Derivation of the equation for HV Gaseous Breakdown?

[Johnny Ghaddar]

Homework Statement

Derive an expression for the growth of current in a gap stressed with the high electric field

Relevant Equations

Main Equation File

Hello,

I am solving a dielectric materials assignment to derive the equation for the growth of current in a gap stressed with the high electric field. The equation is as follows:

The equation combines the anode, cathode and attachment process as shown below:

I have derived the two equations with α and η & α and ϒ processes combined. But when I start to derive the final equation for η and ϒ I get stuck in the start as I am unsure of how to add the currents to achieve the final equation.

I have referred to the following course books but unable to find any guidance as both mention direct results.

1. Chapter5–ElectricalBreakdowninGasesin“HighVoltageEngineering-Fundamentals”,2ndEdition,E.Kuffel,W.S.Zaengl,andJ.Kuffel,Newnes,2000.
2. Chapter2–Conductionandbreakdowningases,inHighVoltageEngineering,2ndEdition,M.S.NaiduandV.Kamaraju,McGrawHill,2009.

I will appreciate any help from this forum. Please, this is my first post here

 

[anathema]

Hello there,

Thank you for reaching out to this forum for help with your assignment. It sounds like you have already made some progress in deriving the equations for α and η & α and ϒ processes. I would recommend taking a step back and starting by clearly defining your variables and their relationships.

For example, what do α, η, and ϒ represent in your equation? How do they relate to each other and to the growth of current in a gap stressed with high electric field? Once you have a clear understanding of these variables, it will be easier to combine the equations and derive the final equation for η and ϒ.

Additionally, I would suggest looking for other resources beyond the course books you mentioned. Have you tried searching for similar equations in scientific journals or online databases? Sometimes, seeing how other scientists have approached a similar problem can provide valuable insights and help you overcome any roadblocks you may be facing.

I hope this helps and good luck with your assignment! Don't hesitate to ask for further clarification or assistance from this forum. We are all here to support each other in our scientific pursuits.