Thermal Superconductors vs Pulse Lasers...in atmosphere

Question

Based of a conversation with @Starfish Prime regarding the answers from this question here.

In short, while the question itself had a satisfactory answer with it being that pulse lasers would absolutely shred thermal superconductors, Starfish Prime pointed out that due to the fact that I neglected to mention that I was envisioning the question to apply to terrestrial pulse lasers; the answers given were instead made with the assumption that I was talking about pulse lasers and thermal superconductors in space.

With that little embarrassing oversight now glaring at me. Let me ask:

How well would thermal superconductors fair against pulse lasers in atmosphere at sea level?

Answer 1

TL;DR: in an atmosphere, thermal superconductors might actually be less useful than in space.

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In an atmosphere, your laser power is limited by atmospheric breakdown... the point at which the beam is intense enough that the small portion of it that is absorbed by the atmosphere is enough to cause ionization. You then get a cascade of ionization products amd a cloud of plasma which is effectively opaque to your laser beam, and all the energy gets absorbed into the plasma with a bang and a flash of broadband light.

The physics of atmospheric breakdown are fiddly, but Luke Campbell has a convenient approximation for breakdown of averagely dusty air: $$I_{th} = {3.6\times10^{-5} \over {\lambda^2 \left (p \tau \right)^{0.6}}}$$ where $p$ is the air pressure in atmospheres (multiples of 10⁵ Pa), $\lambda$ is the wavelength of light in meters and $\tau$ is the pulse duration in (presumably) seconds, given a breakdown threshold intensity $I_{th}$ in W/cm². Remember, this is just an approximation and can vary by at least one order of magnitude in either direction depending on the cleanliness of the air, but it gives you an idea of the relationship of the interesting parameters.

Now, the longer the pulse (eg. as $\tau$ gets larger) the lower $I_{th}$ gets, because there's more time for electrons to get loose and be accelerated into neighbouring molecules and an ionization cascade cause the cloud of laser-absorbing plasma to appear. Also, the longer the pulse, the more the effects of the laser are thermal in nature. This means that the kind of lasers that thermal superconductors are most effective against are also the ones most likely to cause atmospheric breakdown.

It turns out that once you've got hold of sufficiently tough and refractory armor (boron nitride nanotubes are good in an atmosphere with lots of oxygen, like Earth's, and carbon materials are better in reducing atmospheres as they have a slightly higher melting/boiling point) then in anything but squeaky clean air you may well find that longer-pulse (≫ 1 ns) lasers powerful enough to punch a hole in the armor just can't reach the targets. Even if the air was squeaky clean, once you start firing megawatt and gigawatt lasers about there'll be plenty of smoke and dust arising.

Ultrafast lasers with subnanosecond pulses have a large $I_{th}$, which means they can have peak energies sufficient to punch holes in that kind of armor. They also cause enough nonlinear optical effects on the target that they no longer cause strictly thermal damage, and peak power levels are pretty high anyway so they're unlikely to be fazed by thermally superconducting armor, which in any case is unlikely to be nanotube-tough and therefore highly vulnerable to projectile and fragment damage.

This means that you almost always want to use some kind of nanotube material based armor, because it'll shrug off insufficiently powerful lasers and it'll be effective against projectile weaponry of the sort that can past through dirty smoky air unhindered. There's not obviously much use in having thermal superconductors as armor.

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_{Note, for those of you thinking of using plasma to protect you from lasers: plasma is energetically costly to produce, generally quite hot, and exceedingly difficult to confine with sufficient density to be opaque to enemy lasers. It is also extremely visible, and won't protect you at all from projectiles or blasts, and you won't be able to see through it. It is very much a case of the cure being worse than the disease. You'd be better off with a low-density fog generator.}

Answer 2

There is no different answer than those you got already.

Any weapon designer worth their title would account for atmospheric induced distortion and disturbance on the beam path, to ensure the target is reached by the needed amount of laser power.

This means that the effect will be the same, unless there is something like a heavy sandstorm in the path of the beam, which would severely affect and dampen the beam intensity. But also in that case I would expect the user manual to mention "do not fire the laser through a sandstorm".