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Consider a collimated light beam in a vacuum (I am being unspecific about the frequency, anything from radio to gamma). If the beam power/cross section was increased indefinitely would new phenomena occur at certain energy densities?

I gather that pair-production couldn't occur due to momentum considerations but would there be some interaction with the quantum vacuum?

At sufficiently high power is there a self-gravitation effect of the beam, a point touched on by a previous question? What if the beam was reflected back on itself by a mirror?

Note: the motivation for this question relates to theoretical limits for beam weapons.

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Well, for one thing, if the beam was very energetic then the mirror wouldn't help you at all because photons also carry momentum which translates to pressure on the surface and so they would pound the mirror and there's only so much pressure any material can withstand... Of course, I am ignoring lots of other effects of why the mirror wouldn't work at high intensities (e.g. every mirror also absorbs a little, so with a powerful enough beam you would burn it...). –  Marek May 11 '11 at 12:27
With the surface of a mirror defence system scattering some of the incident beam, I wonder whether you would also see electron-positron pair production if you were using, e.g. a gamma ray beam. That would certainly encourage the mirror to ablate further. –  Nigel Seel May 11 '11 at 13:17
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You have some information about photon-photon scattering in vacuum on the Extreme-Light Infrastructure's website. In particular, they say

For electric fields $E\sim mc^2/λ_C ~ 10^{29} {\mathrm W}/{\mathrm cm}^2$, where $λ_C$ is the Compton wavelength (Schwinger (1951)), virtual electron-positron pairs will be able to separate and become real.

Which means that various interesting effects happens here, even in vacuum, limiting the power of the light beam.

While ELI's website shows that it these effects will probably seen in not too futuristic experiment, this density is expected to be reached in very short (attosecond) pulses at a low repetition rate. For a weapon, the relevant quantity is the average power, and making a weapon which concentrates the power of $10^{20}$ nuclear reactor in one cm² doesn't seam very realistic, except if you build a Death Star ;-)

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I did a crude back of the envelope estimate of gamma ray burst intensity, and came up with 1e23 W/cm^2, so that is a really extreme power density you are taking about. Anything actually doable would be many many orders of magnitude weaker than that. –  Omega Centauri Jun 10 '11 at 17:57
As I understand it, momentum conservation requires that two photons with opposite momenta have to interact in order for real pair-production to occur at these extreme energy densities. This would preclude a non-reflected beam hitting a limiting power (unless interaction with the CMB would do it?). –  Nigel Seel Jun 10 '11 at 19:42
@Nigel I agree. For any given beam, you can find a frame where it has negligible power. –  mmc Jun 11 '11 at 3:06
@Nigel what you describe is first order diagrams. Second and higher order diagrams in a coherent beam can materialize pairs out of the vacuum. The momentum of the pair will be following the beam direction but the individual electron and positron will acquire a transverse momentum which is what will destroy the beam in addition to presenting a target to the following photons. –  anna v Jun 11 '11 at 7:53
@Omega Centauri : You're right on the average power (which, again, is the relevant figure for a weapon). But pulsed lasers can perform miracles in terms of peak power, and the number cited are a long term goal for the ELI, which is will be a building-sized laser. With all these caveats, the numbers cited are realistic. (And certainly more than the gravitational effect of light ;-) ) –  Frédéric Grosshans Jun 13 '11 at 17:36
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OK Georg, I am replying to this because it is coming around once more, and good answers exist in wikipedia. as I am too rusty to sit and calculate.

Laser beams begin to cause plasma breakdown in the air at energy densities of around a megajoule per cubic centimeter. This effect, called "blooming," causes the laser to defocus and disperse energy into the atmosphere. Blooming can be more severe if there is fog, smoke, or dust in the air.

So the effect of strong energy in a laser beam ( the one known coherent electromagnetic weapon grade) turns air into plasma after a certain energy density. It will melt whatever it hits at those energies, which after all is the purpose of the weapon. Mirrors are out because the reflecting surface absorb part of the radiation and will be destroyed at such energy densities.

In principle a coherent high energy density beam of soft photons could also pair produce by higher order diagrams, but one would have to calculate at what energy density this would destroy the beam even in vacuum.

If the question is really "how to defend a target from a laser weapon", the answer is "smoke", aluminum confetti and such.

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