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 azimuthal symmetry 483

3.15.4. Results of numerical calculations 486

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

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

3.16.2. Basic equations and their solutions 490

3.16.3. Summary of main results 494

Chapter 4. Cosmic Ray Acceleration in Space Plasmas 495

4.1. Acceleration particles in space plasmas as universal phenomenon in the Universe 495

4.2. The Fermi mechanism of statistical acceleration 497

4.3. Development of the Fermi model: head-on and overtaking collisions 499

4.3.1. Non-relativistic case 499

4.3.2. Relativistic case 500

4.4. Development of the Fermi model: inclusion of oblique collisions 502

4.4.1. Non-relativistic case 502

4.4.2. Relativistic case 507

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

4.5.1. The expected variations of the acceleration mechanism parameters as a particles gain energy 510

4.5.2. 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 X and u on energy 511

4.5.3. Particle acceleration and formation of the spectrum in relativistic energy range including the variations in the parameters X and u with total particle energy E increasing 514

4.5.4. The nature of the constraint of the accelerated particle's energy 516

4.6. Formation of the particle rigidity spectrum during statistical acceleration 518

4.6.1. General remarks and basic relations 518

4.6.2. Non-relativistic range; X and u are independent of R 519

4.6.3. Non-relativistic case; Xand u are functions of R 521

4.6.4. Relativistic range; X and u are independent of R 529

4.6.5. Relativistic range; X and u are functions of R 532

4.7. Statistical acceleration by scattering on small angles 535

4.7.1. Small-angle scattering 535

4.7.2. Energy gain in head-on collisions in non-relativistic case for small angle scatterings 538

4.7.3. Energy change in non-relativistic case for oblique collisions 540

4.7.4. Energy change in relativistic case 543

4.7.5. The mode of particle energy change in time 543

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

4.8.1. Injection energy in the statistical acceleration mechanism 544

4.8.2. The injection from background plasma: conditions for acceleration of all particles 545

4.8.3. The injection from background plasma: quasi-stationary acceleration of a small part of the particles 546

4.8.4. The problem of injection and acceleration of heavy nuclei from background plasma 546

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

4.9.1. The magnetic field effect on plasma turbulence 548

4.9.2. Particle acceleration by plasma fluctuations 548

4.9.3. Acceleration by magneto-sound and Alfven waves 549

4.9.4. Cyclotron acceleration of ions by plasma waves 550

4.9.5. Cyclotron acceleration of ions by the combination frequency 550

4.9.6. Acceleration by electron plasma waves 551

4.9.7. Acceleration by nonlinear waves 551

4.9.8. Acceleration by electrostatic waves 552

4.9.9. Stochastic Fermi acceleration by the turbulence with circularly polarized Alfven waves 553

4.10. Statistical acceleration of particles by electromagnetic radiation 553

4.10.1. Effectiveness of charged particle acceleration by electromagnetic radiation;

comparison with the Fermi mechanism 553

4.10.2. On the injection in the particle acceleration by radiation 554

4.10.3. On the maximum energy and maximum density of accelerated particles in the case of particle acceleration by radiation 554

4.10.4. Cyclotron acceleration of relativistic electrons by lateral waves 555

4.10.5. Electron acceleration by the radiation during their induced Compton scattering 555

4.10.6. Acceleration of charged particles by electromagnetic radiation pressure 556

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

4.11.1. Alfren's idea of particles acceleration by magnetic pumping 557

4.11.2. Relative change of the momentum, energy, and rigidity ofparticles in a single cycle of magnetic field variation in the presence of scattering 558

4.11.3. The rate of the gain in energy and rigidity for the mechanism of acceleration by magnetic pumping 561

4.11.4. Formation of the energy and rigidity spectra in the case of particle acceleration by magnetic pumping 563

4.11.5. Formation of the particle spectrum in the magnetic pumping mechanism including absorption in the source 565

4.11.6. The magnetic pumping mechanism in the case of field variations according to the power law 566

4.11.7. Kinetic theory of particle acceleration by magnetic pumping 566

4.12. Accelerated particle flux from sources 570

4.12.1. Particle flux from a source in stationary case 570

4.12.2. Particle flux from the source in non-stationary case 571

4.12.3. Accelerated particles in the space beyond the stationary sources 571

4.12.4. The accelerated particle spectrum beyond non-stationary sources 572

4.13. Induction acceleration mechanisms 574

4.13.1. The discussion on the problem of induction acceleration mechanisms 574

4.13.2. Charged particle acceleration up to very high CR energies by rotating magnetized neutron star 575

4.13.3. On the maximal energy of accelerated particles from fast rotated magnetic star 578

4.13.4. On the expected energy spectrum and total flux of accelerated particles from fast rotated magnetic star 579

4.14. Particle acceleration by moving magnetic piston 580

4.14.1. Acceleration and deceleration at a single interaction of particles with magnetic piston 580

4.14.2. Acceleration and deceleration of particles at the multiple interactions with magnetic piston 581

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

4.15.1. Acceleration for single passage of a laterally incident particle (the shock front is unlimited) 582

4.15.2. Acceleration in a single passage of a transversely incident particle (the shock front is limited) 585

4.15.3. Exact integration of the particle motion equations for an oblique incidence of a non-relativistic particle onto a shock front 585

4.15.4. Particle acceleration by a transverse shock wave at v >> u in general case (including oblique incidence of particles) 586

4.15.5. Particle acceleration by oblique shock waves 589

4.15.6. Particle acceleration by rotational discontinuities 592

4.15.7. Particle acceleration at a multiple reflection from a shock wave front 595

4.16. Acceleration of particles in case of magnetic collapse and compression 604

4.16.1. Non-relativistic case of particle acceleration during magnetic collapse 604

4.16.2. Relativistic case of particle acceleration during magnetic collapse 606

4.16.3. The case ofparticle acceleration from very low energies up to relativistic energies 607

4.16.4. The particle injection conditions for acceleration in a magnetic trap 609

4.16.5. Diffusive compression acceleration of charged particles 610

4.16.6. Acceleration at fluid compressions and comparison with shock acceleration 613

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

4.17.1. Injection-less acceleration ofparticles and the mechanism of magnetic field annihilation 619

4.17.2. Current sheets and rapid rearrangement of magnetic fields 620

4.17.3. A development of magnetic field annihilation models and the model of magnetic force line reconnection; on the role of discharge phenomena in some astrophysical processes and particle acceleration 626

4.17.4. Particle acceleration in the neutral current sheets 628

4.17.5. 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 mechanisms of solar flares, turbulence, percolation and particle acceleration 630

4.18.1. The problem of solar flare origin, particle acceleration and ejection into solar wind 630

4.18.2. The prominence channel of flares 631

4.18.3. Non-evolutionary channels of triggering of the prominence type of flares 633

4.18.4. The coronal channel of flares 633

4.18.5. Powerful proton flares 636

4.18.6. The problem ofparticle acceleration in the current layer of solar flares 637

4.18.7. The spatial diffusion in the electric field of the sheet in the case of two-dimensional geometry with pure anti-parallel magnetic field 639

4.18.8. The spatial diffusion in the electric field of the sheet in the case of three-dimensional geometry 640

4.18.9. Comparison of the quasi-diffusive acceleration and stochastic acceleration on the Langmuir plasmons 642

4.18.10. On the chemical composition of accelerated particles 642

4.18.11. Development of solar flare models and mechanisms ofparticle 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 646

4.18.13. Acceleration of particles in a fragmented turbulent current sheet 648

4.19. Particle acceleration in shear flows of space plasma 650

4.19.1. Space plasma's shear flows in different objects 650

4.19.2. Particle acceleration in the two-dimensional shear flow ofcollisionless plasma 650

4.19.3. Some examples ofpossible particle acceleration in shear flows 652

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

4.20.1. Two types of scatters in space plasma as additional source of particle acceleration 653

4.20.2. General theory of CR propagation and acceleration in space plasma with two types of scatters moving with different velocities 653

4.20.3. The diffusion approximation 654

4.20.5. Space-homogeneous situation 656

4.20.6. Estimation ofpossible additional acceleration of CR particles in the Galaxy 657

4.20.7. Estimation ofpossible additional acceleration of CR particles in the region of galaxies collision 658

4.20.8. Estimation ofpossible additional acceleration of CR particles in the Heliosphere and in stellar winds 658

4.20.9. On the effectiveness of additional particle acceleration in the double star systems 659

4.20.10. Main results on the mechanism of CR particle additional acceleration and applications 660

4.21. Shock wave diffusion (regular) acceleration 661

4.21.1. Two types of particle interaction with shock wave 661

4.21.2. Elementary model of diffusive shock-wave acceleration 661

4.21.3. Acceleration by the plane shock wave; diffusion approximation 664

4.21.4. The case of particle injection by mono-energetic spectrum 665

4.21.5. On the space distribution of accelerated particles 665

4.21.6. The effect of finite width of shock wave front 665

4.21.7. Effect of finite dimension of shock wave 666

4.21.8. Effect of energy losses during particle shock acceleration 667

4.21.9. Simultaneously regular and statistical acceleration 669

4.21.10. Regular acceleration by spherical shock wave 672

4.21.11. Acceleration by spherical standing shock wave in the solar or stellar wind 672

4.21.12. Acceleration by spherical standing shock wave in the case of accretion 675

4.21.13. Acceleration by spherical running shock wave 677

4.21.14. Effects of finite duration shock acceleration 680

4.21.15. CR acceleration at quasi-parallel plane shocks (numerical simulations) 684

4.22. Simplified 'box' models of shock acceleration 688

4.22.1. Principles of 'box' models of shock acceleration 688

4.22.2. Physical interpretation of the 'box' model 689

4.22.3. Inclusion of additional loss processes 690

4.22.4. Including nonlinear effects in the 'box' model 691

4.22.5. Main peculiarities of 'box' models 692

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

4.23.1. Bulk CR transport in space plasma and diffusive shock wave acceleration 693

4.23.2. Simulating CR particle acceleration in shocks modified by CR non-linear effects 695

4.24. Thermal particle injection in nonlinear diffusive shock acceleration 698

4.24.1. Comparison semi-analytical and Monte Carlo models 698

4.24.2. Injection models 699

4.24.3. Models of momentum dependent diffusion 699

4.24.4. Thermalization 700

4.24.5. Main results for both models and comparison 700

4.25. Time evolution of CR modified MHD shocks 703

4.25.1. The matter of problem 703

4.25.2. Methods of calculations 704

4.25.3. Main results and discussion 706

4.26. Particle injection and acceleration at non-parallel shocks 709

4.26.1. The matter of problem 709

4.26.2. Analytical considerations 710

4.26.3. Numerical calculations for test-particle simulations 712

4.26.4. Numerical calculations for self-consistent hybrid simulations 714

4.27. Numerical studies of diffusive shock acceleration at spherical shocks 715

4.27.1. The matter of problem 715

4.27.2. Comoving spherical grid 716

4.27.3. Numerical models and results 717

4.28. Particle acceleration by the electrostatic shock waves 720

4.28.1. Formation of electrostatic shock waves in space plasma 720

4.28.2. The two-dimensional simulation model 721

4.28.3. Generated electric and magnetic fields, and particle acceleration (results of simulation) 722

4.29. Particle acceleration by relativistic shock waves 725

4.29.1. Peculiarities of particle acceleration by relativistic shock waves 725

4.29.2. First-order Fermi particle acceleration at relativistic shock waves with a 'realistic'

magnetic field turbulence model 725

4.29.3. Particle acceleration at parallel relativistic shocks in the presence of finite-amplitude magnetic field perturbations 728

4.29.4. Electron acceleration in parallel relativistic shocks with finite thickness 730

4.29.5. Small-angle scattering and diffusion: application to relativistic shock acceleration 734

4.30. CR acceleration at super-luminal shocks 737

4.30.1. The matter of the problem 737

4.30.2. Monte Carlo simulations 738

4.30.3. Main results 739

4.30.4. 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 into energetic particles as result of diffusive shock acceleration 742

4.31.1. The problem of diffusive shock acceleration effectiveness 742

4.31.2. Estimation of SEP and CME kinetic energies 743

4.31.3. Main results of comparison 745

Conclusion and Problems 747

References 753

References to Monographs and Books 753

References to Chapter 1 757

References to Chapter 2 766

References to Chapter 3 793

References to Chapter 4 801

Object Index 821

Author Index

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