How to Build a Laser Death Ray
Atmospheric Breakdown
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How to Build a Laser Death RayAtmospheric Breakdown |
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Consider an electron floating in the air when a ray of light comes by. Electrons are electrically charged. Light is a wave in the electromagnetic field. This means the light causes an oscillating electrical field as it passes. The electrical field will exert a force on the electron, accelerating it first in one direction, then the other. If the electron can accelerate in one direction for long enough, before the field changes direction or before it bumps into another molecule, it can gain enough energy to knock an electron off another atom or molecule. Thus, when the electron does hit another air molecule, it creates another electron. This new electron can then create more electrons through the same process. Pretty soon the air breaks down in a cascade of ionization and becomes a dense plasma. Plasma will attenuate light of long enough wavelength, and a dense atmospheric plasma will rapdily absorb beams in the infrared, visible, and near ultraviolet such that they will not reach their target.*
This process requires an electron to be illuminated by the laser light. The shorter wavelengths can make their own electrons by absorbing several photons at once. Air with dust or other aerosols in it can create electrons by the laser being absorbed by the aerosol until it is heated to an ionized state. Even if you have clean air and a wavelength too long to create multi-photon ionization you can often get your seed electron from loosely bound negative ions in the air. For long wavelength light this can often result in breakdown being rather hit-or-miss, sometimes the beam encounters a dust speck or ion, sometimes it doesn't. How can you avoid it? The more intense your light, the faster the electrons are accelerated so the more energy they gain. Lowering the intensity will therefore stop cascade ionization. But we want a very intense beam to make a death ray! So, if the electric field of the light changes direction faster, the electrons will not have enough time to build up much energy before they start slowing down again. This means we want to use light of a higher frequency, which means we must use shorter wavelengths. In addition, very short pulses do not allow time for the electron cascade to multiply, allowing higher intensities. The interaction of lasers with the atmosphere to produce a plasma, and the propagation of the laser through that plasma, is an involved physical problem and we could not hope to give a complete treatment in these web pages. Some quick and dirty estimates are given below, appropriate for atmospheres of mostly nitrogen (such as that of Earth). These estimates cannot be expected to hold in all cases, and for some cases they may be off by an order of magnitude or more. Nevertheless, for a believable death ray for use in a science fiction setting these stimates should be sufficient. In dirty air - air with normal amounts of dust and lint and pollen and other impurities, a relation that works reasonably well for predicting breakdown for pulses longer than a few tenths of a microsecond is
Ith = 0.31 / (λ p0.6)2
where p is the pressure in atmospheres (105 Pa), λ is the wavelength in meters, and Ith is the breakdown intensity in watts per square centimeter. Thus, for example, air can withstand near infrared light of 1 micron (10-6 m) wavelength at intensities of up to 300 GW/cm2. Due to uncertainties in the quality of the air, actual breakdown intensities can differ from this by a factor of about 5 in either direction.
For short pulses in air, it is found that for a pulse of length τ, the threshold breakdown intensity scales roughly as Ith (p τ)0.6 = constant. To the same accuracy of our above equation we can write
Ith = 3.65×10-5 / (λ2 (p τ)0.6).
If this value is larger than the long-pulse length value, use it, otherwise use the long pulse length limit.
In Earth-like atmospheres, the creation of a plasma in the beam will result in rapid attenuation of the beam. However, for thin enough atmospheres the plasma will be sufficiently diffuse that the beam can propagate through the plasma. A mature breakdown plasma in a standard atmosphere will have a free electron density of around 1023/m3, and the beam will have an absorption length on the order of (10-12 / λ2) m. As the atmospheric density drops, the absorption length increases roughly in inverse proportion to the density. * Vacuum ultraviolet, extreme ultraviolet, x-rays and gamma rays can go through even the densest plasmas produced by air but, as described in the section on single photon ionization, the wavelengths that can go through plasma have difficulty going through anything that is not a plasma. Acknowledgements Thanks to Anthony Jackson for stimulating discussions and useful references on this subject. Reference
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