Diagnostics of laser-induced plasma with soft X-ray (13.9�nm) bi-mirror interference microscopy

Tang, Huajing; Guilbaud, Olivier; Jamelot, G.; Ros, D.; Klisnick, A.; Joyeux, D.; Phalippou, D.; Kado, M.; Nishikino, Masaharu; Kishimoto, Maki; Sukegawa, Kouta; Ishino, Masahiko; Nagashima, Keisuke; Daido, Hiroyuki

doi:10.1007/s00340-004-1439-0

Cited by 36 publications

(35 citation statements)

References 10 publications

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“…Similar anomalies were observed in interference patterns of an Al plasma produced by a 13.9 nm Ni-like Ag laser at the Advanced Photon Research Center of the Japan Atomic Energy Research Institute [19]. The free-electron model leads to the conclusion that the square of the plasma frequency u 0 2 is negative!…”

Section: Application To Plasma Opticssupporting

confidence: 58%

“…The ratio of n(u) À 1 to n free À 1 for Al at ion density 10 20 /cc. The ratio is negative at the frequencies of Ni and Ag lasers explaining the effects of anomalous dispersion observed in experiments [18,19].…”

Section: Resultsmentioning

confidence: 94%

“…In Ref. [19] this behavior was correctly attributed to the 2p-3d transition in Al þ2 . To examine such anomalous dispersion in terms of the average-atom model, we compare n(u) À 1 predicted by the average-atom model with its free-electron counterpart n free À 1 in Fig.…”

Section: Application To Plasma Opticsmentioning

confidence: 81%

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High-Energy-Density Physics

Davison¹,

Horie²

2006

Shock Wave and High Pressure Phenomena

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a b s t r a c tThe quantum-mechanical average-atom model is reviewed and applied to determine scattering phase shifts, mean-free paths, and relaxation times in warm-dense plasmas. Static conductivities s are based on an average-atom version of the Ziman formula. Applying linear response to the average-atom model leads to an average-atom version of the Kubo-Greenwood formula for the frequency-dependent conductivity s(u). The free-free contribution to s(u) is found to diverge as 1/u 2 at low frequencies; however, considering effects of multiple scattering leads to a modified version of s(u) that is finite and reduces to the Ziman formula at u ¼ 0. The resulting average-atom version of the Kubo-Greenwood formula satisfies the conductivity sum rule. The dielectric function e(u) and the complex index of refraction n(u) þ ik(u) are inferred from s(u) using dispersion relations. Applications to anomalous dispersion in laser-produced plasmas are discussed.Ó 2009 Elsevier B.V. All rights reserved. Average-atom and static conductivityLet us briefly reprise the average-atom model, which is a quantum-mechanical version of the temperature-dependent Thomas-Fermi theory of a plasma introduced sixty years ago by Feynman etal. [1]. In the average-atom model, the plasma is divided into neutral spherical cells, each containing a single nucleus (charge Z) and Z electrons. The radius of each cell is the Wigner-Seitz (WS) radius, determined from the material density r m (gm/cc), the atomic weight A (gm/mol), and Avogadro's number A ¼ 6:023 Â 10 23 , by R WS ¼ (3U/4p) 1/3 , where U ¼ A=Ar m is the cell volume. Individual electrons (bound and continuum) inside a neutral cell are assumed to move in a self-consistent potential. Outside the cell boundaries the potential vanishes. The continuum electrons penetrate the cell boundary and move into the region between atoms where the electron density approaches a constant value r 0 determined by the temperature T and chemical potential m. In the quantum-mechanical version of the average-atom model, the density oscillates about r 0 outside the cell with a small and ever decreasing amplitude [2]. To insure electrical neutrality, it is necessary to assume a uniform positive background charge r þ that precisely cancels r 0 . The average atom floats in this positive ''jellium'' sea. The average ionic charge of sea is Z * ¼ r þ U. The picture that evolves is an average atom of nuclear charge Z with Z bound and continuum electrons moving self-consistently inside a sphere of radius R WS ; outside is a neutral plasma consisting of electrons (density r 0 ) balanced by positive sea of ions (charge Z * ). The electron density is determined using the quantum-mechanical self-consistent field method. The average-atom model introduced here is a nonrelativistic version of Liberman's Inferno model [3] and is very similar to the model described previously by Blenski and Ishikawa [4].In the quantum-mechanical model, each electron is assumed to satisfy the central-field Schrö dinger equationwhere a ¼ (n, l) for bo...

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Section: Application To Plasma Opticssupporting

confidence: 58%

Section: Resultsmentioning

confidence: 94%

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High-Energy-Density Physics

Davison¹,

Horie²

2006

Shock Wave and High Pressure Phenomena

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“…Since experiments typically measure an electron density that is much less than the critical density the formula above is approximated by n = 1 -(N elec / 2N crit ). In typical interferometer experiments [3][4][5][6][7] that probe plasma of length L using a source with wavelength λ, the number of fringe shifts is equal to…”

Section: Traditional Analysis Of Interferometer Experimentsmentioning

confidence: 99%

Impact of anomalous dispersion on the interferometer measurements of plasmas

Nilsen

Johnson

Iglesias

et al. 2006

Journal of Quantitative Spectroscopy and Radiative Transfer

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For many decades optical interferometers have been used to measure the electron density of plasmas. During the last ten years X-ray lasers in the wavelength range 14 to 47 nm have enabled researchers to use interferometers to probe even higher density plasmas. The data analysis assumes that the index of refraction is due only to the free electrons, which makes the index of refraction less than one and the electron density proportional to the number of fringe shifts. Recent experiments in Al plasmas observed plasmas with an index of refraction greater than one and made us question the validity of the usual formula for calculating the index of refraction. Recent calculations showed how the anomalous dispersion from the bound electrons can dominate the index of refraction in many types of plasma and make the index greater than one or enhance the index such that one would greatly overestimate the electron density of the plasma using interferometers. In this work we calculate the index of refraction of C, Al, Ti, and Pd plasmas for photon energies from 0 to 100 eV (12.4 nm) using a new average-atom code. The results show large variations from the free electron approximation under many different plasma conditions. We validate the average-atom code against the more detailed OPAL code for carbon and aluminum plasmas. During the next decade X-ray free electron lasers and other sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths so understanding the index of refraction in plasmas will be even more essential.

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“…L'étape suivante a consisté à coupler l'interféromètre à un miroir imageur permettant ainsi de disposer d'une microscopie interférentielle, particulièrement adaptée pour décrire in situ des processus nécessitant une résolution spatiale à l'échelle micrométrique et temporelle à l'échelle de la durée de l'impulsion laser X-UV. Nous avons notamment démontré l'intérêt d'un tel outil dans le cadre d'expériences de sonde de plasmas denses créés par laser [7].…”

Section: Introductionunclassified

Microscopie interférentielle X-UV : un outil pour l'étude des endommagements des surfaces optiques

et al. 2006

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Résumé. Nous présentons des résultats récents concernant des premières investigations de microscopie interférentielle par laser X-UV d'endommagement optique. Le laser X-UV utilisé est un laser collisionnel en régime quasi-stationnaire émettant à 21.2 nm, développé au Prague Asterix Laser System (PALS, Prague, République Tchèque). Des échantillons de silice fondue de haute qualité, avec ou sans rayure, étaient irradiées en face avant par un laser bleu, correspondant au 3 ème harmonique du laser à iode du PALS (1.315 m), servant également à réaliser le laser X-UV à 21.2 nm. Celui-ci était utilisé, 5 ns après l'irradiation pour réaliser une imagerie microscopique et interférentielle de la face arrière de l'échantillon. Les résultats font apparaître des déformations locales transitoires. Des premières analyses mettent en évidence une probable variation de la rugosité de la surface. Cette démonstration expérimentale encourageante ouvre la voie à de futures investigations, notamment sur notre prochaine installation laser : LASERIX.

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Diagnostics of laser-induced plasma with soft X-ray (13.9�nm) bi-mirror interference microscopy

Cited by 36 publications

References 10 publications

High-Energy-Density Physics

High-Energy-Density Physics

Impact of anomalous dispersion on the interferometer measurements of plasmas

Microscopie interférentielle X-UV : un outil pour l'étude des endommagements des surfaces optiques

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