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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 model used 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

2.33.3. Kinetic coefficients and transport mean free paths 309

2.33.4. 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 ofparticle 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 problem 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 ofpredicted SEP intensity time variation with NM observations 367

2.43.4. The checking of the model by comparison ofpredicted 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 >106 and >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. Nonlinear Cosmic Ray Effects in Space Plasmas 405

3.1. The important role of nonlinear CR effects in many processes and objects in space

3.2. Effects of CR pressure

3.3. Effects of CR kinetic stream instability

3.4. On the structure and evolution of CR-space plasma systems

3.4.1. Principles of hydrodynamic approach to the CR-space plasma nonlinear system

3.4.2. Four-fluid model for description CR-plasma system

3.4.3. Steady state profiles of the CR-plasma system

3.5. Nonlinear AlfVén waves generated by CR streaming instability

3.5.1. Possible damping mechanisms for Alfvén turbulence generated by CR streaming instability 3.5.2 Basic equations described the nonlinear Alfvén wave damping rate in presence of thermal collisions

3.5.3. On the possible role of nonlinear damping saturation in the CR-plasma systems

3.6. Interplanetary CR modulation, possible structure of the Heliosphere and expected CR nonlinear effects

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

3.6.2. Long - term CR spectrum modulation in the Heliosphere

3.6.3. CR anisotropy in the Heliosphere

3.6.4. Possible structure of the Heliosphere and expected nonlinear effects

3.6.5. Studies of the termination shock and heliosheath at > 92 AU: Voyager 1 magnetic field measurements

3.7. Radial CR pressure effects in the Heliosphere

3.7.1. On a necessity of including non-linear large-scale effects in studies ofpropagation of solar and galactic CR in interplanetary space

3.7.2. Radial braking of solar wind and CR modulation: effect of galactic CR pressure

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

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 are investigations of Heliosphere's termination shock 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

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