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Free-free matrix-elements for two-photon opacity

Journal Article · · High Energy Density Physics
 [1];  [2];  [3];  [3];  [3]
  1. National Inst. for Fusion Science, Toki, Gifu (Japan)
  2. Alternative Energies and Atomic Energy Commission (CEA), Arpajon (France)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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Recent opacity measurements have inspired a close study of the two-photon contributions to the opacity of hot plasmas. The absorption and emission of radiation is controlled by dipole matrix-elements of electrons in an atom or ion. This paper describes two independent methods to calculate matrix-elements needed for the two-photon opacity and tests the results by the f-sum rule. The usual f-sum rule is extended to a matrix f-sum that offers a rigorous test for bound-bound, bound-free and free-free transitions. An additional higher-order sum-rule for the two-photon transition amplitudes is described. In this work, we obtain a simple parametric representation of a key plasma density effect on the matrix-elements. The perturbation theory calculation of two-photon cross-sections is compared to an independent method based on the solution of the time-dependent Schroedinger equation for an atom or ion in a high-frequency electromagnetic field. This is described as a high frequency Stark effect or AC Stark effect. Two-photon cross sections calculated with the AC Stark code agree with perturbation theory to within about 5%. In addition to this cross check, the AC Stark code is well suited to evaluating important questions such as the variation of two-photon opacity for different elements.
Research Organization:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Fusion Energy Sciences (FES)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1772045
Report Number(s):
SAND--2021-3001J; 694759
Journal Information:
High Energy Density Physics, Journal Name: High Energy Density Physics Vol. 34; ISSN 1574-1818
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS