Plasma polarization spectroscopy, Takashi Fujimoto, Atsushi Iwamae

Springer Series on atomic, optical, and plasma physics 44 Springer Series on atomic, optical, and plasma physics The Springer Series on Atomic, Optical, and Plasma Physics covers in a comprehensive manner theory and experiment in the entire f ield 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 f ields 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 f ield 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 f ield 36 Atom Tunneling Phenomena in Physics, Chemistry and Biology Editor: T Miyazaki 37 Charged Particle Traps Physics and Techniques of Charged Particle Field Confinement By V.N Gheorghe, F.G Major, G Werth 38 Plasma Physics and Controlled Nuclear Fusion By K Miyamoto 39 Plasma-Material Interaction in Controlled Fusion By D Naujoks 40 Relativistic Quantum Theory of Atoms and Molecules Theory and Computation By I.P Grant 41 Turbulent Particle-Laden Gas Flows By A.Y Varaksin 42 Phase Transitions of Simple Systems By B.M Smirnov and S.R Berry 43 Collisions of Charged Particles with Molecules By Y Itikawa 44 Plasma Polarization Spectroscopy Editors: T Fujimoto and A Iwamae 45 Emergent Non-Linear Phenomena in Bose–Einstein Condensates Theory and Experiment Editors: P.G Kevrekidis, D.J Frantzeskakis, and R Carretero-Gonz´alez Vols 10–35 of the former Springer Series on Atoms and Plasmas are listed at the end of the book Takashi Fujimoto (Editors) Atsushi Iwamae Plasma Polarization Spectroscopy With 180 Figures 123 Professor Dr Takashi Fujimoto Dr Atsushi Iwamae Kyoto University, Graduate School of Engineering Department of Mechanical Engineering and Science Kyoto 606-8501, Japan E-mail: t.fujimoto@z04r2005.mbox.media.kyoto-u.ac.jp, iwamae@kues.kyoto-u.ac.jp ISSN 1615-5653 ISBN 978-3-540-73586-1 Springer Berlin Heidelberg New York Library of Congress Control Number: This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Violations are liable to prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting and prodcution: SPI Publisher Services Cover design: eStudio Calmar Steinen Printed on acid-free paper SPIN: 12038763 57/3180/SPI - Preface Excited atoms and ions in a plasma produce line radiation, and continuumstate electrons emit continuum radiation This radiation has been the subject of traditional plasma spectroscopy: the observed spectral distributions of the radiation or the intensities of the line and continuum radiation are reduced to the populations of electrons in the excited or continuum states, and these populations are interpreted in terms of the state of the plasma As the word intensity suggests, it is implicitly assumed that this radiation is unpolarized This is equivalent to assuming that the plasma is isotropic If the plasma is under a magnetic and/or electric field, however, this assumption naturally breaks down: the atoms and ions are subjected to the Zeeman or Stark effect A spectral line splits into several components and each component is polarized according to the field This polarization is due to the anisotropy of the space in which the atoms or ions are present Light or the radiation field, except for the case of an isotropic field like the blackbody radiation, is usually anisotropic A polarized laser beam is an extreme example Such a field can create anisotropy in atoms or ions when they are excited by absorbing photons from the field Electrons having an anisotropic distribution in velocity space can create atomic anisotropy when these electrons excite the atoms or ions Thus, it may be expected that we encounter many anisotropic plasmas, so that the radiation emitted by them is polarized The polarization phenomena noted above have been recognized, of course, and the Zeeman or Stark effect is an important element of standard plasma diagnostic techniques Other polarization phenomena have also been investigated to a certain extent, especially in the solar atmosphere research In the laboratory plasma research, however, relatively little attention has been paid to the polarization of radiation Given the fact that polarization is one of the important features of light, this situation may be regarded rather strange This lack of interest in polarization may be ascribed to the fact that an electron velocity distribution is rather easily thermalized, especially in dense plasmas Another factor may be experimental: if we want to detect polarization, and further, to measure it quantitatively, we have to substantial preparations to perform such an experiment Especially, VI Preface if our plasma is time dependent or unstable or the wavelength of the radiation to be detected is outside the visible region, performing an experiment itself is extremely difficult In the past, there have been several plasma spectroscopy experiments in which an emphasis was placed on the polarization properties of the plasma radiation Still these experiments are rather exceptional Therefore, investigations in this direction may form a new research area; this new discipline may be named plasma polarization spectroscopy (PPS) As the brief account above suggests, PPS would provide us with information to which no other techniques have an access or information about finer details of the plasma, e.g., the anisotropic velocity distribution function of plasma electrons; this last aspect is important in plasma physics, e.g., the plasma instabilities There have been groups of workers who are interested in PPS, and, in the last decade, a series of international workshops have been held as the forum among them It was agreed by the participants that PPS has now reached the point of some maturity and a book be published which summarizes the present status of PPS These discussions have resulted in the present monograph As the editors of this book, we tried to make this book rather easy to understand for beginners, so that it should be useful for students and researchers who want to enter this new research area We believe this book can be a step forward to establish PPS as a standard plasma diagnostic technique Kyoto, Japan (August 2007) Takashi Fujimoto Atsushi Iwamae Contents Introduction T Fujimoto 1.1 What is Plasma Polarization Spectroscopy? 1.2 History of PPS 1.3 Classification of PPS Phenomena 1.4 Atomic Physics References 10 Zeeman and Stark Effects M Goto 2.1 General Theory 2.2 Zeeman Effect 2.3 Stark Effect 2.4 Combination of Electric and Magnetic Fields References 13 13 17 20 25 27 Plasma Spectroscopy T Fujimoto 3.1 Collisonal-Radiative Model: Rate Equations for Population 3.2 Ionizing Plasma and Recombining Plasma 3.2.1 Ionizing Plasma Component 3.2.2 Recombining Plasma Component 3.2.3 Ionizing Plasma and Recombining Plasma References 29 29 34 34 39 45 49 Population-Alignment Collisional-Radiative Model T Fujimoto 4.1 Population and Alignment 4.2 Excitation, Deexcitation and Elastic Collisions: Semiclassical Approach 4.2.1 Monoenergetic Beam Perturbers and Cross Sections 4.2.2 Axially Symmetric Distribution 51 51 55 56 58 VIII Contents 4.2.3 Rate Equation in the Irreducible-Component Representation 4.2.4 Rate Equation in the Conventional Representation 4.3 Ionization and Recombination 4.4 Rate Equations 4.4.1 Ionizing Plasma Component 4.4.2 Recombining Plasma Component References Definition of Cross Sections for the Creation, Destruction, and Transfer of Atomic Multipole Moments by Electron Scattering: Quantum Mechanical Treatment G Csanak, D.P Kilcrease, D.V Fursa, and I Bray 5.1 General Theory 5.2 Inelastic Scattering 5.3 Alignment Creation by Elastic Electron Scattering 5.3.1 Semi-Classical Background 5.3.2 Wave-Packet Formulation of Alignment Creation by Elastic Scattering 5.3.3 Discussion and Conclusions References 61 62 64 66 66 67 68 69 69 76 81 82 83 87 88 Collision Processes T Fujimoto 91 6.1 Inelastic and Elastic Collisions 91 6.1.1 Excitation/Deexcitation and Ionization, Q0,0 (r, p), and Q0,0 (p, p) 91 6.1.2 Alignment Creation, Q0,2 (r, p), and Alignment-to-Population, Q2,0 (r, p) 93 6.1.3 Alignment Creation by “Elastic” Scattering, Q0,2 (p, p) 98 6.1.4 Alignment Transfer, Q2,2 (r, p), and Alignment q Destruction, Q2,2 q (p, p) 101 6.2 Recombination 110 6.2.1 Radiative Recombination 110 6.2.2 Dielectronic Recombination: Satellite Lines 113 6.2.3 Ionization 116 6.3 Alignment Relaxation by Atom Collisions 117 6.3.1 LIFS Experiment: Depopulation and Disalignment 117 6.3.2 Alignment Relaxation Observed by the Self-Alignment Method 124 References 125 Radiation Reabsorption T Fujimoto 127 7.1 Alignment Creation by Radiation Reabsorption: Self-Alignment 127 Contents IX 7.1.1 Basic Principle 127 7.1.2 Latent Alignment 131 7.1.3 Self-Alignment 132 7.2 Alignment Relaxation: Alignment Destruction and Disalignment 136 References 142 Experiments: Ionizing Plasma T Fujimoto, E.O Baronova, and A Iwamae 145 8.1 Gas Discharge Plasmas 145 8.1.1 Direct Current Discharge 146 8.1.2 High-Frequency Discharge 150 8.1.3 Neutral Gas Plasma Collision 152 8.2 Z-Pinch Plasmas 154 8.2.1 Vacuum Spark and X-Pinch 156 8.2.2 Plasma Focus and Gas Z-Pinch 159 8.3 Laser-Produced Plasmas 163 8.4 Magnetically Confined Plasmas 166 8.4.1 Tokamak Plasmas 166 8.4.2 Cusp Plasma 167 References 176 Experiments: Recombining Plasma A Iwamae 179 9.1 Introduction 179 9.2 Laser-Produced Plasmas 179 References 184 10 Various Plasmas Y.W Kim, T Kawachi, and P Hakel 185 10.1 Charge Separation in Neutral Gas-Confined Laser-Produced Plasmas 185 10.1.1 Nonideal Plasmas and Their 3D Plasma Structure Reconstruction 186 10.1.2 Polarization Spectroscopy of LPP Plumes Confined by Low-Density Gas 192 10.1.3 Analysis and Discussion 196 10.1.4 Polarization-Resolved Plasma Structure Imaging 197 10.1.5 Concluding Remarks 199 10.2 Polarization of X-Ray Laser 201 10.2.1 Introduction 201 10.2.2 Observation of the Polarization of QSS Collisional Excitation X-Ray Laser 202 10.3 Atomic Kinetics of Magnetic Sublevel Populations and Multipole Radiation Fields in Calculation of Polarization of Line Emissions 206 Appendix C Density Matrix: Light Observation and Relaxation ⎛ 369 ⎞ ρ10 ρ1−1 ρ d ⎜ 11 ⎟ ρ00 ρ0−1 ⎠ ⎝ ρ01 dt ρ−11 ρ−10 ρ−1−1 ⎞ ⎛ 3(ρ10 − ρ0 −1 ) 6ρ1 −1 ρ11 − 2ρ00 + ρ−1−1 h2 ⎜ ⎟ =− ⎝ 3(ρ01 − ρ−10 ) −2(ρ11 − 2ρ00 + ρ−1 −1 ) 3(ρ0 −1 − ρ10 ) ⎠ 6ρ−11 3(ρ−10 − ρ01 ) ρ11 − 2ρ00 + ρ−1 −1 (C.47) The reader may verify that the three elements of the alignment, ρ20 , ρ21 , and ρ22 , in Table C.1 decay with the same rate (g0 + h2 = g2 ) This is the property on which the experiment in Sect 6.1.4 was based (see (C.32a) and (C.32b)) References A Omont, Prog Quant Electron 5, 69 (1977) K Blum, Density Matrix Theory and Applications, 2nd edn (Plenum, New York, 1996) Appendix D Hanle Effect In this appendix, we introduce the Hanle effect, which played an important role in developing PPS D.1 Classical Picture The classical atom consists of an electron which is attracted by the ion core with the harmonic force Suppose the atom is located at the origin A pulsed beam of light propagating in the z direction with its polarization directed in the y direction illuminates the atom and the atomic electron is accelerated by the electric field The electron begins to oscillate in the y direction, and the oscillation decays with the natural lifetime, i.e., the spontaneous decay The emitted light, the resonance fluorescence, is polarized in the y direction and it also decays with the same rate Suppose, a magnetic field is applied in the z direction In the oscillation motion, the electron is exerted by the Lorentz force, and its trajectory is modified; the oscillation direction rotates around the z-axis, i.e., the Larmor precession The direction of the polarization of the emitted light accordingly rotates Suppose we observe the y-polarized component and the x-polarized component of the emitted light separately, and integrate the signals over the whole decay time Owing to the presence of the magnetic field, the averaged polarization degree becomes smaller The rate of decrease is determined by the balance between the decay time of the atom and the Larmor precession frequency, which is proportional to the strength of the applied magnetic field Therefore, the observed polarization degree against the magnetic field has a Lorentzian profile with its FWHM (full width at half maximum) given by the natural lifetime Here we have assumed that the Land´e g-factor is known This effect is known as the Hanle effect, and the plot of the polarization degree against the magnetic field strength is called the Hanle signal 372 Appendix D Hanle Effect If the excitation-observation geometry is different, the observed profile can be of a dispersion shape For example, when our polarizer is directed in the ±45◦ with respect to the y direction, we obtain a dispersion shape profile When our atom suffers collisional relaxation, the effective lifetime shortens, and the FWHM increases Thus, FWHM against, for example, the atom density gives a straight line From this plot, we can determine the natural lifetime from the intercept in the zero-density limit and the collisional relaxation rate coefficient from the slope of this line D.2 Quantum Picture We have an atomic ensemble at the origin, and this system is illuminated by the beam of light in the same way as the above We assume the 0–1 angular momentum pair for our transition The initial density matrix is given by (C.30), and its time development is given by (C.41) To be realistic, we include the spontaneous decay Then, the density matrix is multiplied by the decay factor e−g0 t , and the intensity of the emitted radiation with our polarizer directed in the y direction is given by (C.42) with the same decay factor multiplied The time-integrated signal is Sy ∝ 1 1+ g0 + (2ω/g0 )2 , (D.1) where we have dropped the constant factor Here, the Larmor (angular) frequency is ω = µB gJ B See (C.37) and below The observed intensity of the x polarized component is, as noted after (C.42), given by (D.1) with the plus sign between the two terms in the brackets in (D.1) replaced by the minus sign Therefore, the polarization degree is given as P = S y − Sx = , Sy + Sx + (2ω/g0 )2 (D.2) From the FWHM of the Lorentzian profile, we can obtain g0 , the spontaneous decay rate Now, we include collisional relaxation as expressed by h1 and h2 (see Sect C.5) g0 may include collisional depopulation (see Fig E.2) It is interesting to note that the disorientation, h1 , has no influence on the Hanle signal The disalignment, h2 , affects the Hanle signal exactly in the same way as the spontaneous decay That is, the observed polarization degree is given by (D.2) with g0 replaced by g2 (see (C.45)) The proofs are left with the reader Appendix E Method to Determine the Population In this Appendix, we consider one of the practical, but basic, problems: i.e., by observing an emission line from excited atoms, how we can determine the population of the upper-level atoms This problem may seem rather trivial, but, if these atoms are anisotropically excited, it is less straightforward A typical example is the beam excitation experiment as mentioned in the beginning of Chap (see (6.2)) Suppose we want to determine n(p) from the observed line intensity of the transition p → s from a certain direction with respect to the z-axis, the symmetry axis This may be for the purpose of, e.g., in the beam excitation experiment, determining the excitation cross section Q0,0 (r, p), or some other purposes in which n(p) should be known without ambiguities A typical example is determination of natural lifetime of the upper-level atoms Since f2 (v) is present in this example, an alignment is also created in level p (see (6.4)) As (4.5) shows, the observed intensity, in general, is given not only by the population but also by the alignment, the second term in the brackets, so that we have to eliminate the contribution from the term proportional to a(p)/n(p) One configuration which immediately meets this requirement is to have a polarizer, the transmission axis of which is directed in η = 54.7◦ , the magic angle, so that cos2 η = 1/3 In many cases, however, the light source itself is already weak and adding a polarizer further reduces the signal-to-noise ratio in the observation In the vuv (vacuum ultraviolet) region, we even not have a polarizer with sufficient efficiency So, this configuration is rather undesirable Instead, we could observe the radiation emitted by the atoms from the direction of 54.7◦ with respect to the z-axis We may call this the magic angle observation In this case, for the π light η = 35.3◦ so that (1 − cos2 η) = −1 and for the σ light η = π/2 so that (1 − cos2 η) = By adding these two component intensities, we eliminate the contribution from the alignment When we use a grating spectrometer to resolve this line, however, it usually has different efficiencies for different polarized components with respect to 374 Appendix E Method to Determine the Population the line of sight of the spectrometer When the angle of incidence of the light incident on the grating surface is close to the blaze angle, at which the reflection efficiency is about the maximum, both the components, i.e., the polarized light whose electric vector oscillates in the parallel direction or the perpendicular direction to the grooves of the grating, have approximately the same efficiency At shorter wavelengths, the former component tends to have higher efficiencies and at longer wavelengths, the latter component has higher efficiencies This tendency is seen in Fig 14.8: the π-light is the light polarized in the perpendicular direction to the grooves of the grating, i.e., the p-light For the purpose of making the efficiencies of the grating virtually equal for both the π and σ components of the emission line, the spectrometer may be tilted by 45◦ around its line of sight This method is, however, sometimes inconvenient, since the entrance slit is not parallel or perpendicular to the symmetry axis of the experimental geometry any more Another method almost equivalent to the magic-angle observation is that, by applying a magnetic field in the direction of the line of sight, we rotate the aligned atom system in time around the line of sight Figure E.1 shows an example [1] In this experiment neon atoms in the metastable state (1s3 : Paschen notation; see Figs 6.19 and 7.1.) in a glow discharge plasma is excited by a linearly polarized laser pulse to the 2p2 level, and the subsequent fluorescence of the 1s2 –2p2 transition line is observed The polarization direction of the laser light with respect to the line of sight is 54.7◦ , the magic angle This excitation is virtually equal to the beam excitation at the excitation threshold (within the classical arguments), as discussed in the beginning of Chap The direction of polarization of the excitation laser light corresponds to the beam direction in the beam excitation By this excitation an alignment is created in the upper level atoms along with the population The alignment may further be relaxed by atom collisions and/or radiation reabsorption during the lifetime These relaxation phenomena are discussed in Sects 6.3 and 7.2, respectively In this demonstration experiment, for the purpose of illustration, the polarization effect is made pronounced: A plastic polarizer is placed in front of the entrance slit of our spectrometer, and our system is made sensitive only to the component of the fluorescence polarized in the direction of the laser beam In the absence of the magnetic field (0 G), the observed intensity decays with a certain apparent decay time constant When a magnetic field is applied in the direction of the line of sight, an oscillation appears in the decay curve This is due to the Larmor precession of the produced alignment, or the magnetic dipoles, around the magnetic field (see Appendix C) With the increase in the magnetic field strength, the oscillation frequency increases, and finally it becomes too high to be resolved by our observation system At the magnetic field of 30 G, the oscillation virtually disappears and the effect of the alignment is smeared out In this limit, the decay curve represents correctly the decay of the population, being independent of the alignment and its relaxation Appendix E Method to Determine the Population 375 log I Population Density (Arbitary Units) 3.0 Torr 0.11 mA 30 G 20 G 10 G 0G 20 40 60 80 time (ns) Fig E.1 Temporal decay of the observed emission line intensity subsequent to excitation by a laser pulse, which is polarized in the magic angle A magnetic field is applied in the direction of the line of sight “0 G” means the absence of the magnetic field The apparent decay is substantially different from the population decay as determined from the intensity decay at “30 G” (Quoted from [1], with permission from The Royal Swedish Academy of Science.) It is seen that the apparent decay of the observed intensity without a magnetic field is substantially different from the true decay of the population This difference is due to the disalignment, i.e., a decay of a(p)/n(p) with time, which is due to atom collisions and/or radiation reabsorption As noted above these processes are discussed in the text It may be noted that when disalignment is absent, the apparent decay coincides with the population decay in any excitation-observation geometry In this case, there should be no magnetic field, of course If the situation permits, (4.6) could be directly adopted for the present purpose; Iπ and Iσ are measured separately and the decay of (Iπ + 2Iσ ) is 376 Appendix E Method to Determine the Population De-population Rate (107 s−1) Atom Density (1017 cm−3) 5.5 5.4 5.3 5.2 10 Pressure (Torr) Fig E.2 Depopulation rate of the neon 2p2 level in a neon discharge plasma (circle): from (4.6); (triangle): by the effective magic-angle excitation method (Quoted from [1], with permission from The Royal Swedish Academy of Science.) determined Figure E.2 compares the depopulation rates determined by these two methods [1] It is seen that both the methods give virtually identical results Reference T Fujimoto, C Goto, K Fukuda, Phys Scripta 26, 443 (1982) Index 3-j symbol, 16, 222, 351 6-j symbol, 16, 54, 352 Abel inversion, 190 absorption coefficient, 132, 137 ADP, 157 alignment, 51, 53, 210, 227, 361 alignment creation, 81, 93, 98 alignment creation cross section, 69, 78, 82, 83, 86, 87 alignment destruction, 101, 103, 117, 120, 368 alignment destruction rate, 138 alignment relaxation, 103, 124, 137 alignment transfer, 101, 102 alignment-to-population, 93 alignment-transfer cross section, 80 αBBO, 314 aluminum plasma, 182 anisotropic electron collisions, 148 anisotropic excitation, 8, 233 anisotropic geometry, 127 anisotropic radiation trapping, 205 A-O (alignment-to-orientation), 272, 277, 285 asymmetry, 294 asymmetry parameter, 111 atom plus electron system, 70 atom temperature, 121 atomic polarizability, 198 atomic state, 70 autoionizing state, 228, 234 axial symmetry, 51, 226, 228, 229 axially symmetric excitation, 234 bandpass filter, 304 beam collision experiment, 91 beam-like electron, 152 Bennet equation, 154 beryllium-like satellite, 115 birefringent, 314 Bloch equation, 293 Bohr magneton, 17, 291, 366 Bragg angle, 156 Bragg reflection, 327 Bravais indices, 336, 339 Brewster angle, 156 Byron’s boundary, 43 calcite, 307 calibrated photodiode, 322 capture-radiative-cascade (CRC) phase, 43 cathode fall region, 148 charge separation, 185 cigar-like, 165 circular polarization, 219, 229, 231, 275 circularly polarized, 14, 123, 251, 349 classical atom, 347 classical electric dipole, 2, 130 classical oscillator, 136 classical picture, 2, 258, 347 Clebsch-Gordan coefficient, 52, 79, 209, 351, 360 coherence, 52, 102, 218–220, 243, 254, 365 coherence relaxation, 103 coherence transfer, 102 coherence transfer cross section, 57, 80 378 Index coherency matrix, 251 coherent excitation, 225, 226, 230, 231 collision broadening, 103 collision frequency, 189 collisional depolarization, 146 collisional disalignment, 103 collisional-excitation scheme, 201 collisional-radiative model, 34, 155, 218, 219, 228, 234 complete frequency redistribution, 134 completeness relation, 71 Cormack-Hounsefield algorithm, 190 corona phase, 36 Coulomb length, 189 CR ionization rate coefficent, 46 CR model, 162 CR recombination rate coefficient, 46 creation of alignment, 67 critical density, 164 cross section, 57 crossed electric and magnetic fields, 219, 222, 230 cubic crystals, 337 cusp plasma, 167, 311 ‘cyclic rearrangement’ rule, 342 cylindrical plasma, 134 data base, 93 Debye length, 188 Debye model, 188 decoherence, 236, 238, 240 deexcitation, 57 degree of ionization, 188 degree of polarization, 194 density matrix, 5, 52, 72, 75, 84, 86, 128, 219, 220, 223, 224, 243, 291, 359 dephasing collisions, 105 depopulation, 58, 117, 120, 368 depopulation rate, 105, 138, 368 dichroism polarization, 268 dielectronic recombination, 66, 113, 219, 228 diffuse reflectance standard plate, 305 dipole radiation, directed-electron collisional excitation, 217, 221, 233 directional electron collisions, directional electron impact, 148 disalignment, 103, 117, 118, 120, 139, 205 disalignment factor, 137 disalignment rate, 105, 138 disalignment rate coefficient, 107 disorientation, 123 dispersion profile, 146 Doppler shift, 195 double-electron-capture, 95 drifting ions, 148 EBIT (electron beam ion trap), 9, 217 ECR heating, 290 Einsterin A coefficient, 366 elastic collision, 57, 99, 120 elastic scattering, 83 electric dipole, 347 electric dipole transition, 127 electric field, 20, 148, 223, 280 electromagnetic-multipole, 220, 222 electron beam, 156, 159 electron magnetic moment, 291 electron-impact excitation, deexcitation, 220 electronic partition function, 188 ensemble, 51 equation of state, 188 escape factor, 135, 138 Euler angle, 59, 109, 354 EVDF (electron velocity distribution function), 8, 112, 173 evolution operator, 253, 292 excitation transfer, 107, 118, 137, 139 extraordinary (e-)ray, 307 FAC code, fast-ignitor, 165 Fermi acceleration, 151 Feynman diagram, 253 final-state projection operator, 239 fine structure, 13, 272, 274, 281 flat-spectrum approximation, 254 Floquet method, 292 Fokker-Planck, 165 fractional alignment, 261 free-fall model, 148 fundamental decay mode, 135 Gaussian profile, 131 generalized Fermi golden-rule, 239 Index generalized Master equation, 242 geometrical defocusing, 333 Glan –Taylor polarizer, 313 –Thompson polarizer, 310 graphite polarizer, 328 Griem’s boundary, 38, 43 H-Sheet, 303 Hamiltonian, 291 Hanle, Hanle effect, 103, 107, 117, 125, 145, 256, 371 heavy particle scattering, 69, 81 helicity, 128 helium-like fluorine, 180 helium-like ion, 155 helium-like satellite, 114 hollow-cathode discharge plasma, 148 Holtsmark field, 107, 280, 285 hot spot, 155, 329 hydrogen-like fluorine, 180 hyperfine interaction, 165 ICCD, 322 ideal crystal, 327 incoherent superposition, 128 inelastic collisions, 57 inelastic scattering, 76 infinite slab, 130 initial-state density operator, 239, 242 inner-shell excitation, 116 inner-shell ionization, 206 inner-shell-electron ionization, 234 intensified CCD, 199 intensity, 30, 362 intensity ratio, 164 interfacial instability, 199 ion collision, 107 ion drift motion, ion-atom collision, 94 ionization, 64 ionization balance, 47 ionization rate coefficient, 63 ionizing plasma, 9, 34, 49 ionizing plasma component, 34, 66 IR /II ratio, 161 irreducible, 360 irreducible basis, 56 379 irreducible spherical component, 60, 259 irreducible spherical tensor, 222, 226, 257 iso-electronic sequence, 94 isotropic excitation, 365 isotropic plasma, 131 Johann spectrometer, 156, 157, 159, 328 Johansson spectrometer, 328 Kastler diagram, 130, 204 kinetics, 206 Klein-Rosseland relationship, 92 ladder-like excitation, 38 Land´e g-factor, 282, 366, 371 Langevin function, 198 Larmor frequency, 258, 268, 274, 282, 366, 372 Larmor precession, 5, 123, 131, 371 laser-induced-fluorescence spectroscopy, 103 latent alignment, 127, 131, 148 Legendre polynomial, 60, 111 level-crossing, 103, 273 linear polarization, 1, 229, 251, 262, 265 linearly polarized, 14, 347 Liouville equation, 252 lithium-like satellite, 114, 210 local reflection coefficient, 332 local thermodynamic equilibrium (LTE), 39, 188, 218 longitudinal alignment, 23, 94, 105, 109, 115, 120, 171 Lorentz force, 152 Lorentzian profile, 146 lowering of ionization potential, 188 LTE phase, 45, 280 macroscopic alignment, 131 magic-angle excitation, 365 magnetic field, 17, 52, 152, 223, 258, 271, 272, 276, 366 magnetic kernel, 273 magnetic sublevel, 14, 52, 98, 204, 206, 210 Markov approximation, 243 Master equatio, 220, 228, 242 Mather type, 159, 329 380 Index Maxwell distribution, 30, 121, 173 MCP, 322 mechanical plane, 336, 338 MHD model, 155, 162 microscopic alignment, 131 minus 6th power distribution, 38, 45 mixed Stark-Zeeman, 295 modified Abel inversion, 186 Monte Carlo, 98, 134, 138, 140 mosaic, 328 motional electric field, 280 motional Stark, 289, 295 MSE (motional Stark effect), multi level, 206 multipole intensities, 209 multipole moment, 129, 132 multipole radiation, 208 natural lifetime, 125, 372 natural line width, 105 NCP (net circular polarization), 275, 277, 285 non-ideal plasma, 185 non-ideality parameter, 189 nonlinear optical processes, 290 nuclear fusion, 154 nuclear spin, 289 opacity, 155, 161 optical coherence, 104 optical electron, 29 optical fiber, 310 optical pumping, optical theorem, 84 optical thickness, 158, 276 optically thick, 136, 255, 268 optically thin approximation, 208 ordinary (o-)ray, 307 orientation, 227, 274, 283, 361 orientation destruction, 368 pancake-like, 166 phase correlation, 104 photon helicity, 222, 232, 233 photon-polarization density operator (matrix), 223, 225, 226 π light, 2, 347 π-light excitation, 363 pinch, 154 plasma electric field, 161 plasma focus, 159, 329 plasma frequency, 189 plasma luminosity, 199 polarimeter, 334 polarizability, 108, 265, 299 polarization-dependent intensity, 208 polarizing plane, 335, 338 population, 52, 120, 218, 220, 361 population coefficient, 33 population imbalance, 102, 104 population transfer, 104 population-alignment collisionalradiative (PACR) model, 9, 55 positive column, 127, 146 prominence, 269, 276, 278 proton collision, 107 pulsed LIFS, 124 quadrupole moment, 6, 148 quantization axis, 14, 26, 51, 56, 130, 136, 167, 173, 180, 221, 230, 249, 258 quantized electromagnetic field, 220, 241, 243 quantum beat, 110 quantum mechanical interference, 224, 233, 241 quartz crystal, 156, 329, 335 quasi-static field, 107 quasi-steady-state (QSS) approximation, 66, 202 radiant flux, 31 radiant power, 31 radiation reabsorption, 106, 120, 127, 146, 147 radiation transport, 137 radiationless electron capture, 217, 228 radiative coupling, 133 radiative transfer, 254, 280 rank, 60, 368 rate coefficient, 63, 107, 121, 175 rate equation, 29, 31, 66, 207 raw data format, 306 Rayleigh-Taylor, 191 recombination, 64, 110 recombination continuum, 179, 182 Index recombining plasma, 9, 34, 49, 179, 201 recombining plasma component, 39, 67 rectilinear path, 97 reduced electron density, 39 reduced matrix element, 16, 364 relative alignment, 55, 105, 120 relative angle, 66, 116 relative intensity, 155, 159, 160 relativistic mass-shift, 291 relaxation matrix, 55, 60 relaxation process, 220, 240 relaxation time, 31 resolvent operator, 235, 239, 243 resonance scattering, 253 resonant microwave field, 297 rf electric field, 150 Richtmyer-Meshkov, 191 rigid wall model, 151 rocking curve, 333 rotation matrix, 59, 258, 354 rydberg hydrogen atom, 98 S matrix, 56 S operator, 71, 73 Saha equations, 188 Saha-Boltzmann coefficient, 39 Saha-Boltzmann equilibrium, 48, 206 saturation phase, 36, 43 scaling constant, 186 scaling exponent, 186 scaling relation, 186 scattering amplitude, 74, 83 scattering operator, 71 screening length, 186 screening radius, 188 self alignment, 5, 103, 124, 127, 145, 146, 150 self-absorption, 186 self-absorption method, 120, 138 self-alignment method, 125 self-energy operator, 240, 242 semiclassical approximation, 56, 69, 82 sheet polarizer, 304 σ light, 4, 349 σ-light excitation, 364 ‘skip one’ rule, 342 solar chromosphere, 266 solar corona, 262, 265 solar filament, 269 381 spectral irradiance standard lamp, 309 spin–orbit interaction, 291, 295 stabilized electric arc, 149 Stark broadening, 105, 150, 161, 182, 184 Stark effect, 20, 108 Stark splitting, 294 Stark-Zeeman spectral pattern, 218, 235 state vector, 70 state–multipoles, 75, 77 statistical equilibrium, 254, 266 Stokes parameter, 145, 149, 229, 230, 251, 350 Stokes vector, 255, 265, 268, 276, 278 straight-line trajectory approximation, 69, 82 streak photography, 190 sublevel populations, 207 T operator, 73 temperature dependence, 121 thermodynamic equilibrium, 39 three-body recombination, 30, 64 time-dependent Schroedinger equation, 292 total angular momentum, 7, 52, 70 total electron scattering cross section, 85 transfer of alignment, 67 transient collisional-excitation (TCE) laser, 202 transition operator, 73, 219, 224, 239 transmission probability, 137, 138 trigonal, 340 trigonal structure, 335, 337 two-crystal scheme, 328, 334 two-stream instability, 153 uncertainty of polarization degree, 315 unpolarized light, 129 uv-visible region, 303 vacuum spark, 156 Van Vleck angle, 263 vector spherical harmonics, 208 Wannier, 116 wave packet, 70 wave vector, 70, 219 weak anisotropy, 266 382 Index Wigner rotation operator, 222, 225 Wigner-Eckart theorem, 16, 209, 222, 227, 364 WT-3 tokamak, 167, 307 X-pinch, 156, 158 X-ray laser, 201 X-ray polarimeter, 163 X-ray spectroscopy, 155 z-pinch, 154 Zeeman coherence, 52, 56, 104 Zeeman effect, 17, 221, 234, 241, 250, 262, 268, 272, 295 Zeeman multiplets, 52 Zeeman pattern, 235, 294 Zeeman splitting, 268 Zwanzig projection operators, 238, 240 Springer Series on atomic, optical, and plasma physics Editors-in-Chief: Professor G.W.F Drake Department of Physics, University of Windsor 401 Sunset, Windsor, Ontario N9B 3P4, Canada Professor Dr G Ecker Ruhr-Universit¨at Bochum, Fakult¨at f¨ur Physik und Astronomie Lehrstuhl Theoretische Physik I Universit¨atsstrasse 150, 44801 Bochum, Germany Professor Dr H Kleinpoppen Fritz-Haber-Institut Max-Planck-Gesellschaft Faradayweg 4–6, 14195 Berlin, Germany Editorial Board: Professor W.E Baylis Department of Physics, University of Windsor 401 Sunset, Windsor, Ontario N9B 3P4, Canada Professor U Becker Fritz-Haber-Institut Max-Planck-Gesellschaft Faradayweg 4–6, 14195 Berlin, Germany Professor B.R Judd Department of Physics The Johns Hopkins University Baltimore, MD 21218, USA Professor K.P Kirby Harvard-Smithsonian Center for Astrophysics 60 Garden Street, Cambridge, MA 02138, USA Professor P.G Burke Professor P Lambropoulos, Ph.D Brook House, Norley Lane Crowton, Northwich CW8 2RR, UK Max-Planck-Institut f¨ur Quantenoptik 85748 Garching, Germany, and Foundation for Research and Technology – Hellas (F.O.R.T.H.), Institute of Electronic Structure and Laser (IESL), University of Crete, PO Box 1527 Heraklion, Crete 71110, Greece Professor R.N Compton School of Mathematics and Physics David Bates Building Queen’s University Belfast BT7 1NN, UK Professor M.R Flannery Professor G Leuchs School of Physics Georgia Institute of Technology Atlanta, GA 30332-0430, USA Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg Lehrstuhl f¨ur Optik, Physikalisches Institut Staudtstrasse 7/B2, 91058 Erlangen, Germany Professor C.J Joachain Professor P Meystre Facult´e des Sciences Universit´e Libre Bruxelles Bvd du Triomphe, 1050 Bruxelles, Belgium Optical Sciences Center The University of Arizona Tucson, AZ 85721, USA Springer Series on atomic, optical, and plasma physics 10 Film Deposition by Plasma Techniques By M Konuma 23 Atomic Multielectron Processes By V.P Shevelko and H Tawara 11 Resonance Phenomena in Electron–Atom Collisions By V.I Lengyel, V.T Navrotsky, and E.P Sabad 24 Guided-Wave-Produced Plasmas By Yu.M Aliev, H Schl¨uter, and A Shivarova 12 Atomic Spectra and Radiative Transitions 2nd Edition By I.I Sobel’man 13 Multiphoton Processes in Atoms 2nd Edition By N.B Delone and V.P Krainov 14 Atoms in Plasmas By V.S Lisitsa 15 Excitation of Atoms and Broadening of Spectral Lines 2nd Edition, By I.I Sobel’man, L Vainshtein, and E Yukov 16 Reference Data on Multicharged Ions By V.G Pal’chikov and V.P Shevelko 17 Lectures on Non-linear Plasma Kinetics By V.N Tsytovich 18 Atoms and Their Spectroscopic Properties By V.P Shevelko 19 X-Ray Radiation of Highly Charged Ions By H.F Beyer, H.-J Kluge, and V.P Shevelko 20 Electron Emission in Heavy Ion–Atom Collision By N Stolterfoht, R.D DuBois, and R.D Rivarola 21 Molecules and Their Spectroscopic Properties By S.V Khristenko, A.I Maslov, and V.P Shevelko 22 Physics of Highly Excited Atoms and Ions By V.S Lebedev and I.L Beigman 25 Quantum Statistics of Nonideal Plasmas By D Kremp, M Schlanges, and W.-D Kraeft 26 Atomic Physics with Heavy Ions By H.F Beyer and V.P Shevelko 27 Quantum Squeezing By P.D Drumond and Z Ficek 28 Atom, Molecule, and Cluster Beams I Basic Theory, Production and Detection of Thermal Energy Beams By H Pauly 29 Polarization, Alignment and Orientation in Atomic Collisions By N Andersen and K Bartschat 30 Physics of Solid-State Laser Physics By R.C Powell (Published in the former Series on Atomic, Molecular, and Optical Physics) 31 Plasma Kinetics in Atmospheric Gases By M Capitelli, C.M Ferreira, B.F Gordiets, A.I Osipov 32 Atom, Molecule, and Cluster Beams II Cluster Beams, Fast and Slow Beams, Accessory Equipment and Applications By H Pauly 33 Atom Optics By P Meystre 34 Laser Physics at Relativistic Intensities By A.V Borovsky, A.L Galkin, O.B Shiryaev, T Auguste 35 Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation Editors: J Ullrich and V.P Shevelko ... listed at the end of the book Takashi Fujimoto (Editors) Atsushi Iwamae Plasma Polarization Spectroscopy With 180 Figures 123 Professor Dr Takashi Fujimoto Dr Atsushi Iwamae Kyoto University, Graduate... Kyoto, Japan (August 2007) Takashi Fujimoto Atsushi Iwamae Contents Introduction T Fujimoto 1.1 What is Plasma Polarization Spectroscopy?... paid to the polarization of radiation Given the fact that polarization is one of the important features of light, this situation may be regarded rather strange This lack of interest in polarization