# Derivation of the equation for HV Gaseous Breakdown?

In summary, you are struggling with deriving the final equation for η and ϒ in your assignment on dielectric materials and high electric fields. You have already derived equations for α and η & α and ϒ processes, but you are unsure of how to combine them to achieve the final equation. You are seeking guidance from this forum and have also referred to course books, but have not found any helpful information yet. You are open to any suggestions and appreciate the support from this community.
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

#### Attachments

• Main Equation.png
3.9 KB · Views: 110
berkeman
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.

## 1. What is HV gaseous breakdown?

HV gaseous breakdown is a phenomenon that occurs when a gas, such as air, is subjected to a high voltage electric field. This causes the gas to ionize and become conductive.

## 2. How is the equation for HV gaseous breakdown derived?

The equation for HV gaseous breakdown is derived using the Townsend discharge theory, which takes into account the rate of ionization, the energy lost by electrons, and the electric field strength. The final equation is known as the Paschen's law.

## 3. What factors affect the HV gaseous breakdown?

The HV gaseous breakdown is affected by the gas composition, pressure, and temperature, as well as the geometry of the electrodes and the applied voltage. These factors can alter the rate of ionization and the energy needed for breakdown.

## 4. What are the applications of the HV gaseous breakdown equation?

The HV gaseous breakdown equation is used in various fields, such as electrical engineering, physics, and atmospheric science. It helps determine the critical voltage needed for breakdown in different gas environments and can aid in the design of high voltage systems.

## 5. Can the HV gaseous breakdown equation be applied to all gases?

No, the HV gaseous breakdown equation is only valid for gases that follow the Townsend discharge theory. This includes gases like air, nitrogen, and argon. Other gases, such as sulfur hexafluoride, have their own breakdown equations due to their unique properties.