Modern Methods in Collisional-Radiative Modeling of Plasmas

220 Pages·2016·6.978 MB·English

by  Yuri Ralchenko (eds.)

Springer Series on Atomic, Optical and Plasma Physics 90
Yuri Ralchenko Editor
Modern Methods
in Collisional-
Radiative
Modeling of
Plasmas
Springer Series on Atomic, Optical,
and Plasma Physics
Volume 90
Editor-in-chief
Gordon W.F. Drake, Windsor, Canada
Series editors
James Babb, Cambridge, USA
Andre D. Bandrauk, Sherbrooke, Canada
Klaus Bartschat, Des Moines, USA
Philip George Burke, Belfast, UK
Robert N. Compton, Knoxville, USA
Tom Gallagher, Charlottesville, USA
Charles J. Joachain, Bruxelles, Belgium
Peter Lambropoulos, Iraklion, Greece
Gerd Leuchs, Erlangen, Germany
Pierre Meystre, Tucson, USA
The Springer Series on Atomic, Optical, and Plasma Physics covers in a
comprehensive manner theory and experiment in the entire field of atoms and
molecules and their interaction with electromagnetic radiation. Books in the series
provide a rich source of new ideas and techniques with wide applications in fields
such as chemistry, materials science, astrophysics, surface science, plasma
technology, advanced optics, aeronomy, and engineering. Laser physics is a
particular connecting theme that has provided much of the continuing impetus for
new developments in the field, such as quantum computation and Bose-Einstein
condensation. The purpose of the series is to cover the gap between standard
undergraduate textbooks and the research literature with emphasis on the
fundamental ideas, methods, techniques, and results in the field.
More information about this series at http://www.springer.com/series/411
Yuri Ralchenko
Editor
Modern Methods
in Collisional-Radiative
Modeling of Plasmas
123
Editor
YuriRalchenko
National Institute ofStandards and
Technology
Gaithersburg, MD
USA
ISSN 1615-5653 ISSN 2197-6791 (electronic)
SpringerSeries onAtomic, Optical, andPlasma Physics
ISBN978-3-319-27512-3 ISBN978-3-319-27514-7 (eBook)
DOI 10.1007/978-3-319-27514-7
LibraryofCongressControlNumber:2016930267
©SpringerInternationalPublishingSwitzerland2016
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor
foranyerrorsoromissionsthatmayhavebeenmade.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland
Preface
The light coming from plasmas has always been one of the primary sources of
knowledge on their properties. Be it multi-million-degree magnetic or inertial
confinementplasmas,dazzlingstreamersofthesolarcorona,photoionizedplasmas
generated by powerful z-pinches, or industrial plasmas for lithography, their
spectra, from hard X-rays to infrared and beyond, can give us a great deal of
informationaboutdiversecharacteristicssuchastemperatureanddensity,turbulent
motions,ionizationdistributions,andelectricandmagneticfields,tonameafew.In
mostcasesthemeasuredplasmaemissionandabsorptionspectraarequitecomplex
due to a large number of spectral lines with varying intensities and line shapes, as
well as the presence of continuum photons. As a result, a reliable interpretation of
spectroscopic experiments is mostly achieved with rather sophisticated methods
capableofadequatelydescribingtheorigin,propagationandpossibledestructionof
plasma photons.
Oneofthemostgeneralapproachestocalculationofplasmapopulationkinetics
andspectraisthecollisional-radiative(CR)modeling.Firstintroducedmorethan50
years ago in a seminal paper by Bates, Kingston, and McWhirter, it addresses
determinationofstatepopulationsandensuingspectrafromamicroscopicpictureof
interactions between emitters (i.e., atoms and ions in plasma) and other plasma
particles.Thusitaccountsforthemostrelevantcollisionalandradiativeprocesses,
hence the name. The variety of terrestrial and astrophysical plasmas results in a
considerablediversityofpossibleinteractionsandenvironments,fromsimpleelec-
tron–atom (ion) collisions in a stationary optically thin plasma to non-Maxwellian
particle distribution functions to relatively weak forbidden radiative transitions to
heavy-particle interactions to transient and/or optically thick plasmas, and so on.
Unlike equilibrium descriptions of plasma population kinetics, for example, local
thermodynamicequilibrium(LTE),ageneralCRapproachcallsforafairlydetailed
(and of course reasonably accurate!) representation of relevant elementary interac-
tions. This approach connects plasma modeling with the powerful apparatus of
contemporaryatomicphysics,whichmayrequireutilizationofveryextensivesetsof
atomicdata.
v
vi Preface
The idea for this book originated from invigorating discussions among the
participants of the series of non-LTE code comparison workshops. The present
collection of chapters is aimed at providing an overview of the modern methods
employedincollisional-radiativemodelingwithemphasisonrecentdevelopments.
Suchareviewseemstobelongoverdue,notwithstandingextensiveapplicationsof
CR models to various plasmas as witnessed by hundreds, if not thousands, of
articles on this subject.
The eight chapters presented here address both general topics, such as the bal-
ancebetweendetailandcompletenessinCRmodelsandself-consistentlarge-scale
CR modeling, and more specific issues, such as simulations with different repre-
sentations of atomic structure, applications in radiation hydrodynamics and inter-
action of monochromatic X-rays with matter, astrophysical applications, and
validation and verification of CR models. This collection is not an introductory
textbook and thus is intended for advanced students and young researchers who
alreadyhave some knowledge in CR approach. We hopealso that it will be useful
for scientists and researchers working in general plasma spectroscopy.
Whenthisbookwasinafinalstageofpreparation,oneofthecontributors,Prof.
VladimirG.NovikovoftheKeldyshInstituteofAppliedMathematicsinMoscow,
Russia,suddenly passed away.He was anexcellentphysicist with a wide range of
interests and one of the leading specialists in quantum-statistical methods for
high-temperature plasmas. We dedicate this book to his memory.
Gaithersburg, MD, USA Yuri Ralchenko
Contents
1 Balancing Detail and Completeness in Collisional-Radiative
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Stephanie B. Hansen
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State-Space Completeness. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Degree of State Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Application-Driven Approaches to Balancing Detail
and Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Coronal Fine-Structure Models . . . . . . . . . . . . . . . . . . . 10
1.4.2 General Models for Moderate-Density Plasmas. . . . . . . . 10
1.4.3 Self-consistent Field Models for Dense Plasma . . . . . . . . 13
1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Self-consistent Large-Scale Collisional-Radiative Modeling. . . . . . . 17
Christopher J. Fontes, James Colgan and Joseph Abdallah Jr
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Large-Scale Collisional-Radiative Modeling . . . . . . . . . . . . . . . 20
2.2.1 The Los Alamos Suite of Atomic Physics Codes. . . . . . . 20
2.2.2 Selecting a List of Configurations . . . . . . . . . . . . . . . . . 22
2.2.3 Selecting the Level of Refinement. . . . . . . . . . . . . . . . . 26
2.2.4 Constructing the Rate Matrix . . . . . . . . . . . . . . . . . . . . 28
2.2.5 Steady-State Solutions Versus Time-Dependent
Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.6 Boundary Conditions for the Steady-State CR
Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.7 Different Methods of Solving the Steady-State CR
Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Summary and Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
vii
viii Contents
3 Generalized Collisional Radiative Model Using Screened
Hydrogenic Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
H.-K. Chung, S.B. Hansen and H.A. Scott
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.1 Generalized Collisional-Radiative Atomic Levels. . . . . . . 53
3.2.2 Atomic Transition Rates. . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.3 Plasma Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.4 Spectroscopic Emissivity and Opacity . . . . . . . . . . . . . . 66
3.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.1 Steady-State Plasmas Generated by Long-Pulse Lasers. . . 68
3.3.2 Two-Temperature Plasmas Generated by Short-Pulse
Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.3 Photoionization Equilibrium Plasmas. . . . . . . . . . . . . . . 70
3.3.4 Photo-Ionized Plasmas Generated by X-Ray Free
Electron Lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.5 Radiative Loss Rates of Heavy Elements . . . . . . . . . . . . 73
3.4 Validities and Limitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.1 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.4.2 Improvement on SH Model Spectra. . . . . . . . . . . . . . . . 75
3.4.3 Dielectronic Recombination . . . . . . . . . . . . . . . . . . . . . 76
3.4.4 Radiative Power Losses . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4.5 Continuum Lowering. . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.6 CR Models in High-Energy-Density Radiation-
Hydrodynamic Simulations. . . . . . . . . . . . . . . . . . . . . . 78
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Collisional-Radiative Modeling for Radiation Hydrodynamics
Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Howard A. Scott
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3 Non-LTE Material Response. . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4 High Density Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5 Detailed Balance, Energy Conservation and Discretization . . . . . 98
4.6 Conservation and Consistency in Non-LTE Thermal
Radiation Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Average Atom Approximation in Non-LTE Level Kinetics. . . . . . . 105
Vladimir G. Novikov
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 Level Kinetics Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Contents ix
5.3 The Rates of Collisional and Radiative Processes. . . . . . . . . . . . 108
5.3.1 Excitation by Electron Impact. . . . . . . . . . . . . . . . . . . . 108
5.3.2 Electron-Impact Ionization and Three-Body
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3.3 Autoionization and Dielectronic Capture. . . . . . . . . . . . . 113
5.3.4 Rates of Radiative Processes. . . . . . . . . . . . . . . . . . . . . 114
5.4 Configuration Accounting in the Extended CR-AA Model . . . . . 116
5.5 Reducing Detailed Level Kinetics to Extended CR-AA Model. . . 117
5.6 The Calculation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.7 Results of Calculation for Tin Plasma . . . . . . . . . . . . . . . . . . . 121
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6 Collisional-Radiative ModelingandInteractionofMonochromatic
X-Rays with Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
O. Peyrusse
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.2 Atomic Model Construction for the Modeling of X-Ray
Interaction with Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.3 Interaction with Gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Interaction with Small Objects. . . . . . . . . . . . . . . . . . . . . . . . . 135
6.5 Interaction with Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.5.1 Population Kinetics and Atomic Structure at Solid
Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.5.2 Temperature and Population Evolution. . . . . . . . . . . . . . 139
6.5.3 Energy Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.5.4 Modeling of Al, V and Ag Samples Irradiated
in the X-UV or X-Ray Range. . . . . . . . . . . . . . . . . . . . 146
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7 Spectral Modeling in Astrophysics—The Physics of Non-
equilibrium Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
G.J. Ferland and R.J.R. Williams
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.2 Working with Real Nebulae: The Observational
Questions We Are Trying to Answer. . . . . . . . . . . . . . . . . . . . 155
7.3 Approaches to Astronomical Spectral Modelling . . . . . . . . . . . . 162
7.4 Spectral Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.4.1 The Ionization Balance in the ISM Limit . . . . . . . . . . . . 166
7.5 The Physics of the Astronomical Problem. . . . . . . . . . . . . . . . . 173
7.6 Future Opportunities and Challenges . . . . . . . . . . . . . . . . . . . . 174
7.6.1 New Spectroscopic Opportunities . . . . . . . . . . . . . . . . . 174
7.6.2 And the Grand Challenges to Exploiting Them. . . . . . . . 177
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178