ELEC5205 Chap.2 Nonuniform Fields, Pressure and Vacuum
Nonuniform Fields, Pressure and Vacuum
Three regimes, three controlling questions
A nonuniform gap requires integration of the local effective ionisation coefficient because field varies along the electron path. Compressed gas increases the influence of electrode asperities, particles and emitted starting electrons.
Near vacuum suppresses ordinary avalanche multiplication through long mean free paths, yet intense emission can heat the anode and release enough gas for a local discharge. Classification must precede equation selection.
Replace one gap field with a field path
In coaxial, point-plane and other nonuniform arrangements, the strongest field exists near the smaller or sharper electrode and decays with distance.
The effective ionisation coefficient therefore changes along the trajectory. Divide the path into physically justified intervals or integrate the supplied relation continuously. The accumulated exponent, not the maximum coefficient by itself, determines multiplication.
Record where attachment overtakes ionisation because extending the geometric gap beyond that point may add little active avalanche length.
Treat compressed gas as a surface-sensitive system
Increasing pressure raises gas density and can improve ideal dielectric performance, but it also shortens collision distances and makes a tiny region of extreme field more influential.
Protrusions, metallic particles and surface contamination may supply initiating electrons or create local avalanches. Statistical time lag matters when few starting electrons are available.
A pressure-vessel answer should therefore include field uniformity, electrode finish, particle control and inspection, rather than extrapolating a uniform Paschen curve without qualification.
Do not describe vacuum as an empty perfect insulator
At sufficiently low pressure, an electron may cross much of the gap without the collisions needed for ordinary avalanche multiplication.
Breakdown can instead begin through field emission from microscopic cathode features. The emitted beam may heat the anode, release adsorbed gas or vaporise material, creating a temporary medium in which a discharge grows. Surface preparation, conditioning, electrode material and stored energy become central variables.
This mechanism explains why simply lowering pressure does not guarantee unlimited withstand.
Choose the regime before the formula
Start by stating pressure range, geometry and likely initiating surface. For an ordinary nonuniform gas, calculate the local field and integrate net ionisation. For compressed equipment, examine particles, asperities and starting-electron probability alongside the gas relation.
For near vacuum, trace emission, heating and desorption. Finish with a discriminating observation: pressure trend, conditioning history, surface inspection, pulse timing or post-event damage. That observation tests the proposed mechanism rather than merely restating it.
What this chapter covers
- 01
Nonuniform Integral
- 02
Coaxial Field
- 03
Quasi-Uniform Gap
- 04
Electrode Conditioning
- 05
Compressed Gas
- 06
Vacuum Breakdown
Worked example · free
Estimate coaxial avalanche growth
- 2Calculate the local radial field at each representative point.
- 3Evaluate alpha prime and integrate across the bands.
- 2Compare with the streamer threshold and state numerical sensitivity.
Key terms
- Quasi-Uniform Field
- Quasi-Uniform Field is a mildly varying gap field that may still be treated with a controlled nonuniform calculation.
- Electrode Conditioning
- Electrode Conditioning is the removal or melting of surface defects through repeated discharge, often raising later breakdown voltage.
- Mean Free Path
- Mean Free Path is the average collision distance that determines whether electrons can multiply through enough ionising events.
Nonuniform Fields, Pressure and Vacuum FAQ
Why does compressed gas expose electrode defects?
High pressure can make the ideal bulk-gas prediction very strong, so local field enhancement and electron emission from microscopic hills or particles become comparatively important. Many starting electrons can reach streamer size with less avalanche gain.
Why can vacuum still break down?
A near vacuum provides too few collisions for a large ordinary avalanche, but a microscopic cathode feature can emit a narrow energetic electron beam. Heating at the anode may release trapped gas and create a local discharge path.
How should a coaxial gap be calculated?
Write the field from the radius-dependent geometry, evaluate the effective ionisation coefficient along the radial path and integrate it. An average field can conceal the strong inner-electrode region that controls avalanche growth.
Exam move
Build a comparison table for quasi-uniform gas, compressed gas and near vacuum. For each, record the initiating charge source, collision role, dominant surface effect and likely evidence. Practise one radial numerical integration and one verbal explanation of why Paschen scaling fails for opposite reasons at the two extremes.
Refine the integration near the smaller electrode and compare it with a coarse equal-band estimate to expose numerical sensitivity. For the surface-controlled regimes, pair every proposed mechanism with a test: repeated shots for conditioning, electrode inspection for asperities, pressure sweep for collision scaling, and post-event residue for heating or desorption.
Report the uncertainty introduced by radial step size, since threshold decisions near the boundary should not be reversed silently by coarse numerical sampling.
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