From the Preface: "In this book, we attempt to sketch the different paths followed by fusion research from initial ignorance to present understanding, be it the understanding of why a particular scheme would not work, or why it was more profitable to concentrate, at least for the time being, on the mainstream— tokamak development. We do not regard ourselves as historians, but we hope that our account will help future historians as well as scientists in other fields to find their way through this difficult terrain.
Physics and applications of complex plasmas by Vladimirov, Sergey V. From Preface: "The physics of complex plasma systems containing a colloid "macroscopic" particle component "dust" is a rapidly emerging area at the forefront of the physics and chemistry of plasmas and gas discharges, space physics and astrophysics, and materials science and engineering. Treumann ISBN: The present book provides a contemporary systematic treatment of shock waves in high-temperature collisionless plasmas as are encountered in near Earth space and in Astrophysics. It consists of two parts. Such shocks are naturally magnetised implying that the magnetic field plays an important role in their evolution and dynamics.
This part treats subcritical shocks which dissipate flow energy by generating anomalous resistance or viscosity. The main emphasis is, however, on super-critical shocks where the anomalous dissipation is insufficient to retard the upstream flow. These shocks, depending on the direction of the upstream magnetic field, are distinguished as quasi-perpendicular and quasi-parallel shocks which exhibit different behaviours, reflecting particles back upstream and generating high electromagnetic wave intensities.
Particle acceleration and turbulence at such shocks become possible and important. Part II treats planetary bow shocks and the famous Heliospheric Termination shock as examples of two applications of the theory developed in part I. Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter by Atzeni, Stefano Abstract: The book is devoted to targets for nuclear fusion by inertial confinement and to the various branches of physics involved.
It first discusses fusion reactions and general requirements for fusion energy production. It then introduces and illustrates the concept of inertial confinement fusion by spherical implosion, followed by detailed treatments of the physics of fusion ignition and burn, and of energy gain. The next part of the book is mostly devoted to the underlying physics involved in inertial fusion, and covers hydrodynamics, hydrodynamic stability, radiative transport and equations-of-state of hot dense matter, laser and ion beam interaction with plasma.
It discusses different approaches to inertial fusion direct-drive by laser, indirect-drive by laser or ion beams , including recent developments in fast ignition. The goal of the book is to give an introduction to this subject, and also to provide practical results even when derived on the basis of simplified models. Physics of Plasmas by T.
Boyd, J. Sanderson ISBN: The Physics of Plasmas provides a comprehensive introduction to the subject, illustrating the basic theory with examples drawn from fusion, space and astrophysical plasmas. A particular strength of the book is its discussion of the various models used to describe plasma physics and the relationships between them. These include particle orbit theory, fluid equations, ideal and resistive magnetohydrodynamics, wave equations and kinetic theory.
The reader will gain a firm grounding in the fundamentals, and develop this into an understanding of some of the more specialised topics. Throughout the text, there is an emphasis on the physical interpretation of plasma phenomena. Exercises are provided throughout.
Advanced undergraduate and graduate students of physics, applied mathematics, astronomy and engineering will find a clear but rigorous explanation of the fundamental properties of plasmas with minimal mathematical formality. This book will also appeal to research physicists, nuclear and electrical engineers. Low-temperature radio frequency plasmas are essential in various sectors of advanced technology, from micro-engineering to spacecraft propulsion systems and efficient sources of light.
The subject lies at the complex interfaces between physics, chemistry and engineering. Focusing mostly on physics, this book will interest graduate students and researchers in applied physics and electrical engineering. The book incorporates a cutting-edge perspective on RF plasmas.
It also covers basic plasma physics including transport in bounded plasmas and electrical diagnostics. Its pedagogic style engages readers, helping them to develop physical arguments and mathematical analyses. Worked examples apply the theories covered to realistic scenarios, and over in-text questions let readers put their newly acquired knowledge to use and gain confidence in applying physics to real laboratory situations. Cravens ISBN: Physics of Solar System Plasmas provides a comprehensive introduction to the plasma physics and magnetohydrodynamics that are needed to study the solar wind and magnetosphere.
The text includes a broad introduction to plasma physics, including important discussions of kinetic theory, single particle motion, magnetohydrodynamics, geomagnetically trapped energetic particles and the physics of magnetic reconnection. This leads into a thorough description of the Sun and the solar wind, and, finally, the author addresses magnetospheric physics. Among the topics covered here are magnetospheric morphology, bow shocks, magnetospheric convection and electrical currents, substorms, ionospheric physics, magnetosphere-ionosphere coupling, auroral physics and the interaction of the solar wind with the planets.
Problem sets at the end of each chapter make this a useful text for advanced undergraduate students in astrophysics, geophysics, or atmospheric sciences. Graduate students and researchers will also find it a valuable source of information. Space plasma is so hot that the atoms break up into charged particles which then become trapped and stored in magnetic fields.
When critical conditions are reached the magnetic field breaks up, releasing a large amount of energy and causing dramatic phenomena. The largest space plasma activity events observed in the solar system occur on the Sun, when coronal mass ejections expel several billion tons of plasma mass into space. This book provides a coherent and detailed treatment of the physical background of large plasma eruptions in space. It provides the background necessary for dealing with space plasma activity, and allows the reader to reach a deeper understanding of this fascinating natural event. The book employs both fluid and kinetic models, and discusses the applications to magnetospheric and solar activity.
This will form an interesting reference for graduate students and academic researchers in the fields of astrophysics and plasma physics. Physics of Strongly Coupled Plasma by Fortov, Vladmir Abstract: This book concerns the physics of plasma at high density, which is compressed so strongly that the effects of interparticle interactions, nonideality, govern its behavior.
The interest in this non-traditional plasma has emerged during the last few years when states of matter with high concentration of energy, constituting the basis of the modern technologies and facilities, became accessible for impulse experiments. The greatest part of the Universe matter is in this exotic state. In this book, the methods of strongly coupled plasma generation and diagnostics are considered. The experimental results on thermodynamic, kinetic, and optical properties are given, and the main theoretical models of the strongly coupled plasma state are discussed.
Particular attention is given to fast developing modern directions of strongly coupled plasma physics, such as metallization of dielectrics and dielectrization of metals, nonneutral plasma, complex dusty plasma, and its crystallization. Physics of the Plasma Universe by Anthony L. Peratt ISBN: Today many scientists recognize plasma as the key element to understanding new observations in near-Earth, interplanetary, interstellar, and intergalactic space; in stars, galaxies, and clusters of galaxies, and throughout the observable universe.
Physics of the Plasma Universe, 2nd Edition is an update of observations made across the entire cosmic electromagnetic spectrum over the two decades since the publication of the first edition. It addresses paradigm changing discoveries made by telescopes, planetary probes, satellites, and radio and space telescopes. The contents are the result of the author's 37 years research at Livermore and Los Alamos National Laboratories, and the U.
Department of Energy.
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This book covers topics such as the large-scale structure and the filamentary universe; the formation of magnetic fields and galaxies, active galactic nuclei and quasars, the origin and abundance of light elements, star formation and the evolution of solar systems, and cosmic rays. Chapters 8 and 9 are based on the research of Professor Gerrit Verschuur, and reinvestigation of the manifestation of interstellar neutral hydrogen filaments from radio astronomical observations are given. This volume is aimed at graduate students and researchers active in the areas of cosmic plasmas and space science.
The supercomputer and experimental work was carried out within university, National laboratory, Department of Energy, and supporting NASA facilities. Plasma and Fluid Turbulence by Itoh, Kimitaka This monograph is founded on the belief that the cooperation of theory and modelling with direct numerical simulation and experimental observations is indispensable for forming a firm understanding of the evolution of nature, in this case the theory and modelling of plasma and fluid turbulence. For researchers and graduate students in plasma physics.
This well-illustrated monograph is devoted to classic fundamentals, current practice, and perspectives of modern plasma astrophysics. The first part of the book is unique in covering all the basic principles and practical tools required for understanding and work in plasma astrophysics. The second part represents the physics of magnetic reconnection and flares of electromagnetic origin in space plasmas in the solar system, single and double stars, relativistic objects, accretion disks, their coronae. The lectures were intended as an introduction to the basic ideas about the boundary or scrape-off layer, SOL, of magnetic fusion device —particularly of tokamaks—for people with a plasma physics education.
Concepts about the SOL have largely been developed during the s and s and, as yet, little of this has found its way into plasma texts. The first part of this book was written with the intention of filling this gap. Plasma Electronics by Petrovic, Z. From Preface: "This book is based on a series of lectures presented at Keio University as part of its graduate program We believe that the book is well suited as an instrument for self-instruction through its topical exercises and problems arranged in each chapter. Plasma-Material Interaction in Controlled Fusion deals with the specific contact between the fourth state of matter, i.
A comprehensive analysis of the main processes of plasma-surface interaction is given together with an assessment of the most critical questions within the context of general criteria and operation limits. It is shown that the choice of plasma-facing materials can be reduced to a very limited list of possible candidates. Plasma Medicine by M. Laroussi Editor ; M.
Kong Editor ; G. Morfill Editor ; W. The introduction of low temperature plasma technology to medical research and to the healthcare arena in general is set to revolutionise the way we cure diseases. This innovative medium offers a valid and advantageous replacement of traditional chemical-based medications. Its application in the inactivation of pathogens in particular, avoids the recurrent problem of drug resistant microorganisms.
This is the first book dedicated exclusively to the emerging interdisciplinary field of plasma medicine. The opening chapters discuss plasmas and plasma chemistry, the fundamentals of non-equilibrium plasmas and cell biology. The rest of the book is dedicated to current applications, illustrating a plasma-based approach to wound healing, electrosurgery, cancer treatment and even dentistry. The text provides a clear and integrated introduction to plasma technology and has been devised to answer the needs of researchers from different communities.
It will appeal to graduate students and physicists, engineers, biologists, medical doctors and biochemists. The primary objectives of this book are, firstly, to present the essential theoretical background needed to understand recent fusion research and, secondly, to describe the current status of fusion research for graduate students and senior undergraduates.
It will also serve as a useful reference for scientists and engineers working in the related fields. Plasma physics and fusion energy by Freidberg, Jeffrey P. From Preface: "Plasma Physics and Fusion Energy is a textbook about plasma physics, although it is plasma physics with a mission - magnetic fusion energy. The goal is to provide a broad, yet rigorous, overview of the plasma physics necessary to achieve the half century dream of fusion energy. As noted in the statement of task Appendix A , the objective of the study was to provide a scientific assessment and strategy for the study of magnetized plasmas in the solar system.
By emphasizing the connections between locally occurring solar system structures and processes and their astrophysical counterparts, the study would contribute to a unified view of cosmic plasma behavior. Plasma Physics gives a comprehensive introduction to the basic processes in plasmas and demonstrates that the same fundamental concepts describe cold gas-discharge plasmas, space plasmas, and hot fusion plasmas.
Starting from particle drifts in magnetic fields, the principles of magnetic confinement fusion are explained and compared with laser fusion. Collective processes are discussed in terms of plasma waves and instabilities. The concepts of plasma description by magnetohydrodynamics, kinetic theory, and particle simulation are stepwise introduced.
Plasma physics: confinement, transport and collective effects by Dinklage, A. Beginning with a broad introduction, the book leads graduate students and researchers — also those from related fields - to an understanding of the state-of-the-art in modern plasma physics. Furthermore, it presents a methodological cross section ranging from plasma applications and plasma diagnostics to numerical simulations, the latter providing an increasingly important link between theory and experiment.
Effective references guide the reader from introductory texts through to contemporary research. Plasma Committee. The study was to focus on progress in plasma research, identify the most compelling new scientific opportunities, evaluate prospects for broader application of plasmas, and offer guidance to realize these opportunities. The report provides an examination of the broad themes that frame plasma research: low-temperature plasma science and engineering; plasma physics at high energy density; plasma science of magnetic fusion; space and astrophysical science; and basic plasma science.
Within those themes, the report offers a bold vision for future developments in plasma science. Plasma Spectroscopy by Fujimoto, Takashi Abstract: This book presents a theoretical framework of plasma spectroscopy, in which the observed spectral line intensities or the populations of excited levels of atoms or ions immersed in plasma are interpreted in terms of the characteristics of the plasma. Following a review of important atomic processes in plasma, the rate equation governing the populations in excited levels and the ground state is solved in the collisional-radiative model.
In this model, plasmas are classified into the ionizing plasma and the recombining plasma. Various features of these plasmas are examined. Ionization and recombination of atoms and ions are also treated in the model. An emission-line intensity is proportional to the ionization flux or to the recombination flux, and thus the ionization-balance plasma produces less intense emission lines.
The recombination continuum intensity continues smoothly to the series lines, originating from levels in local thermodynamic equilibrium, so that the Boltzmann plot of the population of these levels is extended to the continuum-state electrons. Line broadening mechanisms are discussed, including the Stark broadening. Radiation transport gives rise to a modification to the emission line profile and to an effective decrease in the transition probability; the latter problem is treated in two alternative approaches.
Phenomena characteristic of dense plasma are discussed, including the excitation and deexcitation processes of ions involving doubly excited levels and a modification to the Saha relationship. The book includes modern and complete treatments of electron cyclotron emission, collisions, relativistic effects, Landau damping, quasilinear and nonlinear wave theory, and tunneling equations. The broad scope encompasses waves in cold, warm, and hot plasmas and relativistic plasma waves. Special chapters deal with the effects of boundaries, inhomogeneities, and nonlinear effects.
The author derives all formulae and describes several fundamental wave experiments, allowing for a greater appreciation of the subject. Nuclear fusion research is entering a new phase, in which power exhaust will play a vital role. This book presents a complete and up-to-date summary of this emerging field of research in fusion plasmas, focusing on the leading tokamak concept.
Emphasis is placed on rigorous theoretical development, supplemented by numerical simulations, which are used to explain and quantify a range of experimental observations. The text offers a self-contained introduction to power exhaust, and deals in detail with both edge plasma turbulence and edge localized modes, providing the necessary background to understand these important, yet complicated phenomena. Combining an in-depth overview with an instructive development of concepts, this is an invaluable resource for academic researchers and graduate students in plasma physics.
This textbook provides a modern and accessible introduction to magnetohydrodynamics MHD. It describes the two main applications of plasma physics, laboratory research on thermo-nuclear fusion energy and plasma astrophysics of the solar system, stars and accretion disks, from the single viewpoint of MHD. This approach provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, from the laboratory to the universe. It equips the reader with the necessary tools to understand the complexities of plasma dynamics in extended magnetic structures.
The classical MHD model is developed in detail without omitting steps in the derivations and problems are included at the end of each chapter. This text is ideal for senior-level undergraduate and graduate courses in plasma physics and astrophysics. Principles of Plasma Diagnostics by I. Hutchinson ISBN: This book provides a systematic introduction to the physics behind measurements on plasmas. It develops from first principles the concepts needed to plan, execute, and interpret plasma diagnostics.
The book is therefore accessible to graduate students and professionals with little specific plasma physics background, but is also a valuable reference for seasoned plasma physicists. Most of the examples are taken from laboratory plasma research, but the focus on principles makes the treatment useful to all experimental and theoretical plasma physicists, including those interested in space and astrophysical applications. This second edition is thoroughly revised and updated, with new sections and chapters covering recent developments in the field.
Specific areas of added coverage include neutral-beam-based diagnostics, flow measurement with mach probes, equilibrium of strongly shaped plasmas and fusion product diagnostics. The Second Edition has been carefully updated and revised to reflect recent developments in the field and to further clarify the presentation of basic principles. Along with in-depth coverage of the fundamentals of plasma physics and chemistry, the authors apply basic theory to plasma discharges, including calculations of plasma parameters and the scaling of plasma parameters with control parameters.
Principles of Plasma Spectroscopy by Hans R. Griem ISBN: This monograph presents a comprehensive description of the theoretical foundations and experimental applications of spectroscopic methods in plasma physics research. The first three chapters introduce the classical and quantum theory of radiation, with detailed descriptions of line strengths and high density effects. The next chapter describes theoretical and experimental aspects of spectral line broadening.
The following five chapters are concerned with continuous spectra, level kinetics and cross sections, thermodynamic equilibrium relations, radiative energy transfer, and radiative energy losses. The book concludes with three chapters covering the basics of various applications of plasma spectroscopy to density and temperature measurements and to the determination of some other plasma properties. Over one thousand references not only guide the reader to original research covered in the chapters, but also to experimental details and instrumentation.
This will be an important text and reference for all those working on plasmas in physics, optics, nuclear engineering, and chemistry, as well as astronomy, astrophysics and space physics. Reaction-Diffusion Problems in the Physics of Hot Plasmas by Lazzaro, Enzo The physics of hot plasmas is of great importance for describing many phenomena in the Universe and is fundamental for the prospect of future fusion energy production on Earth. Non-trivial results of nonlinear electromagnetic effects in plasmas include the self-organization an self-formation in the plasma of structures compact in time and space.
These are the consequences of competing processes of nonlinear interactions and can be best described using reaction-diffusion equations. This book is focused on paradigmatic problems of reaction-diffusion type, met in many branches of science and concerning in particular the nonlinear interaction of electromagnetic fields with plasmas. This guidance is intended for the managers, designers, operators, and other personnel with safety responsibilities for facilities designated as magnetic fusion facilities.
Using a risk-based prioritization, the concepts presented here may also be applied to other magnetic fusion facilities. This Standard is oriented toward regulation in the Department of Energy DOE environment as opposed to regulation by other regulatory agencies. As the need for guidance involving other types of fusion facilities or other regulatory environments emerges, additional guidance volumes should be prepared.
The concepts, processes, and recommendations set forth here are for guidance only. They will contribute to safety at magnetic fusion facilities. This Standard identifies safety requirements for magnetic fusion facilities. Safety functions are used to define outcomes that must be achieved to ensure that exposures to radiation, hazardous materials, or other hazards are maintained within acceptable limits. Requirements applicable to magnetic fusion facilities have been derived from Federal law, policy, and other documents.
In addition to specific safety requirements, broad direction is given in the form of safety principles that are to be implemented and within which safety can be achieved. Spectroscopy of Astrophysical Plasmas by Edited by A. Dalgarno, D. Layzer ISBN: A group of acknowledged experts describe the use of spectroscopy as a diagnostic probe of astronomical environments. The broad sweep of the book enables good coverage to be given to all the situations in which plasmas are encounteres in astronomical investigations.
Specifically, the articles include quasars, Seyfert galaxies, active galactic nuclei, the solar chromosphere and corona, galactic HII regions, circumstellar shells, interstellar gas, supernova remnants and interstellar clouds. The book includes an account of the basic aspects of spectroscopy in a chapter on laboratory astrophysics. The book was stimulated by the extraordinary contributions to astronomical spectroscopy of Leo Goldberg, and is dedicated to him.
Throughout, this book is written with the needs of students in astronomy and astrophysics in mind. Each chapter includes a summary or conclusions about the future direction of research. Furthermore there are extensive bibliographies. This textbook is therefore an excellent introduction to research in astrophysics and it will act as a pathfinder to the primary literature.
Theory of Photon Acceleration by Mendonca, J. Theory of Space Plasma Microinstabilities by S.
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The ionized material that constitutes plasma permeates almost all of the universe beyond the planets and their atmospheres and satellites. This book describes the linear theory of many different waves and instabilities that may propagate in a collisionless plasma. Electrostatic and electromagnetic fluctuations, and a variety of instability sources are considered.
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Applications of the theory are discussed with respect to spacecraft observations in the solar wind, terrestrial magnetosheath, magnetosphere and magnetotail and at the bow shock and magnetopause. Tables at the end of most chapters summarize wave and instability nomenclature and properties, and problems for the reader to solve are interspersed throughout the text. Together these make this book of great value to both the student and research worker in space physics. Turbulence in space plasmas by Vlahos, L. Over the years, many leading European graduate schools in the field of astrophysical and space plasmas have operated within the framework of the research network, "Theory, Observations, and Simulations in Turbulence in Space Plasmas.
It emphasizes applications on solar coronae, solar flares, and the solar wind. Waves and Oscillations in Plasmas by Hans L. The author would like to thank students and colleagues for their assistance. Her patience and help are gratefully acknowledged. The author is also indebted to Prof.
Kristian Dysthe, the University of Bergen, Prof. Mitsuo Kono, Chuo University for valuable discussion on the chapters discussing nonlinear waves in fluids and plasmas.
Jan Trulsen, Institute for Theoretical Astrophysics, the University of Oslo, has offered help and given advice at all stages of the work. His friendly support has been indispensable. Also comments form numerous students over the years have helped to clarify many points in the text. A sabbatical year at the Norwegian Centre for Advanced Study CAS , in the academic year , was most pleasurable and stimulating. I would like to express my appreciation to the staff at that institute. I am very grateful to Dr. Wojciech Miloch who patiently and carefully read large parts of the text and offered many useful comments and valuable criticism.
Whistler-mode Waves in a Hot Plasma by Sergei Sazhin The book provides an extensive theoretical treatment of whistler-mode propagation, instabilities and damping in a collisionless plasma. This book fills a gap between oversimplified analytical studies of these waves, based on the cold plasma approximation, and studies based on numerical methods. Although the book is primarily addressed to space plasma physicists and radio physicists, it will also prove useful to laboratory plasma physicists.
Mathematical methods described in the book can be applied in a straightforward way to the analysis of other types of plasma waves. Problems included in this book, along with their solutions, allow it to be used as a textbook for postgraduate students. Anya Bartelmann. This set of data has a wide spectral range, which covers the appropriate wavelengths for all ion stages of carbon.
The irradiances were cross checked with the higher resolution radiances which have been given by Curdt et al. Its narrow range meant it was not suitable to be used for the rates, but comparisons showed good overall agreement with the radiances derived from Woods et al. The main source was Malinkovsky et al. It is noted that these are irradiance observations obtained when the Sun was very active see Del Zanna ; it is not straightforward to convert irradiances to radiances in this case.
The analytical fits to the Opacity Project, R-Matrix cross section backgrounds derived by Verner et al. In this CR model it would not take into account photo-ionisation of ions in excited levels nor the differing ionisation rates of those levels. Consequently, level resolved cross sections were used, as calculated by Badnell and made available on the APAP Network website 3.
These were checked by comparing the total rates of the ground level with the Verner et al. In ionisation equilibrium,. The usual method to calculate ion charge states at zero density as in e. The relative population of two ions is then obtained directly from the ratio of the total ionisation and recombination rates at each temperature. To take into account density, a level resolved model was developed in which all the main fine structure levels for the carbon ions were included. Matrices which included all the rates were built for each ion. The matrix elements for the processes occurring within one ion were obtained in the same way as in the Chianti package; they included collisional excitation and de-excitation by electron and proton impact, photo-excitation and -de-excitation, plus radiative decay.
The other elements of the matrices, for transitions between ions, were populated using the ionisation and recombination rates for the ground and metastable levels which were described earlier. The populations of all the levels for all ions were solved at once. This was a novel approach; it used a significant modification of the Chianti codes, and was written in IDL. Part of these codes have been included in v. The rate coefficients for the ground and metastable levels have been made available at the CDS.
Comparisons were made with available experiments and theoretical calculations in order to validate the results. Experiments where ions in metastable levels were present provided a valuable way of validating cross sections for both ground and metastable levels at the same time, so long as the populations of ions in metastable levels were known within a reasonable degree of accuracy.
Abdel-Naby et al. However, they do not give a sufficiently high energy range to be able to use the results for ionisation rates. Calculations of ionisation cross sections were made with FAC, whilst bearing in mind the known shortcomings of the DW approximation for nearly neutral charge states. The main experiment used for comparison has been Brook et al. For rate coefficients, accuracy in the cross section near the threshold is important, which can be another shortcoming of the DW approach.
To solve the problem and provide rates for the model, the recommended data of Bell et al. The scaled energies of Bell et al. A later experiment by Yamada et al. Figure 2 shows that the FAC ground level cross section follows a very similar energy distribution and peaks just a few per cent above Bell et al..
Chianti uses the ground level cross section of Dere , who also used FAC. The R-Matrix result of Ludlow et al. The only available comparison for the metastable term is with the work of Ludlow et al.. The Fogle et al. Woodruff et al. Falk et al. It is seen that the theoretical cross sections are almost entirely within the experimental uncertainties. R-Matrix rate coefficients for this ion. Bell et al. The Dere cross section is close to the Knopp et al. The cross sections from Dere are close to Crandall et al.. To calculate the cross sections for EA requires data from several processes: collisional excitation, auto-ionisation and radiative decay.
A bound electron is collisionally excited to an auto-ionising state above the threshold, and then it may either spontaneously ionise or decay. Calculating EA cross sections involves multiplying the excitation cross section to a level by the auto-ionisation branching ratio from that level, and summing over all levels which lie above the ionisation threshold. The auto-ionisation branching ratio is the probability that auto-ionisation takes place instead of decay. The sum over p is for excitations to all levels within the ion over the ionisation limit, the sum over q is for all final levels in the next higher charge-state to which the ion may spontaneously ionise, and the sum over s is for all levels to which radiative decay may take place within the existing ion.
Autostructure was used to obtain data for the required processes, which were then combined to create level resolved rate coefficients for ground and metastable levels, which have been made available online. As mentioned in Sect. To resolve this, the structure used by Liang et al. At the same energy, the Ludlow et al. This accords with the conclusion of Ludlow et al. The uncertainty observed in the cross sections, which arose from differences in structure, was also seen in the rate coefficients.
Because of this variability, the EA rate coefficients were computed using the R-Matrix, thermally averaged collision strengths from Liang et al. Since the R-Matrix collision strengths only include outer shell excitations, inner shell EA has been added to the rate coefficients by using AS DW excitation and auto-ionisation data with the same structure. Inner shell EA contributes significantly less to the total EA over most of the temperature range for this ion.
As an example of the contribution made by EA for this ion, at 40 K the ground level EA rate coefficient is one-third of the ground level DI value. Loch et al. This is seen in the cross section shown in Fig. The main contributions for the ground level come from weaker two-electron transitions, whereas for the metastable, 2s 2p 3 P , term the dominant contributions come from one-electron excitations.
Consequently, the metastable term EA cross section is an order of magnitude higher, which is in agreement with the value given by Loch et al. However, owing to sensitivity of the collision strengths to the mixing coefficients and weak, two-electron excitations from the ground, EA rate coefficients were affected by which approximation was used for the scattering computation. Using the R-Matrix data also had the advantage of including the resonance contributions.
Inner shell EA becomes important in the rate coefficients for temperatures above 10 6 K when calculated with a Maxwellian electron distribution. It may be possible to observe some peaks close to the relevant thresholds, but, given that the combined uncertainties in the metastable population and cross section measurements are greater than the EA contribution, these may simply be scatter in the results. Teng et al. Hahn et al. Double, direct ionisation produces cross sections which are between 0. Triple DI is two orders of magnitude less than double DI, and was not included in the modelling.
Another factor to bear in mind for the CR model is that the threshold for double ionisation is much higher, and so, compared to single ionisation, the rates will be significantly lower. The rates may be more significant with non-Maxwellian electron distributions which have an enhanced population at high energies.
As described in Sect. The effect of each process was determined by first running the model in the coronal approximation, that is, ions in a single, ground level with total rates connecting neighbouring charge states. This assisted identifying the primary effect each process has on the charge-state distribution. Thereafter, the model was switched to modelling resolved by levels for each atomic process to determine the effect on ion populations.
The remaining charge states were each modelled as a single level. It is densities which redistribute ion populations to terms above the ground term that produce the first noticeable effects of shifting the temperature formation of ions in the level resolved model, compared to the single level model. Effect with density of level-resolved, collisional ionisation on the CR model; blue dotted line — Chianti v.
The changes in the ionisation balance also affect the temperature at which ions peak in their abundance. However, the threshold energy is far above the formation temperatures of the ions, and EA makes negligible changes to the ion populations. Goldberg et al. With carbon EA is seen to be important for both B-like and Be-like ions. Multiple ionisation has no noticeable influence on the charge-state distribution in these conditions.
Although DR suppression is approximated here, it gives clues to the behaviour seen in full CR models, in which high n levels are included. Suppressing these rates will have little impact on the charge-state distribution. Effect with density of DR suppression on the ground-to-ground CR model; blue dotted line — Chianti v. This is similar to the effect level resolved, collisional ionisation has on the model.
The ions will be almost completely in the ground level, which requires free electrons to have high energies in order to excite bound, K -shell electrons to the next, L -shell level in order for DR to occur. Considering the combination of level resolved, collisional ionisation and dielectronic recombination suppression Fig. Combined effect with density of level-resolved, collisional ionisation and DR suppression on the CR model; blue dotted line — Chianti v.
There is a consequent shift towards lower temperatures and higher peak populations. Since the PI rates are independent of temperature and density, in conditions of higher density the collisional rates will dominate. Since the PI rates depend on the particular radiances present for each of the transitions, it is difficult to determine systematic differences when switching between the coronal approximation and level resolved models. The scenario demonstrates, as with collisional ionisation, level resolved photo-ionisation produces greater populations in the next higher charge states because of the faster ionisation rates from metastable levels.
Stronger radiances in other conditions, when active regions are present or during flares, for instance, should result in greater population shifts towards higher charge states. Now that the basic model has been built, it is possible to compare it with the results of earlier works Fig. Although there are many processes at play in a full model, it may be possible to explain several of the differences between the two models.
As noted in Sect. It suggests the model may have used either slower ionisation or faster recombination rates, or a combination of both. Comparing the case with photo-ionisation included Fig. Allowing for this, the similarities in the overall charge-state distribution are recognised, especially with the difference in collisional ionisation rates taken into consideration, which was noted in the case without PI. In order to test how much the present ion populations could affect plasma diagnostics, a means of comparing the results with observations is now discussed.
A diagnostic technique which uses ion populations involves predicting line intensities from a given set of ion populations and comparing the results with observed intensities. This provides a way of determining the plasma conditions which produced the observed emission. Since the conditions to which this CR model most applies is the solar TR tests against the line emission from this region will be made.
The technique used to calculate the theoretical line intensities is known as differential emission measure DEM modelling, as described e. It uses the observed line intensities to estimate the amount of plasma present along the line of sight and its density distribution. The technique can be used in situations where the temperature distribution of the plasma varies smoothly along the field of view, which is a reasonable assumption for these solar conditions. It uses ion and level populations from the modelling, radiative decay rates and solar elemental abundances, along with the plasma density distribution with height, in order to calculate the expected intensity of each line.
The DEM technique is also used for other purposes, such as determining elemental abundances, for instance. The DEM modelling is dependent on ion populations, which is the very quantity being tested here. As a result, ion populations which have been previously published should be used to calculate the density distribution of the plasma with height.
Once the density distribution has been established, the predicted intensities can be calculated using carbon ion populations from different sources and compared with observations. The modelling of the quiet Sun TR observed on the disc was considered. It also differs from the analysis which has been presented in Parenti et al. The radiances used to calculate the photo-ionisation rates in Sect. However, as has been pointed out by Wilhelm et al. The Skylab radiances were therefore supplemented with a few among those which have been reported by Wilhelm et al.
Often, good agreement is found with the quiet Sun radiances which have been obtained by OSO-4 Dupree Chianti v. The DEM modelling was carried out with the improved version released in Chianti v. The intensity of the vast majority of the strongest spectral lines is largely independent of density. However, some TR lines are sensitive to the varying density in the lower part of this region. The effective temperature of a line is given by:. As the DEM increases exponentially towards lower temperatures, T eff is normally much lower than T max , the temperature where the contribution function G T of a line has a maximum.
In turn, T max is normally higher than the temperature of maximum ion population in equilibrium. As a baseline, the charge-state distributions at zero density from Chianti were used for all ions in order to determine the DEM from the observed lines. Once the DEM was determined, the ratios of predicted to observed intensities for all of the lines were calculated. The ratios using the Chianti ion populations are shown in column R 1 of Table 1. The ratios using the ion populations from this work are given in column R 2. Table 1. Since both pairs of lines from these nitrogen ions are largely independent of density, it suggests the cause is more likely to be related to the formation temperatures of the lines.
Based on the evidence of modelling carbon, it is reasonable to infer that modelling which is dependent on density would show shifts in the formation temperatures of the nitrogen ions and provide improved theoretical values.