Stability Analysis and Reconstruction of Wave Distribution Functions in Warm Plasmas by Tord Oscarsson IRF Scientific Report 201 ISSN 0284-1703 INSTITUTET FÖR RYMDFYSIK Swedish Institute of Space Physics Umeå Division Stability Analysis and Reconstruction of Wave Distribution Func- tions in Warm Plasmas T. E. Oscarsson Swedish Institute of Spare Physics, Umeå Division, University of Umeå, S-901 87 Umeå, Sweden Abstract The purpose of this thesis is first, to describe stability analysis and reconstruction of the wave distribution function (VVDF) separately, and then to show how the two approaches can be combined in an investigation of satellite data. To demonstrate the type of stability investigation that is often used in space physics we study instabilities below the local proton gyrofrequency which are caused by anisotropic proton distributions. Arbitrary angles between the wavevector and the background magnetic field are considered, and effects of warm plasma on the wave propagation properties arc included. We also comment briefly given on an often-used scheme for classifying instabilities. In our discussion on VVDF analysis we develop a com- pletely new and general method for reconstructing the WDF. Our scheme can be used to reconstruct the distribution function of waves in warm as well as cold plasmas. Doppler effects introduced by satellite motion are included, and the re- constructions can be performed over a broad frequency range simultaneously. The applicability of our new WDF reconstruction method is studied in model problems and in an application to observations made by the Swedish satellite Viking. In the application to Viking data we combine stability and WDF analyses in a unique way that promises to become an important tool in future studies of wave-particle interactions in space plasmas. Keywords: Space plasma, magnet osphere, satellite observations, wave-particle interactions, warm plasma, stability analysis, wave distribution function, WDF analysis, Viking ISSN 0284-1703 Printed in Sweden Swedish Institute of Space Physics Kiruna 1989 Stability Analysis and Reconstruction of Wave Distribution Functions in Warm Plasmas T. K. Oscarsson R G. Swedish Institute of Space F'hysics, Umea Division. University of Umeä. S-901 87 I'mea. Sweden Akademisk avhandling som ined tillstånd av Rektorsämbetet vid Umeå Univer- sitet fiamlägges till offentlig granskning vid Fysiska institutionen, hörsal I). 1,1' 0. fredagen den 2 juni 1989 kl 13.00. The thesis is based on the following papers: I Oscarsson ' ?, and M. André, Waves with frequencies below the proton gyrofrequ i in a multicomponent plasma, Ann. Gropliysiraf. .-/. 319, HKSfi. II Oscarsso ' r .. and K. CJ. Rönnmark, Comments on the theory of absolute and conv A instabilities, Geophys. His. it It.. 13. 13S1, 1986. III Oscarsson 7 K., and K. (i. Rönnmark, Reconstruction of wave distribution functions n warm plasmas, ,/. Grophys. lies,, !)/,. 2117. 1989. IV Oscars; . T. E., and K. C Rönnmark, A general method for reconstructing wave di. d»ution functions and its application to Viking observations, l!)Sf). Stability Analysis and Reconstruction of Wave Distribution Functions in Warm Plasmas T. E. Oscarsson Swedish Institute of Space Physics, Umeå Division, University of Umeå, S-901 87 Umeå, Sweden IRF Scientific Report 201 May 1989 Cover illustration Waveform data recorded during Viking orbit 1402 (center panel, supplied by Gunnar Holmgren, IRF Uppsala Divi- sion, Sweden) . The UV-image obtained earlier during the same orbit shows part of the auroral oval (lower right-hand panel, supplied by Sandy Murphree, Uni- versity of Calgary, Canada). Northern Scandinavia is indicated in the lower left corner of the UV-irnage, and a # indi- cates the "footprint" of the Viking satel- lite. ISSN 0284-1703 Printed in Sweden Swedish Institute of Space Physics Kiruna 1989 Stability Analysis and Reconstruction of Wave Distribution Func- tions in Warm Plasmas T. E. Oscarsson Swedish Institute of Space Physics, Umeå Division, University of Umeå, S-901 87 Umeå, Sweden Abstract The purpose of this thesis is first to describe stability analysis and reconstruction of the wave distribution function (WDF) separately, and then to show how the two approaches can be combined in an investigation of satellite data. To demonstrate the type of stability investigation that is often used in space physics we study instabilities below the local proton gyrofrequency which are caused by anisotropic proton distributions. Arbitrary angles between the wavevector and the background magnetic field are considered, and effects of warm plasma on the wave propagation properties are included. We also comment briefly given on an often-used scheme for classifying instabilities. In our discussion on WDF analysis we develop a com- pletely new and general method for reconstructing the WDF. Our scheme can be used to reconstruct the distribution function of waves in warm as well as cold plasmas. Doppler effects introduced by satellite motion are included, and the re- constructions can be performed over a broad frequency range simultaneously. The applicability of our new WDF reconstruction method is studied in model problems and in an application to observations made by the Swedish satellite Viking. In the application to Viking data we combine stability and WDF analyses in a unique way that promises to become <m important tool in future studies of wave-particle interactions in space plasmas. Keywords: Space plasma, magnetosphere, satellite observations, wave-particle interactions, warm plasma, stability analysis, wave distribution function, WDF analysis. Viking HI Papers The thesis is based on the following papers refrrred to in the text by their numbers: I Oscarsson T. E. and M. André, Waves with frequencies below the proton gyrofrequency in a multicomponent plasma, Ann. Geophysicae, 4, 319, 1986. II Oscarsson T. E.. and K. C Rönnmark, Comments on the theory of absolute and convective instabilities, Cleophys. Res. Lett., 13, 1384, 1986. III Oscarsson T. E., and K. G. Rönnmark, Reconstruction of wave distribution functions in warm plasmas, J. Ceophys. Res., 94, 2417, 1989. IV Oscarsson T. E., and K. G. Rönnmark, A general method for reconstructing wave distribution functions and its application to Viking observations, 1989. IV Contents 1 Introduction 1 2 Stability analysis 4 2.1 Instabilities below the local proton gyrofrequency 4 2.2 Effects of warm ion distributions on the propagation properties of ion cyclotron waves 7 2.3 Absolute and convective instabilities 8 3 Reconstruction of the wave distribution function 10 3.1 The WDF reconstruction problem 10 3.2 WDF analysis in warm plasmas 11 3.3 Applications to simulated data and Viking observations 12 4 A combined stability and WDF analysis 14 5 Summary 15 Acknowledgements 16 References 17 Papers I-IV 1 Introduction Satellite observations made during the last decades have clearly demonstrated the existence of a tremendous number of plasma wave phenomena occurring through- out the earth's magnetosphere and in interplanetary space. The study of plasma waves and their interactions with charged particles is an important branch of space physics. Space plasmas provide natural "laboratories" where it is possible to study plasma wave phenomena under conditions that are difficult to set up in any research laboratory. Thus, experiments in space plasmas provide unique opportunities for investigating fundamental plasma wave processes that otherwise would be hard to study. Investigations of space plasma waves can provide valuable information relevant for applications to laboratory plasmas and to fusion research. However, most importantly, investigations of space plasma waves contribute to our understanding of the processes controlling the dynamics of the earth's magneto- sphere, and its interaction with the interplanetary medium. Our knowledge about plasma waves in the earth's magnetospheric system has increased tremendously during the last decades, as more and more detailed ob- servations of waves and particles in space plasmas have become available. Mea- surements performed with ground based equipment, balloons, and rockets have provided invaluable information, but only through in .situ observations made by satellites has it been possible to make probing investigations of wave-particle in- teractions occurring in space plasmas. Since the launch of Sputnik 1 in 1957, numerous satellites have been launched for the purpose of studying different parts of the earth's magnetospheric system, the solar wind, magnetospheres of other planets, and comets. The first Swedish scientific satellite, Viking, was launched in 1986 to study processes in the earth's auroral acceleration regions. Observations made by satellites are of great importance for our understanding of wave phenomena in space plasmas. Particle detectors carried on board satellites are designed to make detailed measurements of the velocity distribution of plasma particles, and wave experiments are usually designed to perform efficient obser- vations of frequency spectra. Such wave and particle observations are among the most important sources of information about space plasma waves that we have available. To a large extent they form the basis of our present understanding of magnetospheric wave-particle interactions, and only through a continued investi- gation of wave and particle observations can we gain further knowledge about how plasma waves are generated in space, and how these waves can affect the dynamics of the particles comprising