The book consists of four Chapters. Chapter 1 shortly describes main properties of space plasmas and primary CR, different types of CR interactions with space plasmas components (matter, photons, and frozen in magnetic fields). Chapter 2 considers the problem of CR propagation in space plasmas described by the kinetic equation and different types of diffusion approximations (diffusion in momentum space and in pitch-angle space, anisotropic diffusion, anomaly CR diffusion and compound diffusion, the influence of magnetic clouds on CR propagation, non-diffusive CR particle pulse transport). Chapter 3 is devoted to CR non-linear effects in space plasmas caused by CR pressure and CR kinetic stream instabilities with the generation of Alfvèn turbulence (these effects are important in galaxies, in the Heliosphere, in CR and gamma-ray sources and in the processes of CR acceleration). In Chapter 4 different processes of CR acceleration in space plasmas are considered: the development of the Fermi statistical mechanism, acceleration in the turbulent plasma, Alfven mechanism of magnetic pumping, induction mechanisms, acceleration during magnetic collapse and compression, cumulative acceleration mechanism near the zero lines of a magnetic field, acceleration in shear flows, shock-wave diffusion (regular) acceleration. The book ends with a list providing more than 1,300 full references, a discussion on future developments and unsolved problems, as well as Object and Author indexes. This book will be useful for experts and students in CR research, Astrophysics and Geophysics, and in Space Physics.
xxii CONTENTS In 1957 I was invited to work on special problems in Magnetic Laboratory of the Academy of Sciences of USSR as a Head of Department of Magnetic Hydrodynamics. In few years this Laboratory was transfered into the I. V. Kurchatov Institute of Atomic Energy, and I continued to work in this Institute up to 1965. In parallel I also worked at Moscow State University as Professor in the CR and Space Research Team. I also gave lectures in Irkutsk, Alma-Ata, Nalchik, Tbilisi, Erevan, Samarkand, and others places. Over about 40 years of teaching under my supervision more than hundred graduate students and scientists in USSR and some other countries gained their Ph. D. and several tenths became Doctors of Science. As my hobby I continued to work in CR research, and as Vice-President of All-Union Section of Cosmic Rays and Radiation Belts, took an active part in preparing the Soviet net of CR stations to the IGY (International Geophysical Year, 1957-1958): we equipped all soviet stations in USSR and in Antarctica with standard cubic and semi-cubic muon telescopes and with neutron monitors of IGY (or Simpson's) type. In connection with preparing for the IQSY (the International Quiet Sun Year, 1964-1965), the soviet net of CR stations was extended about two fold and they were equipped with neutron super-monitors of IQSY type (with an effective surface about 10 times bigger than the previous monitor of IGY type).
This book provides an extended review on energetic particles interactions, propagation and acceleration in space plasmas. Its four chapters address key problems in CR Astrophysics and CR Geophysics. The book contains more than 1,300 full references.
Chapter 1 briefly describes the main properties of space plasmas and primary CR. Chapter 2 considers the problem of CR propagation in space plasmas described by the kinetic equation and different types of diffusion approximations. Chapter 3 is devoted to CR non-linear effects in space plasmas caused by CR pressure and CR kinetic stream instabilities with the generation of Alfvèn turbulence. In Chapter 4 different processes of CR acceleration in space plasmas are considered. The book ends with a list providing more than 1,300 full references, a discussion on future developments and unsolved problems, as well as Object and Author indexes.
CONTENTS
Preface xxi
Acknowledgments xxvii
Frequently used Abbreviations and Notations xxix
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 Debay 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 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 low 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 range and the
expected dependence of and on 11
1.2.8. Chemical composition in the energy range
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 L on particle rigidity R from solar modulation data
of protons, electrons, and nuclei with various Z 13
1.2.11. The dependence of L on 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, g - 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. Interactions of CR nucleus 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
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 32
1.8.4. Scattering by cylindrical fibers with homogeneous field 32
1.8.5. Scattering by cylindrical fibers with field of type 33
1.8.6. Three-dimensional model of scattering by inhomogeneities of the type
against the background of general field 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
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 47
1.9.7. Transport path of scattering by inhomogeneities of the type
against the background of the regular field 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) 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 1-st factor: solar FEP space-time distribution 78
1.13.3. The 2-nd factor: space-time distribution of solar wind matter 82
1.13.4. The 3-rd factor: gamma ray generation by FEP in the Heliosphere 83
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 of gamma rays generated by FEP
interactions with solar wind matter; the perspectives of the model developing 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 1-st factor: galactic CR space-time distribution in the Heliosphere 92
1.14.3. The 2-nd factor: space-time distribution of solar wind matter 96
1.14.4. The 3-rd 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 at 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 propagation of CR at presence of strong regular field in
low-turbulence magnetized plasma in which the Alfven 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
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 including of the variations of particle energy 202
2.14.5. 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 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 Alfven wave heated
space plasma 217
2.19.1. Space plasma heated by Alfvén waves and how it influenced on particle
propagation and acceleration 217
2.19.2. Determining of the Alfven 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
2.22. On the cosmic ray cross-field diffusion in the presence
of highly perturbed magnetic fields 236
2.22.1. The matter of problem 236
2.22.2. Description of Monte Carlo particle simulations 236
2.22.3. Wave field models 237
2.22.4. Simulations for Alfvenic turbulence models A, B1, B2 238
2.22.5. Simulations for oblique MHD waves models C-AF, C-AK, C-MF, and C-MK 240
2.23. Dispersion relations for CR particle diffusive propagation 242
2.23.1. The matter of the problem and denominations 242
2.23.2. Dispersion relations for diffusion and telegrapher's equations 243
2.23.3. Dispersion relations in general case 244
2.23.4. Dispersion relations for isotropic pitch-angle scattering 245
2.23.5. Dispersion relations for the cases with dominant helicity 246
2.23.6. Dispersion relations for focusing scattering 246
2.23.7. Dispersion relations for hemispherical scattering 247
2.24. The dynamics of dissipation range fluctuations with application
to CR propagation theory 248
2.24.1. The matter of problem 248
2.24.2. Magnetic helicity according to WIND spacecraft measurements 250
2.24.3. Anisotropy according to WIND spacecraft measurements 250
2.24.4. Slab waves and 2D turbulence according to WIND spacecraft measurements 251
2.25. A path integral solution to the stochastic differential equation of the Markov process for CR transport 252
2.25.1. The matter of the problem 252
2.25.2. Diffusion and Markov stochastic processes; used definitions 253
2.25.3. Path integral representation for the transition probability of Markov processes 255
2.25.4. Main results and method's checking 257
2.26. Velocity correlation functions and CR transport (compound
diffusion) 258
2.26.1. The matter of problem 258
2.26.2. Compound CR diffusion 259
2.26.3. The Kubo formulation applied to compound diffusion 260
2.26.4. Main results 263
2.27. The BGK Boltzmann equation and anisotropic diffusion 263
2.27.1. The matter of problem 263
2.27.2. Description of the model 264
2.27.3. The diffusion approximation 265
2.27.4. Evaluation of the Green function 266
2.27.5. Long-scale, large-time asymptotics 269
2.27.6. Pitch angle evolution and perpendicular diffusion 271
2.27.7. Summary of main results 272
2.28. Influence of magnetic clouds on the CR propagation 273
2.28.1. The matter of the problem 273
2.28.2. The numerical model 273
2.28.3. Numerical results 275
2.28.4. Comparison with observations 278
2.29. Non-diffusive CR particle pulse transport 280
2.29.1. The matter of problem 280
2.29.2. Kinetic equation 281
2.29.3. Pitch angle response function for neutron monitors 282
2.29.4. Time-finite injection 282
2.29.5. Three parts of resulting solution 282
2.29.6. Expected temporal profiles for neutron monitors and comparison with observations 284
2.30. Pitch angle diffusion of energetic particles by large amplitude
MHD waves 288
2.30.1. The matter of the problem 288
2.30.2. The used model 289
2.30.3. Main results of simulation 289
2.31. Particle diffusion across the magnetic field and the anomalous
transport of magnetic field lines 293
2.31.1. On the anomalous transport of magnetic field lines in quasi-linear regime 293
2.31.2. Quasi-linear theory for magnetic lines diffusion 294
2.31.3. Quasi-linear spreading of magnetic field lines 295
2.31.4. The transport exponent and transport coefficient for magnetic field lines 297
2.31.5. Comparison with the original quasi-linear prediction 299
2.31.6. Summary of main results and discussion 301
2.32. CR transport in the fractal-like medium 301
2.32.1. The matter of problem and main relations 301
2.32.2. Formation of CR spectrum in the frame of anomaly diffusion in the fractal-like medium 303
2.32.3. Parameters of the model and numerical calculations 304
2.32.4. Application to the problem of galactic CR spectrum formation 305
2.33. CR propagation in large-scale anisotropic random and regular
magnetic fields 306
2.33.1. The matter of problem 306
2.33.2. Main equations and transforming of collision integral 307
2.33.4. Kinetic coefficients and transport mean free paths 309
2.33.5. Comparison with experimental data 311
2.34. CR perpendicular diffusion calculations on the basis of MHD
transport models 312
2.34.1. The matter of problem 312
2.34.2 Three models for perpendicular diffusion coefficient 312
2.34.3. The main results for diffusion coefficients 315
2.34.4. Summarizing and comparison of used three models 318
2.35. On the role of drifts and perpendicular diffusion in CR propagation 319
2.35.1. Main equations for CR gradient and curvature drifts in the interplanetary magnetic field 319
2.35.2. The using of Archimedean-spiral model of interplanetary magnetic field 321
2.35.3. The illustration results on the nature of CR drift modulation 322
2.36. Drifts, perpendicular diffusion, and rigidity dependence of
near-Earth latitudinal proton density gradients 324 < 2.36.1.="" the="" matter="" of="" the="" problem="" 324="">
2.36.2 The propagation and modulation model, and diffusion tensor 324
2.36.3. Latitudinal gradients for CR protons 327
2.36.4. Discussion on the nature of CR latitudinal transport 328
2.37. CR drifts in dependence of Heliospheric current sheet tilt angle 329
2.37.1. The matter of the problem 329
2.37.2 CR propagation and modulation model; solar minimum spectra 329
2.37.3. Tilt angle dependence of CR protons at Earth 330
2.37.4. Tilt angle dependence of CR intensity ratios at Earth orbit 332
2.37.5 Discussion of main results 333
2.38. CR drifts in a fluctuating magnetic fields 334
2.38.1. The matter of problem 334
2.38.2. Analytical result and numerical simulations for CR particle drifts 336
2.38.3. Numerical simulations by integration of particle trajectories 337
2.38.4. Summary of main results 339
2.39. Increased perpendicular diffusion and tilt angle dependence of
CR electron propagation and modulation in the Heliosphere 339
2.39.1. The matter of the problem 339
2.39.2 The propagation and modulation model 340
2.39.3. Main results and discussion 342
2.39.4. Summary and conclusions 346
2.40. Rigidity dependence of the perpendicular diffusion coefficient and the Heliospheric modulation of CR electrons 346
2.40.1. The matter of problem 346
2.40.2. The propagation and modulation model, main results, and discussion 347
2.41. Comparison of 2D and 3D drift models for galactic CR
propagation and modulation in the Heliosphere 352
2.41.1. The matter of problem 352
2.41.2. The propagation and modulation models 353
2.41.3. Main results of comparison, and discussion 355
2.41.4. General comments to the Sections 2.34-2.41 358
2.42. The inverse problems for solar CR propagation 358
2.42.1. Observation data and inverse problems for isotropic diffusion, for anisotropic
diffusion, and for kinetic description of solar CR propagation 358
2.42.2. The inverse problem for the case when diffusion coefficient depends only from
particle rigidity 359
2.42.3. The inverse problem for the case when diffusion coefficient depends from particle
rigidity and from the distance to the Sun 361
2.43. The checking of solution for SEP inverse problem by comparison
of predictions with observations 364
2.43.1. The checking of the model when diffusion coefficient does not depend from
the distance from the Sun 364
2.43.2. The checking of the model when diffusion coefficient depends from the distance to the Sun 366
2.43.3. The checking of the model by comparison of predicted SEP intensity time variation
with NM observations 367
2.43.4. The checking of the model by comparison of predicted SEP intensity time variation
with NM and satellite observations 368
2.43.5. The inverse problems for great SEP events and space weather 370
2.44. The inverse problems for CR propagation in the Galaxy 370
2.45. The inverse problem for high energy galactic CR propagation and modulation in the Heliosphere on the basis of NM data 371
2.45.1. Hysteresis phenomenon and the inverse problem for galactic CR propagation
and modulation in the Heliosphere 371
2.45.2. Hysteresis phenomenon and the model of CR global modulation in the frame
of convection-diffusion mechanism 372
2.45.3. Even-odd cycle effect in CR and role of drifts for NM energies 373
2.45.4. The inverse problem for CR propagation and modulation during solar
cycle 22 on the basis of NM data 376
2.46. The inverse problem for small energy galactic CR propagation and modulation in the Heliosphere on the basis of satellite data 382
2.46.1. Diffusion time lag for small energy particles 382
2.46.2. Convection-diffusion modulation for small energy galactic CR particles 384
2.46.3. Small energy CR long-term variation caused by drifts 386
2.46.4. The satellite proton data and their corrections on solar CR increases and jump
in December 1995 389
2.46.5. Convection-diffusion modulation and correction for drift modulation of
the satellite proton data 392
2.46.6. Results for ³ 106 and ³ 100 MeV protons (IMP-8 and GOES data) 393
2.46.7. The satellite alpha-particle data and their main properties 395
2.46.8. Results for alpha-particles in the energy interval 330- 500 MeV 395
2.46.9. Main results of the inverse problem solution for satellite alpha-particles 400
2.46.10. Peculiarities in the solution of the inverse problem for small energy CR particles 402
Chapter 3. Cosmic Ray Nonlinear Effects in Space Plasmas 405
3.1. The important role of CR nonlinear effects in many processes
and objects in space 405
3.2. Effects of CR pressure 406
3.3. Effects of CR kinetic stream instability 407
3.4. On the structure and evolution of CR-space plasma nonlinear systems 409
3.4.1. Principles of hydrodynamic approach to the CR-space plasma nonlinear systems 409
3.4.2. Four-fluid model for description CR-plasma system 410
3.4.3. Steady state profiles of the CR-plasma system 411
3.5. Nonlinear Alfven waves generated by CR streaming instability 415
3.5.1. Possible damping mechanisms for Alfven turbulence generated by CR streaming instability 415
3.5.2 Basic equations described the nonlinear Alfven wave damping rate in presence
of thermal collisions 416
3.5.3. On the possible role of nonlinear damping saturation in the CR-plasma systems 420
3.6. Interplanetary CR modulation, possible structure of the Heliosphere
and expected CR nonlinear effects 421
3.6.1. CR hysteresis effects and dimension of the modulation region; importance of CR
nonlinear effects in the outer Heliosphere 421
3.6.2. Long - term CR spectrum modulation in the Heliosphere 423
3.6.3. CR anisotropy in the Heliosphere 425
3.6.4. Possible structure of the Heliosphere and expected nonlinear effects 426
3.6.5. Studies of the termination shock and heliosheath at > 92 AU: Voyager 1
magnetic field measurements 428
3.7. Radial CR pressure effects in the Heliosphere 433
3.7.1. On a necessity of including non-linear large-scale effects in studies of propagation
of solar and galactic CR in interplanetary space 433
3.7.2. Radial braking of solar wind and CR modulation: effect of galactic CR pressure 434
3.7.3. Radial braking of solar wind and CR modulation: effects of galactic CR pressure
and re-exchange processes with interstellar neutral hydrogen atoms 439
3.8. Expected change of solar wind Mach number accounting the effects of radial CR pressure and re-charging with neutral interstellar atoms 444
3.9. On the type of transition layer from supersonic to subsonic fluid
of solar wind 445
3.10. Non-linear influence of pickup ions, anomalous and galactic CR
on the Heliosphere's termination shock structure 447
3.10.1. Why investigations of Heliosphere's termination shock are important? 447
3.10.2. Description of the self-consistent model and main equations 448
3.10.3. Using methods of numerical calculations 450
3.10.4. Expected differential CR intensities on various heliocentric distances 450
3.10.5. Different cases of Heliospheric shock structure and solar wind expansion 452
3.10.6. The summary of obtained results 456
3.11. Expected CR pressure effects in transverse directions in Heliosphere 458
3.11.1. CR transverse gradients in the Heliosphere and its possible influence on solar wind moving 458
3.11.2. The simple model for estimation of upper limit of CR transverse effects on solar wind 458
3.11.3. The effect of the galactic CR gradients on propagation of solar wind in meridianal plane 463
3.12. Effects of CR kinetic stream instability in the Heliosphere 466
3.12.1. Rough estimation of stream instability effect at constant solar wind speed 466
3.12.2. Self - consistent problem including effects of CR pressure and kinetic stream
instability in the Heliosphere 470
3.12.3. Main results for Heliosphere 475
3.13. CR nonlinear effects in the dynamic Galaxy 475
3.13.1. CR propagation in dynamic model of the Galaxy 475
3.13.2. Geometry of galactic wind and possible role of CR 476
3.13.3. Expected distribution of galactic wind velocity and CR density
in the halo (ellipsoidal geometry model) 477
3.14. Self-consistent problem for dynamic halo in rotating Galaxy 479
3.14.1. Solution for galactic wind and magnetic field 479
3.14.2. Solution for CR propagation in the rotating Galaxy 480
3.15. On the transport of random magnetic fields by a galactic wind
driven by CR; influence on CR propagation 482
3.15.1. Random magnetic fields in the galactic disc and its expanding to the dynamic halo 482
3.15.2. Basic equations described the transport of the random magnetic fields 482
3.15.3. The random magnetic field effects in the galactic wind flow with azimuthally symmetry 483
3.15.4. Results of numerical calculations 486
3.16. Nonlinear Alfvén waves generated by CR streaming instability
and their influfence on CR propagation in the Galaxy 489
3.16.1. On the balance of Alfvén wave generation by CR streaming instability
with damping mechanisms 489
3.16.2. Basic equations and their solutions 490
3.16.