# Single Photon Ionization

Light is composed of individual packets, or quanta, of energy. A single quanta of light is called a photon. The energy of one photon is 1.24×10-6 divided by the light's wavelength in meters. The energy is in units of electron volts, or eV, a common unit used for describing energies on the atomic or molecular scale. One eV = 1.602×10-19 Joules.

When the energy of one photon is greater than the energy which holds an electron to an atom, the atom can absorb the photon and be ionized. This is a linear process, so all the effects of single photon ionization can be handled using the methods described in the section on Linear Absorption and Scattering.

It takes 13.6 eV to ionize atmospheric oxygen and 14.5 eV to ionize atmospheric nitrogen, so the shortest wavelength of light that can shine through air without ionizing it is around 1×10-7 meters. This is the boundary between the near ultraviolet, where light can shine through air, and the vacuum ultraviolet, where light is absorbed almost immediately and cannot go farther than a few millimeters. Even the soft x-rays cannot go more than a few centimeters through air. It is only when you reach the very short hard x-ray and gamma ray wavelengths that ionizing light can travel an appreciable distance in air, but even these have attenuation lengths of less than a kilometer. As a result, VUV, x-ray, and gamma ray lasers are primarily useful in the vacuum of space where their short wavelength allows them to be focused at great distances due to limited diffraction effects.

There is, however, a possible way around this limit. If the atoms in the air have lost so many electrons that there are no more electrons with low enough binding energies for the light to knock out, then air can no longer absorb light by being ionized by that light. This is called bleaching. So if an intense pulse from an x-ray death ray shines through the air, the leading edge of the pulse can be sacrificed to knock all of the electrons off air atoms that are bound by less than the photon energy, allowing the rest of the pulse to shine through. This, of course, absorbs energy from the beam so the further the beam goes the less energy it has to deliver to the target. Since the higher the energy of the photons in the beam, the more electrons that can be knocked out, higher energy beams lose more energy for a given volume of air that is bleached.

There is still a limit to how far bleaching can get you. This happens because free electrons can scatter light out of the beam - a process called Thompson scattering. As you might expect, when there are more electrons in the air, the light gets scattered more rapidly. Thus, for beams with higher photon energies going through bleached air - and thus going through denser free electrons - the light scatters more. Thompson scattering is linear scattering, as described in the section on Linear Absorption and Scattering.

Still, there is a way around the Thompson scattering limit, too. Shoot a pulse with just enough energy to bleach the air out to somewhat less than the Thompson scattering length. Wait a short amount of time for the super-heated air to expand to a semi-vacuum. The rarefied air in the beam path now has many fewer electrons to scatter the death ray's light. Thus, another pulse shot down the same path can get to the unbleached air while losing very little light to scattering. In this manner, subsequent pulses can blast their way through the air, burning a hole in the atmosphere in order to reach their target.

The same pulse-and-wait method used to overcome Thompson scattering can also be used to decrease the energy needed to ionize a transparent path through the air. A leading pulse partially ionizes the air without fully bleaching it. The hot air-plasma then expands to a lower density, and a subsequent pulse can strip the remaining electrons to a fully bleached state. Since there are fewer atoms to be bleached, less energy is required.

For earth air at sea level, this is summarized in the table below. Each line corresponds to a threshold photon energy - if that energy is not reached the extra absorption and scattering do not occur. For example, a 14.4 eV photon beam has the same bleaching energy and scattering length as a 13.6 eV photon beam, since it has not yet reached the 14.5 eV threshold that would cause extra asborption and scattering.
 photon energy (eV) wavelength (m) bleaching energy (J/cm3) scattering length (m) 13.6 9.07×10-8 22 1500 14.5 8.50×10-8 115 300 29.7 4.17×10-8 306 166 35.2 3.52×10-8 362 150 47.6 2.60×10-8 667 107 55.1 2.25×10-8 756 100 77.7 1.60×10-8 1380 75 98.2 1.26×10-8 2010 62 114.3 1.08×10-8 2190 60 138.6 8.95×10-9 2410 58 554.0 2.24×10-9 5960 50 669.3 1.85×10-9 10300 44 741.8 1.67×10-9 11400 43 874.4 1.42×10-9 12800 42
Once you get above 874.4 eV of photon energy, the beam will be ionizing all of the electrons in the air and you don't suffer any worse performance as you increase the photon energy. Note that when converting values to use consistent units, J/cm3 = MJ/m3 - remember this when using the formulas below and keep everythin in terms of meters for calculations (or convert everything in meters into cm, as long as you are consistent it will all work out).

So far, it seems that the higher in photon energy you go, the worse your performance becomes. However, because of diffraction the shorter wavelength, higher photon energy beams can remain tighly focused for longer. This means that they can start out with a narrower beam so that they have to ionize less air overall. This can actually increase the range in some cases.

A beam with wavelength λ that initially starts with a width of S can maintain a width of approximately S for a distance of

b = π S2 / (2 λ).
In this range, every meter will absorb an energy equal to π S2 /4 times the bleaching energy given in the table above. At a distance of approximately b and 1.5 b, the beam will be approximately twice as wide and thus will absorb approximately 4 times as much energy per meter. Between 1.5 b and 2 b, the beam will be three times as wide and will thus absorb approximately 9 times as much energy per meter. Each additional 0.5 b increases the multiple of the original beam with by one, and the energy absorption increases by the square of that. Thus, beyond the distance b the beam quickly balloons and will absorb all the beam energy.

For example, to get a 100 meter range of near constant width with an 3.53×10-8 m wavelength, you need a width of 1.5 mm. This will absorb 540 J per meter over this length. Compare this to a 2.25×10-9 m beam. To get a near constant width over 100 m it needs a width of 0.038 mm, which means it will absorb 270 J/m. Depsite absorbing more energy for a given volume of bleached air, it can be made narrow enough that it doesn't need to bleach as much air and ends up wasting less energy burning a hole through the air.

### Effects on Target

When the beam reaches its target, it will interact with the target in the same way it interacts with the air. To a reasonable approximation, the energy to absorb the beam depends only on the mass of target per unit area the beam has to go through. Since a human body is about 800 times denser than air, it will take about 800 times as much energy to go through a given length of meat and bone as it takes to go through air. Heavy metals in the target can make it more effective at absorbing the beam for high energy photons, but it will not make too much of a difference for the energies listed on the table.

Since the beam is pulsed, it will act like a blaster. However, these EUV and soft x-ray beams are not absorbed by the plasma they create - they will just shine through the plasma to ionize to a bleahced plasma the first un-ionized matter they touch. All of the energy absorbed in this process remains in the high pressure plasma, which will explode outward to create a wound channel significantly wider than the initial beam diameter. (This only strictly applies to beams with wavelengths shorter than about 6×10-8 meters in material with the density of meat, or about 2×10-8 meters when going through steel. Longer wavelength VUV beams will be absorbed and cause surface explosions, like the usual blasters).