Plasma Lasers
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Approximate magnitudes in some typical plasmas

Plasma Type ne cm-3 Te eV wpe sec-1 lD cm ne lD3 nenei sec-1
Interstellar gas 1 1 6 ´ 104 7 ´ 102 4 ´ 108 7 ´ 10-5
Gaseous nebula 103 1 2 ´ 106 20 107 6 ´ 10-2
Solar Corona 109 102 2 ´ 109 2 ´ 10-1 8 ´ 106 60
Diffuse hot plasma 1012 102 6 ´ 1010 7 ´ 10-3 4 ´ 105 40
Solar atmosphere,
gas discharge		 1014 1 6 ´ 1011 7 ´ 10-5 40 2 ´ 109
Warm plasma 1014 10 6 ´ 1011 2 ´ 10-4 103 107
Hot plasma 1014 102 6 ´ 1011 7 ´ 10-4 4 ´ 104 4 ´ 106
Thermonuclear
plasma		 1015 104 2 ´ 1012 2 ´ 10-3 107 5 ´ 104
Theta pinch 1016 102 6 ´ 1012 7 ´ 10-5 4 ´ 103 3 ´ 108
Dense hot plasma 1018 102 6 ´ 1013 7 ´ 10-6 4 ´ 102 2 ´ 1010
Laser plasma 1020 102 6 ´ 1014 7 ´ 10-7 40 2 ´ 1012
electron density     ne
electron temperature     Te
electron plasma frequency     wpe = (4pnee2 / me)1/2 = 5.64 ´ 104 ne1/2 rad/sec
Debye length   lD = (kTe / 4pnee2)1/2 = 7.43 ´ 102 Te1/2 ne1/2 cm
electron collision rate   nei = 2.91 ´ 10-6 ne ln L Te-3/2 sec-1
from page 40 of NRL Plasma Formulary (see diagram on page 41 and LANL site diagram from P-24 Plasma Physics Group in the Physics Division Annual Report, 1994)

Cool circumstellar dust and gas is constantly accumulating around a star which is rapidly ejecting plasma; the rapid cooling of the plasma when it encounters this shell can significantly enhance the non-equilibrium effects of adiabatic expansion. Gas contact is so effective at producing rapid cooling that Oda et al. (1987) have successfully operated an extreme ultraviolet plasma laser using this mechanism alone, without the slightest amount of expansion :

TPD-I, The Plasma Machine :
Gas-Contact Cooling Plasma Laser (TPD-I) : Magnetically confined stationary helium plasma lasing in XUV 164 nm when the column is cooled by hydrogen gas -contact. (Institute of Plasma Physics (IPP) Nagoya, Japan).

Another advantage in stellar atmospheres are the typically very large distance scales, a small population inversion produces radiation whose intensity would exponentially grow in amplitude over the large distances to the point where it dominates the spectrum with a strong broad emission line. The strongest manifestation of natural lasers occur in quasars.

Another disadvantage of laboratory plasma lasers is erosion damage.

'IT IS ALL DONE WITH MIRRORS'

In laboratory plasma lasers the lasing medium is of necessity limited to small scales compared to astrophysical lasers. This drawback is partly compensated by the advantage that we can place mirrors at both ends of the lasing medium to produce a laser which seems to be much longer in effective 'virtual' extent. By repeatedly bouncing off the mirrors the photons make many back and forth passes, effectively lengthening the lasing medium. Place yourself between a pair of parallel mirrors and see infinitely repeated images of yourself, until you can no longer see the images due to the greenish absorption of the glass and finite reflectivity of the mirrors.

Placing the lasing medium within a pair of mirrors also produces a Fabry-Perot resonant cavity whose spectral response is equivalent is the Airy function consisting of a sequence of cavity 'modes'. Each mode correspond to an electromagnetic standing wave which can occupy the cavity. With careful design, the laser can be made to oscillate in only one of these modes which results in a highly monochromatic collimated beam with extremely sharp spectral response.

NATURALLY OCCURRING, FUSION POWERED PLASMA LASERS

The maximum number of passes than a photon can make within a mirrored laboratory laser cavity is limited by absorption and upper level depletion, which is ultimately limited by the finite amount of energy pumped into the population inversion. The shorter the wavelength the faster the energy must be pumped into the upper levels. Although there are no mirrors in outer space, no such power restrictions occur in astrophysical plasma lasers, which are pumped by an enormously powerful fusion furnace.

AMPLIFIED SPONTANEOUS EMISSION

Even though most commercial lasers are designed to operate within a cavity and produce very sharp emission lines; this is not necessarily so for lasers without mirrors, especially in astrophysical environments where usually the spectral line is broadened by Doppler effects, turbulence and rapid plasma ejections. The stimulated emission occurs from many spontaneous emissions 'seeds' simultaneously, i.e. amplified spontaneous emission; a technical name for the phenomena of cooperative photon emission in the absence of mirrors. Since the amplification is exponential over distance the gain is strongest along an axis through which the longest path through the plasma can be attained. If the plasma is very elongated the emission occurs almost exclusively along that axis.

Table Top Laser Diagram 100 kilowatt Homebuilt Air Laser : pumped by electrical gas discharge, it produces coherent 337 nm UV radiation from a molecular nitrogen transition. There are no mirrors so the laser emits amplified spontaneous emission both in the forward and backward direction simultaneously. (Scientific American June 1974)

PRACTICAL USES OF PLASMA LASERS

PLASMA LASERS : HIGH-POWER, HIGH-EFFICIENCY LASERS

The simple fact the lasing medium is a highly ionized plasma readily lends itself to virtually unlimited power amplification.

High Power

Continuous high power lasing is possible by using the geometry of a plasma expanding away from a nozzle; since the decay of different parts of the plasma occur at different times the active lasing portion of the jet is constantly being replenished while simultaneously the depleted lasant is rapidly carried out of the active zone. This dual combination are two crucial ingredient in most high power lasers,
  1. Rapid overpopulation of the upper quantum level relative to the lower level.
  2. Rapid de-population of the lower lasing level by transport of depleted plasma out of the active lasing medium.

High Efficiency

High power can be achieved simultaneously with high efficiency by a suitable choice of initial plasma parameters before the rapid cooling takes place : In certain temperature ranges the thermodynamic population of certain ion species is almost exclusively dominated by the ion consisting of a closed electron shell. The ionization energy of an inert-gas like electron configuration is much larger than the energy required to ionize less stable configurations. The inert gas-like stage of ionization persists over a much larger range of temperatures, and for certain particular temperatures the competing ionic stages have negligible concentrations.

During the rapid cooling stage, almost all of these stable 'parent' ions within the plasma contribute to the rapid three-body recombination of the free-electrons into the upper laser level. This means that every ion in the plasma can potentially contribute a stimulated photon to the amplification process.

The extent to which the excited ions can coherently amplify the light is limited only by unwanted spontaneous emissions, and the requirement of maintaining a suitable inversion rate for the specific ratio of stimulated emission versus spontaneous emissions that the particular application requires.

The potential for high efficiency, unlimited power lasers is enormous, and its practical uses in industry are too numerous to mention here.

REFERENCES

  1. Oda,T. et al.: 1987, Short Wavelength Laser and Their Applications, Springer Verlag.
  2. Science on High-Energy Lasers: From Today to the NIF