Dielectric Breakdown

An electron is happily mining its own business floating freely around in the air when suddenly a high power laser beam comes by. How rude! The electric field of the laser beam starts tugging on the electric charge of the electron, accelerating it to faster and faster speeds. Soon, the electron has more than enough energy to knock out other electrons that are stuck on to atoms. Now the electric field starts tugging on these newly freed electrons, too, and they start knocking off more free electrons of their own. Soon, you get a runaway process where the air turns into an electron soup. This electron soup is called a plasma, and the air has just experienced dielectric breakdown.

You need to get a couple things right in order to get dielectric breakdown. First, if the electrons bump into air molecules before they gain enough energy to knock out additional electrons, then they just get scattered in random directions and need to be re-accelerated by the field. So too dense of air or not strong enough laser light means free electrons just bounce off air molecules without ever starting the breakdown cascade.

Second, light is a wave, and it has a frequency. This means the electric field periodically turns around and pulls the electrons the other way. All that energy they’d been getting from the field is now being drained away. If the laser light’s frequency is high enough, the electrons just jiggle up and down slightly without ever getting enough energy to start the breakdown process.

As you might have guessed by now, this process is not good if it happens part-way along your beam when you are trying to shoot a bad guy. Ripping off all those electrons takes a lot of energy, energy that comes from your beam! Not only that, but plasma is hot, low density, and has funky electrical properties that turn it into a lens. The light it doesn’t absorb gets scattered out of your beam and away from your target. And finally, if the wavelength of your beam is longer than somewhere between 5 and 2 μm (65 to 150 THz or0.3 to 0.7 eV, in sea level density air and depending on how much ionization occurs), the plasma just directly absorbs your beam, using your beam’s energy to heat itself up even more so it can absorb and scatter your beam further. Not nice, plasma! Are you working for my target, perhaps?

But will your design for a laser beam death annihilation ray suffer from breakdown? Here’s a way to get a quick estimate. Find the threshold intensity $I_{Th}$

${\begin{array}{lll}I_{Th,CW}&=&0.31\left[{\dfrac {1\,{\mbox{m}}}{\lambda }}\,\left({\dfrac {10^{5}\,{\mbox{Pa}}}{p}}\right)^{0.6}\right]^{2}\\I_{Th,pulse}&=&6.35\times 10^{-5}\left[\left({\dfrac {1\,{\mbox{m}}}{\lambda }}\right)^{2}\,\left({\dfrac {10^{5}\,{\mbox{Pa s}}}{p\,t}}\right)^{0.6}\right]\end{array}}$

where $P$ is the beam power, $E$ is the beam energy, $t$ is the beam duration, $p$ is the air pressure, and $\lambda$ is the beam wavelength; and take $I_{Th}$ as the larger of these two. If

$I={\frac {4\,P}{S^{2}}}={\frac {4\,E}{tS^{2}}}$

is close to $I_{Th}$, there’s a risk you’ll start a cascade breakdown, If it is much larger than $I_{Th}$, you will almost certainly cause an air breakdown. If it is much less, you’re safe. Go ahead and blaze away!