ELEC5205 Chap.1 Gas Avalanche and Paschen Law
Gas Avalanche and Paschen Law
From collision to conducting channel
Gas breakdown begins when free electrons gain enough energy between collisions to ionise molecules. The effective coefficient alpha prime subtracts electron attachment from ionisation, and its path integral controls avalanche multiplication. Once space charge becomes strong enough, photoionisation seeds secondary avalanches and a streamer develops.
Paschen law connects the ideal uniform-gap breakdown voltage to pressure times distance, but electrode roughness and near-vacuum collision limits define where that shortcut fails.
Begin with an electron-energy balance
An electron accelerates between collisions and gives energy back when it strikes a molecule.
If the field and mean free path permit ionisation, one electron can create additional free electrons and positive ions. Attachment removes electrons from that multiplying population. The net coefficient is therefore more useful than the ionisation coefficient alone.
Write its units as inverse length, state whether the field is uniform, and treat the exponential as accumulated multiplication along a path rather than as an unexplained memorised law.
Recognise the avalanche-to-streamer transition
A Townsend avalanche initially develops without greatly changing the imposed field. As its charge grows, the head and trailing ions create space charge that reshapes the local field.
Photons can create seed electrons away from the original path, allowing new avalanches to merge into a streamer. This is a change in mechanism: the discharge no longer depends only on primary multiplication.
A numerical criterion estimates onset, but the explanation should also describe why growth can continue faster and over a larger region.
Use pressure-distance scaling within its regime
Pressure changes molecular number density and therefore collision spacing; gap distance changes the available acceleration and multiplication path. Their product captures the balance for an ideal uniform field and a specified gas.
Near the Paschen minimum, neither too many short collisions nor too few collision opportunities dominate. At high pressure, small electrode asperities and particles can control local stress.
At very low pressure, ordinary gas avalanche reasoning weakens and surface emission or desorbed gas can become decisive.
Audit a breakdown calculation
First convert the stated avalanche population or streamer criterion to a natural logarithm.
Next obtain the required effective coefficient, invert the supplied empirical relation for field, and multiply by distance only when the uniform-field assumption is justified. Preserve units through every inversion.
Finally, compare the result with the geometry and environment: a calculated uniform-gap voltage does not prove that real electrodes are smooth, that pressure is in range, or that the initiating electron supply is adequate.
What this chapter covers
- 01
Effective Ionisation
- 02
Avalanche Growth
- 03
Streamer Criterion
- 04
Paschen Law
- 05
Pressure-Distance Boundary
- 06
Uniform-Field Assumption
Worked example · free
Invert an avalanche threshold
- 2Convert the streamer population to the required net ionisation coefficient.
- 2Invert the empirical relation for field magnitude.
- 2Multiply by gap length and qualify the model.
Key terms
- Effective Ionisation
- Effective Ionisation is the net electron-growth rate per distance after attachment is subtracted from ionisation.
- Streamer Criterion
- Streamer Criterion is the avalanche size or integrated growth used to mark transition into a space-charge-driven conducting channel.
- Paschen Minimum
- Paschen Minimum is the lowest region of a gas breakdown-voltage curve as pressure-distance product changes.
Gas Avalanche and Paschen Law FAQ
Why does avalanche size grow exponentially?
Each ionising electron can create additional electrons that undergo the same process, so the growth rate is proportional to the population already present. Integrating that proportional rate over distance produces an exponential rather than a linear relation.
When does Paschen law become unreliable?
It becomes unreliable when the assumed uniform gas process no longer dominates. High pressure-distance products expose field enhancement from roughness and particles, while near vacuum provides too few collisions across the gap for ordinary avalanche growth.
What changes when an avalanche becomes a streamer?
The avalanche space charge becomes large enough to distort the applied field. Recombination photons create new electrons around the original avalanche, and secondary avalanches combine into a fast ionised channel that can drive the gap toward breakdown.
Exam move
Derive the exponential once from a proportional growth statement, then practise converting a population threshold into alpha prime and voltage. Redraw the Paschen curve with its invalid high-pressure and near-vacuum regions. Finish by explaining why the streamer transition changes the mechanism, not only the electron count.
Maintain a unit table for pressure, distance, field and inverse-length coefficients, and run the calculated field back through the empirical relation as an independent check. Change one input at a time and predict the direction before calculating. For every pressure-distance answer, write one sentence identifying the geometry or surface assumption most likely to fail in practical hardware.
Compare that prediction with a deliberately sharp electrode case to decide when local inception replaces the uniform-gap model as the controlling analysis.
Working through Gas Avalanche and Paschen Law in ELEC5205? Sia is AskSia’s AI Electrical Engineering tutor — ask any ELEC5205 Gas Avalanche and Paschen Law question and get a clear, step-by-step explanation grounded in how ELEC5205 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
