COSMIC RAY INTERACTIONS,PROPAGATION, AND

ACCELERATION IN SPACEPLASMAS

By

LEV I. DORMANIsrael Cosmic Ray & Space Weather Center and Emilio Segre Observatory,

affiliated to TelAviv University, Israel Space Agency, and Technion, Qazrin, Israel;Cosmic Ray Department oflZMIRAN, Russian Academy of Science, Troitsk, Russia

4y Springer

CONTENTSPAGES

Preface xxiAcknowledgments xxviiFrequently used Abbreviations and Notations xxxi

Chapter 1. Cosmic Ray Interactions in Space Plasmas 11.1. Main properties of space plasma 1

1.1.1. Neutrality of space plasma and Debye radius 11.1.2. Conductivity and magnetic viscosity of space plasma I1.1.3. The time of magnetic fields dissipation; frozen magnetic fields 11.1.4. Transport path of ions in space plasma and dissipative processes 21.1.5. Space plasma as excited magneto-turbulent plasma 21.1.6. Main channels of energy transformation in space plasma 21.1.7. Particle acceleration in space plasma and the second fundamental law of thermodynamics 3

1.2. Main properties and origin of CR 41.2.1. Internal and external CR of different origin 41.2.2. On the main properties of primary and secondary CR 41.2.3. Five intervals in the observed CR energy spectrum 51.2.4. Main CR properties and origin ofCR in the interval 1 71.2.5. The anisotropy in energy intervals 1 and 2 71.2.6. 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 10 eV/nucleon < E^ < 3 x 10 eV/nucleon range and the

expected dependence of AQIE/I) and Asicj\Ejt) on E^ - 11

1.2.8. Chemical composition in the energy range 3x10 eV/nucleon < E^ < 10 eV/nucleon

and the nature of the scattering elements in the Galaxy 111.2.9. The nature of the energy boundary between intervals 3 and 2 121.2.10. The mode of the dependence of A on particle rigidity Rfrom solar modulation data

of protons, electrons, and nuclei with various Z 13 .

1.2.11. The dependence of A on E^ from data of solar CR propagation 15

1.2.12. The features of the solar modulation of the CRspectrum and the measurementsof 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 161.3.1. Cross sections, paths for absorption, and life time of CR particles relative to nuclear

interactions in space plasma 161.3.2. CR fragmentation in space plasma 171.3.3. Expected fluxes of secondary electrons, positrons, y- quanta, and neutrinos 191.3.4. 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 231.5.1. Ionization energy losses by CR nuclei during propagation in the space 231.5.2. Ionization and bremsstrahlung losses for CR electrons 25

1.6. CR interactions with photons in space 261.6.1. CR nuclei interactions with space photons 261.6.2. CR electron interactions with the photon field • 27

1.7. Energy variations of CR particles in their interactions with magnetic fields 271.7.1. Synchrotron losses of energy by CR particles in magnetic fields 271.7.2. Acceleration and deceleration of particles in their interactions with moving magnetic fields 29

vii

Vlll CONTENTS

1.8. CR particle motion in magnetic fields; scattering by magnetic inhomogeneities 301.8.1. CR particle motion in the regular magnetic fields frozen into moving plasma formations 301.8.2. CR particle moving in essentially inhomogeneous magnetized plasma 311.8.3. Two-dimensional model ofCRparticle scattering by magnetic

inhomogeneities of type H = (0,0,//)

1.8.4. Scattering by cylindrical fibers with homogeneous field 32

1.8.5. Scattering by cylindrical fibers with field of type h = M/r" 33

1.8.6. Three-dimensional model of scattering by inhomogeneities of the type h = (0, h(x)fi)

against the background of general field H o =(//„,0,0) 35

1.9. The transport path of CR particles in space magnetic fields 381.9.1. The transport path of scattering by magnetic inhomogeneities of the type of

isolated magnetic clouds of the same scale 381.9.2. Transport scattering path in case of several scales of magnetic inhomogeneities 391.9.3 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 = Mj 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/r" 47

1.9.7. Transport path of scattering by inhomogeneities of the type h = (0,h(x)fi)

against the background of the regular field Ho — (Hofifl) 481.9.8. The transport scattering path including the drift in inhomogeneous fields 521.9.9. The transport scattering path in the presence of the regular background field 531.9.10. The transport path for scattering with anisotropic distribution of magnetic

inhomogeneities in space 561.10. Magnetic traps of CR in space 57

1.10.1. Types of CR magnetic traps and main properties 571.10.2. Traps of cylindrical geometry with a homogeneous field 591.10.3. Traps with strength-less structure of the field 591.10.4. The effect of magnetic field inhomogeneities 591.10.5. Traps with an inhomogeneous regular field 601.10.6. Traps with a curved magnetic field 611.10.7. Traps with a magnetic field varying along the force lines 621.10.8. Traps with a magnetic field varying with time 62

1.11. Cosmic ray interactions with electromagnetic radiation in space plasma 631.11.1. Effects ofCompton scattering of photons by accelerated particles 631.11.2. The influence of the nuclear photo effect on accelerated particles 701.11.3. Effect of the universal microwave radiation on accelerated particles 711.11.4. Effect of infrared radiation on accelerated particles 72

1.12. CR interaction with matter of space plasma as the main source ofcosmic gamma radiation 73

1.12.1. The matter of the problem 731.12.2. Gamma rays from neutral pions generated in nuclear interactions ofCR with

space plasma matter 731.12.3. 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 flareenergetic particles with solar and stellar winds 77

1.13.1. The matter of problem and the main three factors 771.13.2. The 1st factor: solar FEP space-time distribution 781.13.3. The 2nd factor: space-time distribution of solar wind matter » 821.13.4. 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 forobservations inside the Heliosphere during FEP events 85

1.13.6. Gamma rays from interaction of FEP with stellar wind matter 891.13.7. Expected gamma ray fluxes from great FEP events - 891.13.8. 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 galacticCR with solar and stellar winds 91

1.14.1. The matter of problem and the main three factors 911.14.2. The 1st factor: galactic CR space-time distribution in the Heliosphere 921.14.3. The 2nd factor: space-time distribution of solar wind matter 961.14.4. The 3rd factor: gamma ray generation by galactic CR in the Heliosphere 961.14.5. Expected angle distribution of gamma ray fluxes from solar wind 981.14.6. Gamma ray fluxes from stellar winds • 1001.14.7. Summary of main results and discussion 100

1.15. On the interaction of EHE gamma rays with the magnetic fieldsof the Sun and planets 103

1.15.1. The matter of the problem 1031.15.2. Magnetic e* pair cascades in the magnetosphere of the Sun 1041.15.3. The possibility that extra high energy CR spectrum at > 1019 eV contains

significant proportion of photons 1051.15.4. Summering of main results and discussion 107

Chapter 2. Cosmic Ray Propagation in Space Plasmas 1092.1. The problem of CR propagation and a short review of a development of the basically

concepts 1092.2. The method of the characteristic functional and a deduction of kinetic equation

for CR propagation in space in the presence of magnetic field fluctuations 1112.3. Kinetic equation in the case of weak regular and isotropic random fields 1152.4. Kinetic equation for CR propagation including fluctuations of plasma velocity 1172.5. Kinetic equation for propagation of CR including electric fields in plasma 1242.6. 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 1262.6.1. Formulation of the problem and deduction of the basic equation 1262.6.2. The case of large wave lengths 1302.6.3. The case of small wave lengths 130

2.7. Green's function of the kinetic equation and the features of propagationof low energy particles 13 2

2.8. Kinetics of CR in a large scale magnetic field 1392.8.1. The kinetic equation deriving on the basis of the functional method 1392.8.2. Diffusion approximation 1452.8.3. Diffusion ofCR in a large-scale random field 1482.8.4. CR transport in the random girotropic magnetic field 150

2.9. CR diffusion in the momentum space 1552.10. CR diffusion in the pitch-angle space 1582.11. Fokker-Planck CR transport equation for diffusion approximation 165

2.11.1. Diffusion approximation including the first spherical mode 1652.11.2. Including of magnetic inhomogeneities velocity fluctuations 1672.11.3. Diffusion approximation including the second spherical harmonic 1682.11.4. Drift effects in a diffusion propagation of CR ' 1742.11.5. General poloidal magnetic field effects in a diffusion propagation ofCR 1772.11.6. Derivation of the Fokker-Planck CR transport equation from variational principle 179

; CONTENTS

2.12. Phenomenological description of CR anisotropic diffusion 1822.12.1. Deduction of general equation 1822.12.2. The case of propagation in a galactic arm 1832.12.3. The case of CR propagation in interplanetary space 1842.12.4. On rotation ofCR gas in the interplanetary space 1882.12.5 Temporal variations and spatial anisotropy ofCR in the interplanetary space 1892.12.6. The region where CR anisotropic diffusion approximation is applicable 190

2.13. On a relation between different forms of the equation ofanisotropic diffusion of CR 190

2.14. Spectral representations of Green's function of non-stationaryequation of CR diffusion 194

2.14.1. Formulation of the problem 1942.14.2. Determining of the radial Green's function for a non-stationary diffusion

including convection 1942.14.3. Green's function of the three-dimensional transfer equation including convection 1992.14.4. Possible inclusion of the variations of particle energy 2022.14.5. 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 velocitiesand pitch-angle and spatial coefficients of diffusion 203

2.15.1. Correlation function of particle velocities 2032.15.2. 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 expandingmagnetic fields 206

2.17. The second order pitch-angle approximation for the CRFokker-Planck kinetic equation 210

2.17.1. The matter of the problem 2102.17.2. The first order approximation 2112.17.3. The second order approximation 2112.17.4. Peculiarities of the second pitch-angle approximation 213

2.18. Anomalous diffusion: modes of CR diffusion propagation 2142.18.1. Three modes of particle propagation: classical diffusion, super-diffusion and sub-diffusion 2142.18.2. Simulation of particle propagation in a two-dimensional static magnetic field turbulence 214

2.19. Energetic particle mean free path in the Alfven wave heatedspace plasma 217

2.19.1. Space plasma heated by Alfven waves and how it influences on particlepropagation and acceleration 217

2.19.2. Determining of the Alfven wave power spectrum 2182.19.3. Determining of the energetic particle mean free path 219

2.20. Bulk speeds of CR resonant with parallel plasma waves 2212.20.1. Formation of the bulk speeds that are dependent on CR charge/mass and momentum 2212.20.2. Dispersion relation and resonance condition 2222.20.3. Effective wave speed 2232.20.4. Bulk motion of the CR in space plasma 225

2.21. Non-resonant pitch-angle scattering and parallel mean-free-path 2272.21.1. The problem of the non-resonant pitch-angle scattering 2272.21.2. Derivation of the non-resonant scattering process 2292.21.3. Resulting mean free path and comparison with gyro-resonant model 2322.21.4. Contribution from slab and oblique Alfven waves to the non-resonant pitch-angle scattering 2332.21.5. Parallel mean free path: comparison of the theoretical predictions with the measurements 234

CONTENTS XI

2.22. On the cosmic ray cross-field diffusion in the presenceof highly perturbed magnetic fields 236

2.22.1. The matter of problem 2362.22.2. Description of Monte Carlo particle simulations 2362.22.3. Wave field models 2372.22.4. Simulations for Alfvenic turbulence models A, Bl, B2 2382.22.5. 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 2422.23.1. The matter of the problem and denominations 2422.23.2. Dispersion relations for diffusion and telegrapher's equations 2432.23.3. Dispersion relations in general case 2442.23.4. Dispersion relations for isotropic pitch-angle scattering 2452.23.5. Dispersion relations for the cases with dominant helicity 2462.23.6. Dispersion relations for focusing scattering 2462.23.7. Dispersion relations for hemispherical scattering 247

2.24. The dynamics of dissipation range fluctuations with applicationto CR propagation theory 248

2.24.1. The matter of problem 2482.24.2. Magnetic helicity according to WIND spacecraft measurements 2502.24.3. 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 Markovprocess for CR transport 252

2.25.1. The matter of the problem 2522.25.2. Diffusion and Markov stochastic processes; used definitions 2532.25.3. Path integral representation for the transition probability of Markov processes 2552.25.4. Main results and method's checking 257

2.26. Velocity correlation functions and CR transport (compounddiffusion) 258

2.26.1. The matter of problem 2582.26.2. Compound CR diffusion 2592.26.3. The Kubo formulation applied to compound diffusion 2602.26.4. Main results 263 :

2.27'. The BGK Boltzmann equation and anisotropic diffusion 2632.27.1. The matter of problem \ 2632.27.2. Description of the model 2642.27.3. The diffusion approximation 2652.27.4. Evaluation of the Green function 2662.27.5. Long-scale, large-time asymptotics 2692.27.6. Pitch-angle evolution and perpendicular diffusion 2712.2 7.7. Summary of main results 2 72

2.28. Influence of magnetic clouds on the CR propagation 2732.28.1. The matter of the problem 2732.28.2. The numerical model 2732.28.3. Numerical results 2 752.28.4. Comparison with observations 278

2.29. Non-diffusive CR particle pulse transport 2802.29.1. The matter of the problem 2802.29.2. Kinetic equation 2812.29.3. Pitch-angle response function for neutron monitors 2822.29.4. Time-finite injection 2822.29.5. Three parts of resulting solution 2822.29.6. Expected temporal profiles for neutron monitors and comparison with observations 284

Xll CONTENTS

2.30. Pitch-angle diffusion of energetic particles by large amplitudeMHD waves 288

2.30.1. The matter of the problem 2882.30.2. The model used 2892.30.3. Main results of simulation 289

2.31. Particle diffusion across the magnetic field and the anomaloustransport of magnetic field lines 293

2.31.1. On the anomalous transport of magnetic field lines in quasi-linear regime 2932.31.2. Quasi-linear theory for magnetic lines diffusion 2942.31.3. Quasi-linear spreading of magnetic field lines 2952.31.4. The transport exponent and transport coefficient for magnetic field lines 2972.31.5. Comparison with the original quasi-linear prediction 2992.31.6. Summary of main results and discussion 301

2.32. CR transport in the fractal-like medium 3012.32.1. The matter of problem and main relations , 3012.32.2. Formation ofCR spectrum in the frame of anomaly diffusion in the fractal-like medium 3032.32.3. 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 regularmagnetic fields 306

2.33.1. The matter of problem 3062.33.2. Main equations and transforming of collision integral 3072.33.3. Kinetic coefficients and transport mean free paths 3092.33.4. Comparison with experimental data 311

2.34. CR perpendicular diffusion calculations on the basis of MHDtransport models 312

2.34.1. The matter of problem 3122.34.2 Three models for perpendicular diffusion coefficient 3122.34.3. The main results for diffusion coefficients 3152.34.4. Summarizing and comparison of used three models "- 318

2.35. On the role of drifts and perpendicular diffusion in CR propagation 3192.35.1. Main equations for CR gradient and curvature drifts in the interplanetary magnetic field 3192.35.2. The using of Archimedean-spiral model of interplanetary magnetic field 3212.35.3. The illustration results on the nature ofCR drift modulation 322

2.36. Drifts, perpendicular diffusion, and rigidity dependence ofnear-Earth latitudinal proton density gradients 324

2.36.1. The matter of the problem 3242.36.2 The propagation and modulation model, and diffusion tensor 3242.36.3. Latitudinal gradients for CR protons 3272.36.4. Discussion on the nature ofCR latitudinal transport 328

2.37. CR drifts in dependence of Heliospheric current sheet tilt angle 3292.37.1. The matter of the problem 3292.37.2 CR propagation and modulation model; solar minimum spectra 3292.37.3. Tilt angle dependence of CR protons at Earth 3302.37.4. Tilt angle dependence ofCR intensity ratios at Earth orbit 3322.37.5 Discussion of main results 333

2.38. CR drifts in a fluctuating magnetic fields 3342.38.1. The matter of problem 3342.38.2. Analytical result and numerical simulations for CRparticle drifts 3362.38.3. Numerical simulations by integration of particle trajectories 3372.38.4. Summary of main results 339

2.39. Increased perpendicular diffusion and tilt angle dependence ofCR electron propagation and modulation in the Heliosphere 339

2.39.1. The matter of the problem 339

CONTENTS Xlll

2.39.2 The propagation and modulation model 3402.39.3. Main results and discussion 3422.39.4. Summary and conclusions 346

2.40. Rigidity dependence of the perpendicular diffusion coefficient and theHeliospheric 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 CRpropagation and modulation in the Heliosphere 352

2.41.1. The matter of problem 3522.41.2. The propagation and modulation models 3532.41.3. Main results of comparison and discussion 3552.41.4. General comments to the Sections 2.34-2.41 358

2.42. The inverse problem for solar CR propagation 3582.42.1. Observation data and inverse problems for isotropic diffusion, for anisotropic

diffusion, and for kinetic description of solar CR propagation 3582.42.2. The inverse problem for the case when diffusion coefficient depends only from

particle rigidity 3592.42.3. The inverse problem for the case when diffusion coefficient depends from particle

rigidity and from the distance to the Sun 361

2 A3. The checking of solution for SEP inverse problem by comparisonof predictions with observations 364

2.43.1. The checking of the model when diffusion coefficient does not depend fromthe distance from the Sun 364

2.43.2. The checking of the model when diffusion coefficient depends from the distance to the Sun 3662.43.3. The checking of the model by comparison of predicted SEP intensity time variation

with NM observations 3672.43.4. The checking of the model by comparison of predicted SEP intensity time variation

with NM and satellite observations 3 68

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 3702.45. The inverse problem for high energy galactic CR propagation and

modulation in the Heliosphere on the basis of NM data 3712.45.1. Hysteresis phenomenon and the inverse problem for galactic CR propagation

and modulation in the Heliosphere '•• 3712.45.2. Hysteresis phenomenon and the model ofCR global modulation in the frame

of convection-diffusion mechanism 3 722.45.3. Even-odd cycle effect in CR and role of drifts for NM energies 3732.45.4. 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 andmodulation in the Heliosphere on the basis of satellite data 382

2.46.1. Diffusion time lag for small energy particles 3822.46.2. Convection-diffusion modulation for small energy galactic CR particles 3842.46.3. Small energy CR long-term variation caused by drifts 3862.46.4. The satellite proton data and their corrections on solar CR increases and jump

in December 1995 3892.46.5. Convection-diffusion modulation and correction for drift modulation of

the satellite proton data 3922.46.6. Results for >106 and >100 MeV protons (IMPS and GOES data) 3932.46.7. The satellite alpha-particle data and their main properties t 3952.46.8. Results for alpha-particles in the energy interval 330—500 MeV 3952.46.9. Main results of the inverse problem solution for satellite alpha-particles 4002.46.10. Peculiarities in the solution of the inverse problem for small energy CR.particles 402

XIV CONTENTS

Chapter 3. Nonlinear Cosmic Ray Effects in Space Plasmas 4053.1. The important role of nonlinear CR effects in many processes

and objects in space 4053.2. Effects of CR pressure 4063.3. Effects of CR kinetic stream instability 4073.4. On the structure and evolution of CR-space plasma systems 409

3.4.1. Principles of hydrodynamic approach to the CR-space plasma nonlinear system ' 4093.4.2. Four-fluid model for description CR-plasma system 4103.4.3. Steady state profiles of the CR-plasma system 411

3.5. Nonlinear Alfven waves generated by CR streaming instability 4155.5./. Possible damping mechanisms for Alfven turbulence generated by CR streaming instability 4153.5.2 Basic equations described the nonlinear Alfven wave damping rate in presence

of thermal collisions 4163.5.3. On the possible role of nonlinear damping saturation in the CR-plasma systems 420

3.6. Interplanetary CR modulation, possible structure of the Heliosphereand expected CR nonlinear effects 421

3.6.1. CR hysteresis effects and dimension of the modulation region; importance ofCRnonlinear effects in the outer Heliosphere 421

3.6.2. Long - term CR spectrum modulation in the Heliosphere 4233.6.3. CR anisotropy in the Heliosphere 4253.6.4. Possible structure of the Heliosphere and expected nonlinear effects 4263.6.5. 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 4333.7.1. On a necessity of including non-linear large-scale effects in studies of propagation

of solar and galactic CR in interplanetary space 4333.7.2. Radial braking of solar wind and CR modulation: effect of galactic CR pressure 4343.7.3. 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 ofradial CR pressure and re-charging with neutral interstellar atoms 444

3.9. On the type of transition layer from supersonic to subsonic fluidof solar wind 445

3.10. Non-linear influence of pickup ions, anomalous and galactic CRon the Heliosphere's termination shock structure 447

3.10.1. Why are investigations of Heliosphere's termination shock important? 4473.10.2. Description of the self-consistent model and main equations 4483.10.3. Using methods of numerical calculations 4503.10.4. Expected differential CR intensities on various heliocentric distances 4503.10.5. Different cases of Heliospheric shock structure and solar wind expansion 4523.10.6. The summary of obtained results 456

3.11. Expected CR pressure effects in transverse directions in Heliosphere 4583.11.1. CR transverse gradients in the Heliosphere and its possible influence on solar wind moving 4583.11.2. The simple model for estimation of upper limit ofCR transverse effects on solar wind 4583.11.3. The effect of the galactic CR gradients on propagation of solar wind in meridional plane 463

3.12. Effects of CR kinetic stream instability in the Heliosphere 4663.12.1. Rough estimation of stream instability effect at constant solar wind speed 4663.12.2. Self-consistent problem including effects ofCR pressure and kinetic stream

instability in the Heliosphere 4703.12.3. Main results for Heliosphere 475

CONTENTS XV

3.13. CR nonlinear effects in the dynamic Galaxy 4753.13.1. CR propagation in dynamic model of the Galaxy 4753.13.2. Geometry of galactic wind and possible role of CR 4763.13.3. 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 4793.14.1. Solution for galactic wind and magnetic field 4793.14.2. Solution for CR propagation in the rotating Galaxy 480

3.15. On the transport of random magnetic fields by a galactic winddriven by CR; influence on CR propagation 482

3.15.1. Random magnetic fields in the galactic disc and its expanding to the dynamic halo 4823.15.2. Basic equations described the transport of the random magnetic fields 4823.15.3. The random magnetic field effects in the galactic wind flow with azimuthal symmetry 4833.15.4. Results of numerical calculations 486

3.16. Nonlinear Alfven waves generated by CR streaming instabilityand their influfence on CR propagation in the Galaxy 489

3.16.1. On the balance of Alfven wave generation by CR streaming instabilitywith damping mechanisms 489

3.16.2. Basic equations and their solutions 4903.16.3. Summary of main results 494

Chapter 4. Cosmic Ray Acceleration in Space Plasmas 4954.1. Acceleration particles in space plasmas as universal phenomenon

in the Universe 4954.2. The Fermi mechanism of statistical acceleration 4974.3. Development of the Fermi model: head-on and overtaking collisions 499

4.3.1. Non-relativistic case 4994.3.2. Relativistic case 500

4.4. Development of the Fermi model: inclusion of oblique collisions 5024.4.1. Non-relativistic case 5024.4.2. Relativistic case 507,

4.5. Statistical acceleration of particles during the variations in theacceleration mechanism parameters as particles gain energy 510

4.5.1. The expected variations of the acceleration mechanism parameters as a particles gain energy 5104.5.2. The mode of particle energy change and formation of the spectrum in the non-relativistic range

for the statistical acceleration mechanism including the dependence of A and u on energy 5114.5.3. Particle acceleration and formation of the spectrum in relativistic energy range including

the variations in the parameters Xandu with total particle energy E increasing 5144.5.4. The nature of the constraint of the accelerated particle's energy 516

4.6. Formation of the particle rigidity spectrum during statistical acceleration 5184.6.1. General remarks and basic relations 5184.6.2. Non-relativistic range; Xandu are independent ofR 5194.6.3. Non-relativistic case; Xandu are functions ofR 5214.6.4. Relativistic range; X and u are independent ofR 5294.6.5. Relativistic range; X and u are functions ofR 532

4.7. Statistical acceleration by scattering on small angles 5354.7.1. Small-angle scattering 5354.7.2. Energy gain in head-on collisions in non-relativistic case for small angle scatterings 5384.7.3. Energy change in non-relativistic case for oblique collisions 5404.7.4. Energy change in relativistic case 5434.7.5. The mode of particle energy change in time 543

XVI CONTENTS

4.8. Injection energy and the portion of the accelerated particlesin the statistical mechanism 544

4.8.1. Injection energy in the statistical acceleration mechanism 5444.8.2. The injection from background plasma: conditions for acceleration of all particles 5454.8.3. The injection from background plasma: quasi-stationary acceleration

of a small part of the particles 5464.8.4. The problem of injection and acceleration of heavy nuclei from background plasma 546

4.9. Statistical acceleration in the turbulent plasma confinedwithin a constant magnetic field 547

4.9.1. The magnetic field effect on plasma turbulence 5484.9.2. Particle acceleration by plasma fluctuations 5484.9.3. Acceleration by magneto-sound and Alfven waves 5494.9.4. Cyclotron acceleration of ions by plasma waves 5504.9.5. Cyclotron acceleration of ions by the combination frequency 5504.9.6. A cceleration by electron plasma waves 5514.9.7. Acceleration by nonlinear waves 5514.9.8. Acceleration by electrostatic waves 5524.9.9. Stochastic Fermi acceleration by the turbulence with circularly polarized Alfven waves 553

4.10. Statistical acceleration of particles by electromagnetic radiation 5534.10.1. Effectiveness of charged particle acceleration by electromagnetic radiation;

comparison with the Fermi mechanism 5534.10.2. On the injection in the particle acceleration by radiation 5544.10.3. On the maximum energy and maximum density of accelerated particles in the case

of particle acceleration by radiation 5544.10.4. Cyclotron acceleration of relativistic electrons by lateral waves 5554.10.5. Electron acceleration by the radiation during their induced Compton scattering 5554.10.6. Acceleration of charged particles by electromagnetic radiation pressure 556

4.11. Statistical acceleration of particles by the Alfven mechanism ofmagnetic pumping 557

4.11.1. A Ifven 's idea of particles acceleration by magnetic pumping 5574.11.2. Relative change of the momentum, energy, and rigidity of particles in a single cycle

of magnetic field variation in the presence of scattering 5584.11.3. The rate of the gain in energy and rigidity for the mechanism of acceleration

by magnetic pumping 5614.11.4. Formation of the energy and rigidity spectra in the case of particle acceleration

by magnetic pumping 5634.11.5. Formation of the particle spectrum in the magnetic pumping mechanism including

absorption in the source 5654.11.6. The magnetic pumping mechanism in the case of field variations according to the power law 5664.11.7. Kinetic theory of particle acceleration by magnetic pumping 566

4.12. Accelerated particle flux from sources 5704.12.1. Particle flux from a source in stationary case 5704.12.2. Particle flux from the source in non-stationary case 5714.12.3. Accelerated particles in the space beyond the stationary sources 5714.12.4. The accelerated particle spectrum beyond non-stationary sources 5 72

4.13. Induction acceleration mechanisms 5744.13.1. The discussion on the problem of induction acceleration mechanisms 5744.13.2. Charged particle acceleration up to very high CR energies

by rotating magnetized neutron star 5754.13.3. On the maximal energy of accelerated particles from fast rotated magnetic star 5784.13.4. On the expected energy spectrum and total flux of accelerated particles from

fast rotated magnetic star 5 79

4.14. Particle acceleration by moving magnetic piston 5804.14.1. Acceleration and deceleration at a single interaction of particles with magnetic piston 5804.14.2. Acceleration and deceleration of particles at the multiple interactions with magnetic piston 581

CONTENTS xvn

4.15. Mechanisms of particle acceleration by shock waves and other movingmagneto-hydrodynamic discontinuities during a single interaction 582

4.15.1. Acceleration for single passage of a laterally incident particle (the shock front is unlimited) 5824.15.2. Acceleration in a single passage of a transversely incident

particle (the shock front is limited) 5854.15.3. Exact integration of the particle motion equations for an oblique incidence

of a non-relativistic particle onto a shock front 5854.15.4. Particle acceleration by a transverse shock wave at v » u in general

case (including oblique incidence of particles) 5864.15.5. Particle acceleration by oblique shock waves 5894.15.6. Particle acceleration by rotational discontinuities 5924.15.7. Particle acceleration at a multiple reflection from a shock wave front 595

4.16. Acceleration of particles in case of magnetic collapseand compression 604

4.16.1. Non-relativistic case of particle acceleration during magnetic collapse 6044.16.2. Relativistic case of particle acceleration during magnetic collapse 6064.16.3. The case of particle acceleration from very low energies up to relativistic energies 6074.16.4. The particle injection conditions for acceleration in a magnetic trap 6094.16.5. Diffusive compression acceleration of charged particles 6104.16.6. Acceleration at fluid compressions and comparison with shock acceleration 613

4.17. The cumulative acceleration mechanism near the zero linesof magnetic field 619

4.17.1. Injection-less acceleration of particles and the mechanism of magnetic field annihilation 6194.17.2. Current sheets and rapid rearrangement of magnetic fields 6204.17.3. A development of magnetic field annihilation models and the model of magnetic force

line reconnection; on the role of discharge phenomena in some astrophysicalprocesses and particle acceleration 626

4.17.4. Particle acceleration in the neutral current sheets 6284.17.5. Mechanism of magnetic field dissipation in a current sheet including

non-anti-parallelism of magnetic field, instabilities, and turbulence 629

4.18. Tearing instability in neutral sheet region, triggering mechanismsof solar flares, turbulence, percolation and particle acceleration 630

4.18.1. The problem of solar flare origin, particle acceleration and ejection into solar wind 6304.18.2. The prominence channel of flares 631 '4.18.3. Non-evolutionary channels of triggering of the prominence type of flares 6334.18.4. The coronal channel of flares 6334.18.5. Powerful proton flares 6364.18.6. The problem of particle acceleration in the current layer of solar flares 6374.18.7. The spatial diffusion in the electric field of the sheet in the case of two-dimensional

geometry with pure anti-parallel magnetic field 6394.18.8. The spatial diffusion in the electric field of the sheet in the case

of three-dimensional geometry 6404.18.9. Comparison of the quasi-diffusive acceleration andstochastic acceleration

on the Langmuir plasmons 6424.18.10. On the chemical composition of accelerated particles 6424.18.11. Development of solar flare models and mechanisms of particle acceleration

in the turbulent current sheet (Tearing mode instability - 643; Pinch type instabilities(Sausage, kink, etc.) - 645; Overheating of turbulent regions in the current sheet - 645;Splitting of current sheet at regions of discontinuous conductivity - 646) 643

4.18.12. Unsteady state of turbulent current sheet and percolation 6464.18.13. Acceleration of particles in a fragmented turbulent current sheet 648

4.19. Particle acceleration in shear flows of space plasma 6504.19.1. Space plasma's shear flows in different objects > 6504.19.2. Particle acceleration in the two-dimensional shear flow of collisionless plasma 6504.19.3. Some examples of possible particle acceleration in shear flows 652

XV111 CONTENTS

4.20. Additional regular particle acceleration in space plasma withtwo types of scatters moving with different velocities 653

4.20.1. Two types of scatters in space plasma as additional source of particle acceleration 6534.20.2. General theory ofCR propagation and acceleration in space plasma with two

types of scatters moving with different velocities 6534.20.3. The diffusion approximation 6544.20.4. The case Bo = 0 6564.20.5. Space-homogeneous situation 6564.20.6. Estimation of possible additional acceleration of CR particles in the Galaxy 6574.20.7. Estimation of possible additional acceleration of CR particles in the

region of galaxies collision 6584.20.8. Estimation of possible additional acceleration of CR particles in

the Heliosphere and in stellar winds 6584.20.9. On the effectiveness of additional particle acceleration in the double star systems 6594.20.10. Main results on the mechanism of CR particle additional acceleration and applications 660

4.21. Shock wave diffusion (regular) acceleration 6614.21.1. Two types of particle interaction with shock wave 6614.21.2. Elementary model of diffusive shock-wave acceleration 6614.21.3. Acceleration by the plane shock wave; diffusion approximation 6644.21.4. The case of particle injection by mono-energetic spectrum 6654.21.5. On the space distribution of accelerated particles 6654.21.6. The effect of finite width of shock wave front 6654.21.7. Effect of finite dimension of shock wave 6664.21.8. Effect of energy losses during particle shock acceleration 6674.21.9. Simultaneously regular and statistical acceleration 6694.21.10. Regular acceleration by spherical shock wave 6724.21.11. Acceleration by spherical standing shock wave in the solar or stellar wind 6724.21.12. Acceleration by spherical standing shock wave in the case of accretion 6754.21.13. Acceleration by spherical running shock wave 6774.21.14. Effects of finite duration shock acceleration 6804.21.15. CR acceleration at quasi-parallel plane shocks (numerical simulations) 684

4.22. Simplified 'box' models of shock acceleration 6884.22.1. Principles of 'box' models of shock acceleration 6884.22.2. Physical interpretation of the 'box' model 6894.22.3. Inclusion of additional loss processes 6904.22.4. Including nonlinear effects in the 'box' model 6914.22.5. Main peculiarities of 'box' models 692

4.23. Diffusive shock wave acceleration in space plasmawith accounting non-linear processes 693

4.23.1. Bulk CR transport in space plasma and diffusive shock wave acceleration 6934.23.2. Simulating CR particle acceleration in shocks modified by CR non-linear effects 695

4.24. Thermal particle injection in nonlinear diffusive shock acceleration 6984.24.1. Comparison semi-analytical and Monte Carlo models 6984.24.2. Injection models 6994.24.3. Models of momentum dependent diffusion 6994.24.4. Thermalization 7004.24.5. Main results for both models and comparison 700

4.25. Time evolution of CR modified MHD shocks 7034.25.1. The matter of problem 7034.25.2. Methods of calculations 7044.25.3. Main results and discussion 706

4.26. Particle injection and acceleration at non-parallel shocks 7094.26.1. The matter of problem 7094.26.2. Analytical considerations 7104.26.3. Numerical calculations for test-particle simulations 7124.26.4. Numerical calculations for self-consistent hybrid simulations 714

CONTENTS XIX

4.27. Numerical studies of diffusive shock acceleration at spherical shocks 7154.27.1. The matter of problem 7154.27.2. Comoving spherical grid 7164.27.3. Numerical models and results 717

4.28. Particle acceleration by the electrostatic shock waves 7204.28.1. Formation of electrostatic shock waves in space plasma 7204.28.2. The two-dimensional simulation model 7214.28.3. Generated electric and magnetic fields, and particle acceleration (results of simulation) 722

4.29. Particle acceleration by relativistic shock waves 7254.29.1. Peculiarities of particle acceleration by relativistic shock waves 7254.29.2. First-order Fermi particle acceleration at relativistic shock waves with a 'realistic'

magnetic field turbulence model 7254.29.3. Particle acceleration at parallel relativistic shocks in the presence of finite-amplitude

magnetic field perturbations . 7284.29.4. Electron acceleration in parallel relativistic shocks with finite thickness 7304.29.5. Small-angle scattering and diffusion: application to relativistic shock acceleration 734

4.30. CR acceleration at super-luminal shocks 7374.30.1. The matter of the problem 7374.30.2. Monte Carlo simulations 7384.30.3. Main results 7394.30.4. Expected diffuse signal from sources with super-luminal shock fronts 740

4.31. On the fraction of the kinetic energy of moving space.plasma goes intoenergetic particles as result of diffusive shock acceleration 742

4.31.1. The problem of diffusive shock acceleration effectiveness 7424.31.2. Estimation of SEP and CME kinetic energies 7434.31.3. Main results of comparison 745

Conclusion and Problems 747

References 753References to Monographs and Books 753References to Chapter 1 757References to Chapter 2 766 'References to Chapter 3 V 793 :

References to Chapter 4 801

Object Index 821

Author Index 831