Influence of Microfield Directionality on Line Shapes
Abstract
:1. Introduction
2. Spectral Line Shape Calculations
2.1. The Different Codes and Approaches
- The SimU code [11]: The perturbing fields are simulated by the particle field generator, where the motion of a finite number of plasma particles (electrons and ions) is calculated assuming that classical trajectories are valid. Then, using this field as a perturbation, the radiator dipole oscillating function is calculated by the Schrödinger solver. Finally, using the fast Fourier transformation (FFT) method, the power spectrum of the radiator dipole oscillating function is evaluated, giving the spectral line shape. The results of repeated runs of this procedure are then averaged to obtain a smooth spectrum. Although, in principle, the particle field generator may account for interactions between all particles, for the cases presented in this study, perturbing protons were modeled as reduced-mass Debye quasiparticles interacting only with the stationary radiator via the Debye potential.
- The BinGo code [12]: This code uses standard classical MD simulation to compute the perturbing fields. In this work, the plasma model consists of classical point ions interacting together through a Coulombic potential screened by electrons and localized in a cubic box with periodic boundary conditions. Newton’s equations of particle motion are integrated by using a velocity-Verlet algorithm using a time-step consistent with energy conservation. The simulated time-depending field histories are used in a step-by-step integration of the Schrödinger equation to obtain and, thus, in the Liouville space. An average over a set of histories is necessary to evaluate . Again, the spectral line shape is obtained using FFT.
- The Euler–Rodrigues (ER)-simulation code [13]: The plasma model for the simulation of time-dependent field histories consists of an emitter at rest in the center of a spherical volume and set in a bath of statistically independent charged quasi-particles moving along straight line trajectories. A reinjection technique ensures statistical homogeneity and stability. The simulated electric field histories are used in a solver for the evolution of the atomic system. For hydrogen, if the SO (4) symmetry is valid, Euler–Rodrigues (ER) parameters are used; otherwise the diagonalization process is done using Jacobi’s method.
- The DM-simulation code [14]: This code uses the same solver as the ER-simulation code, but the time-dependent field histories are simulated using the MD simulation technique in order to account for the particle interactions.
- The multi-electron line shape (MELS) code [24]: The “standard” theory (quasi-static ions and impact electrons) and the Boerker-Iglesias-Dufty (BID) model [15] to account for ion dynamics effects. The microfield distribution is from the adjustable-parameter exponential approximation (APEX) model [25,26].
- The PPP code [27]: The Stark broadening is taken into account in the framework of the standard theory by using the static ion approximation and an impact approximation for the electrons or including the effects of ionic perturber dynamics by using the fluctuation frequency model [16,17]. The microfield distribution functions required are calculated using the APEX model or an external MD simulation code.
2.2. Plasma Characteristics
Ne (cm−3) | T(eV) | Γ | α | ωpi (rad/s) | vdyn (rad/s) |
---|---|---|---|---|---|
1018 | 1 | 0.23 | 0.83 | 1.32 × 1012 | 1.77 × 1012 |
1018 | 10 | 0.02 | 0.26 | - | 5.57 × 1012 |
1019 | 1 | 0.50 | 1.22 | 4.16 × 1012 | 3.80 × 1012 |
1019 | 10 | 0.05 | 0.39 | - | 1.20 × 1013 |
3. Results
3.1. Generalities
3.2. Code Comparisons
3.2.1. Full Cases
3.2.2. Vibration Case
3.2.3. Rotation Case
4. Discussion
Acknowledgments
Author Contributions
Appendix A: Field Correlation Function in the BID Model
Conflicts of Interest
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Calisti, A.; Demura, A.V.; Gigosos, M.A.; González-Herrero, D.; Iglesias, C.A.; Lisitsa, V.S.; Stambulchik, E. Influence of Microfield Directionality on Line Shapes. Atoms 2014, 2, 259-276. https://doi.org/10.3390/atoms2020259
Calisti A, Demura AV, Gigosos MA, González-Herrero D, Iglesias CA, Lisitsa VS, Stambulchik E. Influence of Microfield Directionality on Line Shapes. Atoms. 2014; 2(2):259-276. https://doi.org/10.3390/atoms2020259
Chicago/Turabian StyleCalisti, Annette, Alexander V. Demura, Marco A. Gigosos, Diego González-Herrero, Carlos A. Iglesias, Valery S. Lisitsa, and Evgeny Stambulchik. 2014. "Influence of Microfield Directionality on Line Shapes" Atoms 2, no. 2: 259-276. https://doi.org/10.3390/atoms2020259