---
title: "Streamer theory of breakdown in gases"
subject: "High Voltage Engineering"
chapter: 6
key: "semester_8/high_voltage_engineering:streamer-theory-gases"
source: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/streamer-theory-gases
site: BCT Engineering
---

# Streamer theory of breakdown in gases

High Voltage Engineering · Chapter 6: Dielectric Breakdown

- Asked in: 2071 Magh, 8 marks
- Video: [Streamer Theory | Breakdown in Gas | High Voltage Engineering #streamer #highvoltage #viral](https://www.youtube.com/watch?v=lUvwdVv2Cxc) — Prasant Decodes
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/high_voltage_engineering/streamer-theory-gases
- Whole chapter: https://www.bctengineer.com/md/semester_8/high_voltage_engineering/chapter-6

## Question

Describe the streamer theory of breakdown in gases.

## Short answer

Streamer theory explains high-pd breakdown: a single avalanche with ~10^8 charges distorts the field, photo-ionization creates secondary avalanches, and a plasma channel grows rapidly to bridge the gap. Meek's criterion E_r = E and Raether's alpha x_c = 17.7 + ln x_c define the critical condition.

## Answer

The **streamer theory** (Raether and Meek, also Loeb) explains spark breakdown of gases at high $pd$ (above about 1000 torr·cm, e.g. long gaps in atmospheric air), where Townsend's theory fails. It states that a **single electron avalanche**, when it becomes large enough, distorts the field by its own space charge, and **photo-ionization** in the gas then produces a conducting plasma channel (streamer) that rapidly bridges the gap.

#### Why a new theory was needed

- Observed formative time lags ($\sim10^{-8}$ s) are much shorter than Townsend's prediction (time for ions to cross the gap, $\sim10^{-5}$ s).
- Breakdown at high $pd$ does not depend on the cathode material.
- Sparks are thin, bright, branched channels, not diffuse glows.

#### Mechanism

```text
 (a) avalanche          (b) space charge
 C|  e- ->  ->  ->|A    C|      - - +++++|A
                         field enhanced near head

 (c) photo-ionization   (d) streamer
 C|   . <- . <- +++|A   C|<======plasma===|A
     secondary avalanches   channel bridges gap
```

1. **Primary avalanche:** a free electron near the cathode starts an avalanche ($e^{\alpha x}$ electrons) that moves to the anode.
2. **Space charge:** electrons move about 100 times faster than ions, so the avalanche head carries electrons while a cone of slow **positive ions** is left behind. When the avalanche reaches the anode, the electrons are absorbed and the positive space charge remains.
3. **Field distortion:** the space-charge field $E_r$ adds to the applied field near the space charge and becomes comparable to it once the avalanche has about $10^8$ charges.
4. **Photo-ionization:** excited atoms in the avalanche emit photons, which ionize gas molecules near the positive space charge, creating new electrons.
5. **Secondary avalanches:** these electrons start avalanches in the enhanced field and flow into the positive space charge, forming a quasi-neutral plasma. The positive tip moves forward.
6. **Streamer propagation:** the process repeats, so a conducting **cathode-directed streamer** grows very fast (about $10^8$ cm/s) towards the cathode. When it reaches the cathode, a highly conducting channel connects the electrodes: **spark breakdown**.

If the voltage is well above minimum, the avalanche can become critical mid-gap, and **mid-gap streamers** grow towards both electrodes.

#### Breakdown criteria

**Meek's criterion:** breakdown occurs when the radial space-charge field at the avalanche head equals the applied field ($E_r \approx E$):

$$
E_r = 5.27\times10^{-7}\,\frac{\alpha\,e^{\alpha x}}{(x/p)^{1/2}}\ \text{V/cm}
$$

Putting $E_r = E$ and $x = d$ gives the minimum breakdown voltage for the gap.

**Raether's criterion:** a critical avalanche size is needed:

$$
\alpha x_c = 17.7 + \ln x_c \quad (\text{about } e^{\alpha x_c} \approx 10^8)
$$

#### Features explained

| Observation | Streamer explanation |
|---|---|
| Very short time lag | Photons travel at light speed; no ion transit needed |
| Independence from cathode | Secondary electrons come from gas (photo-ionization) |
| Thin, branched channel | Streamer follows photo-ionized paths |
| Valid at high $pd$ | Large avalanches build enough space charge |

The two theories complement each other: Townsend's mechanism applies to short, low-pressure gaps (low $pd$), and the streamer mechanism to long gaps at atmospheric and higher pressures.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which observation was Townsend's theory unable to explain?
   A. Exponential current growth
   B. Short time lags, thin channels and cathode independence
   C. Existence of ionization
   D. Paschen's law
   Answer: B. These led to the Raether-Meek theory. (Key point: Why streamer)

2. Why does a positive space charge remain after the avalanche?
   A. Ions move faster
   B. Electrons are not produced
   C. Ions are neutral
   D. Electrons move ~100 times faster than ions
   Answer: D. Electrons are absorbed at the anode; slow ions remain. (Key point: Space charge)

3. What role does photo-ionization play?
   A. Photons create electrons near the space charge, starting secondary avalanches
   B. Photons knock electrons from the cathode
   C. Photons slow ions
   D. Photons recombine electrons
   Answer: A. Secondary avalanches feed the plasma streamer. (Key point: Photo-ionization)

4. What is the critical avalanche size?
   A. About 10^2 charges
   B. About 10^12 charges
   C. About 10^8 charges, alpha x_c = 17.7 + ln x_c
   D. One electron
   Answer: C. At that size space-charge field equals applied field. (Key point: Raether's criterion)

## Related in High Voltage Engineering

- [Townsend current growth with secondary ionization](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Atownsend-current-growth-secondary) — High Voltage Engineering, chapter 6, asked 2×