Attenuation of a laser in space?

The equation for the power emitted by a laser beam at a distance in a circle of radius $r$ at a distance $z$ where the beam diameter is $w(z)$ is $$P(r,z)=\frac{1}{2}\pi I_0{w}_0^2(1-e^{-2r^2/w^2(z)})$$ where $I_0$ is the initial intensity and $w_0$ is the initial beam diameter (see these course notes). If we assume that the entire diameter of the beam hits the target, then we can set $r=w(z)$ and get $$P=\frac{1}{2}\pi I_0{w}_0^2(1-e^{-2})$$ We could write $I_0$ as a function of the electric field amplitude $E$ and the characteristic impedance $\eta$ (see this presentation), but it might be better to just work off of numbers. At any rate, this equation assumes that all of the beam hits the target, which isn't necessarily the case. Were we to use the world's most powerful laser, we could get around 1.3$\times$10¹⁵ watts of power - for half of a trillionth of a second.

Let's think about beam divergence, and the Rayleigh length. This is the value of $z$ for which $w(z)=2w_0$. It is given by $$z_R=\frac{\pi w_0^2}{\lambda }$$ The NIF laser operates at a wavelength of 351 nm (Haynam et al. (2007)), with all 192 beams being focused through a hole less than 1 mm in diameter. Assuming that our lasers have beam widths of about this much, then we have a $z_R$ of ~22 meters. That's not good.

However, this is because the beams must be so small. The Boeing YAL-1 could have been effective at up to 300 kilometers (see a summary of a report). So if we up the power, then we could in theory get results more like the ones seen at NIF - really, really explosive. A couple hundred kilometers should be achievable.

Laser shielding is a whole different problem. At these energies, there's not a whole lot that can stop these lasers. Most things will catch fire or blow up (or both). Heck, that's why the NIF uses them!

One option is to use a shield of "trash" - basically, laser cannon fodder. It gradually gets eaten away by laser attacks.

Problems:

1. It blocks the vessel from doing anything (seeing the opponent, launching missiles, etc.).
2. It's temporary, must be replaced, and may not last long.

A second solution might be to use a shielding gas. This is commonly used in industrial welding to absorb some heat from welding lasers. I have absolutely no idea if it could work. You would likely need to rig up a magnetic field to contain it (if possible), and it would obscure visible light. But it might be better than nothing.

posted about 9 years ago

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