This document discusses John Sealy Townsend's theories on breakdown in gases and his current growth equation. Townsend studied the process of ionization where an electron liberates an atom, forming a positive ion and two electrons. He found that current first increases proportionally with voltage, then remains constant, and finally increases exponentially at higher voltages due to electron collision ionization of gas. Townsend's current growth equation models how the number of electrons increases exponentially based on the number of ionizing collisions per unit distance, represented by Townsend's first ionization coefficient, and the distance from the cathode.

1. HIGH VOLTAGE
ENGINEERING
 TOWNSEND’S
THEORY&CURRENT
GROWTH EQUATION
IN SIMPLE
LAUNGUAGE
LEC # 04
BREAKDOWN
IN GASES

2. TOWNSEND’S THEORIES
 The Townsend discharge is named
after John Sealy Edward Townsend,
(7 June 1868 – 16 February 1957) a
mathematical physicist of Oxford
University.
 The process of liberating an
electron from a gas molecule with
the simultaneous production of a
positive ion is called ionization. This
process is represented as-
A is atom, A+ is positive ion. Study of a Townsend discharge
𝑒− + 𝐴 →
𝜀>𝑉𝑖
𝑒− + 𝐴+ + 𝑒−

3. TOWNSEND’S CURRENT GROWTH EQUATION
 The variation of current as a function of voltage was studied by Townsend.
 He found that the current at first increased proportionally as the voltage is
increased and then remains constant.
 At still higher voltages, the current increases exponentially.
 The exponential increase in current is due to ionization of gas by electron
collision.

4. TOWNSEND’S CURRENT GROWTH EQUATION
 When one electron collides with a neutral particle, a positive ion and an
electron are formed. This is called an ionizing collision.
 Assume n0 is electrons emitted from cathode. Let α be the average
number of ionizing collisions made by an electron per cm travel in the
direction of the field where it depends on gas pressure (P) and E/P, and is
called the Townsend’s first ionization coefficient or primary ionization
coefficient.
 x is a distance from cathode and nx is number of electrons.
 When these nx electrons travel a further distance of dx they give rise to
(α nx dx)Electrons.

5. Therefore the average current in the gap, which is equal to the number
of electrons travelling per second will be
TOWNSEND’S CURRENT GROWTH EQUATION

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