COSMIC RAY INTERACTIONS, PROPAGATION, AND ACCELERATION IN SPACE PLASMAS i i i CONTENTS ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 339 EDITORIAL BOARD Chairman W.B. BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A. ([email protected]); University of Leiden, The Netherlands ([email protected]) Executive Committee J. M. E. KUIJPERS, University of Nijmegen, The Netherlands E. P. J. VAN DEN HEUVEL, University of Amsterdam, The Netherlands MEMBERS F. BERTOLA, University of Padua, Italy J. P. CASSINELLI, University of Wisconsin, Madison, U.S.A. C. J. CESARSKY, European Southern Observatory, Garching bei München, Germany O. ENGVOLD, University of Oslo, Norway P. G. MURDIN, Institute of Astronomy, Cambridge, U.K. A. HECK, Strasbourg Astronomical Observatory, France R. McCRAY, University of Colorado, Boulder, U.S.A. F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India K. SATO, School of Science, The University of Tokyo, Japan F. H. SHU, National Tsing Hua University, Taiwan B. V. SOMOV, Astronomical Institute, Moscow State University, Russia R. A. SUNYAEV, Space Research Institute, Moscow, Russia Y. TANAKA, Institute of Space and Astronautical Science, Kanagawa, Japan S. TREMAINE, Princeton University, U.S.A. N. O. WEISS, University of Cambridge, U.K. CONTENTS iii COSMIC RAY INTERACTIONS, PROPAGATION, AND ACCELERATION IN SPACE PLASMAS By LEV I. DORMAN Israel Cosmic Ray & Space Weather Center and Emilio Segré Observatory, affiliated to TelAviv University, Israel Space Agency, and Technion, Qazrin, Israel; Cosmic Ray Department of IZMIRAN, Russian Academy of Science, Troitsk, Russia i v CONTENTS A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-5100-X (HB) ISBN-13 978-1-4020-5100-5 (HB) ISBN-10 1-4020-5101-8 (e-book) ISBN-13 978-1-4020-5101-2 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. CONTENTS v Dedicated to the memory of my eldest brother Abraham Argov (1914-2003), whom I met for the first time in 1989 in Paris (see the picture above, he is on the left). In 1925 he emigrated with our great grand parents Globman (on our mother’s side) from Ukraine to Palestine. Later he took part in the foundation and governing of the prominent kibbutz Beit-Hashita in the Yizreel Valley. As an officer, he took part in the War of Independence in 1948 (when his family name was changed to Hebrew, Argov). Abraham, together with my cousin Michal Govrin-Brezis, organized my first visit to Israel in 1990 and arranged my meeting with Prof. Yuval Ne'eman. Ne'eman, who soon became the Minister of Science, played an important role in the formation of the Israel Cosmic Ray and Space Weather Centre and the Emilio Segre' Observatory. CONTENTS vii CONTENTS PAGES Preface xxi Acknowledgments xxvii Frequently used Abbreviations and Notations xxxi Chapter 1. Cosmic Ray Interactions in Space Plasmas 1 1.1. Main properties of space plasma 1 1.1.1. Neutrality of space plasma and Debye radius 1 1.1.2. Conductivity and magnetic viscosity of space plasma 1 1.1.3. The time of magnetic fields dissipation; frozen magnetic fields 1 1.1.4. Transport path of ions in space plasma and dissipative processes 2 1.1.5. Space plasma as excited magneto-turbulent plasma 2 1.1.6. Main channels of energy transformation in space plasma 2 1.1.7. Particle acceleration in space plasma and the second fundamental law of thermodynamics 3 1.2. Main properties and origin of CR 4 1.2.1. Internal and external CR of different origin 4 1.2.2. On the main properties of primary and secondary CR 4 1.2.3. Five intervals in the observed CR energy spectrum 5 1.2.4. Main CR properties and origin of CR in the interval 1 7 1.2.5. The anisotropy in energy intervals 1 and 2 7 1.2.6. Relationships between the observed CR spectrum, the anisotropy, the relative content of the daughter nuclei, and the transport scattering path 9 1.2.7. Chemical composition in the 109eV nucleon≤Ek ≤3×1011eV nucleon range and the expected dependence of ΛG(Ek) and Asid(Ek) on Ek 11 1.2.8. Chemical composition in the energy range 3×107eV nucleon≤Ek ≤109eV nucleon and the nature of the scattering elements in the Galaxy 11 1.2.9. The nature of the energy boundary between intervals 3 and 2 12 1.2.10. The mode of the dependence of Λ on particle rigidity R from solar modulation data of protons, electrons, and nuclei with various Z 13 1.2.11. The dependence of Λ on Ek from data of solar CR propagation 15 1.2.12. The features of the solar modulation of the CR spectrum and the measurements of the radial gradient 16 1.2.13. The nature of the CR in energy intervals 3 - 5 16 1.3. Nuclear interactions of CR with space plasma matter 16 1.3.1. Cross sections, paths for absorption, and life time of CR particles relative to nuclear interactions in space plasma 16 1.3.2. CR fragmentation in space plasma 17 1.3.3. Expected fluxes of secondary electrons, positrons, γ - quanta, and neutrinos 19 1.3.4. Expected fluxes of secondary protons and antiprotons 22 1.4. CR absorption by solid state matter (stars, planets, asteroids, meteorites, dust) and secondary CR albedo 22 1.5. CR interactions with electrons of space plasma and ionization losses 23 1.5.1. Ionization energy losses by CR nuclei during propagation in the space 23 1.5.2. Ionization and bremsstrahlung losses for CR electrons 25 1.6. CR interactions with photons in space 26 1.6.1. CR nuclei interactions with space photons 26 1.6.2. CR electron interactions with the photon field 27 1.7. Energy variations of CR particles in their interactions with magnetic fields 27 1.7.1. Synchrotron losses of energy by CR particles in magnetic fields 27 1.7.2. Acceleration and deceleration of particles in their interactions with moving magnetic fields 29 vii viii CONTENTS 1.8. CR particle motion in magnetic fields; scattering by magnetic inhomogeneities 30 1.8.1. CR particle motion in the regular magnetic fields frozen into moving plasma formations 30 1.8.2. CR particle moving in essentially inhomogeneous magnetized plasma 31 1.8.3. Two-dimensional model of CR particle scattering by magnetic inhomogeneities of type H=(0,0,H) 32 1.8.4. Scattering by cylindrical fibers with homogeneous field 32 1.8.5. Scattering by cylindrical fibers with field of type h=M rn 33 1.8.6. Three-dimensional model of scattering by inhomogeneities of the type h=(0,h(x),0) against the background of general field Ho=(Ho,0,0) 35 1.9. The transport path of CR particles in space magnetic fields 38 1.9.1. The transport path of scattering by magnetic inhomogeneities of the type of isolated magnetic clouds of the same scale 38 1.9.2. Transport scattering path in case of several scales of magnetic inhomogeneities 39 1.9.3 The transport scattering path in the presence of a continuous spectrum of the cloud type of magnetic inhomogeneities 41 1.9.4. Transport path in a plane perpendicular to cylindrical fibers with a homogeneous field 45 1.9.5. Transport path of scattering by cylindrical fibers with field h=M rn in the two-dimensional case 47 1.9.6. The transport path in the three-dimensional case of scattering by the fields of the type h=M rn 47 1.9.7. Transport path of scattering by inhomogeneities of the type h=(0,h(x),0) against the background of the regular field Ho=(Ho,0,0) 48 1.9.8. The transport scattering path including the drift in inhomogeneous fields 52 1.9.9. The transport scattering path in the presence of the regular background field 53 1.9.10. The transport path for scattering with anisotropic distribution of magnetic inhomogeneities in space 56 1.10. Magnetic traps of CR in space 57 1.10.1. Types of CR magnetic traps and main properties 57 1.10.2. Traps of cylindrical geometry with a homogeneous field 59 1.10.3. Traps with strength-less structure of the field 59 1.10.4. The effect of magnetic field inhomogeneities 59 1.10.5. Traps with an inhomogeneous regular field 60 1.10.6. Traps with a curved magnetic field 61 1.10.7. Traps with a magnetic field varying along the force lines 62 1.10.8. Traps with a magnetic field varying with time 62 1.11. Cosmic ray interactions with electromagnetic radiation in space plasma 63 1.11.1. Effects of Compton scattering of photons by accelerated particles 63 1.11.2. The influence of the nuclear photo effect on accelerated particles 70 1.11.3. Effect of the universal microwave radiation on accelerated particles 71 1.11.4. Effect of infrared radiation on accelerated particles 72 1.12. CR interaction with matter of space plasma as the main source of cosmic gamma radiation 73 1.12.1. The matter of the problem 73 1.12.2. Gamma rays from neutral pions generated in nuclear interactions of CR with space plasma matter 73 1.12.3. Gamma ray generation by CR electrons in space plasma (bremsstrahlung and inverse Compton effect) 76 1.13. Gamma ray generation in space plasma by interactions of flare energetic particles with solar and stellar winds 77 1.13.1. The matter of problem and the main three factors 77 1.13.2. The 1st factor: solar FEP space-time distribution 78 1.13.3. The 2nd factor: space-time distribution of solar wind matter 82 1.13.4. The 3rd factor: gamma ray generation by FEP in the Heliosphere 83 CONTENTS ix 1.13.5. Expected angle distribution and time variations of gamma ray fluxes for observations inside the Heliosphere during FEP events 85 1.13.6. Gamma rays from interaction of FEP with stellar wind matter 89 1.13.7. Expected gamma ray fluxes from great FEP events 89 1.13.8. On the possibility of monitoring gamma rays generated by FEP interactions with solar wind matter; using for forecasting of great radiation hazard 90 1.14. Gamma ray generation in space plasma by interactions of galactic CR with solar and stellar winds 91 1.14.1. The matter of problem and the main three factors 91 1.14.2. The 1st factor: galactic CR space-time distribution in the Heliosphere 92 1.14.3. The 2nd factor: space-time distribution of solar wind matter 96 1.14.4. The 3rd factor: gamma ray generation by galactic CR in the Heliosphere 96 1.14.5. Expected angle distribution of gamma ray fluxes from solar wind 98 1.14.6. Gamma ray fluxes from stellar winds 100 1.14.7. Summary of main results and discussion 100 1.15. On the interaction of EHE gamma rays with the magnetic fields of the Sun and planets 103 1.15.1. The matter of the problem 103 1.15.2. Magnetic e± pair cascades in the magnetosphere of the Sun 104 1.15.3. The possibility that extra high energy CR spectrum at > 1019 eV contains significant proportion of photons 105 1.15.4. Summering of main results and discussion 107 Chapter 2. Cosmic Ray Propagation in Space Plasmas 109 2.1. The problem of CR propagation and a short review of a development of the basically concepts 109 2.2. The method of the characteristic functional and a deduction of kinetic equation for CR propagation in space in the presence of magnetic field fluctuations 111 2.3. Kinetic equation in the case of weak regular and isotropic random fields 115 2.4. Kinetic equation for CR propagation including fluctuations of plasma velocity 117 2.5. Kinetic equation for propagation of CR including electric fields in plasma 124 2.6. Kinetic equation for the propagation of CR in the presence of strong regular field in low-turbulence magnetized plasma in which the Alfvén waves are excited 126 2.6.1. Formulation of the problem and deduction of the basic equation 126 2.6.2. The case of large wave lengths 130 2.6.3. The case of small wave lengths 130 2.7. Green's function of the kinetic equation and the features of propagation of low energy particles 132 2.8. Kinetics of CR in a large scale magnetic field 139 2.8.1. The kinetic equation deriving on the basis of the functional method 139 2.8.2. Diffusion approximation 145 2.8.3. Diffusion of CR in a large-scale random field 148 2.8.4. CR transport in the random girotropic magnetic field 150 2.9. CR diffusion in the momentum space 155 2.10. CR diffusion in the pitch-angle space 158 2.11. Fokker-Planck CR transport equation for diffusion approximation 165 2.11.1. Diffusion approximation including the first spherical mode 165 2.11.2. Including of magnetic inhomogeneities velocity fluctuations 167 2.11.3. Diffusion approximation including the second spherical harmonic 168 2.11.4. Drift effects in a diffusion propagation of CR 174 2.11.5. General poloidal magnetic field effects in a diffusion propagation of CR 177 2.11.6. Derivation of the Fokker-Planck CR transport equation from variational principle 179 x CONTENTS 2.12. Phenomenological description of CR anisotropic diffusion 182 2.12.1. Deduction of general equation 182 2.12.2. The case of propagation in a galactic arm 183 2.12.3. The case of CR propagation in interplanetary space 184 2.12.4. On rotation of CR gas in the interplanetary space 188 2.12.5 Temporal variations and spatial anisotropy of CR in the interplanetary space 189 2.12.6. The region where CR anisotropic diffusion approximation is applicable 190 2.13. On a relation between different forms of the equation of anisotropic diffusion of CR 190 2.14. Spectral representations of Green's function of non-stationary equation of CR diffusion 194 2.14.1. Formulation of the problem 194 2.14.2. Determining of the radial Green’s function for a non-stationary diffusion including convection 194 2.14.3. Green’s function of the three-dimensional transfer equation including convection 199 2.14.4. Possible inclusion of the variations of particle energy 202 2.14.5. The Green’s function for the stationary isotropic diffusion in the case of power dependence of the diffusion coefficient on a distance 202 2.15. On a relation between the correlation function of particle velocities and pitch-angle and spatial coefficients of diffusion 203 2.I5.1. Correlation function of particle velocities 203 2.15.2. Connection between the correlation function of particle velocities, pitch-angle and spatial coefficients of diffusion 204 2.16. On a balance of CR energy in multiple scattering in expanding magnetic fields 206 2.17. The second order pitch-angle approximation for the CR Fokker-Planck kinetic equation 210 2.17.1. The matter of the problem 210 2.17.2. The first order approximation 211 2.17.3. The second order approximation 211 2.17.4. Peculiarities of the second pitch-angle approximation 213 2.18. Anomalous diffusion: modes of CR diffusion propagation 214 2.18.1. Three modes of particle propagation: classical diffusion, super-diffusion and sub-diffusion 214 2.18.2. Simulation of particle propagation in a two-dimensional static magnetic field turbulence 214 2.19. Energetic particle mean free path in the Alfvén wave heated space plasma 217 2.19.1. Space plasma heated by Alfvén waves and how it influences on particle propagation and acceleration 217 2.19.2. Determining of the Alfvén wave power spectrum 218 2.19.3. Determining of the energetic particle mean free path 219 2.20. Bulk speeds of CR resonant with parallel plasma waves 221 2.20.1. Formation of the bulk speeds that are dependent on CR charge/mass and momentum 221 2.20.2. Dispersion relation and resonance condition 222 2.20.3. Effective wave speed 223 2.20.4. Bulk motion of the CR in space plasma 225 2.21. Non-resonant pitch-angle scattering and parallel mean-free-path 227 2.21.1. The problem of the non-resonant pitch-angle scattering 227 2.21.2. Derivation of the non-resonant scattering process 229 2.21.3. Resulting mean free path and comparison with gyro-resonant model 232 2.21.4. Contribution from slab and oblique Alfvén waves to the non-resonant pitch-angle scattering 233 2.21.5. Parallel mean free path: comparison of the theoretical predictions with the measurements 234