# Neon lamp: minimal breakdown voltage

I am looking at this formula from wiki for breakdown voltage in gas discharge lamps, and I see its linear by length (d) (oops, I see it's divided by $ln$)

$$\frac{Bpd}{\mathrm{ln}\ Apd-\mathrm{ln}\ (1+\frac{1}{\gamma_\text{se}})}$$

Does that mean that I can make tiny neon lamp with just 0.1 to 0.05mm spacing between electrodes and it will glow as low as 5V for example?

Are there any gases which have lower minimal breakdown voltage than neon?

I guess using niddles instead of parallel plates would also lower breakdown voltage, as field is stronger?

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Not at all! If there are no other paths than those of .1 mm, the lamp will not ignite at all, even not at the usual 70 to 140 Volts depending on elektrode material. –  Georg Nov 1 '11 at 23:44
@Georg I don't get it... You mean whole spacing will be in 'dark' area? I had an impression that as you narrow distance between electrodes, electric field increases and accelerates electrons faster... –  BarsMonster Nov 2 '11 at 8:43
Look for mechanism of glow discharge, without enough distance to develop a cathode drop, a discharge will not start. Have You ever seen those "candle flicker" glow lamps? The electrodes in that lamps have a distance of about one mm, nevertheless there is no discharge beween them. conrad.de/ce/de/product/550763/FLACKERKERZE-KLAR-230V-3W-E14 –  Georg Nov 2 '11 at 9:55

## 1 Answer

As $A$, $B$ and $\gamma_{se}$ are parameters that do not depend on the distance of the electrodes try to visualize $V=V(d)$ (all in arbitrary units):

The breakdown voltage increases dramatically for smaller electrode distances. In a normal neon lamp the electrons are accelerated by the electric field and excite the neon atoms. This can only happen if the electrons have enough kinetic energy when they collide with the neon atoms. If you reduce the distance between the electrodes and keep the other parameters constant the electrons will not have enough distance to accelerate before the hit the other electrode and you will not get a glow. To still achieve a breakdown you have to increase the voltage quite a bit. For even smaller distances the formula does not work anymore. Such high fields will probably lead to destruction of your electrodes from sparks between them.

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What about niddle electrodes? I had an impression that they give you stronger field -> should allow glow at lower voltages... –  BarsMonster Nov 8 '11 at 5:20
@BarsMonster: Electrodes with sharp features have a higher field gradient, this helps to create Corona discharges wiki article. In a neon lamp the glow is not due a sharp electrode and it would not really be beneficial. With a high field gradient you can ionize air molecules but in a neon lamp you instead sputter atoms out of the cathode which in turn collide with the gas molecules, excite them and you see the specific colors of the gas. –  Alexander Nov 9 '11 at 0:09