Although sometimes line absorption is used to infer the cross section whose frequency integral yields the absorption oscillator strength according to 2. In that case, plasma parameters and size should be selected to avoid significant absorption, so that the emerging intensity is proportional to the product of the desired ,4-value and the integral of the upper level population density along the line of sight chapter 8. Moreover, spectrally integrated line intensities must be measured with great care in background and line wing corrections Wiese , Griem et al.
For the measurement of relative ,4-values within a given ionic species, the most important requirement is that relative upper level populations can be reliably calculated, e.
The critical plasma parameter is therefore the electron temperature, which is usually determined spectroscopically chapter 11 or by Thomson scattering Sheffield , Hutchinson However, in order to estimate any deviations from assumed equilibrium population ratios, it is also necessary to know, e. Generally, equilibrium relations are invoked for the populations, e. For single-species plasmas and invoking quasineutrality, it is again sufficient to have measured values of electron temperature and density Hutchinson , see also chapters 10 and In this case, however, very accurate electron densities are required, because this quantity enters quadratically.
For multi-species plasmas, the difficulties of obtaining accurate level populations are more severe. Moreover, for multiply ionized atoms it is usually impractical to have experiments at sufficiently high densities for the thermal equilibrium relations to apply.
More involved models chapter 6 must then be used, 3. To investigate, e. Another interesting area of study are possible changes of transition probabilities due to dense plasma effects as discussed near the end of section 3. However, claimed observations Chung et al. Reported small changes of transition probabilities in argon ion laser discharges Aumayr et al. Normally this contribution to the width of a spectral line is entirely negligible in applications of plasma spectroscopy, x-ray lines of medium and heavy ions being important exceptions. This is so because Doppler shifts associated with the motions of emitting or absorbing particles and, depending mainly on the density, because level perturbations, etc.
Effects of the second kind were called pressure broadening in the earlier literature and were, specifically for plasmas, the subject of monographs Griem , Sobel'man et al. Usually, but not always, these Doppler and pressure broadening effects can be treated independently see section 4. In many cases, and assuming the radiator or absorber velocities to be nonrelativistic and their distribution to be Maxwellian, i. To obtain the full width at half maximum FWHM , 4. Pressure broadening is less conducive to any general statement, except for a classification according to either the underlying physical mechanism or the basic approximation used in the line profile calculations.
Of the various mechanisms, Stark effects caused by the electric fields produced by nearby ions and electrons, or by collective fields associated with plasma waves section 4. However, in partially ionized gases, interactions with neutral perturbers can be important as well, either due to long range Van der Waals forces or, if a resonance condition between radiators and perturbers of the same species is fulfilled, also due to longer range dipole-dipole interactions.
These two situations will be discussed in section 4. The second traditional classification according to the mathematical approximations to a more general theory of line broadening are the Holtsmark or quasistatic approximation sections 4. The corresponding line shape functions have normally no simple analytic form, with the exception of the impact approximation for isolated lines, i.
The latter is more appropriate for measurements, being the separation between half of maximum intensity points. In the case of doubly peaked lines and provided the profile asymmetry is sufficiently small, one uses the mean of the maxima to define the half intensity points on the outside of the two peaks.
Also shown is the Voigt profile resulting from the convolution of these two profiles. Such Voigt profiles have been widely tabulated, e. Their widths are well approximated by a simple formula due to Whiting The convolution of different line profiles is naturally only a correct procedure if the underlying mechanisms are statistically independent.
This is not the case, e. In that case the resultant profile can even be narrower than the Doppler profile according to 4. Such "collisional narrowing" will be discussed in section 4. It was predicted by Dicke Another word of caution concerns the conversion of line widths and shifts, e. As long as they are small compared with the unperturbed 4.
Also, an additional numerical factor arises if different length units are used for X and c, as is frequently done. It is usually assumed that it is sufficient to consider one radiator at a time, i. This is a reasonable assumption except, perhaps, for resonance broadening. The co4 factor is normally treated as constant, except when profile asymmetries are important section 4.
In most situations, 4. However, if Kirchhoff's law is invalid, or if there are phase correlations between the various contributing initial states, absorption and emission profiles can be different.
To discuss such situations, a density matrix formulation of line broadening much used in laser physics and reviewed by Cooper is more appropriate. If the radiating atom or ion is imbedded in a slowly varying environment, say, of perturbing ions, it may be possible to avoid the complications of a dynamical theory by making the quasistatic approximation, following Holtsmark For a given perturber configuration, time-independent perturbation theory can then be used to calculate corrections to cofj due to the corresponding ion microfield F and, if necessary, also corrections to the dipole matrix elements.
In the case of the linear Stark effect, i. At very high densities, separation of a perturber factor from the density operator is no longer possible, and a molecular-dynamics simulation of clusters containing the radiator and a sufficiently large number of perturbers may be more appropriate Kress, Kwon and Collins The operator t s,O is often called 7 s,0 in the original literature.
Often the lower states, i. This gives instead of 4. The averages are over the initial perturber and radiator states, and u s, 0 is the time evolution operator in the interaction representation.
Also, H is the unperturbed Hamiltonian. A completely quantum mechanical formulation of the following general relaxation theory of line broadening is also possible Smith and Hooper , Smith , Voslamber , as is the inclusion of lower state interactions. See You and Cooper for a discussion of the correspondences between quantum and classical treatments of "doubled" atoms involved in this case.
Average rating: 0 out of 5 stars, based on 0 reviews Write a review. There was a problem with saving your item s for later. Herbert J. The first three chapters introduce the classical and quantum theories of radiation, with detailed descriptions of line strengths and high density effects. Add to basket. Hopcraft, I. Tell us if something is incorrect.
It corresponds to the perturber factor of p 0 in 4. The operator u r;s,0 is the radiator's evolution operator, i. Since g r is time independent, F r,s is clearly also a solution of 4. The major accomplishment of the relaxation theory is to obtain the relevant properties of uav s,0 without explicitly solving the time-dependent Schrodinger equations for the multitude of perturber configurations. This feat was 4.
By applying P and 1 — P to 4. Assuming stationarity, i. Vanishing of the term arising from the projection operator is generally assumed, as well as that of [U r9s U. The two conditions for omitting these terms seem to differ, since the average interaction is J 4. In the vicinity of neutral atoms as radiators, uniform perturber distributions are an excellent approximation, so that the charged perturber contributions by electrons and ions to the average interaction indeed cancel.
This is because of quasineutrality of the plasmas of interest here, and because the contributions of various perturbers to Uf r, t depend on their signs if perturbing ions act only as point charges. The corresponding "plasma polarization shift" Berg et al. Experimental evidence for or against this effect also had been scant and somewhat controversial, but the corresponding red shifts are now better established both experimentally and theoretically see sections 4.
We will nevertheless continue the discussion of the "general" theory omitting the terms related to a nonvanishing average interaction. This omission, together with the neglect of lower state interactions and of initial correlations mentioned below 4. The simplified version of 4. Comparison of the subsequent approximations with such computer simulations see section 4.
The electric fieldstrength F r,s in 4. According to 4. An essential assumption, called the impact approximation by Smith et al. The 4.