HIGH VOLTAGE Breakdown phenomena Assistant Professor Suna BOLAT KRÖGER

Eastern Mediterranean University

Department of Electric & Electronic Engineering

Some basic concepts

Insulation

To prevent electrical conduction between points with different potentials

Insulator

Material used for obtaining electrical insulation in the insulation system

•Gas

•Liquid

•Solid

•Vacuum

Some basic concepts

Electrical discharge

Any dielectric (or insulator) can withstand a voltage applied below a critical value.

If applied voltage across dielectric exceeds this critical value, a discharge occurs in the insulator medium.

Electrical discharges

There are different types of electrical discharge.

• Breakdown: complete electrical discharge through the insulator

• Flashover: complete electrical discharge jumping around the insulator

• Partial discharge: partial breakdown on conductors at points with the highest electrical stress

Electrical breakdown in gases

Gases as insulating medium is often preferred in high voltage technique application because of their self-restoring capability after a breakdown.

(air, SF6 )

Discharge in gases

• Generally, a neutral gas does not conduct electricity when it is conserved from external factors. However, application of electric field can lead the gas to lose its insulating properties at a critical value.

• This conduction in dielectric is called ELECTRICAL DISCHARGE. Electrical discharge occurs in the presence of charged particles which are electrons (negatively charges particles) and ions (negatively or positively charged atoms or molecules).

Structure and excitation of atom and ionization

Nucleous

(protons [positive] and

neutrons [chargeless])

Electron

(negative)

Removing an electron from a neutral atom results in positive ion Adding an electron to a neutral atom results in negative ion

Energy on a charge

𝐹 = 𝑞 𝐸

𝐸 =𝑈

𝑑

𝐹 = 𝑞𝑈

𝑑

𝐹𝑑 = 𝑞𝑈 = 𝑊 (𝑒𝑛𝑒𝑟𝑔𝑦,𝑤𝑜𝑟𝑘)

Excitation energy

We = q Ue

VK VL VM

Nucleus

K L M O P We = q (VK – VL)

Excitation energy

We = q (VK – VL)

When a voltage between two orbits is applied to an electron, electron jumps to the one orbit level up.

Photon energy

• The electron stays at this new orbit level for about 10-8 – 10-9 seconds and it returns to its original position.

• The electron is emits energy as photon (beam energy) energy.

𝑊𝑒 = 𝑞𝑈𝑒 = ℎ 𝑓𝑒 Photon energy (quantum of energy)

h: Planck’s constant; fe: frequency of the radiation

Ionization

Removing an electron from an atom or a molecule is called IONISATION.

Wi = q Ui

Ionization

voltage

W

Free electron positive ion

(which is removed

from the atom)

IONIZATION

Ionization types in gases

1. Ionization by collision • Gas atoms and molecules collect kinetic energy by moving. When

atoms or molecules collide, they transfer their energies to each other.

𝐸𝑘 =1

2𝑚𝑣2 : kinetic energy

𝑊𝑖 ≤1

2𝑚𝑣2 → 𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑏𝑦 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛

• When kinetic energy of an electron exceeds the ionization energy of the atom or molecule (the energy needed to be given to an atom or a molecule in order to remove an electron), ionization occurs. Sometimes ionization occurs progressively.

Ionization types in gases

2. Photo-ionization A molecule in the ground state can be ionized by a photon having frequency f provided that the quantum of energy emitted h f (by an electron jumping from one orbit to another), is greater than the ionization energy of the molecule. (Gas gains photon’s energy)

𝑊𝑝 = ℎ 𝑓𝑝 : Photon energy

h: Planck’s constant = 6.62510-34 Joule.s; fp: frequency of photon

Ionization types in gases

2. Photo-ionization

𝑓 =𝑣

𝜆, 𝜆 ↓ → 𝑓 ↑ → 𝑊 = ℎ 𝑓 ↑ 𝜆 =

𝑐

𝑓

(𝑣: speed & 𝜆: wavelength)

𝑊 = ℎ 𝑓 ≥ 𝑊𝑖 → 𝑝ℎ𝑜𝑡𝑜𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛

Photon with a small wavelength () or high frequency (f) can supply enough energy for ionization.

Ionization types in gases

3. Thermal ionization

3.1. Gas molecules moves faster when heated.

𝐸𝑘 =1

2𝑚𝑣2 : kinetic energy increases

𝑊𝑖 ≤1

2𝑚𝑣2 → 𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑏𝑦 𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛

3.2. Gas emits light when heated 𝑊 = ℎ 𝑓 ≥ 𝑊𝑖 → 𝑝ℎ𝑜𝑡𝑜𝑖𝑜𝑛𝑖𝑠𝑎𝑡𝑖𝑜𝑛

Ionization types in gases

4. Surface ionization 4.1. Electron Bombardment

Electron removed from electrode – – – –

Electrons

Bombardment

Minimum enegy that has to be supplied to the conductor atom or molecule is called output energy

+ –

–

– electrode

conductor

Atom of the conductor

When electrons or positive ions impigne to the electrode, they will remove electron

𝑊𝑜 ≪ 𝑊𝑖 = 2 − 25 𝑒𝑉

0.1 – 1 eV ionization energy

Output energy of the gas

of the electrode

Ionization types in gases

4. Surface ionization 4.2. Surface ionization by light

Electron removed from electrode –

Light source

+ –

–

–

electrode conductor

Atom of the conductor

𝑊𝑜 ≪ 𝑊𝑝= hf Electron is removed

Photon energy

Ionization types in gases

4. Surface ionization 4.3. Surface ionization by heat

Ionization types in gases

4. Surface ionization 4.4. Surface ionization by field effect

E

-

F = q E E = U/d F = q U/d

𝑊𝑜,𝑎𝑡𝑜𝑚 = 1 − 5 𝑒𝑉 𝑊𝑖,𝑔𝑎𝑠 = 2 − 25 𝑒𝑉

𝑊𝑜 < 𝑊𝑖,𝑔𝑎𝑠

it is easier to remove an electron from metal rather than gas!!!

Discharge theorems (breakdown characteristics in gases)

1. Townsend Theorem

Townsend theorem

Electron Avalanche mechanism

Suppose a free electron exists (due to cosmic radiation or some other external effect) in a gas where an electric field exists.

If E is sufficiently high ionization by collision

(very possible)

If we apply E, free electrons are accelarated

kinetic energy

in eV

move toward the anode

Collision

• This process is cumulative.

• The number of electrons will go on increasing as they continue to move under the action of E

Free path law

Free Path (λ) Free path is the distance travelled by a particle between two collisions

- Random movements of gas atoms or molecules

Free path law

Mean Free Path (𝝀𝒂𝒗𝒆 = 𝝀 ) Mean free path is the arithmetic average distance travelled by a moving particle between successice impacts.

or

Arithmetic average distance travelled by more than one particle in a certain period of time.

𝝀 = 𝝀𝒂𝒗𝒆 =𝟏

𝒏𝝀𝟏 + 𝝀𝟐 + ⋯+ 𝝀𝒏

n: number of collision, or number of free paths

Free path law

Probability of a particle to travel a distance equal orgreater than λ

𝑓 𝜆 = 𝑃 𝜆 = 𝑒−

𝜆𝜆𝑎𝑣𝑒

Probability of 𝜆 ≥ 0 𝑒−

0

𝜆𝑎𝑣𝑒 = 𝑒0 = 1 → 100%

Probability of 𝜆 ≥ 𝜆𝑎𝑣𝑒 𝑒−

𝜆𝑎𝑣𝑒𝜆𝑎𝑣𝑒 = 𝑒−1 =

1

𝑒→ 37%

Probability of 𝜆 ≥ 3𝜆𝑎𝑣𝑒 𝑒−

3𝜆𝑎𝑣𝑒𝜆𝑎𝑣𝑒 = 𝑒−3 =

1

𝑒3 → 5%

Probability fuction

λ

P(λ)

P 𝜆 = 𝑒−

𝜆

𝜆𝑎𝑣𝑒

Number of particles

• Number of initial particles: n0

• Number of non-colliding particles: nλ

𝑛𝜆 = 𝑛0 𝑒−

𝜆𝜆𝑎𝑣𝑒

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓

𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠=

𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑙𝑙𝑖𝑑𝑖𝑛𝑔 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠

+𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓

𝑛𝑜𝑛𝑐𝑜𝑙𝑙𝑖𝑑𝑖𝑛𝑔 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠

Free paths depending on particle properties

𝜆𝑎𝑣𝑒 =1

𝜋 (𝑟1 + 𝑟2)2 𝑁

.𝑣𝑎𝑣𝑒

𝑣1𝑎𝑣𝑒2 + 𝑣2𝑎𝑣𝑒

2

𝑟1: radius ofthe 1st particle

𝑟2: radius ofthe 2nd particle

𝑣1𝑎𝑣𝑒: average speed of the 1st particle

𝑣2𝑎𝑣𝑒: average speed of the 2nd particle

N: number of particles in unit volume (1 cm3)

1. Molecule – molecule collision mean free path of molecules

𝑟1 = 𝑟2 = 𝑟

𝑣1𝑎𝑣𝑒 = 𝑣2𝑎𝑣𝑒 = 𝑣𝑎𝑣𝑒

𝜆𝑚,𝑎𝑣𝑒 =1

𝜋 (2𝑟)2 𝑁.

𝑣𝑎𝑣𝑒

𝑣𝑎𝑣𝑒2 + 𝑣𝑎𝑣𝑒

2

=1

4 2𝜋𝑟2. 𝑁

2. Molecule – ion collision mean free path of ion

𝑟𝑖𝑜𝑛 ≅ 𝑟𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 ≅ 𝑟

𝑣𝑖𝑜𝑛 > 𝑣𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 → 𝑖𝑔𝑛𝑜𝑟𝑒 𝑣𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒

𝜆𝑖,𝑎𝑣𝑒 =1

𝜋 (2𝑟)2 𝑁.𝑣𝑖𝑜𝑛

𝑣𝑖𝑜𝑛2

=1

4𝜋𝑟2. 𝑁

3. Molecule – electron collision mean free path of electrons

𝑟𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 ≪ 𝑟𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 = 𝑟

𝑣𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 ≫ 𝑣𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 → 𝑖𝑔𝑛𝑜𝑟𝑒 𝑣𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒

𝜆𝑒,𝑎𝑣𝑒 =1

𝜋 𝑟2 𝑁.𝑣𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛

𝑣𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛2

=1

𝜋𝑟2. 𝑁

Conclusion:

𝜆𝑒,𝑎𝑣𝑒 = 4𝜆𝑖,𝑎𝑣𝑒 = 4 2𝜆𝑚,𝑎𝑣𝑒

Determination of Towndsend’s coefficients

• Reminder:

Due to general gas law:

𝑝 = 𝑘. 𝑇. 𝑁

Gas pressure

Boltzman’s constant k = 1.38x10-23 J/K

Gas temperature K

Number of particles in unit volume

For an electron

𝜆𝑒,𝑎𝑣𝑒 =1

𝜋𝑟2. 𝑁

𝜆𝑒,𝑎𝑣𝑒 =1

𝜋𝑟2.𝑝

𝑘. 𝑇

=𝑘. 𝑇

𝜋𝑟2. 𝑝 = 𝑓(𝑇, 𝑝)

𝜆𝑒,𝑎𝑣𝑒 =1

𝐴. 𝑝

𝑁 =𝑝

𝑘. 𝑇 Substitute this

Constant!!! (if T is constant)

𝑘. 𝑇

𝜋𝑟2 =1

𝐴

Determination of Townsend’s coefficients ,

Townsend’s first ionization coefficient,

is the number of ionizing collisisons, on average, made by one electron per unit drift (1 cm) in the direction of the field.

Townsend’s first ionization coefficient,

x = 0 x = d x

E

Townsend’s first ionization coefficient,

𝛼 = 1

𝜆𝑒,𝑎𝑣𝑒 𝑒

−𝜆𝑒,𝑖

𝜆𝑒,𝑎𝑣𝑒

Number of collisions

Probability of ionization in one collisison

𝜆𝑒,𝑎𝑣𝑒 =1

𝐴. 𝑝

𝜆𝑒,𝑖 =𝑉𝑖𝐸

: minimum distance an electron should travel in order to ionize