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 andDebye 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

1.2.6. 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 109 eV/nucleon < Ek < 3 X1011 eV/nucleon range and the expected dependence of Aq (Ek) and Asid (Ek) on Ek 11

1.2.8. Chemical composition in the energy range 3 X107 eV/nucleon < Ek < 109 eV/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 Aon particle rigidity R from solar modulation data of protons, electrons, and nuclei with various Z 13

1.2.11. The dependence of Aon 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, y- 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

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/

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 = Mrn 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 ofproblem 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

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 ofproblem 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 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 inclusion of the variations of particle energy 202

2.14.5. The Green's function for the stationary isotropic diffusion in the case ofpower 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

2.15.1. 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 ofparticle 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 Alfven waves and how it influences 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

2.22.1. The matter of problem

2.22.2. Description of Monte Carlo particle simulations

2.22.3. Wave field models

2.22.4. Simulations for Alfvenic turbulence models A, B1, B2

2.22.5. Simulations for oblique MHD waves models C-AF, C-AK, C-MF, and C-MK

2.23. Dispersion relations for CR particle diffusive propagation

2.23.1. The matter of the problem and denominations

2.23.2. Dispersion relations for diffusion and telegrapher's equations

2.23.3. Dispersion relations in general case

2.23.4. Dispersion relations for isotropic pitch-angle scattering

2.23.5. Dispersion relations for the cases with dominant helicity

2.23.6. Dispersion relations for focusing scattering

2.23.7. Dispersion relations for hemispherical scattering

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 the 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

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