Townsend (in a glance)

Avalanche based on Townsend occurs in a condition where the quantities of electrons created are less than 108. The electric field where such avalanche occurs is also constant (no changes in electric field). In another book, the product of space between electrodes and the pressure in it is less than 5cm.bar. The source of electrons is due to solely from photo ionization.

Townsend theory on breakdown

There are 2 phases of current generated. First batch of electrons are called primary electrons where they are created from the UV light exposure. These electrons are the one creating second batch of electrons (Secondary) due to the collision between the primary electrons/ions with the atoms within the gap.

Primary ionization

Purpose is to find current growth due to first ionization effect;

i. Number of electrons produced in steady-state per second; nd = noeαd ,

ii. The respective current due to nd is given by; Id = Ioeαd

It can be concluded that current in the gap, Id is due solely on the electrons that are produced from photoionization process only, Io. If there is no UV light, therefore there will be no discharge, no and Id = 0. (That is primary ionization.)

Secondary ionization

This process considers the positive bombardment on the cathode. (+ve bombardment produce electrons from the cathode).Therefore 2 types of electrons produced;

no = no of electron emitted per second in steady state due to UV light. n+ = no of electrons produced from positive ion bombardment process on the cathode.

Total number of electrons reaching anode per second in steady state ;

n = (no + n+)eαd

While these electrons are moving towards anode, some of the collide and producing positive ions. These positive ions ;

n- (no – n+ )

These positive ions contribute to the positive bombardment on the cathode. The number of electrons produced due to this process ;

n = oeαd

ିࢽ(eαd-1) for current, simply replaced no with Io and n with I.

*this is made based on my current understanding on the matter, in a summation way. Should you find any mistake don’t hesitate to let me know. I am also learning. Thank you .~Kak Iza