JNTU B.Tech III HIGH VOLTAGE ENGINEERING Previous Question Paper (August - 2022 - R18)

Ionization by collision is the primary process of gas breakdown where an electron gains sufficient kinetic energy from an electric field to liberate an additional electron upon colliding with a neutral gas molecule. When an electron is accelerated by an electric field, it acquires kinetic energy equal to 1/2mv². If this energy equals or exceeds the ionization potential of the gas atom, the collision results in the ejection of an orbital electron, creating a positive ion and two free electrons.

The process can be visualized as an electron moving from the cathode towards the anode. As it travels, it undergoes successive collisions. Initially, a single electron produces a second electron; these two then produce two more, leading to an exponential increase in the number of charge carriers. This cumulative process is known as an electron avalanche. The diagram would show a single electron path branching into multiple paths as it progresses toward the anode, representing the multiplication of charge carriers through successive ionizing collisions.

To derive the Townsend breakdown criterion, consider a gap between two parallel plate electrodes with a uniform electric field. Let n₀ be the number of electrons emitted from the cathode. As these electrons move a distance dx towards the anode, they produce new electrons due to ionization. Let α be the Townsend's first ionization coefficient, representing the number of ionizing collisions per unit distance.

The increase in the number of electrons dn in distance dx is given by:

Integrating this from x = 0 to x = d (the gap distance), we get:

The number of new electrons produced is n₀(e^αd - 1). If γ is Townsend's second ionization coefficient (representing secondary electron emission from the cathode due to positive ion bombardment), the total number of electrons at the anode becomes:

Breakdown occurs when the current becomes self-sustaining, meaning the denominator approaches zero. Thus, the Townsend criterion for breakdown is:

When this condition is met, the discharge becomes independent of the initial external ionization source, leading to a complete electrical breakdown of the gas.