ELK$473$E Discharge Phenomena in High Voltage Technique

Homework # $1$

Q$1.$

Calculate the breakdown voltage, critical pressure, and minimum breakdown voltage for a parallel plate electrode system of $0\mathrm{.}9$ cm spacing using Townsend discharge theory under $16C$ temperature and $776$ mmHg pressure conditions. Moreover, calculate the breakdown voltage of the same system by using streamer discharge theory, and interpret the results.

under normal atmospheric conditions. Note that the number of electrons is $0\mathrm{.}92{10}^8$ during the transition to the plasma phase$).$

Q$2.$

An experiment was performed to measure $$ by using a parallel plate electrode system at a voltage of $12$ kV $.$ The steady$-$state current was measured as $5{10}^{-7}A$ at a spacing of $0\mathrm{.}4$ cm between the plane electrodes. The current increased to $8{10}^{-6}$A for the same electric field, with the spacing increased to $0\mathrm{.}85$ cm $.$ Determine $$ for the given conditions.

Q$3.$

In a non$-$uniform electric field strength, $$ is defined as

$=A_1-B_1\sqrt[\phantom{2}]{x}(c{m}^{-1})$

where x is the measured distance from the cathode surface in cm $.$ Assuming that one electron starts moving from the cathode surface, determine the expression in terms of given parameters for the number of electrons in an avalanche at a distance of $"$ a $"$ cm $.$

Q$4.$

Under a uniform electric field strength, the number of electrons due to the collision of one electron traveling $"$a$"$ cm in the direction of the electric field is given as $K^{.a}.$ Find the expressions for the self$-$sustaining discharge, the breakdown voltage, and the critical pressure that minimizes the breakdown voltage using Townsend discharge theory.