POLARIZATION SPECTROSCOPY OF IONIZED GASES ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 200 Executive Committee w. B. BURTON, Sterrewacht, Leiden, The Netherlands C. DE JAGER, Foundation Space Research. Utrecht. The Netherlands E. P. J. VAN DEN HEUVEL. Astronomical Institute. University ofA msterdam. The Netherlands H. V AN DER LAAN. Astronomical Institute. University of Utrecht. The Netherlands Editorial Board I. APPENZELLER, Landessternwarte Heidelberg-Konigstuhl, Germany J. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A. F. BERTOLA, Universitd di Padova, Italy W. B. BURTON, Sterrewacht, Leiden, The Netherlands J. P. CASSINELLI, University of Wisconsin, Madison, U.SA. C. J. CESARSKY, Centre d' Etudes de Saclay. GiJ-sur-Yvette Cedex. France C. DE JAGER, Foundation Space Research. Utrecht. The Netherlands R. McCRAY, University of Colorado. JILA. Boulder. U.S.A. P. G. MURDIN, Royal Greenwich Observatory. Cambridge, U.K. F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India F. H. SHU, University of California, Berkeley, U.SA. B. V. SOMOV, Astronomical Institute. Moscow State University, Russia S. TREMAINE, CITA. University of Toronto. Canada Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, Japan E. P. J. VAN DEN HEUVEL, Astronomical Institute, University ofA msterdam, The Netherlands H. V AN DER LAAN, Astronomical Institute. University of Utrecht, The Netherlands N. O. WEISS, University of Cambridge. U.K. POLARIZATION SPECTROSCOPY OF IONIZED GASES by S. A. KAZANTSEV Institute of Physics, St. Petersburg State University, Russia and I.-C. HENOUX Observatoire de Paris, Meudon,France SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress ISBN 978-90-481-4550-8 ISBN 978-94-017-2708-2 (eBook) DOI 10.1007/978-94-017-2708-2 Cover: Electrons and protons accelerated above the surface of the Sun in the corona are precipitating on the solar atmosphere. As a result the atmosphere is heated and a hot ionized plasma rises in the corona. Particle acceleration takes place in regions where magnetic fields are present and the ionized hydrogen plasma is then trapped in gigantic magnetic loops. When it cools, the ionized hydrogen recombines with local electrons, becomes neutral and starts emitting in the Red Balmer a line. At the base of the loop, the accelerated protons and electrons are bombarding the atmospheric neutral hydrogen leading to linearly polarized Balmer a line emission. The measurement of this polarization provides information on the nature and velocity distribution of the accelerated particles. Courtesy of Z. Mouradian, DASOP, URA326, Observatoire de Paris. Printed on acid-free paper All Rights Reserved © 1995 by Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1995 Softcover reprint of the hardcover 1st edition 1995 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. CONTENTS PREFACE 5 INTRODUCTION 6 CHAPTER 1. SPECTROPOLARIMETRIC MANIFESTATION OF SELF-ALIGNMENT 10 1.1 Representation of Stokes parameters by polarization moments 10 1.1.1 Classical and polarization moment formalism 11 1.1.2 Relation to the ordering of angular momenta 16 1.1.3 Stokes parameters within the detector frame of reference 21 1.2 Quadrupole ordering of angular momenta of excited atomic particles 24 1.2.1 Equation for polarization moments 24 1.2.2 Self-alignment under radiation self-absorption 27 1.2.3 Self-alignment by electron impact 30 1.2.4 Connection of Stokes parameters to the quadrupole moment 32 1.3 Electron impact alignment cross-sections 35 1.3.1 Relations to collisional spectroscopic parameters 35 1.3.2 Methods of calculation 39 CHAPTER 2: EXPERIMENTAL METHODS FOR POLARIMETRIC SPECTRAL SENSING 47 2.1 Optical polarimetry techniques 47 2.1.1 Requirements for experimental polarimetric schemes 47 2.1.2 Fourier polarimeter 49 2.1.3 Polarimeters for solar spectra studies 51 2.2 Magnetic spectropolarimetry 53 2.2.1 Polarization moments in presence of a magnetic field. Hanle effect 53 2.2.2 Stokes parameters determination 56 2.2.3 Laboratory magnetic polarization spectrometer 58 2 CONTENTS 2.3 Derivation of local plasma parameters 61 2.3.1 Stokes parameters and polarization moments 61 2.3.2 Axially symmetric ionized gas entities 65 CHAPTER 3: POLARIMETRIC SENSING OF THE POSITIVE COLUMN IN A D.C. DISCHARGE 70 3.1 Experimental characteristics of noble gas self-alignment 70 3.1.1 Cascading self-alignment 70 3.1.2 Self-alignment of highly excited states 79 3.2 Electron impact self-alignment 81 3.2.1 Evidence for electron impact self-alignment 81 3.2.2 Self-alignment in a cylindrical discharge 85 3.3 Electric parameters in the positive column 86 3.3.1 Kinetics of fast electrons 86 3.3.2 Polarization profile across the discharge image 90 3.3.3 Radial electric field 97 CHAPTER 4: POLARIMETRIC SENSING OF A HIGH FREQUENCY DISCHARGE 104 4.1 Self-alignment generation 104 4.1.1 Radiation self-absorption 104 4.1.2 Electron impact 109 4.2 Plasma structural features in a capacitive discharge 110 4.2.1 Radiation polarization in the vicinity of the electrode sheath 110 4.2.2 Electron motion anisotropy near the electrode sheath 111 4.2.3 Spectropolarimetric effects in other parts of the plasma 118 4.3 Electric and energetic characteristics of a capacitive discharge 124 4.3.1 Energy transport through the electrode sheath 125 4.3.2 Amplitude of the alternative electric field in the central part 132 CHAPTER 5: POLARIZATION SPECTROSCOPY OF IONS 140 5.1 Theory of drift self-alignment 140 5.1.1 Theory 140 5.1.2 Characteristic rate constants 142 5.2 Observation of drift self-alignment in a hollow cathode 143 5.2.1 Spectropolarimetric peculiarities 143 5.2.2 Evidence for drift self-alignment 145 CONTENTS 3 5.3 Drift velocity of ions 148 5.3.1 Determination of the rate constants 148 5.3.2 Remote sensing of the hollow cathode 150 CHAPTER 6: ATOMIC CONSTANTS DETERMINATION 155 6.1 Noble gases 155 6.1.1 Relaxation constants 155 6.1.2 Lifetimes and alignment-destroying collision cross-sections 157 6.1.3 Correction for self-absorption 161 6.2 Electron beam excitation 162 6.2.1 Accounting for beam magnetic field bending 163 6.2.2 Radiation self-absorption 166 6.2.3 Alignment cascading 169 CHAPTER 7: POLARIZATION SPECTROSCOPY IN ASTROPHYSICS 175 7.1 Solar magnetic field measurement 175 7.1.1 Zeeman and Hanle effects 175 7.1.2 Solar prominences magnetic field 177 7.1.3 Coronal magnetic field 181 7.2 Impact polarization in solar flares 183 7.2.1 Solar flares 183 7.2.2 Anisotropies associated with energy transport 184 7.2.3 Ha polarization observations 185 7.2.4 Origin of the observed polarization 188 7.3 Energy transport by protons in solar flares 194 7.3.1 Expected proton velocity anisotropy 194 7.3.2 Delivered energy flux 197 7.3.3 Application of the polarization moment formalism 200 CONCLUSIONS 210 REFERENCES 211 5 PREFACE This book describes the physical principles of polarization spectroscopy and its applications to the remote sensing of ionized gases. Recent evolution of this technique allows for quantitative studies of energy transport and dis sipation in various types of ionized gases states. In the theoretical part, the basic phenomena of the ordering of the ve locities of fast exciting charged particles, together with the polarization of the outer electron shells of the ensemble of excited atoms or molecules are described. A general approach based on the irreducible tensorial set representation of the rotation symmetry group is used. The effects of the polarization of the excited atoms or molecules are examined in more de tail. Then the integral equation giving the intensity and polarization of the emitted lines is derived and methods to solve this equation are analysed. Experimental applications of remote sensing are reviewed. Universal spectropolarimetric remote sensing has been applied to laboratory low pres sure gas discharge plasmas and to non-thermal processes taking place in the solar atmosphere, illustrating the possibilities of this new method. This book may be useful for researchers, Ph D students and graduate students utilizing optical methods for the remote sensing of various ionized gases: low temperature plasmas generated in different discharges and beam gas systems, high temperature plasmas, solar plasmas, eruptive processes, ionized gases in the upper atmosphere of the earth where precipitating par ticles are present and various other cases. 6 INTRODUCTION Elaborate remote sensing of ionized gases is based on the study of their optical line spectrum. Whereas the conventional intensity spectroscopic methods already attained the limits of their possibilities, polarization spec troscopy represents by itself a new optical diagnostic technique which ex pands considerably the frontiers of the studies of ionized gases by optical methods. Since the discovery of splitting of atomic lines in polarized compo nents by Zeeman /1/, the main application of polarization spectroscopy, as a remote sensing technique, has been the measurement of the magnetic field strength and orientation in astrophysical objects. These measurements make use of the direct connection between the local vector magnetic field and the observed spectroscopic polarization pecularities. In astronomy, the application of the spectropolarimetry to magnetic field measurements goes back to 1908 when Hale /2/ discovered the magnetic field of sunspots. In locations were the magnetic field is low, like in solar prominences, it can be measured using Hanle effect /3 , 4/. The achievements of the very active field of Zeeman polarimetry in solar physics are presented in detail in J. O. Stenflo's /5/. Polarized radiation can also be generated even in the absence of a mag netic field, and polarization measurements can bring information on plasma anisotropies providing new applications of the polarimetric remote sensing. These possibilities in the optical spectral range and in X-rays have been proposed and used /6, 7, 8/ as a method of sensing non-thermal processes in the solar atmosphere. The implementation of this spectropolarimetric sensing requires the utilization of reliable atomic data and of advanced methods of theoritical atomic physics /9/. Restrospectively, up until the last decade, there was a lack of general theoretical relationships between the polarization spectroscopic parameters and the kinetic characteristics ofthe exciting particles. Therefore spectropo larimetry of ionized gases was not a quantitative tool. Due to the complexity of the spectropolarimetric effects, the absence of specific atomic constants and cross-sections, and the difficulties encountered in measuring the Stokes parameters in the line spectrum of ionized gases, impact spectropolarimet ric effects were not used for the remote sensing of plasma parameters. The history of impact polarization, however, began in 1926 with the detection POLARIZATION SPECTROSCOPY OF IONIZED GASES 7 of the linear polarization of some spectral lines of mercury in a low pressure arc by Skinner /10/. Although the polarization of spectral lines has since been observed in different discharges (positive column of D.C. discharges, hollow cathode discharges, high frequency discharges, etc), only qualitative analysis of the discharge objects were made during those rare spectropo larimetric studies. Polarization of emission and absorption lines is related to the unequal distribution of populations of the magnetic substates of excited atoms, in other words to the ordering of momenta of the outer electron shells of atomic particles (atoms, molecules, ions). From a number of detailed experimental studies it was concluded that for a majority of cases the polarization of the optical line emission of ionized gases is determined by the self-alignment of atomic particles or the quadrupole orientation of momenta of electron shells induced in the excitation process. Different fundamental physical mecha nisms, such as reabsorption of radiation, anisotropic electron or proton im pact excitation and anisotropy of the collisional relaxation are responsible for the formation of the self-alignment. In this respect the self-alignment of atomic ensembles may be regarded as a general feature reflecting the lim ited spatial dimensions and the energy exchange processes in any ionized gas entity /11/. The most promising diagnostic application is the use of the self-alignment induced by the anisotropy of the motion of fast exciting electrons. The en ergy delivered into an ionized gas and the internal electric field distribution lead to a localised anisotropy of the velocity distribution function of fast electrons. Then the resulting anisotropy in the electron velocity space gives rise to the collisional self-alignment of the excited atoms and to the polar ization of the optical emission. Later on, the transformation by collisons of the energy of fast electrons into a thermal form diminishes the degree of anisotropy in velocity space and consequently the degree of linear po larization. Qualitative studies of the polarization degree in the spectra of gas discharges that results from electron impact excitation of atoms have shown the extensive informative possibilities of spectropolarimetric tech niques. New theoretical and experimental studies of the polarization effects in ionized gases under electron impact excitation and of the derivation of plasma parameters enable one to regard the polarization spectroscopy as a new and quantitative remote spectral sensing technique. The principally new potential of polarization spectroscopy results from the general relationship between the alignment tensor of the excited atomic ensemble at the collisional excitation and the quadrupole moment of the ve-