation
can be integrated directly,If
a positive particle starts
from rest at the origin of the
coordinate system,the
integration is:
Putting this vx into
component equation of x
direction,one obtains:
dt
dyv
dt
dv
y
x
yv x
m
Eqy
dt
yd 2
2
2
Its solution is:
Where C1 and C2 are arbitrary constants of integration.
Differentiating this equation can yields the Y component
of velocity:
tCtCm Eqy s inc o s 212
tCtCv y co ss i n 21
If the initial conditions are,a positive
charge starting at the origin with zero initial
x and y velocities at time t=0,then C2=0
and C1=-Eq/mω2,the solution becomes:
Inserting this value into equation about vx
and integrating for the x motion,can yield
)c o s1(2 t
m
Eqy?

)s in(2 tt
m
Eqx

Finally,x and y velocities can be obtained
by differentiating:
t
B
Ev
y?s in?
)c o s1( t
B
E
v x
3.3.2 Crossed-Field Drift velocity
From the equations of vx and vy,it can be seen that the
average value of vy is zero,but the average of vx is not.
Crossed-field drift velocity (average velocity in x
direction):
Vx=vd=E/B
It predicts that both ions and electrons will move in the
E× B direction with the same velocity,and this velocity is
independent of the sign,mass and kinetic energy of the
charge.
tBEv y?s in? )c o s1( tBEv x
3.3.3 Magnetoelectric heating
Crossed electric and magnetic
fields may be used in a
magnetically contained plasma,
the magnetic field provides
gross containment,while the
electric fields are used to heat
the plasma and to improve
containment since they can do
work on it.
An example of a
magnetoelectrically contained
cylindrical plasma is shown in
right figure.
3.4 Charged particle motion in slowly
varying electric or magnetic fields
Slowly varying electric and magnetic fields are
those for which the inertia of charged particles is
small enough that they can respond freely to the
forces exerted by these fields.
Two examples of industrial importance will be
discussed,
the radio frequency resonant heating of a plasma;
the magnetic mirror,
3.4.1 Radio frequency resonant heating
Consider the electrons in a
magnetized plasma gyrating
in a constant magnetic field
which is shown in right figure,
The applied electromagnetic
field has a component in the
x direction in resonance with
the gyrofrequency of
electrons:
Gyrofrequency,ω
Phase:θ
Gyroradius,rg
)s in (0 tEE x
Figure (a),the phase
angle θ=0,At this point,
the electric field vector is
0.
Figure (b),the phase
angle θ=π/2,the electric
field is pointing in the
positive x direction,
opposite the velocity of
the electron,the electron
is accelerated.
Figure (c),the phase angle
θ=π,the electric field is 0.
Figure (d),the phase angle
3π/2,the electron velocity
vector is pointing in the
positive x direction,and the
electric field is again at its
maximum value,pointing in the
negative x direction.
So the x component of electric
field always accelerates the
electron and adds energy to
the electron during its entire
orbit.
The theory originally put forward
by Glasstone and Lovberg(1960).
The work done on the electron
shown in above figure is given by
the dot product of the
instantaneous force and the
differential distance,this
differential energy increase is
given by:
Quantitatively explanation on the process of
RF resonance heating
dsqdsqEsdEqd E s i n 20s i n
The differential energy along the orbit,
ds,is given by:
The gyroradius rg is given by:
Where ε┴is the perpendicular
component of the electron energy,in
joules.
dds r g?
qB
m
qB
m v
r g
2
1
)2(?

If the equation about ds is substitute into energy equation,
one obtains an expression for the differential energy
added to the perpendicular component of the electron
motion,
In one rotation of the electron about its gyrocenter the
energy added is given by:
Finally,the energy added is:
dqd rE g 20 s in
ErrE qdqsdEq gg 00 20 s i n2
B
mE 2
1
0 )2(?


The relationship of the difference in the gyroradius and
the energy increase:
The difference in the gyroradius per rotation is:
Thus,the increase in gyroradius per rotation is
independent of the electron energy,and is same for all
gyroradii,
21)2(
2
1

mqBd
d rr gg
2
0
qB
Emr
g

For an electron with an initial gyroradius,an initial
energy,and a final energy at a final gyroradius,the
number of gyrations,N,is given by:
)(
)2(
2
1
0
2
12
1
0

gg
gg
rqB
m
r
rr
N
)()
2
( 2
1
0
2
1
2
1
0
mE
B
N
The gyration frequency is a constant independent of the
energy.
The heating time required to go from an energy ε┴0 to
the energy ε┴ is given by:
gc
gg
C
H r
rrN

)(22 0
0
2
1
0
2
1
0
2
1
,)(
)2(2
cH
qE
m


In order for heating to be possible,this
heating time must be less than the particle
containment time,?0,or,the particle
collision time,?c,in the plasma,whichever
is smaller,The heating time is
independent of the confining magnetic
field strength,To minimize the heating
time required to achieve a given energy,
one must use as strong an electric field as
technological limitations will permit.
Question,what conditions must be asked for RF
resonance heating?
If charged particles can make several
gyrations between collisions,it then
becomes possible to use RF fields
oscillating at the resonant frequency of
gyration to heat plasmas.
3.4.2 Magnetic mirrors
Since many industrial plasmas are very hot,far from
thermodynamic equilibrium,and require a great deal
of energy to create and maintain,it is often helpful to
use constant magnetic fields to assist in confining
them,or to use magnetic fields instead of material
walls as plasma nozzles and diffusers.
These applications of a magnetic field work best when
the magnetic moment is an approximate constant of
the motion.
If the spatial gradients of the magnetic field are small,
the magnetic moment is approximately constant.
R is the gyroradius of the particle,and Z0 a
characteristic scale length of the magnetic field
gradient.
Magnetic moment,the current flowing around the
boundary of the gyro-orbit timing the enclosed area of
the orbit:
1
00

eB Z
mv
Z
R?
tc o n srIM t a n2
The radius of the orbit is the gyroradius,given by:
Where v┴ is the velocity perpendicular to the magnetic
field.
The current is,
And so the magnetic moment is:
Which is an approximate,but not an exact,constant of
the motion,
qB
mvRr
g

2
eevI
BBmvM 2
2
A magnetic mirror configuration is illustrated in blow figure.
In this cylindrical
coordinate system,the z
axis points along the axis
of the magnetic field.
m in
2
0
2
22 B
mv
B
mv

The right figure illustrates
velocity space for
particles in the region
0≤z≤z0.
The angle is the angle
between the direction,
and the total velocity
vector,such that,
s invv
If the confined plasma is free of electric fields,the
magnetic moment will remain constant as the
particle moves from the boundary of the uniform
plasma region at z=0,to the point of maximum
magnetic field at z=z0,
If the particle still has a non-zero parallel velocity at
the point z=z0,it will be lost to the right,Thus,the
particle that just reaches z=z0 at B=Bmax,and has
v//=0 at that point,is the particle on the verge of
confinement.
)()0( 0zzz
If the magnetic moment remains constant,its value at z=0
and at z=z0 must be the same,
Where θ2 is the escape cone angle in velocity space at z=0,
Within this angle in velocity space,particles in the uniform
plasma region on the left will be lost from containment
because they have too much parallel velocity,Outside the
escape cone,particles will remain confined for as long as
collisions do not knock them from the confined region into
the escape cone,This critical escape cone angle is found
from equation:
m a x
2
m i n
2
22
22
s in
B
mv
B
mv
21
m a x
m i n
2 )(s in B
B
Homeworks:
Using electron cyclotron resonance
heating (ECR) to heat electron,the radio
field being E=500sin107t (V/M),
Question:(1)the magnetic induction
(2)the heating time when a electron
energy being heated from 1eV to 10 eV.
Electron sources include heated filaments,
photoelectric emission,field emission,hollow
cathodes,and secondary electron emission.
5.1 Thermionic emission sources
Vacuum tubes and many other vacuum-
electronic devices require electron emission from a
cathode with current densities up to the Child law
limit.
5 Electron Sources and Beams
5.1.1 Physics of Thermionic Emission
The electrons in metal are trapped in a potential
well,show schematically in figure.
The depth of this potential well is equal to the work
function,Φ.
The band of mobile
electrons in the metal
has a width Φm,
giving a total band depth
Φb=Φ+Φm.
In above figure,the metal surface is at the
position indicated by the hatched line,In order for an
electron to escape the metal,it has to overcome a
potential barrier of Φ eV,At room temperature,this
does not happen to any significant extent,At high
temperature,in excess of 1000 K,electrons in the
metal acquire enough thermal energy so that the
more energetic of them reach the potential Φ and can
escape from the metal.
5.1.2 Richardson Equation
The emission of electrons from surface is given by
(A/m2)
where T,the temperature of the surface,
A,the emission constant,
Φ,the work function is the minimum
energy,in electronvolts,
When electrons are emitted from a
cathode surface according to the Richardson
equation,it is said to be thermionically emitting.
)ex p (2 TeATJ
The constant A and Φ are determined
experimentally by measuring the current density J,
emitted from a J/T2 as a function of 1/T on a semi-
logarithmic Richardson plot,illustrated in
right figure,
The work function Φ
is found from the
slope of the straight
line on this graph,
and the constant A
from the vertical
axis intercept.
Statistical mechanical theory predicts that for all metals
the parameter A appearing in the Richardson equation is
given by
A=4 πmek2/h3=1.2× 106Ak2/m2.
This universal,constant value of A is inconsistent with
experimental,since some metals have a value about half
this great.
For a range of clean refractory metals,the value of the
parameter A can range over the values
Special thermionic emitters include barium-
impregnated tungsten for low work function,and thoriated
iridium for low work function plus oxidation resistance.
2244 /102001030 KmAA
In a space-charge limited diode
with a thermionically emitting
cathode,the current of electrons
can be limited to less than the
Child law value by operating the
cathode at a temperature such
that less than the space-charge
limited current density Jc is
emitted and available,This is
illustrated on right figure,
where T1,T2,and T3 are
successively higher cathode
temperatures,and the straight
line relating the current density
to the cathode V0 across the
diode is the Child law current.
In conclusion:
At electron emitters,heated filaments have the
advantages of being a well known technology,
they are simple to construct,and they do not
require a gas flow to maintain their operation,
Among the disadvantages of heated filaments
as electron sources are a relatively short
lifetime,since the refractory materials of which
filaments are made are subject to chemical
attack,and high power consumption,leading to
cooling problems.
5.2 Photoelectric Emission Sources
5.2.1 Photoelectric effect
Electrons acquire enough energy
from the photons associated with
incident electromagnetic radiation
to overcome the work function,Φ,
of the solid material,For this process
to happen,the frequency of the
incident radiation must be above the photoelectric threshold,
νmin,given by νmin=eΦ/h (Hz),The energy of electrons
emitted from a surface is given by (Albert) Einstein’s
photoelectric equation,
ε=h(ν-νmin) (J)
5.2.2 Photoelectron Current Densities
An upper bound on the electron density possible by
photoelectric emission can be calculated on the assumption that the
incident radiation emission has a frequency ν=νmin,and a power flux
SW/m2,to give a flux of photoelectrons.
Гe=S/eε’min=S/hνmin=S/eΦ (electrons/m2s).
The current density of these electrons is
Je=eГe=S/Φ(A/m2).
For ordinary levels of illumination,exemplified by the solar
constant S=1338W/m2,and a characteristic work function of Φ
=1.5eV,the electron current density would be Je≈93 mA/cm2,If one
had an intense ultraviolet source with S=108 W/m2 and a surface
with a work function Φ=4.5eV,the electron current density would be
as high as 2200 A/cm2.
5.2.3 Applications
Practical limitations on the intensity of ultraviolet
sources have restricted use of the photoelectric effect to
stabilizing dark discharges in the Townsend regime,
stabilizing glow discharges,and to initiating electrical
breakdown between electrodes.
As UV lasers become available for industrial plasma
applications,photoelectric emission in applications
where hot cathodes or strong electric fields are
inconvenient,Also,a photo-emitting cathode can be
operated at room temperature,an advantage in many
applications.
5.3 Field Emission Sources
Field emission sources operate by placing such
a high electric field on a metal (or insulator) that
electrons are pulled out of the surface by
electrostatic forces.
Consider a small hemispherical point of radius
r raised to the potential V0,shown in right figure.
The electric
field at the surface
of the tip is given
by E=V0/R (V/m)
it is not too difficult to apply potentials
V0=10kV to sharp points,the radius of
curvature of which is R=10-6m,Electric fields
at the tip can therefore reach magnitudes of
1010V/m,a value high enough that field
emission can occur.
5.3.1 Physics of field emission
If the electric field given by
equation E=V0/R (V/m) is high
enough,electrons can be pulled
out of the surface by field
emission,the physical
mechanism of which is
illustrated in right figure,
This figure shows a
schematic energy level diagram
for electrons in a metal or
insulator,in which the band of
electron energies is depressed
by the work function Φ below the
reference potential.
Imposition of a strong electric field results in a
potential as a function of distance above the surface
of the metal given by the line ACD,Beyond the point
C,an electron outside the metal would have a
potential lower than its value inside the metal; this
provides a driving force for quantum mechanical
tunneling of electrons from B to C,through the
potential barrier immediately above the surface of the
material,This process was studied by Fowler and
Nordheim:
Jf=CE2exp(-D/E),C and D are constant.
Study indicates the enormous capability
of field emission to emit electrons from
materials,provided only that the electric
field at the surface be above approximately
5 GV/m,Although such electric fields may
appear very large,they can be produced by
potentials of the order of tens of kilovolts,
applied to fine points or asperities with
characteristic dimensions of the order of 1
um.
The advantages of field emission include a
relatively small power consumption,operation at
room temperature,not being space-charge limited,
and a relatively long lifetime,Disadvantages of
field emission as an electron source include the
facts that,to avoid electrical breakdown,these
sources are usually operated in a pulsed mode
only; that very high potentials and/or electric fields
are required to exhibit the phenomenon of field
emission; and that sputter erosion of the emitting
tip can reduced the high electric fields required to
exhibit the phenomenon of field emission.
5.4 Hollow cathode sources
Hollow cathode sources have been
extensively developed since 1965,and have
come into widespread use because of their
several advantages over other electron sources,
such as the thermionic filament,Applications of
this source have proliferated without an
adequate analytical theory of the physical
processes by which they operate.
5.4.1 Alternative Configurations
the Lidsky hollow cathode
In this source,a hollow tube constricting in diameter
to a capillary-like nozzle is operated with gas flowing
axially through the tube and into the plasma chamber on
the right,The Lidsky cathode is maintained at a
negative potential with respect to the surrounding
plasma,so that ion bombardment heats the small
capillary tube,maintaining a plasma inside.
This arrangement is hard to initiate and maintain in
the steady state,so a later modification included a
cylindrical heater to raise the cathode to incandescence.
Among the many modifications developed over
the years,many of them for electrostatic ion
engines intended for space propulsion are the
plasma bridge cathode shown in figure (b) ; the
hot-tube hollow cathode in figure(c),in which the
side wall is heated by electrical currents flowing
through concentric tubes to the thin annular side
wall surrounding the plasma; and the coil-heated
hollow cathode,shown in figure (d),in which
electrical currents flow axially along concentric
tubes,and heat a coiled electrical filament which
surrounds the hollow cathode plasma,Hollow
cathodes are usually run with a ‘keeper’ electrode
about 1cm downstream of the capillary nozzle,
which draws a small current that maintains and
stabilizes the plasma in the hollow cathode.
Homework:
Please design a electron source with
current density of 1A/cm2 and beam
diameter of 2mm,The answer should
include the principle and structure of the
electron source.
5.4.2 Foil-enhanced Hollow Cathodes
Two highly evolved versions of the hollow cathode
include that developed for space applications by
Poeschel et al (1979) shown in figure 5.8,and the
tungsten (1988),These sources were intended to
operate with mercury vapor,the propellant of ion
engines for space applications,Hollow cathode
sources of these designs were capable of operating for
10000 hours or more; they both featured a concentric
keeper electrode a few millimeters downstream of the
exit of the hollow cathode; they were approximately 4
mm in diameter; and they were capable of emitting
several amperes of electron current.
Hollow cathodes have come into relatively widespread use as
electron sources in the last two decades,after having been
extensively developed for the space program by NASA,Advantages
of the hollow cathode include its long lifetime,measured in the best
cases in tens of thousands of hours; small size; small power
consumption,relative to thermionic filaments; and the further
advantage that they can ionize almost any working gas which flows
axially through them,Their disadvantages include a relatively
complex design in which optimum operation depends on proprietary
materials and unpublished lore,The operation of hollow cathodes is
difficult to derive from first principles,and a basic understanding of
the physical processes operating in the devices is lacking,Hollow
cathodes have a major disadvantage in that they require a gas flow
for their operation,to maintain the intense plasma in the final nozzle
from which the electrons are drawn,This gas throughput can be an
advantage when one needs to ionize the working gas,but it can be
a disadvantage in an application for which only electron current is
desired.
5.5 Secondary Electron Emission Sources
Secondary electron emission from the
cathodes plays a key role in maintaining the
currents which flow in the Townsend and in
glow discharge,Because the current densities
available from secondary electron emission
are relatively small compared to the current
densities available from the electron sources
discussed above,electron sources based on
secondary electron emission are relatively
infrequently used.
Secondary electron emission sources,like that shown
schematically in figure 5.10,are based on the secondary
emission of electrons by ion impact,This process is
characterized by the secondary electron emission
coefficient,γe=# of electrons emitted / # of ions incident
on surface,For ions impacting the cathode with keV
energies,the secondary electron emission coefficient
can be grater than one,Secondary electrons may also
be emitted by energetic electron impact on an anode.
The importance of secondary electron emission as an
electron source is most frequently manifested in the
transient initial build-up phrases of normal glow or arc
discharges,In these regimes,secondary electrons
provide a current until the electron-neutral ionization
process can provide a volumetric source of electrons
which maintains a plasma in the steady state.
5.6 Source and Beam Characteristics
Many military,aerospace,and plasma
processing applications require the generation of a
beam of energetic or electrons,If beam focusing
and a monoenergetic energy distribution are not
critical requirements,one or more of the electron
sources discussed in this chapter are often
adequate,However,if an application demands a
parallel or well-focused electron trajectory,or a
monoenergetic energy distribution,then the
electron source of choice is usually based on a
system of plane parallel grids,operating at,or just
below,the space-charge limited current,in
electron beams,and the figures of merits by which
electron sources may be characterized.
5.6.1 Beam Parameters
In a unidirectional beam,such as might be
produced by one of the sources discussed
above,the velocity reached by a particle of mass
m as the result of being accelerated across a
potential V0 is given by the beam velocity,
υb=(2e V0/m)1/2 (m/s),The number density of the
charges in a space-charge limited beam is equal
to that at the acceleration electrode,given by
equation ne(d)=4ε0 V0/9ed2=nA,nb=na=4ε0
V0/9ed2 (electrons/m3)
The particle flux in the space-charge limited beam of
figure5.11 is given by combining the above two
equations,Гb=Jc/e=υb nb=4 ε0 (2e/m)1/2 V03/2/d29e
(electrons /m2) where d is the separation of the two
grids across which the potential V0appears,This
expression is,of course,the child law.
The beam power flux is given by the product of the
accelerating voltage and the space-charge limited
current density floeing between the grids,pb= Jc V0=4 ε0
(2e/m)1/2 V05/2/d29 (w/m2),It should be noted that
because of the very large difference between ion and
electron masses,the power flux carried by electron
beams,thus making it necessary to avoid impingement
of electron beams on accelerating grids,and to provide
adequate cooling of the target on which an electron
beam is collect.
5.6.2 Figures of Merit for Electron Sources
Referring to figure 5.11,the total beam current is
given by Ib=3.14D2J/4 (A) where D is the diameter of
the beam,and j is the current density,the upper limited
of which is the child law current,A source with an
extraction voltage V0 and an initial beam cross sectional
area A=3.14D2/4 will have a perveance ρ≡Ib V03/2
(A/V3/2) where equation Ib=3.14D2J/4 (A) has been
substituted for the total current,The perveance allows
one to compare the performance of a specific,actual
design to an idealized child law diode with no webbing
in the accelerator grids,no beam divergence,etc,For
an electron source with fixed cross-sectional area,ρ
depends only on the geometry of the extractor and
accelerating grids,The larger is the perveance,the
better the source design.
The design required to produced an electron
beam is composed of the beam power pb of
equation pb= Jc V0=4 ε0 (2e/m)1/2 V05/2/d29 (w/m2),
and power required to operated the source,ps the
surce power may be written ps=pd+pf+p0= IbV* (W)
where pd is the power required to maintain a source
discharge (such as a hollow cathode),pf is the
power required to supply filaments or cathodes,and
p0 is other power drain required to maintain the
source,Ib is the beam current,V* is the eV per
beam electron required in the source to produce
each electron,For electron sources,the minimum
valve of V* is the wor kfunction of cathode,shown
for selected materials in table 5.1.
The total power required by the source is
given by pt=pb+ps=Ib(v0+v*) (W),The electrical
efficiency of the source,ηE≡pb/ pt= v0/ (v0+v*)
(W),Equation ηE≡pb/ pt= v0/ (v0+v*) can be
written ηE=1/(1+v*/v0),The electrical efficiency is
plotted as a function of the ratio v*/v0 on figure
5.12,by making a calorimetric measurement of
the beam power,and measuring the total
electrical energy into the source,ηE can be
calculated and v* found from figure 5.12.
5.7.2 Current Density Enhancement
To enhance the current density above the child
law limit,at least two possibilities exist,One is the
bipolar diode shown in figure 5.13,in which one
maintains a potential v0 across a gap of width χ=d.
The effect of the space-charge cloud between the
electrodes is produced by emitting electrons or
negative ions from the cathode,and positive ions from
the anode,It has been shown by Howes (19650) that
this partial neutralization of the space charge between
the electrodes will allow higher than child law currents
to flow,but such an arrangement is to set up in
practice.
5.7.3 Electrostatic Beam Deflection
Many situations arise in which it is desirable
to electro statically deflect beams of charged
particles,Probably the most important and
widely used device incorporating these
principles is the electro statically deflected
cathode ray (electron beam0 tube,found in all
oscilloscopes,The oscilloscope was invented in
the year 1897 by the German physicist
Ferdinand Braun (1850-1912).
The functioning of an electro statically
deflected cathode ray tube is shown on the
diagram in figure 5.15,On the left,an electron
gun accelerates electrons though a potential Va
and forms a small,cylindrical,well-focused
electron beam which travels to the right between
two flat metal deflection plates of length? and
separation d,When no deflection potential Vd is
applied between the deflection plates,the
electron beam travels in a straight line along the
χ axis and impinges at the center of the screen
on the right,When a positive deflection voltage
Vd is applied to the lower plate,the resulting
electric field deflects the electron beam by an
angle θ,and the beam impinges on the screen a
distance D from the centre.
If the deflection plates are plane and parallel,the
electric field between them can be written in terms of the
deflection voltage and separation as E=Vd/d (V/m),While
the electron is between the deflection plates,the
equation of motion in the plate of the diagram may be
written and,Integrating the equation of
motion for the y direction once,one obtains if the
electron enters the deflection region at y=0 and at tine
t=0,Integrating equation (5.34) again,one obtains the y
deflection of the electron as a function of time while it
remains between the deflection plates,since the y
velocity is 0 when the beam enters the region between
the deflection plates,In the χ direction,integration of
equation (5.33) yields,
Thus,the electric field in the y direction does not
affect energy or velocity of the particle in the χ direction
orthogonal to it,The constant χ velocity of the electron
as it moves between the plates is determined by the
conservation of energy in the electron gun at the left,
(formula),Because the χ velocity is constant,the time-of-
flight of the electron between the deflection plates is
given by (formula),Substituting this time-of-flight into
equation (5.34) yield the y vecolity at the time the
electron leaves the deflection region,(formula),This
velocity,when substituted into equation (5.35),yield the
vertical deflection of the electrons as they leave the
deflection region,(formula) where equation(5.37) has
been used to eliminate v0,
If we ignore the effect of fringing field,the electrons will have no
forces acting on them after they leave the deflection region between
the plates,so the tangent of the deflection angle is given by the ratio
of the y and χ velocities as the electron leaves the deflection region,
(formula),Equations (5.37) and (5.39) have been used to get the
right-hand member of equation (5.41),From the trigonometry of
figure 5.15,the final deflection D on the screen is given by (formula).
Substituting equations (5.40) and (5.41) into (5.42) yield the following
expression for the y deflection on the oscilloscope screen,(formula).
The deflection angle and deflection distance on the screen are
independent of the mass and charge of the particle beam being
deflected,and depend only on the geometry and the initial energy of
the particles,Of great practical importance id the fact that deflection
on the screen is directly proportional to the deflection voltage Vd,so
that the oscilloscope is a linear instrument for measuring voltages,In
actual oscilloscope tubes,a second set of deflecting plates,at right
angles to those shown in figure 5.15,deflects the electron beam in
and out of the plane of the figure,thus providing a time base for the
measurement of time-varying electrostatic potentials.
5.7.4 Magnetic Beam Deflection
A second method to deflect a charged particle beam
is the use of a static magnetic field,Since the magnetic
force q (v× B) is perpendicular to the velocity at all times,
magnetic deflection does not add energy to the deflected
particles,As an example of magnetic deflection,we will
use the magnetically deflected cathode ray tube,
illustrated in the figure5.16,In this figure a uniform
magnetic induction B is applied in a region of width? with
sharp boundaries at χ=0 and χ=?,Electrons are
accelerated through a potential Va in an electron gun to
the left,and impinge on the deflection region,within
which they move with a constant radius of curvature R
given by (formula).
After being deflected by an angle θ,the electrons exit
the deflection region at χ=?,at a distant y below the χ
axis,Appling the Pythagorean Theorem,one obtains
(formula),Simplifying,this equivalent to (formula) from
which the final deflection distance y may be obtained
using the quadratic formula,(formula),From the
geometry of the figure,the deflection angle θ of the
electron beam may be written (formula),Substituting
equations (5.47) and (5.48) into equation (5.49) yields for
the total deflection D,(formula),If the width of the
deflection region is much smaller than the radius of
gyration of the electrons in the magnetic induction B,the
usual situation,the expressions involving this small
quantity in equation (5.50) may be simplified using
(formula),Substituting equation (5.51) into equation
(5.50),and neglecting all terms higher than second-order
in?/R,the deflection on the screen may be written with
the help of equation (5.54) as (formula).
The deflection of an electron beam on the screen of a
magnetically deflected cathode ray tube is thus
proportional to the magnetic induction B,The induction B
is generated by two coils,one each above and below the
plane of the diagram of the figure 5.16,This magnetic
induction is proportional to the current flowing in these
coils and thus,foe small deflection angles θ,the
magnetically deflected cathode ray tube is a linear
instrument foe measuring current,in contrast to the
electro statically deflected cathode ray tube,which is a
linear instrument for measuring voltage,In actual tubes,
a second pair of coils deflects the beam in and out of the
plane of the diagram in figure 5.16,providing a time
base.
5.7.5 Comparative Deflection Capabilities
Sometimes it is not obvious whether electric or
magnetic beam deflection is the method of choice,If
equations (5.41) and (5.48) are used to examine the
relative beam deflection capabilities of electric an
magnetic field for the same small deflection angle,θ≈ sin
θ ≈ tan θ,then equations (5.41) and (5.48) yield
(formula),This equation allows us to relate the electric
field and magnetic induction required to produce the
same small deflection angle of a charges particle beam.
Solving equation (5.53) for the electric field,one obtains
(formula),Thus,the electric and magnetic fields required
for the same deflection angle are related by the beam
velocity,vb.
In the presence of a plasma or other source of
ultraviolet radiation,it is difficult to maintain electric
fields higher than approximately 1MV/m,(formula)
where A is the atomic mass number of the species
being deflected,The relationship represented by the
equality in equation (5.55) is plotted on figure 5.17,For
a given particle energy Va,both electrostatics and
magnetic deflection are feasible below the curves; from
the curves to B=1.5T,magnetic deflection is feasible,
and beyond 1.5T,even magnetic deflection becomes
technically difficult,usually requiring superconducting
magnetic.
If the beam current density is high that its
space-charge shields against electrostatic
deflection,magnetic fields may be the deflection
mechanism of choice,Another consideration is
that beam deflection with electric fields is not
mass selective,but magnetic deflection is,Thus,
if a source produces a spread of isotopic
masses which one wishes to maintain in a beam,
electric field deflection can accomplish this,
while magnetic deflection would not.
Finally,because a static magnetic induction
cannot do work on a charged particle,magnetic
deflection does not add energy to the deflected
particle,while electrostatic deflection adds,from
equation (5.39),an amount of energy given by
(formula),This energy added by the electric field
can be substantial,and is often undesirable.
5.7.6 Paraxial Beam Transport
If an accelerating
electrode configuration
is not properly
designed,electrode
impingement,illustrated
in right figure,
and beam divergence,
illustrated in next figure,
can result.
Electrode
impingement leads
to a parasitic drain
on the source
power supply and
a requirement for
electrode cooling;
beam divergence
is undesirable in
many applications,
To maintain a parallel beam of charged particles
through accelerating electrodes,consider the section
between two plane parallel electrodes indicated
schematically by the dotted lines on figure (a),If one
wishes to create a beam equal to the width of the dotted
lines in figure (a),one must ask what configuration of
electrodes required to ‘make up’ for the missing
electrons outside the beam which maintain parallel
trajectories,The answer is the (pierce) configuration,
originally suggested by pierce (1940,1949) and shown
in figure (b),which maintains electric field lines parallel to
the beam,And gives rise to trajectories which do not
interest the electrodes,Such impacts,if they should
occur,lead to parasitic power losses,electrode heating,
and electrode erosion.
5.7.7 Beam Focusing
If one has a well collimated,parallel
beam at its source,like those discussed
in the previous section,it can be
brought to a focus 9or defocused) with
an electrostatic lens like that shown
schematically on figure 5.23,Adjusting
the voltage V? adjusts the focal length of
this configuration.
8 Low pressure electrical
discharge
Most early research on
electrical discharge physics
was performed on the
classical low pressure
electrical discharge tube.
1 dark discharge
(a) background ionization
(b) the saturation regime
(c) the Townsend regime
(d) Corona discharge
(e) Electrical breakdown
2 Glow discharge
(a) The normal glow discharge
(b) The abnormal glow discharge
3 Arc discharge
(a) The glow-to-arc transition
(b) Nonthermal arcs
(c) thermal arcs
Voltage-current
characteristic
8 Dark discharge in gases
8.1 Background ionization
The dominant physical process in the
background ionization division from A to B in
figure is due to ions and electrons created by
ionization from background radiation,Such
radiation,from cosmic rays,radioactive
minerals in the surrounds,or other sources,is
capable of producing a constant and
measurable degree of ionization in air at
atmospheric pressure.
This same ionization process is
active in a classical DC low pressure
dark discharge like that shown in
foregoing figure,When an electric field
is imposed along the axis of such a
cylindrical discharge tube,the ion and
electron pairs formed by ionizing
radiation migrate to the electrodes in
the imposed electric field,giving the
weak current illustrated from A to B in
figure 8.1,
Fig.8.1
Fig.8.2
8.2 SATURATION REGIME
If the voltage between the electrodes on the
DC low pressure discharge tube of figure 8.2 is
increased far enough,eventually all the
available ions and electrons produced in the
volume between the electrodes will be collected,
leading to saturation of the current between the
points B and C on figure 8.1,If the volumetric
source of ions and electrons from ionizing
radiation is given by the source strength,S,it
can be written
S = dn/dt （ electrons or ions/m3-s） (8.1)
The saturation current is given by
IS=AdeS(A) (8.2)
Where A is the cross-sectional
area of the discharge,
d = L is the length of the discharge
The total currents are typically of the
order of picoamperes or nanoamperes.
These currents are independent of the
applied voltage but linearly dependent
on the radiation source strength,S,a
regime useful in some radiation
counters,The saturation current
density JS is given by
Js=Is/A=edS(A/m2) (8.3)
8.3 TOWNSEND DISCHARGE
Processes of industrial
importance occur in the Townsend
discharge,including corona and the
electrical breakdown of dielectric
gases.
Consider an analysis for which the
electric field E is constant along the axis
of the low pressure discharge tube
shown on figure 8.2,In such a
discharge,consisting of two parallel
plates with a uniform electric field
between them,additional electrons can
arise from photo- or secondary electron
emission from the cathode,with a flux
given by:
Ge0 (electrons/m2-s)
A second,volume ionization source can be
present,due to ionization of the background gas
by energetic electrons accelerated in the electric
field,This volume may be written
(Electrons or ions/m3-s)
where the neutral number density density,
and is the Maxwellian-averaged
reaction rate coefficient for electron-neutral
impact ionization.
neeee nnRS0
en
ne
8.3.1 Current Growth
If the voltage across the low
pressure discharge tube is
increased beyond point C on
figure 8.1,the current will rise
exponentially,The physical
process responsible for this is
indicated in figure 8.3.
The electrons initially produced in the creation of
ion-electron pairs by ionizing radiation or from other
sources are accelerated in the electric field of the
discharge tube,If the electric field is high enough,
the electrons can acquire sufficient energy before
reaching the anode to ionize another neutral atom.
As the electric field becomes stronger,these
secondary electrons may themselves ionize a third
neutral atom,thus leading to a chain reaction,or
avalanche of electron and ion production,This
region of exponentially increasing current between
C and E on figure 8.1 is called the Townsend
discharge.
Fig.8.3
8.4 CORONA DISCHARGES
Corona,sometimes referred to as a
unipolar discharge,is a
phenomenon characteristic of
Townsend dark discharges which
occurs in regions of high electric
field near sharp points,edges,or
wires in electrically stressed gases
prior to the point of electrical
breakdown.
If the coronal current are relatively high,corona
can be technically a ‘glow discharge’,visible to the
eye,For low currents,the entire corona is dark,
appropriate to the dark discharges with which we
classify it,Related phenomena include the silent
electrical discharge,an inaudible form of the
filamentary discharge,and the brush discharge,a
luminous discharge in a non-uniform electric field,
in which many corona discharges are active
simultaneously and form streamers which
penetrate the high electrically stressed gas
surrounding the point of initiation.
8.4.1 Phenomenology of Corona
The phenomenology of corona
may be understood with the
assistance of figure 8.4.
Corona should not be confused
with sparking,or electrical
breakdown,Sparking or
electrical breakdown is usually a
transient,localized,high current
discharge,while corona is a
very low current,continuous
phenomenon,the currents of
which are orders of magnitude
smaller than those that flow
during electrical breakdown.
Fig.8.4
The breakdown voltage in kilovolts at standard
temperature and pressure of dry air is given by,
VB = 3000d +1.35 kV (8.35)
for plane,parallel electrodes separated by the
distance d,in meters,The breakdown electric field is
found by dividing equation (8.35) by the gap width d,
to obtain
EB=VB/d=3000+1.35/d (kV/m) (8.36)
Thus,the breakdown electric field for dry air at
standard atmospheric conditions is about 3 MV/m,
or 30 k V/cm.
When the local electric field around
points or fine wires exceeds the
breakdown field given by above
equation (8.36),corona results,Around
a sharp point or a fine wire like that
shown in figure 8.4,the electric field
will be a maximum at the surface of
the inner conductor,and will decrease
with radius and reach a minimum
value at the outer electrode.
When the applied voltage,V0,is higher than
necessary to initiate corona,the electric field will
drop off to the breakdown value given by equation
(8.35) at a radius r0 called the active radius of the
coronal discharge,and it is within this active
volume that most corona-initiated plasma
chemistry occurs,At pressures near one
atmosphere,electrons attach to oxygen quite
readily,and therefore the electrical current
between the active radius and the outer electrode
is carried by either negative or positive ions,
depending on the polarity of the voltage applied to
the inner electrode.
A continuous or intermittent current,usually
of the order of microamperes to
milliamperes per decimeter of length,will
flow to the power supply,with positive
polarity resulting in a continuous,DC
electrical current,and negative polarity
usually resulting in a pulsed or intermittent
current,Electrons may participate in the
current in the active volume,but in air and
other gases are quickly attached to form
negative ion species.
Corona can occur for both positive and negative
polarity,with little difference in their initiation
voltages or coronal current,Corona can initiate on
sharp points at potentials as low as 5 kV,On a fine
wire,corona can manifest itself as a cylindrical
glow (polished polarity),or a string of approximately
equally spaced beads on a polished wire (negative
polarity),Corona can initiate from sharp points,fine
wires,sharp edges,asperities,scratches,or
anything which creates a localized electric field
greater than the breakdown electric field of the
medium surrounding it.
8.4.2 Application of Corona
Corona has many important industrial
applications,including electrostatic
precipitators,xerography,modification of
surfaces to alter their wettability or printing
ink.
Corona is used industrially for antistatic
applications,in which materials such as
photographic film and plastic sheet have
surface charge neutralized by exposure to
corona.
There are many large-scale applications of
corona and corona-like filamentary
discharges to plasma chemistry,probably
the largest scale of which is the
commercial production of ozone in Europe
for use in treating public water supplies.
Many other chemical compounds of
industrial importance can be created in a
coronal discharge,A common feature of
most of these industrial applications is that
they are based on coronal discharges
around fine wires.
8.4.3 Detrimental effect of Corona
In addition to the commercial
applications discussed above,corona
has a variety of effects which must be
dealt with or eliminated,Some of these
effects include power lines loss,in
which coronal losses from high voltage
overland transmission lines can exceed
the resistive losses,particularly in
humid or snowy conditions.
When corona occurs on an electrical
conductor,it is capable of forming
detrimental chemical species in air,
including ozone,NO2,and nitric acid in the
presence of water vapor,These species
can attack the electrical conductor itself as
well as surrounding insulators.
When the voltage on an electrical
conductor exceeds approximately 20
kV,x-rays may be produced by
corona,which become progressively
more penetrating as the voltage
increases,This phenomenon
apparently has not led to
commercially useful x-ray sources,
but it can be a serious personnel
hazard in high voltage equipment.
Finally,corona is capable of
producing audible noise when it
occurs,for example,on high
voltage transmission lines,Under
the proper atmospheric conditions,
coronal noise can exceed
accepted standards for the
exposure of residential
communities.
The detrimental effects of corona
discussed above are mostly the result
of coronal discharges from fine points.
Thus,in order to minimize or
eliminate these effects of corona,it is
necessary to understand theoretically
the generation of corona around fine
points and sharp edges of a kind that
produce corona on high voltage
equipment.
8.5 Corona sources
8.5.1 Corona from a point
As was remarked above,in order to
eliminate the detrimental effects of
corona,it is usually necessary to
understand the generation of
corona by a sharp point.
Consider a sharp point with a spherical
radius r=a at a potential v0 in the center of
a spherical cavity wall with radius r=b and
potential v=0,Both the sharp point and the
surrounding grounded cavity wall are
electrically conducting,The breakdown of
the surrounding air and the visible corona
illustrated in figure 8.15 extend out to the
active radius r=r0.
Fig.8.15
The radius electric field and potential distribution
for low corona current,i.e,ρ(r)≈0,will now be
calculated,For this zero charge density limited,
Poisson’s equation becomes,for a spherically
symmetric point in a spherically symmetric cavity,
(8.37)
Since we have assumed spherical symmetry,the
potential and electric fields are functions of radius
only,From equation (8.37),it follows that
(8.38)
0)(1
0
2
2
Er
dr
d
r
E
tco n srEr t an)(2?
using equation (8.38),we can write
(8.39)
where Es,Eb,and Ew are the electric field
strengths at the surface of the point; the
active radius,where it is equal to the
breakdown electric field; and at the wall,
respectively,Using the two left-hand terms
of equation(8.39),we may write
WBs EbErEaEr
22
0
22
(8.40)
Integrating both sides of equation (8.40)
between the limits a≤r’≤r,one obtains
(8.41)
which gives the electrostatic potential
(8.42)
2
2
r
Ea
dr
dVE s
r
a
S
r
a
S
V
V r
Ea
r
drEarVVdV |)( 2
2
2
0
0

)11()( 20
ar
EaVrV s
We evaluate the electric field at the surface of the
point,where E=Es,by setting V(r)=0 at the radius
r=b,to obtain
(8.43)
Solving for the electric field Es,we obtain from
equation (8.43)
(8.44)
Substituting equation (8.44) into equation (8.40),
the radial electric field at the radius r,we obtain
(8.45)
)1(0
b
aaEV
s
))/(1(
10
baa
VE
s
)(
)( 2 0
abr
a b VrE
If we substitute equation (8.44) into
equation (8.42),the radial potential profile
for the low coronal current case is
obtained,
(8.46)
)(
)(]
)(
)(1[)(
00 abr
rbaV
abr
arbVrV


If the coronal current is significant,so that the coronal charge
density cannot be neglected,the coronal current can be written in
terms of the current density,
(8.47)
The total coronal current flowing between the point and the
surrounding spherical electrode is not a function of radius,The
current density appearing in equation (8.47) can be written as
(8.48)
where the radial drift velocity υd can be written in terms of the ionic
mobilityμi and the radial electric field,
(8.49)
Substituting equations (8.49) and (8.48) into equation
(8.47),and solving for the charge density yields
(8.50)
Substituting this ionic charge density into Possion’s
equation,equation (8.37),yields for the spherical
geometry
(8.51)
Rearranging equation (8.51) yields Possion’s equation
in the form
(8.52)
Integrating both sides of equation (8.52),one obtains
(8.53)
where Es is the electric field at the surface of the point,
where r=a,Equation (8.53) allows us to solve for the
radical electric field at the point r,which is given by
(8.54)
We can relate the voltage on the point,v0,to the
surface electric field,Es,by integrating the potential from
v0,at r=a,to the potential V=0,at r=b:
(8.55)
where the constants A and C are given by
(8.56)
Integrating equation (8.55),the potential V0 is given by
(8.57)
This integral does not appear in standard tables,This
equation relates the surface electric field on the sharp
point to the applied potential V0.
One can be obtained an expression for the radial
potential profile,Returning to equation (8.52),the
potential V(r) is a solution of the differential equation
resulting from Possion’s equation,
(8.58)
The potential distribution V(r) is a solution to the
nonlinear second order differential equation,
(8.59)
Here again,closed form solutions for V(r) do not appear
to be available.
8.6 ELECTRICAL BREAKDOWN
Many industrial applications of plasma involve high
voltage,so the phenomenon of electrical breakdown is
of great importance,both to initiate it when desired,and
to prevent it when necessary,Consider the classical
dark discharge configuration shown in figure 8.3,We
will examine the Townsend discharge with the emission
of a current of secondary electrons from the cathode on
the left,due to ion or photon impact,This is also
pertinent to the parallel plate geometry shown in figure
8.4,which is widely used in electrical breakdown
studies.
8.6.1 Current in the Townsend Discharge
Define a secondary electron emission coefficient?,
#of electrons emitted / # of incident ions or photons (8.124)
which is the number of electrons emitted from the cathode per
incident ion or photon,In classical electrical discharge tubes in the
Townsend region,the ion energies are generally low,and values of?
are characteristically of the order of 10-2 or less,From equation (8.9),
the flux of electrons on the anode is given by
(8.125)
Where d is the separation of the anode and cathode,α is Townsend’s
first ionization coefficient,and Гea is equal to the electron flux at the
anode from all sources.
edecea eG?G
The quantity Гec is the total electron
emission from the cathode,and is equal to
(8.126)
where Gec is the flux of electrons from the
cathode by secondary electron emission,and
Geo is the electron flux from the cathode due
to photoemission,background radiation,or
other processes.
0eesec G?G?G
In the steady state,the ion flux arriving at the
cathode must equal the difference between the
electron flux arriving at the anode,and the
electron flux emitted from the cathode,
(8.127)
Substituting equation (8.125) into equation
(8.127) and re-arranging,one obtains the
cathode flux of electrons due to secondary
emission,
(8.128)
ic
es
ecea G?
G?G?G
)1(?G?G deces e
Making a further substitution of equation (8.128)
into equation (8.126),the total electron flux from the
cathode is
(8.129)
Solving for the electron flux from the cathode,
(8.130)
Substituting equation (8.130) ento equation (8.125),
the electron flux to the anode is
(8.131)
ecdeceesec e GG?G?G?G )1(0
)1(1
0

G?G
d
e
ec e
)1(1
0

G?G
d
d
e
ea e
e
By multiplying both sides by the
electronic charge and the electron
number density,one can write
equation (8.131) in terms of the
current density in a plane parallel to
the electrode surfaces,
(8.132)
)1(10
d
d
e
e
jj
9 DC Electrical Glow Discharge in Gases
The glow discharge regime owes its name to
the fact that the plasma is luminous,This
luminosity arises because the electron energy
and number density are high enough to
generate visible light by excitation collisions.
The glow discharge regime finds
widespread industrial applications in
lighting devices such as the classical
electrical discharge tube used in
fluorescent lights; DC parallel-plate
plasma reactors; ‘magnetron’ discharge
used for depositing thin films; and
electron-bombardment plasma sources,
Some configurations of the glow
discharge are shown next,
9.1 phenomenology of dc glow
discharge
As the voltage across the classical DC
low pressure electrical discharge tube is
increased through the dark discharge
regime,the current increases exponentially
in the Townsend discharge.
As one approaches the breakdown
voltage,one of two things may happen,
depending upon the internal resistance of
the power supply is very high,such that it
can deliver only extremely small currents,
the discharge tube cannot draw enough
current to breakdown the gas,and the
tube will remain in the corona regime with
small corona points or brush discharges
being evident on the electrodes.
If,however,the internal
resistance of the power supply is
relatively low,then the gas will
breakdown at the voltage Vb,and the
discharge tube will move from the
dark discharge regime into the low
pressure normal glow regime.
9.1.1 Low pressure normal glow
discharge
The glow discharge regime is shown in
greater detail in figure 9.2,The left-hand
plot shows a schematic voltage- current
diagram,with total discharge currents on
the abscissa which are intended to be
characteristic in magnitude,On the right is
a corresponding plot of the electrode
current density as a function of the total
current for the glow discharge regime.
After electrical breakdown,a low
pressure electrical discharge tube
connected to a power supply with a low
internal resistance will make a
discontinuous transition,on the current-
voltage diagram,from the breakdown
point E to the point F,The region to the
right of point F is almost flat and the
voltage across the discharge tube rises
only slightly while the current varies over
several orders of magnitude.
normal glow discharge,The region from F
to G,In the region,not only is the voltage
relatively independent of the total current
flowing in the discharge tube,but also the
current density reaching the electrodes is
relatively independent of the total current.
This means that,in the normal glow
discharge regime,the plasma is in contract
with only a small part of the cathode
surface at low currents.
As the current increases,the
contract surface fills more and
more of the total cross section,
until at the point G,the boundary
of the abnormal glow,the plasma
covers the entire surface of the
cathode,in order to deliver the
required total current at a constant
current density.
In the abnormal glow above point G,
the voltage increase significantly with
increasing total current in order to force
the cathode current density above its
natural value and the provide the desired
current,To point H,the electrodes
become sufficiently hot that the cathode
emits electrons thermionically,If the DC
power supply has a sufficiently low
internal resistance,the discharge will
undergo a glow-to-arc transition.
9.1.2 Regions of the normal
glow discharge
The plasma which forms in a classical DC low
pressure electrical discharge in the normal glow
regime can have an appearance like that shown in
the idealized sketch of figure behind,These
structures were first observed in the 1830’s by
Michael Faraday,and later by such early
investigators of the low pressure electrical
discharge tube as Mabria(1848).
These structures appear over a
wide range of operating conditions,
and are so characteristic of the
normal glow discharge regime that
they received individual names.
Often in honor of the 19th century
investigators who were among the
first to observe or investigate them.
The density of the shading of the figure
is intended to represent the luminous
intensity of the structures represented,A
characteristic set of operating conditions
for the normal glow discharge shown in
figure 9.3 might be an anode voltage VA of
one or two kilovolts,a total current of 0.1 A,
and air or argon gas at a pressure of a few
torr.
Characteristic axial profiles of the light
intensity,plasma potential,electric field,
and net charge density are indicated
schematically on figure,with the visible
structures to which they correspond
indicated by the diagram at the top of the
figure.
The characteristics of the low pressure
DC normal glow electrical discharge have
been intensity studied in the hundred-
year period prior to 1940,and an
enormous body of literature is available
on its phenomenology,We will now
summarize some of these observations
by describing the major structures,
starting with the cathode on the left,and
proceeding right toward the anode.
Cathode,The cathode is made of an
electrically conducting metal,the
secondary electron emission coefficient,
γ,of which has a significant effect on
the operation of the discharge tube,The
cathode of the classical discharge tube
is usually a circular disc,and operates
cold; that is,it does not rely on
thermionic electron emission to sustain
the discharge.
The importance of the secondary emission
coefficient is implied by the Townsend theory.
In order to attempt a quantitative prediction
of the behavior of a normal glow discharge,one
needs to know the type of cathode material used,
and have some knowledge of the value of its
secondary electron emission coefficient,one
sometimes uses a hollow cathode in which the
plasma terminates in a cavity,or inside a
cylindrical cathode structure,the purpose of
which is to conserve particles and photons
which lead to ionization and /or emission.
Aston dark space,Immediately to the
right of the cathode is the Aston dark
space,a thin region with a strong electric
field and a negative space charge,which
contains slow electrons which are in the
process of accelerating from the cathode.
In this region,the electrons are of too low
a density and/or energy to excite the gas,
so it appears dark.
Cathode glow,The next structure to the
right in the figure is the cathode glow,
which in air is often a reddish or orange
color due to emission by excited atoms
sputtered off the cathode surface,or
incoming positive ions which are moving
toward the cathode,The cathode glow has
a relatively high ion number density,The
axial length of the cathode glow depends
on the type of gas and the gas pressure.
The cathode glow sometimes clings to
cathode and makes the Aston dark space.
Cathode (Crookes,Hittorf) dark space,This
relatively dark region to the right of the
cathode glow is referred to as the Crookes
dark space in the English literature,and the
Hittorf dark space in the early German
literature of electrical discharges,It has a
moderate electric field,a positive space
charge,and a relatively high ion density.
Cathode region,Most of the voltage drop across
the discharge tube appears between the
cathode and the boundary between the cathode
dark space and the negative glow,This region is
called the cathode region,It is of length dc,from
the cathode surface (χ=0) to the boundary of the
negative glow (χ=dc),The voltage drop is known
as the cathode fall,of Vc volts,Most of the power
dissipation in a glow discharge occurs in the
cathode region,In this region,electrons are
accelerated to energies high enough to produce
ionization and avalanching in the negative glow,
and in regions to the right of the negative glow.
A low pressure glow discharge will adjust the axial length
of its cathode region,dc so that a minimum value of the
product dcp is established,
dcp≈(dp)mim (9.1)
where this product is the Pashen minimum,At the Pashen
minimum,the discharge maintains itself under conditions
of a minimum cathode fall voltage and power dissipation.
In the normal glow discharge,the current density flowing to
the cathode remains approximately constant as the total
current varies,as the area of the discharge plasma in
contact with the cathode increases with total current.
Typical values in air at a pressure of 1 torr might be a
current density of 0.3 mA/cm2,dc≈0.5 cm,and a cathode
fall voltage ranging between 100 and 300V.
Negative glow,Immediately to the
right of the cathode dark space is the
negative glow,the brightest light
intensity in the entire discharge,The
negative glow has a relatively low
electric field,is usually long compared
to the cathode glow,and is most
intense on the cathode side,Electrons
carry almost the entire current in the
negative glow region.
Electrons which have been accelerated
in the cathode region produce
ionization and intense excitation in
the negative glow,hence the bright
light output observed,As these
electrons are slowed down,energy
for excitation is no longer available
and the Faraday dark space begins.
The electron number density in the
negative glow is characteristically
about 1016 electrons/m3.
Faraday dark space,This region is
found to the immediate right of the
negative glow,and in it the electron
energy is slow as a result of ionization
and excitation interactions in the
negative glow,In the Faraday dark
space the electron number density
decreases by recombination and radial
diffusion,the net space charges is very
low,and the axial electric field is
relatively small.
Positive column,The positive column is
quasi-neutral,and is what Irving Langmuir
had in mind when he defined plasma,In
the positive column,the electric field is
small,typically 1V/cm,The electric field is
just large enough to maintain the required
degree of ionization at its cathode end,The
electron number density is typically 1015 to
1016 electrons/m3 in the positive column,
with an electron kinetic temperature of 1 to
2 eV.
In air the positive column plasma is
pinkish to blue,As the length of the
discharge tube is increased at constant
pressure,the length of the cathode
structures remains constant (pdc=constant),
and the positive column lengthens,The
positive column is long,uniform glow,expert
when standing or moving striations are
triggered spontaneously,or ionization wave
are triggered by a disturbance.
Anode glow,The anode glow is a bright
region at the anode end of the positive
column,slightly more intense than the
positive column,and not always
present,This is the boundary of the
anode sheath,
Anode dark space,The anode dark
space,between the anode glow and
the anode itself,is the anode sheath
which has a negative space charge
due to electrons traveling from the
positive column to the anode,and a
higher electric field than the positive
column,The anode pulls electrons out
of the positive column and acts like a
langmuir probe in electron situation in
this respect.
9.2 Theory of DC glow discharge
In this section we will study some
physical processes which relate the major
independent and dependent variables of
DC glow discharge plasma,These
relationships are often useful in
understanding the otherwise surprising
behavior of DC glow discharge,even
though the utility of these relationships is
sometimes more on a qualitative level than
for exact quantitative prediction.
9.2.1 Townsend theory of cathode region
The history of research on glow
discharge in classical electrical
discharge tubes has shown that the
Townsend discharge can be applied
to the cathode region of the normal
glow discharge,if only qualitative or
rough quantitative understanding is
sufficient.
In this application,the parameter dc
is the length of the cathode region in
meters,and Vc is the cathode fall
voltage in volts,To a good
approximation,the plasma
parameters of the normal glow
discharge adjust themselves such
that equation holds,
m i n)( dppd c?
This is the minimum breakdown
parameter of the Paschen curve,
where the cathode fall voltage is given
by
and Vb,min is the breakdown voltage
at the minimum of the Paschen curve.
m i n,bc VV?
Typically,the minimum cathode fall
breakdown parameter pdc ranges
from 5 to 25× 10-3 torr m,and the
minimum cathode fall voltage,Vc for
most gases can range between
approximately 150v and 450v for a
range of common gases and cathode
materials.
In early investigations of the
cathode region,F W Aston (1911)
reported that the electric field in the
cathode region is approximately
linear,
E=C(dc-χ)
By integrating this,the cathode
voltage at the axial position χ can
be obtained
)
2
()()(
2
0 0
x
xdCdxxdCE d xxV c
x x
c
Applying the boundary conditions
χ= dc
at V(dc)=Vc
to equation,the constant of integration
C may be written
C=2Vc/dc2
which,when substituted into above
equation,yields an expression for
the potential along the axis of a
normal glow discharge in the cathode
region,
2
)2(
c
cx
x d
xdxV
V
Differentiating above equation yields the electric
field in the cathode fall region,
which recovers the linear relation of Aston.
In the cathode region one can obtain the net
charge density from Possion’s equation by
defining a net charge number density
2
)(2
c
cc
d
xdV
dx
dVE
ein nZn
Possion’s equation for the axial
dimension of the normal glow
discharge may be written
2
0
2
2 2
c
c
d
Vne
dx
Vd

Solving above equation for the net
charge density yields
which is a constant,positive net ion
number density in the cathode region
of the normal glow discharge,These
functional dependences are indicated
schematically in forward figure.
2
02
c
c
ed
Vn
9.2.2 Unmagnetized lorentzian plasma
We now derive,on a microscopic level,
the power input into an unmagnetized
DC glow discharge,using the parallel
plate geometry,Consider a glow
discharge plasma described by a
Lorentzian model,in which electrons
lose their momentum to the neutral
background gas with the collision
frequency νc.
In the geometry,the equation of motion for
individual electrons is given by
(9.13)
In a DC electric field,equation (9.13) becomes
(9.14)
If we assume initial conditions for the electron
(keeping in mind that this is a steady state
discharge),
(9.15)
Eem
dt
dmamF
ecee
00
e
c m
Ee
dt
d
0)(t
With this initial condition,the solution to equation (9.14) is
(9.16)
The second term in equation (9.16) is a starting transient,
which dies out,leaving the constant velocity in the steady
state,
(9.17)
where μe is the electron mobility.
The work done on the electron by the electric field is
(9.18)
t
ecec
ce
m
eE
m
eEt?
)()( 000
0
0 E
m
eE
e
ec
d
dxeExdFdW 0
The power absorbed by one electron is given by
(9.19)
Substituting equation (9.17) into equation (9.19)
gives the power absorbed by one electron
(9.20)
If the normal glow discharge has an electron
number density ne,the total power absorbed per
unit volume is given by
(9.21)
dveEdt
dxeE
dt
dWp
00
ec m
Eep
2
02?
ec
e
e m
EenpnP
2
0
2

Here,we have ignored collective plasma effects
which might shield a plasma from an externally
imposed electric field.
We can express the power dissipation in terms of the
energy density of the electrostatic field,
(9.22)
and the electron plasma frequency,
(9.23)
Equation (9.21) can be written in terms of equations
(9.22) and (9.23) as follows,
(9.24)
2
00m a x 2
1 EU
e
e
pe m
en
0
2
2

ce
e
m
enEP

2
2
1
0
2
2
00?
Equation (9.24) then becomes
(9.25)
*
m a x
2
m a x
2
UUP
c
pe
where the parameter ν* is the energy transfer
frequency which is the frequency,in hertz,with
which the electrostatic energy density provided by
the external power supply is transferred to a unit
volume of the plasma,For this unmagnetized plasma
the energy transfer frequency is
(9.26)
This frequency,which is fundamental to the transfer
of energy into the plasma,is a function of electron
number density,electron kinetic temperature,the
type of gas,and the neutral background gas
pressure,
c
pe
2
* 2?
DC Electrical Arc Discharges
in Gases
The third major regime of industrially
important DC electrical discharges is the
arc discharge,which has been used for
illumination and high temperature metals
processing for nearly 200 years.
10.1 ARC REGIME
An arc discharge is defined in terms
of its luminosity,current density,and
cathode fall voltage,The current
densities of arcs range from several
amperes per square centimeter to
more than a thousand amperes per
square centimeter,These current
densities contrast with those of glow
discharges,in which current densities
are seldom more than 50mA/cm2,
Arcs are also characterized by a relatively small
cathode fall voltage,approximately 10V or
less,in the region of high spatial gradients
within a few millimeters of the cathode,By
contrast,glow discharges typically have a
cathode voltage drop greater than 100V over
a distance of more than a centimeter,The
total current drawn by an electrical discharge
is not definitive,since arcs can be maintained
at currents of 1A or less,whereas glow
discharges,if they have sufficiently large
electrode surfaces,can draw 10 A or more.
10.1.1 Voltage-Current
Characteristic
Three principal division of the regime:
(1) the glow-to-arc transition,which is
triggered by electron emission from
the cathode,This emission results
from the high heat loads on the
cathode which occur in the high
current density regions of the
abnormal glow discharge,
(2) the non-thermal,low intensity division
of the arc regime,which is determined by
the internal impedance of the DC power
supply and its associated circuit,This
division is characterized by total currents
between approximately 1 and 50 A.
(3)Beyond point J on the diagram,at
approximately flat or slowly rising voltage-
current characteristic,which is called the
thermal or high intensity division of the arc
regime.
Table10.1 plasma parameters of non-thermal (low
intensity) and thermal (high intensity) arc discharges.
Plasma parameter non-thermal arc Thermal arc
Equilibrium state Kinetic LTE
Electron density,ne
(clectrons/m3) 1020< ne<1021 1022< ne<1025
Gas pressure,p (pa) 0.1<p<105 104<p<107
Electron temperature,T’e,(eV) 0.2< T’e<2.0 1.0< T’e<10
Gas temperature,T’g,(eV) 0.025< T’g<0.5 T’g= T’e
Arc current,I (A) 1<I<50 50<I<104
E/p (v/m-Torr) High low
IE (kw/cm) IE<1.0 IE>1.0
Typical cathode emission Thermonic Field
Transparency Transparent Opaque
Ionization fraction Indeterminate Saha equation
Luminous intensity Bright Dazzling
Radiation output Indeterminate LTE
10.2 PHENOMENOLOGY OF
ELECTRICAL ARCS
The arc regime of electrical discharges
was reported by Sir Humphrey Davy in 1808,
and was observed in connection with his
electrochemical experiments with the large
battery bank of the Royal Institution in which
many individual wet cells were connected in
a series-parallel configuration,allowing the
simultaneous generation,for the first time,of
large currents at moderately high voltage.
10.2.1 Classical Arc
Nomenclature
Until the early 20th century,most arcs
were used as lighting devices and
operated as non-thermal arcs,The
features of such an arc discharge are as
follows,moving from left to right:
(1) The cathode is the negative
electrode,which,in non-thermal,low
intensity arc discharges,usually emits
electrons thermionically.
(2) The cathode spots are one or more
points of plasma attachment of high
current density where the cathode material
is very hot,The current density in the
cathode spots can be on the order of 500
to more than 10000 A/cm2,and the positive
ion current of the order of 100 A,The
temperature of the cathode will depend on
the type of gas,the electrode material,and
the current density,but for atmospheric
arcs typically in the range from 2200
to3300 K.
The cathode spots usually move over the
cathode surface with a velocity of the
order of meters per second during the
operation of an arc discharge,Cathode
material is lost by vaporization,since the
cathode spots may be at the extremely hot,
the temperature of the cathode as a whole
is considerably less,as mentioned above,
The electron momentum transfer drives
the axial convection of neutral gases,
which affects the electrodes.
(3) The cathode sheath is located next
to the cathode and is usually less than 1
mm thick,It will typically have a voltage
drop of 10 V,comparable to the ionization
potential of the gas used,This voltage
drop is referred to as the cathode fall.
(4) The positive column contains the
bulk of the arc discharge,and occupies
nearly all of the axial length of the arc.
There is relatively little voltage drop in this
region,which visibly can be separated into
the two regions.
(5) The plasma core is the bulk of the hot
plasma,Most of the gas in this region is
dissociated,and for many arcs which
operate at pressures of an atmosphere or
greater,the plasma core is in
thermodynamic equilibrium and radiates
like a black body,The temperature of the
positive column of an arc discharge
depends on the electrode material,the
operating gas,and the current density,but
typical temperatures for an arc in
atmospheric air will range above 5700 K,
the surface temperature of the sun.
(6) The aureole is a region of flaming
gases,not in thermodynamic equilibrium,
which surrounds the core,where plasma
chemistry can take place.
(7) The anode sheath contains a
relatively large voltage drop over a short
distance,the anode fall,comparable to
the cathode fall,The anode fall is
comparable to or less than the
ionization potential of the gas,and can
range from a few volts to ten volts,The
electric field in the anode sheath
accelerates electrons to the anode spot.
(8) The anode spot is usually a single
‘hotspot’ where the current density is high.
Unlike the cathode spots,there is usually
only a single spot of large area and lower
current density than the cathode spot,The
anode spot forms at a location nearest the
arc,and expands backward on the anode
with increasing total current.
(9) The anode is the electrode which collects
the electrode current,and,like the cathode,is
usually made of high melting point,refractory
metal,At atmospheric pressure,the
temperature of the anode is the same or
slightly higher than the cathode,The value of
the anode temperature depends on the
electrode material,the type of gas,the
current density,and typically ranges from
2500 to 4200 K for atmospheric arcs
operating with carbon,tungsten,copper,or
iron electrode.
10.2.2 Modern arc nomenclature
This schematic drawing shows
the modern nomenclature for the
various regions of an arc,along
with the accompanying voltage
drop along the axis,
Starting at the left,the cathode
emits electrons at very high current
densities,For nonthermal,low
intensity arcs,this current usually
arises from thermionic emission from
one or more relatively large,diffuse
cathode spots,which move over the
surface,
The current density in this cathode
spot might range from 500 to 10 000
A/cm2; for thermal,high intensity arcs
with field emission,many small
microspots move over the cathode
surface,each with current densities in
the range from 106 to 108 A/cm2,
The cathode sheath is comparable to
the electron Debye length,λde≈1-
10μm,The voltage across this sheath
is the cathode fall,about 10 V in most
arcs.
The cathode region is a region of
potential and density gradients,with
an axial extent of perhaps dc≈1mm,
Beyond this region,there is a
cathode flow zone approximately
1cm in axial extent in which the
cathode jet is formed,and external
neutral gas interacts strongly with
the arc column,
The cathode jet is a region of high
velocity,hot gas which entrains external
gas near the cathode,and flows axially
with velocities that can reach several
hundred meters per second,The cathode
jet can reach the anode,and it can,and
usually does,greatly increase the heat
transfer to the anode,The scouring effect
of the cathode jet on the anode also can
remove anode material at a rapid rate,
The arc column is a region of low
axial density gradient and electric
field,and essentially no axial
temperature gradients.
Near the anode,the anode flow zone,
anode region and anode sheath are
comparable in dimensions to the
corresponding cathode region,except
that the diameter of the anode
attachment spot is usually significantly
large than that of the cathode,leading
to a smaller anode jet velocity and
less prominent anode flow effect.
The arc column current density is
typically 1000A/cm2 in thermal,high
intensity arcs,the cathode fall is
typically Vc ≈10V,and the anode fall,
VA,is typically equal to the ionization
potential of the gas used,from 3 to
13 V,
In arcs,the cathode fall is usually too
small for secondary electron
emission to play a significant role in
electron emission from the cathode,
Arcs cannot be sustained without
copious emission of electrons from
the cathodes,and this is
accomplished by two mechanisms,
thermionic emission and field
emission.
In low current (approximately 1-10 A) non-
thermal,low intensity arcs,the primary electron
emission mechanism is sometimes non-self-
sustained thermionic emission,In this regime,
the cathode must be heated externally in order
to bring the cathode surface temperature up to
the level where enough electrons are emitted to
sustain the arc,In most non-thermal arcs,
electrons are emitted from the cathode by self-
sustaining thermionic emission,in which the
cathode surface is raised to and maintained at
electron-emitting temperature by the heat flux
from the arc.
in thermal,high intensity arcs,extremely high
currents and current densities are required to
maintain the arc,and these are supplied by
field emission,In field emission,the cathode
temperature is determined by the
characteristics of the heat transfer to the
cathode and the cathode cooling mechanism,
In order to preserve the electrodes and
lengthen the electrode lifetime,the cathode in
thermal,high intensity arcs is usually too cool
to emit thermionically,Electrons are emitted
into the arc by field emission from many
small spots (microspots),each with current
densities of 106 to 108 A/cm2,
A variety of important phenomena occur at the cathode,
The cathode jet discussed above can be very strong,and
its effects can reach to and significantly heat the anode,
Diffuse attachment of the arc to a significant fraction of
the cathode area can result in thermionic current
densities of 1000 to10000 A/cm2 at the cathode surface,
as the result of emission from a relatively large,
incandescent area,Cathode microspots occur in thermal
arcs,as the result of field emission from tiny spots which
are seen to dance over the cathode surface under close
observation,The surface temperatures of cathode in
field-emitting thermal arcs can range from near room
temperature \s to incandescence,and is determined by
heat transfer considerations,not by the level of
thermionic emission required to maintain the arc,The
cathode power deposition can be very large,and water
cooling is required.
Similar phenomena occur at the anode,The anode jet is
usually significantly less active and of lower velocity than
the cathode jet,because of the lesser constriction of the
arc,and the large anode arc radius,Anodes can operate
in the diffuse attachment mode,in which the current
densities can range from 100to 1000 A/cm2,and in the
so-called constricted or ‘spot’ mode,in which the current
densities reach values from 104 -105 A/cm2,In most arcs,
the anode gets higher heat loads than the cathode,
These higher total heat loads can lead to anode burnout,
so the anodes of thermal arcs are usually actively cooled,
With careful attention to the technological detail of the
heat transfer process,heat transfer rates of 5 KW/cm2
may be achieved,For thermal arcs,the anode fall
voltage is usually less than the ionization potential,since
the gas is ionized almost exclusively by the Maxwellian
electrons in the arc.
10.3 PHYSICAL PROCESSES IN
ELECTRICAL ARCS
The understanding of physical processes in
arcs began with a classical paper by Tonks and
Langmuir (1929),and has reached advanced
levels in recent years,particularly for
axisymmetric,thermal arcs,In the discussion
below,we will not cover the range of computer
models currently used to describe thermal arcs,
but will confine ourselves to simple analytical
theories which describe some of the most
important physical processes and
characteristics of industrial arcs.
10.3.1 Body Forces on arcs
As a result of the high current densities
found in typical arcs,JXB body forces act
on their plasma,A typical geometry for an
axisymmetric cylindrical arc is shown,The
arc has a current density J (r),The total
current is found by integrating this current
density over the radius,
(10.1)

a
drrrJI
0
)(2?
In order to avoid mathematical detail,we
will assure that the current density in the
arc is constant,that is J( r) = J=constant,
Under this constraint,the azimuthally
magnetic field inside an arc with constant
current density is given by
(10.2)
rJB z0
2
1

The body force on the plasma in the arc is
therefore
(10.3)
This body force is radial inward,tending to pinch
the arc to a smaller diameter,If the total arc
current I is of the order of 104 A,the radial body
force given by equation (10.3) may be sufficient
to balance the kinetic pressure of the arc,
irrespective of any electrode attachment,
external gas pressure,or convective stabilizing
effects.
rJFBJF zr 20
2
1
A Bennett pinch (Willard H Bennett,1934)
is a cylindrical arc which has reached an
equilibrium in which the expansionary
kinetic pressure of the plasma on axis is
balanced by the inward radial body force
given by equation (10.3),In most arcs,
however,the radial body force given by
equation (10.3) is less than the kinetic
pressure of the plasma,and other
stabilizing mechanisms,including the
pressure of the surrounding atmosphere
come into play,
The boundary conditions of interest in
analyzing the Bennett pinch can be written
with reference to figure 10.5 as
(10.4a)
(10.4b)
(10.4c)
)0,,0(?BB?
),0,0( zJJ?
0?J
ar?
ar?
In the steady state,the balance of forces on
the arc is given by
(10.5)
which,for the conditions of equations (10.4)
becomes
(10.6)
BJp
dr
dp
BJ z
If we now use Maxwell’s equation in the steady
state,
(10.7)
which is given by,for the geometry of figure
10.5,
(10.8)
JB 0
zJrBdr
d
r 0
)(
1

Since the current density is assumed to be
constant,equation 10.8 can be integrated along
the radius to yield B,given by
rJ
r
a
J
Z
Z
B
02
1
2
02
1
{
ar?
ar?
The radial pressure
distribution inside the
arc may be found,
a
rz
a
r
z rJdrBJrp |)(
22
04
1?

Which yields,for r<a,
The condition for Bennett pinch equilibrium is
found in terms of the axial pressure p0,which is
given by
)()( 222041 raJrp z
22
04
1
0)0( aJpp z
Using the relation I and Jz,p0 may be
rewritten as
The equilibrium radius for the bennett
pinch may be found,
22
2
0
0 4 a
Ip

0
0
2 p
I
a
10.3.2 Electrode Jet Formation
As indicated in figure,arcs neck down to a
smaller diameter near the electrodes,a
defining characteristic of the anode and
cathode flow zones of the arc,This
narrowing down of the arc diameter gives
rise to electrode jets,which flow away
from the electrodes,In some ways the
electrode jets are a counter-intuitive
phenomenon,so it is of interest to analyze
their physical mechanism.
the radial pressure profile may be
written in terms of the total current I,
(10.16))(
4
)( 2242
2
0 ra
a
Irp
In most arcs,the pressure on axis given by
equation (10.16)will be well below the total
kinetic pressure of the arc,The axial
gradient of this pressure,however,drives
the electrode jets,At an axial position in the
arc column where the arc radius rmax=a,the
kinetic pressure on the axis of the arc
column is given by
(10.17)
22
2
0
4
)(
a
I
rp
At the cathode,where the arc diameter
constricts to the much smaller radius
rmax=b,the kinetic pressure or axis is
large,and is given by
(10.18)
22
2
0
4
)(
b
Irp

If the radial arc boundary b<<a,then
the kinetic pressure pb at the location b
is much greater than the kinetic
pressure in the arcs column,pa,so an
axial pressure gradient develops,the
magnitude of which is
(10.19)
22
2
0
222
2
0
4)
11(
4 b
I
ab
Ippp
ab?

This axial pressure gradient drives
neutral gas along the axis away from
the electrodes,,This pumping action
of the axial pressure gradient will then
entrain external gas flowing past the
electrode.
An estimate can be made of the megnitude
of the electrode jet velocity by setting the
pressure difference given by equation (10.19)
equal to the dynamic (stagnation) pressure
which would be produced if the electrode jet
stagnated against a flat surface,1/2*pvo2,
where vois the jet velocity in meters per
second,and p is the plasma mass density in
kilograms per cubic meter,
(10.20)
2
022
2
0
2
1
4


bpb
Ip
Equation (10.20)can be solved to
given an estimate of the jet velocity,
(10.21)
The electrode jets are shown
schematically on figure 10.4,Their
velocity is typically from a few meters
per second to several hundred
meters per second.

2
1
]
2
[ 022
2
0
0
2
1
b
I

The axial electric field is very high in the
electrode sheaths,moderate in the rest of the
electrode region within a centimeter or so of
the electrodes,and least in the arc column,
The total arc voltage may be written
(10.22)
where vc andvA are the cathode and anode
falls,respectively,

A
c
dL
d
AC E d zVVV 1
In general,any arc must have a
minimum total applied voltage v1 given
by
(10.23)
or it will be extinguished,This relation is
important to the design and stabilization
of axially segmented arcs.
AC VVV1
10.3.3 Radiation From Thermal Arcs
Arc discharges operating at or above 1 atm are
often in thermodynamic equilibrium,and thus
radiate like a black body,This leads to their utility
for lighting devices,and to their being an
occupational hazard for ultraviolet radiation when
udsed for industrial processes such as welding,A
medium in thermodynamic equilibrium is one in
which there are no net power flows,and the photo
mean free paths are less than the dimensions of
the medium,In consequence,the surface of the
medium radiates like a black body.
Black bodies emit according to the Planck radiation
law,
(10.24)
where Me is the radiant existence in watts per
square meter,and λ is the wavelength of the
radiation in meters,Equation (10.24) leads to a
distribution of radiant existence as a function of
wavelength shown schematically on figure 10.8,The
radiation goes to zero at very short wavelengths,
rises to a maximum,at λ max,and then falls off
asymptotically to zero at longer wavelengths,One
can determine the wavelength of maximum
emission by differentiating equation (10.24),setting
the derivative equal to zero,and obtaining
(10.25)
The sun is plasma that radiates like a black body at
approximately 5700 K,At that temperature,its
wavelength of maximum emission is in the middle of the
band where the eyes of humans and most other animals
are most sensitive,as a result of our eyes having
evolved to most efficiently utilize the photon emissions of
the sun,At filament temperature of 2500 K,the
wavelength of maximum emission of incandescent bulbs
is in the infrared,thus wasting most of their photons for
lighting purposes,Welding and other arcs typically have
electron kinetic temperatures of 1 or 2 eV,between
approximately 11000 and 22000K,where the wave
length of maximum emission is in the ultra violent,
The radiant existence of an arc,or any other black
body,may be found by integrating the area under
the curve on figure 10.8,
(10.26)
where the parameter ε is a gray body factor or a
gray body coefficient which ranges from 0 to 1.0,
This accounts for the fact that many arcs and other
radiant energy sources do not radiate as effectively
as a black body because of surface dirt,turbulence,
etc,Substituting equation (10.24) into (10.26) and
performing the indicated integration,one obtains the
Stefan-Boltzmann radiation law,
(10.27)
The collection of constants denoted by σ is
Stefan’s constant,and is given in the SI system of
units by.
(10.28)
Arcs at pressures below 1 atm are often
not in thermodynamic equilibrium,but
satisfy only the condition of kinetic
equilibrium,In such arcs,the electron
population can be in kinetic equilibrium
and described by a Maxwell-Boltzmann
distribution,such low intensity,non-
thermal arcs cannot radiate like black
bodies,Equation (10.27) rapresents an
absolute upper limit on the power radiated
from an arc discharge,if it is in
thermodynamic or kinetic equilibrium,
10.3.4 Modeling Electrical Arcs
In modeling arcs,the problem is usually approached
as an exercise in fluid dynamics,rather than relying
upon individual particle equations of motion,or an
approach based on the Lorentzian or Krook models,
In modeling arcs with the fluid dynamic equations for
the conversation of mass,momentum,and energy,
it is usually assumed that the arcs are axisymmetric
and are not functions of time.
One of the simplest of these models is for the
radial power balance of arcs,It is assumed that all
heat is generated by Joule heating in the plasma,
and that all losses are radial and due to a radial
thermal conductivity k,,This gives a power balance
where σ is the electrical conductivity,,If the axial
electric field E is constant or continuous function of
the radius r,if there is no axial variation of the arc
parameters,and if the temperature T is a function of
r only,one can obtain from equation (10.29) the
Elenbaas-Heller equation,
(10.30)
Figure 10.9 Schematic of a wall-stabilized are
discharge studied by Pfender(1978),
Even this simplified equation is very difficult to solve
analytically unless further assumptions are made,
The parabolic model assumes that the electrical
conductivityσ and the thermal conductivity k
are not functions of kinetic temperature T or
radius (usually,bad assumptions),If it is
further assumed that the boundary conditions
on temperature are
on the axis,and
(10.31b)
with Tw the wall temperature,the Elenbaas-Heller
equation can be integrated to obtain
(10.32)
Figure 10.10 Gas dynamic parameters calculated
for the wall-stabilized nitrogen arc shown in
figure 10.9,by Pfender(1978).
DC ELECTRCAL ARC DISCHARGES IN GASES
Figure 10.11 A low pressure vacuum arc operated
in hydrogen by Jobes et al (1969),diagnosed with
the heavy-ion beam probe diagnostic.
This equation and its simplified model contain
important truths about arcs; if the edges of an
arc are cooled (k->0),the central temperature of
the arc increases in order to maintain the arc
equilibrium,This model also predicts a
temperature on axis proportioal to the arc power
dissipation per meter of axial length.
More elaborate models have been developed which
include black body and line radiation,a
functional dependence ofσ and k on the radius and
temperature,and gas dynamic effects such ass
viscosity,This sophistication,however,is
purchased at a substantial price in computational
difficulty,to the point where most arc models are
now the result of computer programs rather than an
analytical formalism,As an example,Pfender (1978)
developed a computational model of a wall-
stabilized arc shown on figure 10.9,and its
calculated performance parameters are shown in
figure 10.10.
When arc discharges have been studied with the highly
sophisticated plasma diagnostic instruments developed for
fusion research,time and space-resolved measurements have
revealed very little reason to assure that arcs are either
axisymmetric or that their characteristics are independent of time.
In one of the early applications of a fusion diagnostic
to a low pressure non-thermal arc,the geometry of which is
shown in figure 10.11,the arc was probed with a time-and
space-resolved plasma diagnostic method known as heavy ion
beam probing (Jobes et al 1969),The arc was operated at
approximately 1 Torr,The heavy-ion beam probing system was
capable of a time resolution of several hundred kilohertz,
and a spatial resolution on the order of 1mm,On figure
10.12 is a contour plot of the electron number density
profile at a particular instant in time,The mountain-like
structure shown in this figure was gyrating a center of
rotation indicated on the diagram with a frequency of
approximately 185 KHz,Thus,neither the instantaneous
appearance of the arc,nor its dynamics were axisymmetric,nor were they independence of time.
Figure 10.12 A three-dimensional time–and
space-resolved plot of the electron number
density in the linear,Low pressure hydrogen
arc-shown in figure 10.11,The approximate
center of rotation is indicated,The
structure shown rotates about this axis with
a frequency of 185 KHz
It is probably significant that the first and
almost the only time that heavy ion beam probing
has been applied to a non-thermal,low intensity
arc of potential industrial interest,it has been
found that many of the common assumptions used to
theoretically describe arcs do not apply,Further
advances in understanding the physical processes
going on in thermal and non-thermal arc discharges
probably will require time-and space-resolved
measurements and more sophisticated diagnostics
and physical modeling,rather than increasing
sophisticated computer models,the input
assumptions of which do not reflect the underlying
physical reality of arc discharges
10.5.1 Power Supplies
Arcs require for their operation real
currents rather than displacement
currents,and these currents are
provided to the electrodes by their AC
or DC power supplies,The power
supplies for AC arcs are invariable at
the supply frequently,either 50 or 60 Hz,
although it is possible to sustain arcs at
AC frequencies of kilohertz,
Except for arcs used in lighting
devices,the AC power supplies for
industrial thermal arcs typically
operate at kilowatt to megawatt levels;
may be one or,more usually,three
phase; and typically consist of
switchgear,step down transformers,
and inductors and/or filter to maintain
power quality,
10.6 Initiating mechanisms for arcs
Arcs are hard to start because they
require either thermionic or field
emission,Over the years,a number
of initiating mechanisms have been
developed,which can be divided into
three major approaches,
The first of these is electrical
breakdown,the process implied by
progress on the voltage-current
characteristic of figure 10.1 from the
point G through the point J,This is a
brute force approach,in which the
voltage across the electrode is raise to
a high enough value to initiate the
grow-to-arc transition.
This method of initiating electrical
arcs presents a safety hazard with
high voltage on the electrodes,and
places difficult requirement on the
electrical supply,which must be
capable of high initiating voltage as
well as the high currents at low
voltage required to maintain the arc in
the steady state.
The second major initiating mechanism is
‘drawing an arc’,which consists simply of
separating electrodes which are initially in
contact,This invariably results in high
current densities at small asperities or
contact points which heat these points
locally,and provide the thermionic
emission necessary to sustain the arc.
Finally,there are a variety of widely used
initiating mechanisms based on external
ionization of the electrode gap,These
include an RF spark,provided,for example,
by an induction or tesla coil; an exploding
wire between the electrodes which can
consist of a carefully placed single wire,or
simply a wad of steel wood jammed
between the electrodes,a single shot
approach; the use of a plasma gun,such
as a spark plug for example ;
the use of ionizing radiation,including
alpha and beta emitters; irradiation of the
electrodes with ultraviolet,x-rays,or
gamma rays; or the irradiation of the
electrode with a high energy laser,Arcs
may also be initiated by smaller plasma
jets,as might be approach for high power
gas heaters,where the electrode
separation is relatively large; and finally,
arcs may be initiated by chemical
ionization in a flame,such as provided by
a match.
Surface interactions in plasma processing
1 industrial plasma processing
1.1 industrially significant plasma
characteristics:
high power or energy density
active species
1.2 benefits of plasma processing
Reduction of the carbon dioxide
emissions and global warming
Reductions in energy comsumption
Increases in the efficiency of energy
use
Reduction of pollution and
enviormental contaminants
Producing unique effects of
commercial value
Resulting in significantly reduced
inputs
Reducing occupational hazards at the
point of manufacture
Reducing unwanted byproducts
3 conventional and plasma surface
treatment wool
The objective of the treatment
processes under study was to
achieve printability of patterns on
woolen cloth
Convention,chemical chlorination
process
Used in textile industry,relatively
difficult and expensive,occupational
hazards to the worker,significant
volumes of unwanted or toxic
wastes,the wool smelling like chlorine
25MJ/kg of wool,
Requring 840MWhr to treat 120
tonnes of wool
Low-pressure plasma treatment process:
being implemented on a pilot prodution
line,The wool exposed to an RF glow
discharge plasma operating at pressures
from 267-800Pa(2-6 torr)
The continuous feed of cloth into andout of
the vaccum system required four
differential stages of vaccum pumping
The vaccum pumping power was the
major energy input and economic expense
in this continuous process
Treatment period,10-15 s
Woolen cloth moved velocity,10-15 m/min
Compared to the conventional chlorination
process:plasma modification of 120 tonnes per
year of wool saves:44 tonnes of sodium
hypochlorite,11 tonnes of sulfuric acid
(H2SO4),16 tonnes of bisulate,27000m3 of
water and 685MWhr of electrical energy
If an atmospheric glow discharge
process were used to treat the wool
and achieved equivalent results,only
1-4 kW would be requried for the
plasma power supply.
Plasma treatment of surfaces
Plasma active species interact only very
superficially with the material,i.e,with the
adsorbed surface monolayers with the first
few monolayers of the surface material
itself,Such interactions can significantly
affect the surface
energy,wettability,printability,adhesion,and
other commerically important properties of
surface.
Objectives of plasma surface treatment
1.1 plasma surface treatment
Plasma surface treatment is the use of active
species produced by a plasma to modify the
surface charateristics of solid materials.
May add or remove adsorbed monolayers;
May involve chemical reactions with the
surface
May add or remove surface charge
May change the physical or chemical state of
the superficial monolayers of a material
Plasma surface treatment
Does not employ energetic lasma with
power densities above a few watts per
cubic centimeter
Does not damage or alter the bulk material
Does not inject ion or atoms below the
surface (ion implantation)
Does not remove bulk material(sputtering
or etching)
Does not add more than a feww
monolayers to the surface (deposition)
1.2Plasma cleaning of workpieces
Plasma cleaning is the removal of
adherent layers of adsorbed
contaminant:monolayers of an
ambient gas,oxides or other chemical
reaction product; hydrocarbons,such
as vacuum pump or maching oils
1.3 altering surface energy
1.3.1 Phenomenology of surface energy
The surface energy is the work done
against surface tension forces in
creating a unit area of liquid on the
surface at constant temperature,and is
associated with the ability of water or
inks to wet surfaces,Unit:J/m2 or
dynes/cm
When the surface energy of a material
is low,from 30 to 40 dynes/cm,it is
relatively unwettable,and water will
bead up on its surface; if the surface
energy is above 60 dynes/cm,the
surface will be very wettable,and a
water drop will spread over a large
area,with a contact angle below 10o
1.3.2 surface-energy-related
characteristics
Wettability:wettability is the ability to adsorb
a liquid on a solid surface,or to absorb the
liquid in the bulk of fibrous materials such as
paper or fabrics.
Wickability,is a measure of the bulk
absorptivity of porous or fibrous
materials,such as papers or fabrics,It is
usually defined in terms of the upward
speed of the wetted boundaryin a vertical
sample dipped in the liquid.
Printability,is the ability to take a printed
pattern or ink on the surface of
paper,film,or fabric.
hydrocarbon-based inks adhere well with
surface energies of only 30-40 dynes/cm,
water-based inks require surface
energies in the range of 40-60 dynes/cm,
this surface energy is higher than the
natural surface energy of many papers
and packaging materials,so plasma
surface treatment may be required.
Dyeability:is the ability of a porous or
fibrous material such as a fabric to be
dyed in bulk,Dyeing is most
effectively done if the fabric to be
dyed is wettable and wickabe to the
dyeing solution.
Washability,is the ability to shed dirt
and stains and withstand laundering.
1.4 altering cohesive properties
Cohesion is the property of a material
that enables it to cling together and
oppose forces tending to tear it apart.
cross-linking of parallel polymer
chains;
surface-to-surface contact cohesion;
three-dimensional cross-linkages
among fibers
1.5 altering adhesive properties
Adhesion is the interaction of two
surface,close to each other or in
contact,which causes them to stick
together.
A common problem in industry is
getting paints to adhere to plastic
surface,such as automotive bumpers
and body panels.