Breakdown in gaseous dielectrics

A gas is normally an excellent insulator because it contains very few free charges. Electrical breakdown of a gas is the change from this insulating state to a highly conducting state (spark or arc) when the applied field is high enough. It happens by collision ionization: free electrons accelerated by the field ionize gas molecules and multiply in avalanches.

How breakdown occurs (general process)

1. A few free electrons are always present (cosmic rays, UV, radioactivity).
2. In the field each electron gains energy $eE\lambda$ between collisions.
3. If this exceeds the ionization energy, a collision releases a new electron and a positive ion.
4. The new electrons are also accelerated: the number grows exponentially as an electron avalanche ($e^{\alpha d}$).
5. Secondary processes (ion impact and photons at the cathode, photo-ionization in the gas) produce new electrons that start new avalanches.
6. When the process becomes self-sustaining, current rises sharply and a spark channel forms.

Other processes: excitation, photo-ionization, attachment (electronegative gases like SF₆ capture electrons and so raise strength), and recombination.

The two main theories are the Townsend mechanism and the streamer mechanism.

1. Townsend mechanism (low $pd$, short gaps)

• Primary ionization: $I = I_0 e^{\alpha d}$, where $\alpha$ = ionizing collisions per electron per cm.
• Secondary ionization: positive ions, photons and metastables release $\gamma$ electrons per ion from the cathode. The current becomes

$$I = \frac{I_0\,e^{\alpha d}}{1 - \gamma\left(e^{\alpha d} - 1\right)}$$

• Breakdown criterion: $\gamma\left(e^{\alpha d} - 1\right) = 1$, or $\gamma e^{\alpha d} \approx 1$. The discharge then sustains itself without the external source.
• It leads to Paschen's law $V_b = f(pd)$ and is valid for $pd$ below about 1000 torr·cm.
• Limitations: predicts formative time lag of about $10^{-5}$ s (observed $\sim10^{-8}$ s) and a diffuse discharge, not the observed thin channel.

2. Streamer (Raether–Meek) mechanism (high $pd$, long gaps)

 cathode                          anode
   |   e- avalanche ---->  +++++ |
   |      photons  *  *   +++++  |
   |   <---- streamer (plasma)   |
   |      channel grows to       |
   |      cathode -> spark       |

• A single avalanche crossing the gap leaves behind a dense positive space charge near the anode, because electrons move fast and ions are slow.
• When the avalanche contains about $10^8$ charges, the space-charge field $E_r$ becomes comparable to the applied field.
• Photons from the avalanche head ionize gas nearby (photo-ionization); the new electrons form secondary avalanches that flow into the positive space charge.
• A conducting plasma channel (streamer) grows rapidly towards the cathode and bridges the gap: breakdown.
• Meek's criterion: breakdown when space-charge field equals applied field:

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

• Raether's criterion: $\alpha x_c = 17.7 + \ln x_c$, i.e. critical avalanche size $e^{\alpha x_c} \approx 10^8$.
• Explains short time lags ($10^{-8}$ s), the thin branched spark channel and independence from cathode material.

Comparison