LEADER 08079nam 22004333 450 001 9910878068603321 005 20240802080341.0 010 $a9789819975242$b(electronic bk.) 010 $z9789819975235 035 $a(MiAaPQ)EBC31572187 035 $a(Au-PeEL)EBL31572187 035 $a(CKB)33566469100041 035 $a(EXLCZ)9933566469100041 100 $a20240802d2024 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElectron-Photon Cascades $eA Probabilistic Point of View 205 $a1st ed. 210 1$aSingapore :$cSpringer Singapore Pte. Limited,$d2024. 210 4$dİ2024. 215 $a1 online resource (510 pages) 225 1 $aNonlinear Physical Science Series 311 08$aPrint version: Uchaikin, Vladimir V. Electron-Photon Cascades Singapore : Springer Singapore Pte. Limited,c2024 9789819975235 327 $aIntro -- Preface -- Contents -- 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). 327 $a6.2.2 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 Longitudinal Moment Method -- 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 LPM Effect -- 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 ? -- 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. 327 $a9.8 Scintillation and Ionization Chambers -- 9.9 Transition Effect in Electromagnetic Calorimetry -- 9.10 Determination of the pi?-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. 327 $a12.7 Fluctuations in the Cherenkov Light Amplitude -- 12.8 Time Structure of the Cherenkov Signal -- 12.9 Cherenkov Image of EPC -- References -- 13 Relativistic EPC in Intergalactic Medium -- 13.1 Introduction -- 13.2 The Ivanenko-Sizov Theory -- 13.3 EPC From Monoenergetic Source -- 13.4 EPC in Monochromatic Photon Field -- 13.5 Variational Analysis -- 13.6 EPC in Magnetic Fields -- References -- 14 Cascade Ages, Similarity, Universality, and All That -- 14.1 Longitudinal Parameterizations and Uncertainties -- 14.2 EAS with Respect to the Shower Age -- 14.3 Lateral Distribution Fitting -- 14.4 The TAP-LAP Analysis -- 14.5 Space-Time Similarity Relations in Inclined Air Showers -- References -- Appendix A Method of Integral Transformations -- A.1 The Laplace Transformation -- A.2 The Inversion of Transformation -- A.3 The Fourier Transformation -- A.4 Spherical Harmonics and Legendre Polynomials -- A.5 The Mellin Transformation -- A.6 Relation to Laplace and Fourier Transformations -- A.7 Integral Representation of the Series -- Appendix B An Excerpt From Ivanenko-Roganova Book -- Appendix C A Few Images From Prof. Ivanenko Scientific Group Archiv -- Index -- Author Index. 410 0$aNonlinear Physical Science Series 676 $a539.756 700 $aUchaikin$b Vladimir V$0520680 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910878068603321 996 $aElectron-Photon Cascades$94196851 997 $aUNINA