前辅文
1 Introduction
References
2 Basic Concepts of Cascade Theory
2.1 The General Scheme of the Cascade Process
2.2 Mathematical Expectation of a Measurand
2.3 Multiparticle Densities
2.4 Fluctuations of a Functional from a Random Measure
2.5 Characteristic and Generating Functionals
2.6 Interrelations Between Multiparticle Densities
References
3 Forward (Basic) Equation for CP
3.1 The Generating Functional
3.2 Equations for GF
3.3 One-Particle Direct Equations
3.4 Multiparticle Direct Equations
3.5 Green’s Function
3.6 The Diagrammatic Representation
3.7 Dynamics of Correlation Forms
References
4 Backward (Adjoint) Equation
4.1 Processes with a Single-Particle Initial State
4.2 Backward Equations for GFs and Multiparticle Densities
4.3 Multiparticle Importance Functions
4.4 Adjoint Equations and Adjoint Functions
4.5 The Perturbation Theory
4.6 Fluctuations and Correlations in Linear Functionals
4.7 Equations for Moments and Distribution of a Linear Functional
4.8 Fluctuations in an Arbitrary Additive Functional
References
5 Electrons and Photons
5.1 Photon Birth (Classical Sketch)
5.2 Electromagnetic Field Operators
5.3 Bremsstrahlung (Quantum Sketch)
5.4 Compton Scattering
5.5 Photo Absorption and Pair Production
5.6 Continuous Energy Loss Model
5.7 Electron Multiple Scattering
5.7.1 Energy Losses and Straggling (After Bohr)
5.7.2 Fluctuations in Energy Losses (After Landau)
5.7.3 The Link with the Generalized Limit Theorem
5.7.4 The Angular Distribution (After Fermi)
5.8 Electron–Photon Cascades
5.9 Cascade Equations in Mellin’s Transforms
References
6 Analytical Theory
6.1 Basic Equation of EPC Theory
6.2 Cascade Curves
6.2.1 Electron Cascade Curve (From Primary Electron)
6.2.2 Electron Cascade Curve (From Primary Photon)
6.3 Degradation Spectrum Problem
6.3.1 Electron Energy Degradation Spectrum
6.3.2 Photon Energy Degradation Spectrum
6.3.3 On Accuracy of Degradation Spectra
6.4 LongitudinalMomentMethod
6.4.1 Cascade Curve Phenomenology
6.4.2 Cascade Curves’ Reconstruction
6.5 Including Electron Scattering
6.6 Beyond Small-Angle Approximation
6.7 Nishimura–Kamata Theory
References
7 SBCE Method
7.1 Lagrange Polynomial Interpolation
7.2 Straight-Ahead Equation System
7.3 Solving Straight-Ahead System
7.4 Integral Terms in SBCE for Statistical Moments
7.5 Some Details in Bremsstrahlung Term
7.6 The SBCE Results Review
7.6.1 The Total Electron Trace Length in an Infinite Medium
7.6.2 Cascade Curves
7.6.3 Particle Number Fluctuations
7.6.4 Cherenkov Radiation in Atmosphere
7.6.5 LPMEffect
7.7 Small-Angle Approximation
7.8 Angular Electron Distributions
7.9 Lateral Electron Distribution
References
8 Statistical Fluctuations in EPC
8.1 Fluctuations in Electron Number
8.2 The Electron Total Trace Length
8.3 Fluctuations of Electron Path in a Layer
8.4 On the First Free Path in EPC Fluctuations
8.5 Random Moments Method (Longitudinal Development)
8.5.1 Fluctuations in Cascade Curves
8.5.2 Correlations in Cascade Curves
8.5.3 Moment Covariance Matrix Equation
8.5.4 Some Parameter Estimations
8.5.5 On the Detector Reading Probability Distribution
8.6 Transverse Random Moments
References
9 Cascades in Calorimeters
9.1 The Transition Effects
9.2 The Perturbation Theory Formulas
9.3 Adjoint Functions for Transition Effect
9.4 Flux Perturbation by Boundaries
9.5 Belenky’s Comment of the Transition Effect
9.6 Transition Effect at Shower Maximum
9.7 Total Particle Flux at a Boundary
9.8 Scintillation and Ionization Chambers
9.9 Transition Effect in Electromagnetic Calorimetry
9.10 Determination of the π-Meson Beam Composition
References
10 Monte Carlo Modeling
10.1 Introduction
10.2 Random Numbers
10.3 Non-branching Trajectory in a Homogeneous Medium
10.4 The Measured Characteristics of Particle Transport
10.5 Non-analog Simulations of Detector Response
10.6 Non-analog Simulation of Trajectories
10.7 The Variance of Estimators
10.8 Examples of Weight MC Modifications
10.9 Weighting Estimation of Correlations in Branching Processes
10.9.1 Equations for the Distribution Function and Its Moments
10.9.2 The First Moment Modified Estimation
10.9.3 Some Examples
10.9.4 The Modified Estimation of the Second Moment
10.10 AEGIS Code
References
11 Stochastic Phenomenology of EAS
11.1 EAS Structure
11.2 Multiple Process Models
11.3 Parametric Sensitivity Analysis
11.4 Functional Sensitivity Analysis
11.5 Solving Equations for Second Moments
11.6 EAS Covariance Matrix
11.7 Inelasticity and Multiplicity Fluctuations
11.8 Two-Component Model of Fluctuations
References
12 Cherenkov Radiation of EPC
12.1 Radiation in a Homogeneous Medium (B-Approximation)
12.2 Cherenkov Radiation in Water (Monte Carlo)
12.3 Cherenkov Radiation in Atmosphere
12.4 ALTAI Code
12.4.1 Electromagnetic Cascade
12.4.2 Emission of Cherenkov Light
12.4.3 Hadron-Nuclei Cascade
12.4.4 Nucleus-Nucleus Interactions
12.4.5 Comparison with Other Codes and Data
12.5 Semianalytical Monte Carlo Method
12.5.1 The SAMC Philosophy
12.5.2 Equations for Equivalent Sources
12.5.3 Sampling From the Equivalent Source
12.5.4 Primary-Energy Correction
12.5.5 The SAMC Errors and CTMC Estimation
12.6 The Lateral Light Distribution
12.7 Fluctuations in the Cherenkov Light Amplitude
12.8 Time Structure of the Cherenkov Signal
12.9 Cherenkov Image of EPC
References
13 Relativistic EPC in Intergalactic Medium
13.1 Introduction
13.2 The Ivanenko–Sizov Theory
13.3 EPC From Monoenergetic Source
13.4 EPC in Monochromatic Photon Field
13.5 Variational Analysis
13.6 EPC in Magnetic Fields
References
14 Cascade Ages, Similarity, Universality, and All That
14.1 Longitudinal Parameterizations and Uncertainties
14.2 EAS with Respect to the Shower Age
14.3 Lateral Distribution Fitting
14.4 The TAP-LAP Analysis
14.5 Space–Time Similarity Relations in Inclined Air Showers
References
Appendix A: Method of Integral Transformations
Appendix B: An Excerpt From Ivanenko–Roganova Book
Appendix C: A Few Images From Prof. Ivanenko Scientific Group Archiv
Index
Author Index
