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"Prof Dr. Suhail Aftab Qureshi" 1

High Voltage Engineering

Prof Dr. Suhail A. Qureshi.



Book: 1.0 High-Voltage Engg. (Text Book)

(Abdullah & Kuffel).

Book: 2.0 High-Voltage Engg. (Reference Book).

(Alstom).

Book: 3.0 High-Voltage Engineering. (Reference Book)

(Subir Ray).



B.Sc Electrical Engineering

Ionization and Decay Processes.

Electric Breakdown in Gases.

The Breakdown in Solid and Liquid Dielectrics.

Generation of High Voltages.

Measurement of High Voltages.

Non-destructive Insulation Test Techniques.


CONTENTS

Ionization and Decay Processes

i. Ionization by Electron Collision

(Townsend’s First ionization coefficient)

ii. Photoionization

iii. Ionization by Interaction of Metastables with Atoms

iv. Thermal Ionization

v. Electron Detachment

vi. Decay by Recombination

vii. Decay by Attachment-Negative Ion Formation

viii. Mobility of Gaseous Ions and Decay by Diffusion


CONTENTS

Cathode Processes

a) Photoelectric Emission

b) Electron Emission by Positive Ion and

Excited Atom Impact

c) Thermionic Emission

d) Field Emission

Townsend’s Second Ionization Coefficient




Electrical Discharge

Mechanism

Ion-Generation

Photo-

ionization

Metastable

Interaction

Ion Losses

Thermal

Ionization

Electron

Attachment

Recombination

Diffusion

Electron

Collision

Ele

ctro

n

Det

atch

men

t


α = Townsend’s 1st Ionization Coefficient (only include

ion Generation by Electron Collision)

γ = Townsend’s 2nd Ionization Coefficient (Include

some or all ion Generation in gases including

cathode processes).



Ionization by electron impact/collision is probably themost important processes in the breakdown of gases.

Effectiveness of the electron impact ionization dependsupon the electron energy:

Ionization by Electron Collision



N+

-e

A A A

AA

O O O

Electrodes

Force of attraction

between (+) and (-) ion

e = electron

N = Nucleus

O- = - ive ions

= Neutral Atom A

A

O

Gas


1) Very fast and very slow movingelectrons/ions are poor ionizers.

Electrons moving very slowly will not produceionization. At moderate velocities but when theenergy is less than the ionization potential electronmay excite atom on collision and the atom maythen become ionize by collision with another slowmoving electron.



Very fast and very slow moving electrons/ions are

poor ionizers.


A A*e

S

e

S A* A+

2

e

S

e

S = Slow

moving

electron

A = Atom

A* = Excited Atom

A+ = Positive ion


Very fast and very slow moving electrons/ions are

poor ionizers.

This process becomes only significant when densities of

electron are high.

Very fast electrons are also poor ionizers.


e

FA A

e

F

Fast moving electrons may pass near an atom without

ejecting an electron from it.



2) For every gas there exists an optimum

electron energy range which gives a

maximum ionization probability.

See fig 1.1



For every gas there exists an optimum electron

energy range

FIG:1.1 Probability of single ionization by electron impact

(a) in Hg vapour, (b) in air.


Ionization probability or

differential Ionization coefficient

“The number of ions pairs produce by an electron in

traveling 1-cm through gas at one mm-Hg”.


Townsend’s First Ionization Coefficient

Oe-

Oe-

Oe-

Gas



In a gas discharge the initiatory electrons originate from

Cosmic radiation

Radioactivity

Photoelectrically by irradiation of one electrode

In the absence of electric field there is an equilibrium in which:



Rate of production of Rate of Decay

Electrons

And positive ions.

Gas

A



Above equilibrium is disturbed by application of

sufficiently high field between electrodes.

Townsend was the first fellow to study the variation of

current between two parallel plate electrodes as a

function of applied field. See fig 1. 2



Townsend found that the current in the gap at first

increased proportionately with applied voltage and then

remain nearly constant at a value which corresponded

to the photoelectric current produced at the cathode by

external ultraviolet irradiation.

At still higher voltages the current increased above the

value io at a rate which increases rapidly with increasing

the voltages.

The increased in current beyond V2 Townsend ascribed

to ionization of gas by electron collision.



If the field increases, electron leaving the cathode i.e

accelerated more and more between collision until they

gain enough energy to cause ionization on collision with

gas atoms or molecule. The additional electrons so

formed also gain energy from the field and then

themselves make ionizing collision.



eO

eO

eO

eO

eO

eO

eO

eO2 eO

eO eO

eO eO

eO eO

eO eO

eA A O

eA A O

A



α =Townsend’s first ionization coefficient.

Defined as “the number of electrons produce in a

path of single electron traveling a distance of 1cm

in the direction of the field.”

dn=increase in the number of electrons

dx=over a distance in a gap



dn=α n dx

n=no exp(α x)

I= Io exp (αd)

no=number of electrons leaving the cathode

Io=current leaving the cathode

d=gap length (cm)

α=Townsend first coefficient

Note: Experiments and theoretical considerations show

that α/p is a function of E/p.

α/p= f(E/p)

E= field gradient

p=gas pressure



See fig 1.3 showing the variation in the ionization

coefficient “α” in N2, air, H2 and A with variation in E.


PHOTOIONIZATION

2e 2e

N N

1e

1e

Photo-excitation


PHOTOIONIZATION

7 10

1 2 2

10 10

1

2 2 1

2

*

( )

( )

* ( )

to

Seconds

A e e

A h quantum of energy photon

A h A e Photoionization

OR

A h Photo excitation

Electrons of lower energy then ionization potential Vi may

on collision excite the gas atoms to higher energy states


PHOTOIONIZATION

On recovering from this state in 10-7 to 10-10 seconds. The

atom radiates a quantum of energy or photon (hν) which

may in turn ionize another atom whose ionization potential

is equal to or less than the photon energy.

The process is known as photo-ionization and may be

represented as

. *A e K E A e

A h A e


PHOTOIONIZATION

Where A=represents a neutral atom or molecule.

hּט=Photon energy

A+ = Positive ion of Atom A

For ionization to occur

hν ≥ e Vi Vi =ionization potential

If the quantum of energy (hν) exceeds (eVi) the excess

may be imparted to the released electron as kinetic energy.

The probability of photon ionization is maximum when (hν-

eVi) is small (0.1-1eV).


PHOTOIONIZATION

If the photon energy is less than eVi , it may still be

absorbed by the atom and raised the atom to a higher

level, photo excitation.

Photo-ionization is a secondary process and may be acting

in the Townsend breakdown mechanism and is essential in

the Streamer mechanism and in some corona discharges.


IONIZATION BY INTERACTION OF

METASTABLES WITH ATOMS

Metastable A* Excited

atom with longer periods

In certain elements (inert gases and group-II element of the

Periodic table) the life time in some of the excited electronic

states extends to seconds. These states are known as

metastable states.

“Metastable” and the atoms in that state are simply referred to

as metastables represented by Am.


IONIZATION BY INTERACTION OF METASTABLES

WITH ATOMS

If Vm, the energy of metastable (Am) exceeds Vi , the

ionization energy of another atom B, then on collision,

ionization may results according to the reaction.

Am + B A + B+ + e- (Vm ≥ Vi)

Am + B A + B* (Vm < Vi)

Another possibility for ionization by metastables is when 2 Vm

> Vi for A, then the reaction may proceed as


IONIZATION BY INTERACTION OF METASTABLES

WITH ATOMS

Am + Am A+ + A + e- + K.E.

Am + 2A A2* + A

A2* A + A + hv

The photon released in the last reaction is of too low energy

to cause ionization in pure gas but it may release electron

from the cathode.

Ionization by metastable interactions thus comes into

operation long after excitation and it has been shown that

these reactions are responsible for the long time lags

observed in certain gases.


THERMAL IONIZATION

Where A = represents a neutral atom

A+ = Ionized atom

e- = electron removed from the ion

ui = Ionization energy

Heat

iA A e u


THERMAL IONIZATION

If a gas is heated to sufficiently high temperature many of the

neutral atoms will acquire adequate (enough) energy to

ionize the atoms they strike. In general the term thermal

ionization is applied to the ionizing action of molecular

collision, radiation and electron collision occurring in gases at

higher temperature. “Thermal Ionization is the principle

source of ionization in flames and high pressure arcs”.


ELECTRON DETACHMENT

“Under certain conditions in high electronic field electron may

become detach from negative ions”. This process however

requires large concentration of negative ions.

A scientist “Loeb” carried out experiments on electron

detachment in O2 and found that it occurred for E/p=90

v/cm/mm-Hg. This process has been suggested to be

significant in negative point corona discharges.


DECAY BY RECOMBINATION

Whenever there are positively and negatively charged

particles present, recombination takes place. The potential

energy and the relative Kinetic energy of the recombining

electron-ion or ion-ion pair is released as quantum of

radiation. Reaction is Represented below.

ReA B AB h verse of Photo ionization



In this expression B- may be an electron or negative ion.

Alternatively, a third body “C” may be involved and may

absorbed the excess energy released in the recombination.

See fig 1.4 for variation in the recombination with gas

pressure.



dn+/dt = dn-/dt = α n+ n-

α= recombination coefficient

In general

n+ = n- = n

and we have dn/dt = α n2

The recombination is particularly important at higher

pressure for which diffusion is relatively unimportant.

The Rate of recombination (α) is proportional to the

concentration of positive and negative ions or electrons

if n+ and n- are the number of positive and negative ions per

unit volume, then


DECAY BY ATTACHMENT

In certain gases electron can combine with neutral atoms or

molecules to form negative ions.

Negative ions formation is an extremely important

process for gases of high dielectric strength. The

negative ions can be found by either a direct electron

capture

*AB e AB h


DECAY BY ATTACHMENT

or by pair production (dissociation process)

*AB e e e


DECAY BY ATTACHMENT

The removal of electrons by attachment from an ionized

gas may be expressed by a relation analogous

(similar) to the expression.

i.e I=Io exp(αd)

η= attachment coefficient

η= Number of attachments produced in a path of a single

electron.


DECAY BY ATTACHMENT

η= Number of attachments produced in a path of a single

electron traveling a distance of 1cm in direction of the field.

Then the loss of electron current in a distance dx , due to this

cause is

dI=-I η dx

I2 = I1 exp (-η x)

Methods for the determination of the attachment coefficients

utilizing above equation have been used by general workers.


DECAY BY ATTACHMENT

“η” is determined from the measurements of the surviving

electronic currents at grids inserted at two points along the

path of the current between two electrodes.

At higher value of E/p it becomes necessary to

measure both ionization coefficient (α) and

attachment coefficient (η) simultaneously.


DECAY BY ATTACHMENT

These coefficients can also be obtained by employing the

Townsend’s methods for study of the pre-breakdown current.

If the process of electron multiplication by electron collision

and electron loss by attachment are considered to operate

simultaneously then as is in the case of attaching gases it

can be shown that the current flowing in the gap is given by

the expression, as below;


DECAY BY ATTACHMENT

where

α= ionization coefficient

η=Recombination/ attachment coefficient

io= Photoelectric emission current

d=gap length

doi i e


DECAY BY ATTACHMENT

In the absence of attachment when the η is equal to zero the

above expression reduces to the form (1.2) and the log i-d

plot of equation (1.6) gives a straight line with α representing

the tangent.

The departure from linearity in plotting “logi” against “d” give

a measure of attachment coefficient (η).


DECAY BY ATTACHMENT


MOBILITY OF GASEOUS IONS AND

DECAY BY DIFFUSION

An ion moving through a gas under the influence of electric

field will have an average “drift velocity”, that varies directly

with the field strength and inversely with the density of gas

through which it moves.

Drift Velocity

(E=field strength d=density of gas)

MOBILITY: The ratio of an average drift velocity in a field to

the velocity in a unit field is called a mobility (K).

Symbolically K=U/E

U= average drift velocity

E=field strength

EDrift Velocity

d


MOBILITY OF GASEOUS IONS AND DECAY BY

DIFFUSION

Mobility is nearly characteristic of gas through which the ion

moves. Experiments shown that K is independent of E/p over

a wide range. See table 1.2 for mobility of single charge

gases ions at 0oC and 760mm-Hg.


MOBILITY OF GASEOUS IONS AND DECAY BY

DIFFUSION


DIFFUSION

In electrical discharges whenever there is a non-uniform

concentration of ions there will be migration of ions from

regions of higher concentration to regions of lower

concentration. This process which is known as diffusion will

cause a “deionizing effect”. In the regions of higher

concentrations and an “ionizing effect” in the regions of lower

concentration.


DIFFUSION

The presence of walls confining a given volume

arrangements (enhances) deionizing effect as the ions

reaching the walls will loose their charge.

Diffusion process are of importance in studying streamer

discharge and spark channels.


CATHODE PROCESSES

Cathode Processes

Photoelectric

Emission

Positive ion and

excited atom impact

Field Emission Thermionic

Emission

+

Gas

Cathode Anode


CATHODE PROCESSES

Electrodes play a very important role in gas discharges by

supplying electron for

Initiation

For the sustain and

For the completion of discharge

a. Under normal conditions electrons are prevented from

leaving the solid electrode by “Electrostatic forces”.


CATHODE PROCESSES

b. To overcome these forces a certain minimum quantum

energy is required

This corresponding potential energy is known as “Work

Function” (φ) and is a characteristics of a given

material.

There are several ways in which the required energy may

be supplied to release the electrons:


CATHODE PROCESSES

1. Photoelectric Emission

2. Positive ions and excited atom impact-Emission

3. Thermionic Emission

4. Field Emission


CATHODE PROCESSES

1- Photoelectric Emission

+

Anode

e

e

Photons

Cathode


CATHODE PROCESSES


Photon incident upon cathode surface whose energy

exceeds the work function (hν ≥ eφ) may eject electrons

from the surface.

When the photon energy exceeds the work function, the

excess energy may be transferred to electron kinetic

energy according to Einstein relation;


CATHODE PROCESSES


m=mass of electron

ve= velocity of electron

hvo = eφ = critical energy required to remove electron

φ= work function

e=electron charge

21

2e omv hv hv


CATHODE PROCESSES

2- ELECTRON EMISSION BY

POSITIVE IONS AND EXCITED ATOM

IMPACT

e e

eCathode Anode

ve ionO


CATHODE PROCESSES

2- ELECTRON EMISSION BY POSITIVE

IONS AND EXCITED ATOM IMPACT

Electrons may be emitted from metal surfaces by

bombardment of positive ions or metastable atoms. To

cause a secondary emission the impinging ion must

release two electrons, one of which is utilized to neutralize

the ion charge.


CATHODE PROCESSES



Minimum energy is required for a positive ion emission is

twice the work function

UK + UP ≥ 2φ

Since the ion is neutralize by one electron and other

electron is ejected.

A+ + K.E cathode surface A+ + 1e- + 1e- A + 1e-


CATHODE PROCESSES



Uk and Up = kinetic and potential energies of the

incident ion.

Neutral excited (metastable) atoms or molecules incident

upon the electrodes surface are also capable of ejecting

electrons from surface.


CATHODE PROCESSES



A+ + K.E A+ + 1e

Cathode surface

A++ K.E + hּט A+ + 2e-

UK + UP ≥ 2φ


CATHODE PROCESSES

3- THERMIONIC EMISSION

Cathode Anode

HEAT

eO

eO


CATHODE PROCESSES


In metals at higher temperatures some of the conduction

electrons near the surface may possess sufficient energy to

overcome the natural potential energy barrier that exists at

the surface and can be emitted.

The potential barrier is known as surface work function (φ)

The electrons receive their energy from violent thermal

lattice vibrations in solid at higher temperature.


CATHODE PROCESSES


The metal temperatures required for Thermionic

emission may be in the region 1500-25000K.

Jz= AT2 ε –eφ/KT

Jz = Emission Current

A = 120 x 104

e = electron charge

m = electron mass

h = plank’s constant


CATHODE PROCESSES


K = Boltzman constant

φ = work function of surface

T = absolute temperature


CATHODE PROCESSES

4- FIELD EMISSION

e

e

V

H.V


CATHODE PROCESSES

4- FIELD EMISSION

Electrons may be drawn out of a metal surface by very high

electrostatic field.

The field require to produce emission currents of few

microamperes are of the order of the 107 - 108 V/cm , for

metals of work function 4.5 eV.

Such fields are observed at very fine wires, sharp points

and other submicroscopic irregularities with average applied

voltages quite low (2-5KV). These fields are much higher than

the break down fields even in compressed gases.


CATHODE PROCESSES

4- FIELD EMISSION

Recent work shows that field emission is possible with

field as low as 104 V/cm. This effect is attributed to a

localize enhancement of electric field by surface

imperfections.

Dust particles have also be shown to be very effective in

causing local spots of intense field emission.


TOWNSEND’S SECOND IONIZATION

COEFFICIENT

Variable H.v

(Gap length)

d

A


TOWNSEND’S SECOND IONIZATION COEFFICIENT

According to the above equation a graph of logi against the

gap length “d” should yield straight line of slope α, if E/P is

kept constant.

In his early measurements of current in parallel plates

gaps, Townsend’s observed that at higher voltages the

current increased at more rapid rate than given by above

equation.

Fig 1.5 shows the kind of curves obtained by plotting logi

against electrodes spacing at a constant pressure.

0.

dI eI



To explain this departure from linearity at higher voltages

Townsend postulated that a secondary mechanism must be

affecting the current.

He first considered liberation of electrons in the gas by

collision of positive ions and later the liberation of electrons

from cathode by positive ion bombardment.

On these assumptions he deduced equations for the

current in the self sustained discharge.



Another process responsible for the upcurving of the (logi –

d) graph in fig 1.5 includes the secondary emission from the

cathode by photon impact.

Following Townsend procedure consider the case for a

sustained discharge where electrons are produced at the

cathode by positive ion bombardment.



Let n = number of electrons reaching the anode per second

no= number of electrons emitted from cathode

n+=number of electrons released from cathode by positive

ion Bombardment.

γ= number of electrons released from cathode per incident

positive ion



Where β represents the number of ion pairs produce by positive

ion in traveling 1cm in the direction of the field.

The case where the secondary emission arises from photon

impact at the cathode may be expressed by

Where θ = Number of photons produce by an electron in

advancing 1cm in the direction of the field.

µ = average absorption coefficient for photons in the gas

g=geometrical represent the fraction of photon that reach the

cathode



η= fraction of photons producing electrons at the cathode

capable of leaving the surface.

In practice both positive ions and the photons may be active

at the same time in producing electrons at the cathode.

Further more metastable atoms may contribute to the

secondary emission at the cathode. Which of the particular

secondary mechanism is predominating depends largely upon

the experimental conditions in question.



There may be more than one mechanism operating in

producing the secondary ionization in discharge gap and it is

now customary to express the secondary ionization by a single

coefficient γ and represent the current by equation

i = io exp (αd) /1-γ(exp (αd)-1)

γ= may represent one or more of the several possible

mechanism

Fig 1.6 shows the experimentally determined γ in hydrogen

plotted as a function of E/p for platinum and sodium. “γ” is

greatly effected by the nature of the cathode surface.



FIG: 1.6 Secondary coefficient

Low work function surface Higher Emission

Higher work function surface Lower Emission

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