Preface ........................................................ XI
Color Plates ................................................... XV
1 Observational Phenomena of Solar Flares ...................... 1
1.1 Observational Constraints ............................... 1
1.2 Hard X-Ray Light Curves and Spectra ..................... 1
1.2.1 Light Curves ..................................... 1
1.2.2 Photon and Electron Energy Spectra ............... 2
1.2.3 Electron Numbers ................................. 4
1.3 Light Curves and Energy Spectra of Gamma-Rays ........... 5
1.3.1 у-Ray Light Curves ............................... 5
1.3.2 Energy Spectra and Abundances of Ions in Flares .. 6
1.3.3 Ion Numbers ...................................... 6
1.4 Geometry of Hard X-Ray and Gamma-Ray Sources ............ 7
1.4.1 Differences in Footpoint Spectral Indices ........ 7
1.4.2 Hard X-Ray and Gamma-Ray Source Locations ........ 9
1.5 Pre- and Postflare Hard X-Ray and Radio Emission ........ 9
1.6 Magnetic Field Changes Associated with Flares .......... 11
1.6.1 Local Magnetic Field Variations ................. 11
1.7 UV and Optical Emission ................................ 15
1.8 Seismic Responses ...................................... 16
1.9 Critical Issues ........................................ 18
2 Particle Acceleration in Flares ............................. 21
2.1 Models of Particle Acceleration ........................ 21
2.1.1 Basic Physics ................................... 21
2.1.2 Magnetic Reconnection Models Associated with
Flares .......................................... 22
2.1.3 Particle Acceleration in a Reconnecting
Current Sheet ................................... 26
2.1.4 Particle Acceleration by Shocks and Turbulence .. 29
2.2 Recent Theoretical Developments ........................ 33
2.2.1 Stochastic Acceleration ......................... 33
2.2.2 Electron Acceleration in Collapsing Current
Sheets .......................................... 35
2.2.1 Particle Acceleration in a Single 3-D RCS with
Complicated Magnetic Topology ................... 40
2.2.4 Estimations of Accelerated Particle Parameters .. 46
2.2.5 Comparison of the Parameters of Accelerated
Particles ....................................... 48
2.2.6 Particle Acceleration in 3-D MHD Models with
Fan and Spine Reconnection ...................... 49
2.3 Limitations of the Test-Particle Approach .............. 54
2.3.1 The Polarization Electric Field ................. 55
2.3.2 Turbulent Electric Fields ....................... 55
2.4 Particle-in-Cell Simulation of Acceleration in a 3-D
RCS .................................................... 57
2.4.1 Problem Formulation ............................. 57
2.4.2 Test-Particle Simulations ....................... 60
2.4.3 PIC Simulation Results .......................... 62
2.5 Particle Acceleration in Collapsing Magnetic Islands ... 70
2.5.1 Tearing-Mode Instability in Current Sheets ...... 70
2.5.2 Particle Acceleration in Magnetic Islands -
PIC Approach .................................... 71
2.6 Limitations of the PIC Approach ........................ 74
2.7 Probing Theories versus Observations ................... 76
2.7.1 Interrelation between Acceleration and
Transport ....................................... 76
2.7.2 Testing Acceleration Models against
Observational Constraints ....................... 77
3 Electron-Beam Precipitation - Continuity Equation
Approach .................................................... 81
3.1 Introduction ........................................... 81
3.2 Particle Energy Losses ................................. 82
3.2.1 Particle Trajectories at Scattering ............. 82
3.2.2 Energy Loss and Momentum Variations ............. 84
3.3 Continuity Equation Approach for Electrons: Pure
Collisions ............................................. 92
3.3.1 Solutions of Continuity Equation for Power-Law
Beam Electrons .................................. 93
3.3.2 Beam Electron Densities ......................... 95
3.3.3 Mean Electron Spectra ........................... 96
3.3.4 Hard X-Ray Bremsstrahlung Emission by Beam
Electrons ....................................... 97
3.3.5 Heating Functions .............................. 102
3.4 Continuity Equation Approach for Electrons - Pure
Electric Field ........................................ 104
3.4.1 Estimation of the Ohmic Loss Effect ............ 105
3.4.2 Kinetic Solutions for a Pure Electric Field .... 109
3.4.3 Estimations of Electron-Beam Stability ......... 118
4 Electron Beam Precipitation - Fokker-Planck Approach ....... 121
4.1 General Comments on Particle and Energy Transport ..... 121
4.2 Problem Formulation ................................... 122
4.2.1 The Fokker-Planck Equation ..................... 122
4.2.2 Normalization of a Distribution Function ....... 124
4.2.3 Dimensionless Equations ........................ 125
4.2.4 Integral Characteristics of an Electron Beam ... 127
4.3 Simulation Method ..................................... 128
4.4 Stationary Fokker-Planck Approach (dƒ / dt = 0) ....... 129
4.4.1 Initial Condition .............................. 329
4.4.2 Beam Electron Distribution Functions ........... 130
4.4.3 Electron-Beam Density Variations with Depth .... 140
4.4.4 Mean Electron Fluxes ........................... 142
4.5 Time-Dependent Fokker-Planck Equation ................. 143
4.5.1 Initial and Boundary Conditions ................ 144
4.5.2 Relaxation to a Steady State ................... 145
4.6 Regime of a Stationary Injection ...................... 147
4.6.1 Distributions of Electron Beams with a Lower-
Energy Part .................................... 147
4.6.2 Variations of Electron-Beam Density ............ 153
4.6.3 Effects of Magnetic Field Convergence .......... 155
4.6.4 Mean Electron Fluxes of a Steady Beam .......... 159
4.6.5 Plasma Heating by a Stationary Beam in
Converging Magnetic Field ...................... 159
4.7 Impulsive Injection ................................... 161
4.7.1 Mean Electron Flux for Beam Impulse ............ 162
4.7.2 Energy Deposition by a Beam Impulse ............ 164
4.8 Conclusions ........................................... 167
5 Proton Beam Kinetics ....................................... 169
5.1 Proton Beam Distribution Function ..................... 169
5.1.1 Effect of Coulomb Collisions on Proton
Precipitation .................................. 369
5.1.2 Effect of a Self-Induced Electric Field on
Proton Precipitation ........................... 172
5.1.3 Effect of Magnetic Field Convergence on
Proton Precipitation ........................... 172
5.1.4 Effect of Wave-Proton Interaction .............. 172
5.1.5 Collisions versus Kinetic Alfven Waves: the
Effect on Proton Precipitation ................. 174
5.1.6 Fokker-Planck Equation for Proton Beams ........ 376
5.2 Precipitation of Proton Beam: Numerical Simulations ... 377
5.2.1 Numerical Calculation of Proton Beam
Distribution Function .......................... 377
5.2.2 Accepted Parameters ............................ 379
5.2.3 Proton Beam Distribution Functions ............. 379
5.3 General Discussion of Proton and Electron
Precipitation ......................................... 382
5.3.1 Beam Spectra at Precipitation .................. 182
5.3.2 Energy and Momentum Transfer ................... 182
6 Hydrodynamic Response to Particle Injection ................ 187
6.1 Hydrodynamic Equations ................................ 187
6.1.1 Additional Equations ........................... 188
6.1.2 Boundary Conditions ............................ 189
6.2 Hydrodynamic Responses to Heating by Electron Beams ... 190
6.2.1 The Heating Functions by High Energy
Particles ...................................... 190
6.2.2 Simulated Heating Functions .................... 190
6.2.3 Hydrodynamics Caused by Electron Beams ......... 192
6.2.4 Hydrodynamics Formed by Mixed Electron and
Proton Beams ................................... 197
6.2.5 Momenta Delivered by Beams and Hydrodynamic
Shocks ......................................... 199
6.2.6 Comparison of Ambient Heating by Electrons
and Protons for 28 October 2003 Flare .......... 200
6.3 Case Study of a Hydrodynamics of the 25 July 2004
Flare ................................................. 204
6.3.1 Observations ................................... 204
6.3.2 Hydrodynamics of Ambient Plasma ................ 211
6.4 Conclusions ........................................... 213
7 Hard X-Ray Bremsstrahlung Emission and Polarization ........ 215
7.1 Introduction .......................................... 215
7.2 Stokes Parameters for HXR Emission .................... 236
7.2.1 Geometry of Observations ....................... 217
7.2.2 Nonrelativistic HXR Cross-Sections ............. 219
7.2.3 Relativistic Angle-Dependent Cross-Sections .... 221
7.3 Simulation Results .................................... 223
7.3.1 Time-Dependent Hard X-Ray Photon Spectra for
a Short Impulse ................................ 223
7.3.2 HXR Emission with Nonrelativistic Cross-
Sections for Steady Injection .................. 224
7.3.3 HXR Emission with Relativistic Cross-Sections
for Steady Injection ........................... 229
7.3.4 HXR Bremsstrahlung Directivity and
Polarization for a Steady Beam Injection ....... 234
7.4 Comparison with Observations .......................... 239
7.4.1 HXR Bremsstrahlung Photon Spectra .............. 239
7.4.2 HXR Bremsstrahlung Directivity and
Polarization ................................... 241
7.4.3 Relationships between Electron and HXR Photon
Spectra and Electron Numbers ................... 244
8 Microwave Emission and Polarization ........................ 247
8.1 General Comments ...................................... 247
8.2 Evaluation of Models for Electron Precipitation ....... 249
8.3 Gyrosynchrotron Plasma Emissivity and Absorption
Coefficient ........................................... 251
8.4 Gyrosynchrotron Emission from a Homogeneous Source .... 253
8.4.1 Depth Variations of MW Emission ................ 253
8.4.2 Gyrosynchrotron Emission from a Whole Coronal
Magnetic Tube .................................. 260
8.5 Comparison with Observations .......................... 263
8.5.1 Flare of 23 July 2002 .......................... 263
8.5.2 Flare of 10 March 2001 ......................... 265
8.5.3 Simulated HXR and MW Emission .................. 270
8.6 Conclusion ............................................ 283
9 Langmuir Wave Generation by Electron Beams ................. 287
9.1 Electron Beams and Their Stability .................... 287
9.2 Basic Equations ....................................... 289
9.2.1 Method of Solution and Model Parameters ........ 290
9.3 Results and Discussion ................................ 291
9.3.1 Electric Field Effects on Langmuir Turbulence .. 291
9.4 Conclusions ........................................... 298
10 Nonthermal Hydrogen Emission Caused by Electron Beams ...... 301
10.1 Introduction .......................................... 301
10.2 Nonthermal Excitation and Ionization Rates ............ 302
10.2.1 Beam Electron Density .......................... 303
10.2.2 Nonthermal Hydrogen Excitation Rates ........... 304
10.2.3 Nonthermal Hydrogen Ionization Rates ........... 306
10.2.4 Comparison of Thermal and Nonthermal
Excitation and Ionization Rates ................ 306
10.3 Hydrogen Emission Produced by Impacts with Beam
Electrons ............................................. 307
10.3.1 Equations of Statistical Equilibrium ........... 309
10.3.2 Radiative Transfer Equations ................... 310
10.3.3 Conservation Equation for a Particle Number .... 311
10.3.4 Method of Solution ............................. 312
10.3.5 Accepted Parameters ............................ 313
10.4 Hydrogen Excitation and Ionization .................... 313
10.4.1 Comparison of Nonthermal and Thermal
Excitation and Ionization Rates ................ 313
10.4.2 Nonthermal Effects on Hydrogen Emission ........ 317
10.4.3 Hydrogen Radiative Losses in Flares ............ 322
10.4.4 Role of Backwarming Heating .................... 322
10.5 Interpretation of Hα Emission in 25 July 2004 Flare ... 324
10.5.1 Fast Changes of Hα Emission in the Main Flare
Event .......................................... 324
10.5.2 Temporal and Spatial Evolution of the Main
Flare Event .................................... 325
10.5.3 Resulting Hα Emission .......................... 328
11 Hα-Line Impact Polarization ................................ 331
11.1 Introduction .......................................... 331
11.2 Basic Models .......................................... 333
11.2.1 Physical Model ................................. 333
11.2.2 Kinetic Model .................................. 333
11.2.3 Radiative Model ................................ 334
11.3 Density Matrix Approach ............................... 336
11.3.1 Steady State Equation .......................... 336
11.3.2 Radiative Tensor ............................... 337
11.3.3 Collisional Tensor ............................. 338
11.3.4 Probabilities of Radiative Transitions ......... 338
11.3.5 Probabilities of Collisional Transitions ....... 339
11.3.6 Stokes Parameters .............................. 339
11.4 Results and Discussion ................................ 340
11.4.1 Hα-Line Polarization Profiles .................. 343
11.4.2 Depth and Time Variations of Hα-Line
Polarization ................................... 344
11.4.3 Interpretation of Observational Features ....... 345
11.5 Interpretation of Polarimetrie Hα Observations ........ 346
11.5.1 Revised Theoretical Model ...................... 349
11.5.2 Results of Observations ........................ 353
11.5.3 Observational Recommendations .................. 356
11.6 Conclusions ........................................... 357
12 Sunquakes Associated with Solar Flares ..................... 359
12.1 First Sunquake of 9 July 1996 Flare ................... 359
12.1.1 Methods of Sunquake Detection .................. 361
12.1.2 Results from First Sunquake Detection .......... 363
12.1.3 Discrepancies between the Parameters Derived
and the Basic Flare Theory ..................... 364
12.2 Observations of Other Sunquakes ....................... 365
12.3 Sunquakes Associated with the Flare of 28 October
2003 .................................................. 367
12.3.1 Hard X-Ray, у-Ray Emission, and Accelerated
Particles in the Earth's Orbit ................ 368
12.3.2 Observed Seismic Sources ...................... 371
12.3.3 Comparison of Momenta Delivered by Beams and
Hydrodynamic Shocks ........................... 376
12.4 Seismic Sources Observed by GONG in 14 December 2006
Flare ................................................. 378
12.4.1 Flare Morphology and Evolution ................. 379
12.4.2 Photospheric and Chromospheric Signatures for
the 14 December 2006 Flare ..................... 379
12.4.3 Photospheric Velocities ........................ 380
12.5 Observations of Solar Interior ........................ 381
12.5.1 Validation of Time-Distance Analysis with
GONG ........................................... 383
12.5.2 Helioseismic Results ........................... 383
12.5.3 Summary of Observed Signatures in Sunquakes .... 387
12.6 Theoretical Implications of Particle Kinetics and
Dynamics Leading to Sunquakes ......................... 388
12.6.1 Topology of Particle Acceleration .............. 388
12.6.2 Particle Precipitation ......................... 389
12.6.3 Plasma Responses to High-Energy Particles ...... 391
12.7 Nonthermal Ionization and Backwarming Heating ......... 395
12.7.1 Hydrogen Nonthermal Excitation and Ionization .. 395
12.7.2 The Role of Backwarming Heating ................ 396
12.7.3 Ni-Line Emission ............................... 397
12.7.4 Generation of Seismic Response by a Pinpoint
Source ......................................... 401
12.7.5 Magnetic Field Change During Flares ............ 402
12.8 Conclusion ............................................ 404
References ................................................. 407
Index ......................................................... 419
|
