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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Effects of dissipation of dense plasmas on spontaneous radiation intensity of ionized atom

Chang-qi Cao, Hui W. Cao

Published Oct 28, 1992• 1 citation
Publisher

Abstract

The effect of dissipation of dense plasmas on spontaneous radiation of ionized atom is investigated by Langevin equations and Weisskopf-Wigner approximation. Analytical expression for emission rate is obtained, the Einstein formula is corrected by a new added term caused by thermal photons, and the Einstein A coefficient is also modified due to damping of the light. The lifetime of the excited ion is modified correspondingly.

DOI
10.1117/12.130403

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The effect of dissipation of dense plasmas on spontaneous radiation of ionized atom is investigated by Langevin equations and Weisskopf-Wigner approximation. Analytical expression for emission rate is obtained, the Einstein formula is corrected by a new added term caused by thermal photons, and the Einstein A coefficient is also modified due to damping of the light. The lifetime of the excited ion is modified correspondingly.
The effect of dissipation of plasmas on the spontaneous radiation of an ionized atom is investigated by Langevin equations and the modified Weisskopf-Wigner approximation to consider the quenching effect of the Einstein A coefficient. The dissipation of field in plasmas results from inverse bremsstrahlung of free electrons and absorption of the ions of the same kind as the radiator. Under certain conditions the Einstein A coefficient may be reduced significantly. The lifetime of the excited ion will be changed correspondingly.
Spontaneous radiation by three-level atoms in a dissipative medium (such as plasma) has been investigated by Langevin equations and the modified Weisskopf-Wigner approximation. General formulae for calculating spontaneous emission coefficients, i.e. Einstein A coefficients, are presented. Numerical calculation shows that the dissipation of plasmas can modify the spontaneous emission coefficients significantly and causes a pit in the coefficient-density curves for relatively low temperature plasmas, and also a pit in the coefficient-temperature curves.
New interesting effects arise, when three-level atoms interact with the plasma, laser field, or a heat bath. If the atoms inside the plasma are excited by the polarized laser pulse or an electron beam, the line wings of the radiation are completely polarized, while the line core is only partially polarized. The Einstein coefficients are generalized to the case, when the atomic decay channels are subject to quantum interference. Such atoms may develop nonzero quantum coherence between upper levels, if they are in contact with the heat bath in thermal equilibrium. This coherency changes the emissivity of the medium and hence can be experimentally observed. In the case when three-level atoms interact with the laser field, spontaneous emission can be suppressed over the whole frequency spectrum.
Introduction The preceding chapters have focused on atomic transitions induced by applied radiation. That is, there is an optical field illuminating the atoms, and their response is calculated. It is implicitly assumed that an excited atom left alone will spontaneously return to the ground state, and conserve energy by emitting light that satisfies E 2 − E 1 = ħ ω 21 in accordance with the Planck and Bohr pictures. But this spontaneous emission process is not addressed quantitatively in these earlier chapters. Spontaneous emission is one of the most pervasive phenomena of atomic physics, and yet its origins remain among the least well-understood. The number of misconceptions is enormous, and they are to be found in textbooks, journal articles, and lecture notes. Because the natural decay of an excited atom adds energy to what is usually an empty mode of the electromagnetic field, the process is fundamentally quantum mechanical. Classical or even semi-classical descriptions cannot be assured to give correct answers. This is not to say that such discussion is to be avoided, but only that caution is needed in interpreting the results. Toward the end of the nineteenth century, many experimental results made it clear that classical mechanics needed to be supplemented by new theories. The first venture into the new physics was Planck's hypothesis that the energy of classical radiating oscillators like those discussed in Chap. 1 would have to be quantized into integer multiples of ħ ω. This notion led to his famous formula for the spectrum of thermal radiation from a non-reflective object (black body), and this formula describes a radiation field in thermodynamic equilibrium with its environment. The result of Planck's hypothesis in the context of thermal equilibrium plays a vital role in the discussion of spontaneous emission. Einstein A - and B -coefficients Soon after Bohr proposed a model of atomic structure consisting of discrete energy levels, connected by radiation whose energy satisfied Δ E = ħω when atoms made transition between them, Einstein published the first serious attempt to connect the absorption and emission processes. Absorption, he reasoned, could occur only in the presence of applied radiation, whereas spontaneous decay occurred without the application of any field.
Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account noncooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and level shifts due to multiple scattering or reabsorption of spontaneously emitted photons. In the Markov limit a nonlinear and nonlocal single-atom density matrix equation is derived. To illustrate the effects of the quantum corrections, we discuss amplified spontaneous emission and radiation trapping in a dense ensemble of initially inverted two-level atoms and the effects of radiative interactions on intrinsic optical bistability in coherently driven systems.
It has recently been shown by Jaynes and collaborators that semiclassical radiation theory contains a description of spontaneous emission of radiation and of radiative level shifts. The present paper gives a gauge-invariant derivation of the radiant energy production rate, using only Maxwell's equations and the usual definitions of electric current and charge density for a many-particle material system described by Schr\"odinger's equation. A complementary derivation, using the time-dependent Schr\"odinger equation, verifies the instantaneous conservation of energy and probability during the radiation process. The semiclassical rate of spontaneous emission differs from the usual formula (Einstein's AAA coefficient) because it depends on the occupancy of both initial and final states of the material system. The implications of this with regard to thermal equilibrium and Planck's law are examined. If a new hypothesis is introduced, postulating the decomposition of the equilibrium radiation into incoherent components, each interacting with a specific pair of energy levels of the material system, then Planck's law is shown to hold for the total intensity of radiation. If this hypothesis is not introduced, the equilibrium conditions for different transitions are incompatible, and the semiclassical radiation theory is incapable of describing thermal equilibrium.