Conditions are examined for which a nonequilibrium hydrogen plasma can be regarded as a medium with a negative absorption sufficient for the creation of a generator operating close to the frequencies of ionization of hydrogen from the ground or low-lying levels.
The analysis of radiation enhancement in a highly ionized plasma with inversely populated energy levels requires taking into account of the entire set of relaxation times (of the collisional radiative model). The detailed solution of this problem is far from complete; even in a qualitative consideration of the processes accompanying the decay of such plasma, it is convenient to distinguish the following three stages: 1) a strongly-ionized plasma with 'instantaneous' cooled free electron when the lower levels are still almost unpopulated; 2) a substantially-ionized plasma in which 'stationary drainage' has been established, with superpopulated upper levels; 3) a weekly-ionized plasma.
Rapid cooling of a megnetized plasma jet that expands into a vacuum is considered. The analysis shows that it is possible, in this way, to produce a medium with a nonequilibrium population inversion.
Some features of relaxation in a dense low-temperature highly ionized plasma of a many-electron chemical element are discussed. It is shown that the decisive role played by the collision transitions and the competition of various relaxation channels cause (under certain conditions) a number a number of levels of such a medium to acquire a population inversion that is practically independent of either the probabilities for spontaneous radiative transitions involving the frequencies in the infrared or visible spectra, or of the reabsorption of the radiation. This is an important property of lasers with a dense, highly ionized plasma (plasma lasers). The negative absorption coefficient in such a medium is very large. Numerical calculations for the case of recombining lithium plasmas illustrate the feasibility of the conditions formulated in the paper.
Numerical calculations based on the collisional-radiative model is made for rate equations of optically thin hydrogen plasma to give the collisional-radiative and population coefficients. Results are tabulated for the range of plasma parameters of Te from 1000 to 256,000 K and ne from 10^6 to 10^20 per cubic cm. Behavior of all the coefficients is analyzed as a function of electron density and as a result the asymptotic expressions of the coefficients at low and high electron-density limits as well as the approximate expressions of the critical electron densities for these asymptotic behaviors are obtained in terms of the rate coefficients for atomic transitions. Effects of trapping of resonance radiation on the coefficients are discussed.
Starting with a plasma of fully stripped ions (arbitrary Z) with an initial temperature and electron density, the set of rate equations governing the population densities of all discrete levels of hydrogenlike ions are solved. The results (population inversion and gain) are presented for a variety of cases, hydrogen through carbon, with emphasis on short-wavelength lasers.
In the rapid expansion of a dense, highly ionized plasma in the plasma laser, the electron gas is cooled, the plasma recombines, and lasing occurs on atomic transitions. A method of calculating these developed using quasistationary analytic population distribution functions over discrete levels. A quenching effect is considered for a hydrogen plasma and a radiative mechanism for emptying the lower level is analyzed. The possibility of an effective collision mechanism for lithium, helium, and beryllium plasmas is pointed out which would permit the use of large plasma volumes for generation. The dependence of population inversion on a number of parameters is studied.
A review is given of the investigations of lasers in which the amplifying medium is a rapidly recombining (supercooled in respect to free electrons) dense plasma. Efficient amplification of visible and ultraviolet radiation is possible in a plasma with free-electron density Ne = 10^13 - 10^18 cm^-3 and an electron temperature Te = 0.05 - 2 eV. At short wavelengths and high energies, the plasma lasers have important advantages over the conventional gas lasers in which the active medium is a gas-discharge overheated plasma which is being ionized. The purpose of the review is to identify the developing trends in the investigations of plasma lasers. An analysis is made of the recombination mechanisms of population inversion of atomic, ionic and molecular levels, of the methods of producing a supercooled plasma, and of the characteristics of different variants of plasma lasers. The general theoretical ideas are illustrated by numerical calculations and experimental results.
Using our time-dependent model we calculate the inversion density and gain for a visible line (6563 A) from hydrogen as a result of rapid cooling of a plasma. A visible plasma dynamic laser is shown to be possible under certain conditions.
Time-dependent inversion density and gain calculations are presented for n=2 to 1 and some n=3 to 2 transitions for cooled He+ and C+5 plasmas. The effects of radiation and the plasma cooling on the inversion density and gain coefficients are emphasized.
The conditions associated with a population inversion of the He I levels with principle quantum numbers 4 and 3 are studied in the supersonic expansion of helium from circular and plane nozzles into a low-pressure region. In an axisymmetric jet the population inversion arises at some finite distance from the nozzle; in plane jets the inversion occurs immediately beyond the slit nozzle. The experimental results are compared with calculations. The experimental data confirm the operation of a recombining mechanism for the population of the He I levels under the experimental conditions and show that a population inversion can be achieved by virtue of the difference in the rate of impact decay of the levels. The population inversion found experimentally corresponds to gain values of the order of 0.1 per meter. Diffusion of nitrogen from the surrounding medium into the jet reduces the population inversion.
The possibility of a hydrogen plasmadynamic recombination laser is experimentally investigated. A high density plasma produced by a high-power quasi-steady MPD arc-jet is cooled by expanding itself into the vacuum chamber. Experimental results confirm that large population inversions between i=4-3 and i=5-3 levels exist over 12-22 cm downstream of the anode. A comparison is made between experimental data and calculated results based on the collisional-radiative model on population of hydrogen levels.
A quasi-steady laser oscillation at 1.88 microns has been observed in a pure hydrogen plasma. The high density plasma produced by a high power quasi-steady MPD arc-jet operating at 8.1 kA of the discharge current and 0.1 g/s of hydrogen flow is cooled by expanding itself into the vacuum chamber. Experimental results confirm that some population inversions occur as a consequence of recombination and subsequent electron thermalization.
Population inversion, which occurs in a recombining plasma when a stationary He plasma is brought into contact with a neutral gas, is examined. With hydrogen as a contact gas, noticeable inversion between low-lying levels of H has been found. The overpopulation density is of the order or 10^8 per cubic cm, which is much higher than that ( about 10^5 per cubic cm) obtained previously with He as a contact gas. Relations between these experimental results and the conditions for population inversion are discussed with the CR model.
A new calculation method is presented, which is suitable for investigating a population inversion between the energy levels of weakly ionized hydrogen plasma in which atom-atom collision processes have been considered. As an example, the plasma conditions required for inversion between energy levels of the principle quantum number 4 and 5 of hydrogen atom are calculated by this method. In contrast to the recombining hydrogen plasma with moderate temperature (kTe greater than 1 eV), it is shown that population inversion is possible in a larger range above the lower bound of the effective recombination rate of the plasma.
Possibilities of a He II plasmadynamic recombination laser are experimentally investigated. It is confirmed by experimental results that large quasi-steady population inversions for i=3-4, i=3-5 and i=4-5 levels of He II exist over 5 cm downstream of the orifice. The maximum population inversion for the transition 4-5 observed corresponds to the single-pass gain of 1.03. A comparison is made between experimental data and calculated results on the basis of the collisional-radiative model on population inversion of He II levels.
Plasma conditions for generating a population inversion between the ground and first excited states in a recombining hydrogen plasma have been investigated on the basis of the CR model. Population inversion can be expected when three-body recombination plays a dominant role; the required regions of electron density and temperature are specified. It is shown that upper bounds exists for the ground-state population density at given electron density and temperature. Larger inversion densities can be obtained between the ground and first excited states than between excited levels. Numerical results are presented.
The plasma condition is investigated theoretically for population inversion between the first two excited states of hydrogen atoms in a recombining plasma. The rate equations, including atom-atom collision terms, is solved consistently with the optical escape factors. The upper bound of the ground level population density (n1)max necessary for inversion in the optically thick plasma at specified electron density and temperature is nearly inversely proportional to the mean radius of the plasma r0. With a decrease in the atom temperature, the upper bounds increase in the optically thin plasma but decrease in the optically thick plasma.
Overpopulation densities Pij, which are defined as the differences between the population densities per unit statistical weight of the upper and lower excited levels i and j, are calculated as a function of the electron density ne for various electron temperatures Te in recombining hydrogen plasmas. Calculation have been made for line pairs with principle quantum numbers (2,3), (3,4) and (4,5). The effect of the ground level population density n1 on Pij is calculated. In this calculation, the atom-atom collision and the self-absorption of the resonance lines are taken into account. The n1-dependence of Pij remains almost constant until the self-absorption becomes significant. The threshold condition for laser oscillation is discussed in relation to the calculated Pij. Laser oscillation is possible for the line pair (2,3) at an electron density and temperature higher than for the other pairs (3,4) and (4,5) when self-absorption is negligible.
The processes leading to the population inversion are investigated in a recombining hydrogen plasma which is interacting with a cool and dense neutral hydrogen by using the rate equations for electrons, ions and neutral particles. The quasi-steady state (QSS) approximation is used only for the level i lying above a certain level i* which is not the first excited level. The calculations have shown that the quasi-steady state cannot be realized while intense energy flows due to the collisional processes exist between different kinds of particles such as the electrons and the ions in the plasma, and that the population inversion is realized only in the quasi-steady state following the transient phase. The effects of initial conditions of the hydrogen plasma and of the introduced neutral hydrogen gas on the overpopulation density are also discussed.
An investigation of gain in a recombining Li-like Al cylindrical plasma and the development of scaling laws on the 3d-4f and 3d-5f transitions is discussed. The work was carried out using a simple model which approximates the hydrodynamic motion to a similarity expansion, thus keeping the run time sufficiently small to enable a large number of configurations of the system to be examined. The laws are formulated both with and without the inclusion of the escape factor in view of the current uncertainty concerning the role of trapping in such systems. Updated versions of the H-like C scaling laws are presented.
The agreement between experimental results and theoretical predictions is improved for the temporal dynamics of the gain coefficient on the 3 to 2 transition of the C VI ion at 182 A. It is shown that nj kinetics improves the description of radiative cleaning of the n=2 level in a partially reabsorbed, expanding plasma, surprisingly increasing the degree of frozen ionization. A detailed description of radiative trapping on the n=2,3 levels is included in the model in the form of the net radiative bracket, calculated through an exact solution of the radiation transfer problem. The accurate treatment of radiative transport is found to convincingly verify the Sobolev formulation of the escape factor.
We describe a scheme for obtaining very short wavelengths (10 A) in recombination lasers. The rapid cooling rates necessary to achieve population inversion during recombination are attained by adiabatic expansion of submicrometer spheres. The spheres are heated impulsively by a powerful picosecond laser. First, they ionize, then as they expand, they cool and recombine. We have calculated the optimum sphere size and initial temperature for maximum gain in the n=3 to 2 transition of hydrogenlike ions of elements with atomic numbers, Z, between 10 and 30. gain of about 250 per cm is calculated in aluminum at 38.8 A. Gain rapidly decreases with Z so that gain in titanium at 13.6 A is about 10 per cm. We have calculated the required pump-laser intensity and found it to be attainable with current lasers. The propagation of the pump through the 'gas' of spheres is considered and the problems arising from pump scattering by the spheres are discussed.
To produce a rapidly cooled recombining plasma for generation of an XUV laser beam, gas-contact cooling has a high potentiality. The approach has two advantages : One is that a stationary population inversion is possible, and the other is a rapid cooling due to inelastic collisions between electrons and atoms. The first experiment on gas-contact cooling was carried out in a magnetically confined stationary plasma column of a TPD-1 device in IPP, Nagoya. It was demonstrated that stationary population inversions were produced between the lower excited levels of the He II when a He plasma was brought into contact with a helium gas. The gain per unit length in the medium of population inversion, however, was quite low because the electron density was relatively low and introduced helium gas pressure was also low. We describe a numerical investigation of a He recombining plasma, rapidly cooled by hydrogen gas-contact, to show the possibility of a stationary laser oscillation of the He II 164 nm line, and we also present measurements of population inversion of He I and II lines in the magnetically confined plasma (TPD-1 in IPP, Nagoya) which is brought into contact with hydrogen gas puffed by a fast-acting valve, and also in a Z-pinch produced plasma. We display the numerical investigation performed on the basis of a collisional-radiative (CR) model and energy equations for electron. Experiments in the TPD-1 plasma and in the Z-pinch plasma are presented.
Up to date, shorter wavelength laser studies by recombining plasma methods have concentrated on hydrogen-like ions. We are investigating recombination lasing of lithium-like carbon ions. There is a possibility that Li-like ions will oscillate with higher efficiency than hydrogen-like ions. The ionization potential of C4+, which is a helium-like ion, is about 6 times that of C3+ and so, the situation for C3+ is very similar to that for a hydrogen-like ion. Consequently, when carbon atoms are strongly ionized, it should be easy to ensure that C4+ is the dominant ion species. This should lead to a higher production efficiency of population inversion in C IV by recombination processes.
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