Van der Waals broadening arises from the dipole interaction of an excited atom with the induced dipole of a ground state atom. In the case of foreign gas broadening, both the perturber and the radiator may be in their respective ground states.
An approximate formula for the FWHM, strictly applicable to hydrogen and similar atomic structures only, is. Stark broadening due to charged perturbers, i. The FWHM for hydrogen lines is. Other tabulations of complete hydrogen Stark profiles exist. Physical Measurement Laboratory. Free Access. Current usage metrics About article metrics Return to article. Initial download of the metrics may take a while. Previous article Next article.
Metrics Show article metrics. Services Articles citing this article CrossRef Bookmarking Mendeley. Reader's services Email-alert. Spectral line broadening is calculated based on a microscopic quantum statistical approach. By using thermodynamic Green's function, plasma correlation effect, electrostatic and dynamic screening, and perturber-radiator interaction are taken into account.
Ions are treated in quasistatic approximation due to Stark effect. A good agreement is shown by comparing the calculated values with the existing experimental and theoretical data. Optical spectroscopy is one of the most important diagnostic tools to characterize warm and dense plasmas.
The emitted radiation from a plasma is perturbed by interaction between a radiating atom and surrounding particles, which leads to spectral line broadening; the most effective mechanism is Stark broadening pressure broadening.
Line profile calculation is an interesting technique to determine the internal plasma parameters, such as density, temperature, and composition, to study the microscopic processes within plasma, and to check the quality of the predicted parameters [ 1 , 2 ].
Several semiclassical and quantum-mechanical approaches have been investigated to calculate spectral line shapes in plasmas [ 1 , 3 — 16 ]. Helium lines were calculated by Griem et al. Furthermore, the convergent theory was improved by Bassalo et al. Recently, molecular dynamics MD simulations have been performed by Calisti et al. The quantum-mechanical Green's function method is considered in this paper to calculate the He I spectral lines in dense plasmas, assuming local thermal equilibrium LTE [ 20 — 26 ].
Spectral line profiles of helium are important in plasma diagnostic. In Section 2 an overview of the spectral line modeling is given. Result and discussion are shown in Section 3. The comparison with other theoretical and experimental results is presented. Finally, conclusion is given in Section 4. A systematic account of medium modifications of the absorption coefficient is possible using the dielectric approach which links the absorption and emission coefficients to the dielectric tensor.
For visible light, the absorption coefficient is given by the long-wavelength limit of the dielectric function where is the index of refraction which in turn reads.
The microscopic treatment of the line shapes in dense plasmas starts form the dielectric approach given by 1 and 2. Neglecting change in the index of refraction, the cluster expansion of the dielectric function together with a systematic perturbative analysis using thermodynamic Green's function shows that the spectral line shape is proportional to the Fourier transform of the dipole-dipole autocorrelation function [ 24 ].
The perturber-radiator interaction leads to a pressure broadening, which contains electronic and ionic contributions. Describing the ionic contribution in the quasi-static approximation by averaging over the ionic microfield [ 24 , 25 ], we have where is identified as a dipole matrix element for the transition between initial and final states. The ionic microfield distribution function is taken according to the Hooper microfield distribution function with field strength normalized to the Holtsmark field [ 49 ].
Equation is the unperturbed transition energy. The function is determined by the self-energy correction of the initial and the final states Both electronic and ionic contributions occur in the self-energy Performing Born approximation with respect to the dynamically screened perturber-radiator potential, the electronic self-energy is obtained as [ 24 ] Here, the level splitting due to the microfield has been neglected [ 23 ], is the Bose distribution function, and is the transition matrix-element given in the following.
The sum over runs from to discrete bound states for the virtual transitions. Dynamical screening effect is accounted for in 6 from imaginary part of the inverse dielectric function The dielectric function is approximated by random phase approximation RPA as where is the kinetic energy of electron.
The Fermi distribution function of electrons in the nondegenerate limit can be approximated by Boltzmann distribution function. Binary collision approximation can be considered, which leads to a linear behavior of the electronic width and shift with respect to the electron density.
Considering Born approximation, the electronic part is overestimated; to avoid this we apply the cut-off procedure and add the strong collision term [ 1 ] in state of partial summation of the three-particle T-matrix, where the result might be slightly modified [ 24 , 26 ]. The transition matrix element describes the interaction of the atom with the Coulomb potential through the vertex function.
In lowest order, it can be determined by the atomic eigenfunctions. The Coulomb interaction with electron-electron-ion triplet depends on the momentum transfer.
For helium and hydrogen atoms, the matrix elements can be represented by the following diagrams [ 20 , 22 ]:. However, the matrix element of helium can be approximated by the one of hydrogen, while the outer electron is screened by inner electron.
The matrix-element of hydrogen reads assuming that the ion with effective charge is much heavier than the electron Expanding the plane wave into spherical harmonics where is the spherical Bessel function, a multipole expansion can be derived, and, for example, gives the monopole, dipole, and quadrupole contributions of the radiator-electron interaction; respectively.
The vertex correction for the overlapping line is related to coupling between the initial and the final states, given by [ 20 , 24 ]. In static limit, static Debye screening can be considered appropriate for the inverse dielectric function such as [ 23 , 50 ] where is the inverse Debye radius.
However, this approximation is valid for virtual transition between states with negligible energy difference. For nonhydrogenic radiator, ionic contribution to the self-energy is related to quadratic Stark effect and quadrupole interaction, further detail is given in [ 25 , 26 ] The microfield can be considered as a static microfield distribution function, while it does not change during the time of interest for the radiation process.
The full line profile is obtained by convolution of pressure broadening with Gaussian distribution of Doppler broadening [ 51 ] where is the mass of the radiating atom. The comparison of available data and our calculated results is shown in this section. The electronic width is compared with the results of the ST of Griem [ 1 ] and of the MD simulations of Gigosos et al. The MD simulations [ 18 , 19 ] results correspond to two different kinds of MD simulations, in the first calculation the independent electrons moving with a constant speed along straight line trajectories.
The correlation between particles is considered by using a screened Coulomb field. The second case is for interacting particles in a one-component plasma, and a regularized potential is used for close collision. The electron-ion interaction is attractive; therefore, configurations involving electrons at distance of the order of de Broglie wavelength or shorter have to be considered.
The Coulomb interaction must be modified in a classical description at such distances. The ion-electron potential regularization provides well-defined classical physics for opposite sign charge systems, and allows the application of the various sophisticated classical many-body methods of classical statistical mechanics [ 52 ]. Moreover, the correlation arises, so the interaction with the emitter is simply the Coulomb potential [ 18 , 19 ]. Figures 1 and 2 show the interaction as well as the correlation between perturbers, they are more important for decreasing temperature.
The discrepancy between both simulations results can be seen at low temperature. Our results in Figure 2 give rather smaller values than the others, especially at low temperature. This might be due to degeneracy in the plasma. Furthermore, the dynamically screened Coulomb interaction is included. The comparison is made with the ST of Griem and his collaborators [ 1 , 3 ] taken from the [ 40 ]; see Figure 3.
Our calculations are also included, and the best agreement is achieved in the case of statical screening effect. The discrepancies at the far wings can be related to the perturbing neighbouring lines. The comparison is made with large number of experimental results and theoretical calculations. This line was investigated by Berg et al. Electron densities were determined from continuum intensity and temperature from intensity ratios of ion and neutral lines. One of the most interesting measurements of Stark broadening of visible neutral helium lines in plasmas has been carried out by Kelleher [ 46 ], where sixteen different spectral lines emitted from a wall-stabilized arc have been studied in detail.
The electron density was determined by interferometry for different wavelengths, and the plasma electron temperature was estimated from a Boltzmann plot or the intensity ratio of the ion and neutral lines. The electron density is measured by laser interferometry. The electron temperature is determined from the intensity ratio of the H-line to the underlying continuum, while the gas temperature is measured from the Doppler broadening [ 45 ].
Plasmas were created under five various discharge conditions using a linear low-pressure pulsed arc as an optically thin plasma source operated in a helium-nitrogen-oxygen gas mixture. Also the measurements of Diatta [ 44 ] and Chiang et al.
Our approach shows a good agreement with the other results. Still some discrepancy can be observed at very low densities, where the dynamical motion of ion is considered in the MD simulation.
0コメント