Final answer:
Townsend's first ionization coefficient is about ion pairs produced by an electron, while the second ionization coefficient refers to secondary ionizations by positive ions. The condition for breakdown in Townsend discharge is when electron/ion production balances with their loss, described by the equation e^(αd) = 1 + 1/γ.
Step-by-step explanation:
Townsend's first and second ionization coefficients are key concepts in the field of gas discharge physics, particularly relating to the mechanisms by which electrical breakdown occurs in a gas. The first ionization coefficient (α) refers to the number of ion pairs produced per unit path length by an electron moving through a gas. The second ionization coefficient (γ) is a measure of the number of secondary ionizations that occur when a positive ion collides with a neutral gas molecule. These ionizations contribute to the overall ionization processes within the discharge.
The condition for electrical breakdown in a Townsend discharge is derived by balancing the rate of production of electrons and ions with their loss processes. This balance occurs when the electrical gain due to ionization equals the loss at the electrodes. Mathematically, it can be represented as breakdown occurring when the product of the first ionization coefficient (α) and electrode separation (d) is such that eαd = 1 + 1/γ.