Safe Approach and High Power
Does electricity arc more easily in a vacuum? I have a
"safe approach" table for high power electrical lines. As altitude
goes up the safe approach distance increases. Why does this happen?
Not in a vacuum, but in low pressure air. An electrical arc involves
the ionization of air molecules. This is an equilibrium process:
the electric field ionizes molecules, and those ions recombine with
any electrons that may be nearby. When air pressure is high, ions
recombine relatively quickly, because ejected electrons cannot go far
away, because they are likely to have collided with other nearby air
molecules. When air pressure is low, ejected electrons are likely to
get farther away, and it takes longer for ions to find electrons to
recombine with. So the recombination rate goes down, the equilibrium
is pushed toward more ionization, and a smaller electric field can
succeed in causing enough ionization to make a path for an arc.
Not so easily in a perfect vacuum, but _very_ easily in thin gasses.
Little Neon bulbs have around 1% of an atmosphere in them,
and it only takes 60v to break down the gas in the 1mm electrode gap.
In 100% of an atmosphere, 1mm takes more like 5000v.
The change in between 1% and 2000% (20 atm) is smooth and steady.
Denser air is a stronger insulator.
Spacecraft on the way up, and unpressurized high altitude aircraft,
have to be really careful with this.
Air with an electric field is like a concrete slope with occasional
each sitting in its own dimple.
If they are too close together or the slope is too shallow,
a ball that escapes its dimple will not have enough downhill run,
and the next ball it bumps will not be dislodged from its dimple.
It requires a chain-reaction, an avalanche,
to be like the abruptly huge conductivity of a spark.
The hillside must be a river of rolling balls to be "conductive".
For a freed electron in air,
the mean-free-path must be long enough to gain about 20V of potential
for it to ionize the next air molecule it impacts.
(For a 2000v air gap, the electron must be able to "free-fall" about
1% of the gap distance before hitting more molecules.)
Otherwise it's just an unnoticeably small bit of static charge in the air,
which slowly works its way over to the positive solid surface and is gone.
web search "Pashcen curve"
here is one:
I would like to suggest wikipedia, but unfortunately there is little
content in its Paschen curve article yet
Maybe it will be better
At higher altitudes, the air is thinner, and the mean-free-path is longer,
so the air is easier to break down.
The safe distance for a given voltage increases proportionately.
The distance that electricity will arc between two conductors is a
complicated function of air pressure and the shape of the conductors.
Rather than tabulating jump distance as a function of voltage, people
usually measure a "breakdown voltage" which is the voltage above which an
electric arc will jump between the conductors. Low breakdown voltage means
Paschen discovered this effect before 1889. He found that at good vacuums,
the breakdown voltage is very high, at 1/1000 of an atmosphere the breakdown
voltage is quite low, and the breakdown voltage increases and keeps going up
with increasing pressure up to atmospheric and beyond.
You might think that the more gas pressure there is, the easier it would be
for the arc to jump. That is not the case.
A very good vacuum is an excellent insulator. A gap of a mm will withstand
a potential across it of tens of thousands of volts. That is because there
is no means of conduction for the electricity. There are no gas molecules
present. Only at tremendous electric fields will electrons be pulled from
the surface of the material itself.
But some gas molecules are added, it becomes VERY easy to a plasma to start
and conduct electricity. The molecules normally hang onto their electrons
and are neutral. It takes a few volts of energy to jar an electron loose.
The molecules provide a source of electrons and ions to conduct electricity.
If a neutral gas molecule loses an electron, the electron moves rapidly
toward the positive plate. (the positive ion moves toward the negative
plate but because it is much heavier it goes slowly.) If the pressure is
low, the electron will travel a small distance, gain energy from the
electric field, and then strike another molecule, and release another
electron or two. And so on and so on. At about 1/1000 of an atmosphere,
the discharge voltage across a 3 mm gap between two plates is about 300
At full atmosphere pressure, the discharge voltage across a 3 mm gap is
about 60,000 volts. That's high, much higher than in a rough vacuum,
because there are so many molecules of air present that it is difficult for
the discharge to start or keep going. Although the voltage might be 60,000
volts, the molecules are packed so close together that neither an electron
or ion can acquire enough energy to start or keep the ionization going. At
very high pressures, the gas is an even better insulator. Sulfur
hexafluoride at high pressure is used in accelerators as an insulating gas.
The easy breakdown at 1/1000 of an atmospheric pressure corresponds to a
height in earth's atmosphere of about 150,000 feet. Missile and spacecraft
designers need to be aware that the kind of electrical insulation and
spacing used on earth does not work in space! At the altitudes which
airplanes fly, it is about ten times easier to initiate an arc discharge
than on the ground.
The shape of the conductors makes a difference too (sphere, wire, flat
plate, etc.) Another factor is whether the electricity is static (DC) or
whether it is alternating, and if so, at which frequency. The snakes of
bright plasma inside "plasma globes" that are purchased in stores are quite
long, and are driven by an alternating voltage of many kilohertz, at many
Industry does plasma processing with alternating current at about 13
megahertz. It is very easy to get a plasma going in side a vacuum chamber
at high frequency with only a few hundred volts.
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Update: June 2012