{"product_id":"foundations-of-plasma-physics-for-physicists-and-mathematicians-isbn-9781119774259","title":"Foundations of Plasma Physics for Physicists and Mathematicians","description":"\u003cp\u003e\u003cb\u003eA comprehensive textbook on the foundational principles of plasmas, including material on advanced topics and related disciplines such as optics, fluid dynamics, and astrophysics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFoundations of Plasma Physics for Physicists and Mathematicians\u003c\/i\u003e covers the basic physics underlying plasmas and describes the methodology and techniques used in both plasma research and other disciplines such as optics and fluid mechanics. Designed to help readers develop physical understanding and mathematical competence in the subject, this rigorous textbook discusses the underlying theoretical foundations of plasma physics as well as a range of specific problems, focused on those principally associated with fusion.\u003c\/p\u003e \u003cp\u003eReflective of the development of plasma physics, the text first introduces readers to the collective and collisional behaviors of plasma, the single particle model, wave propagation, the kinetic effects of gases and plasma, and other foundational concepts and principles. Subsequent chapters cover topics including the hydrodynamic limit of plasma, ideal magneto-hydrodynamics, waves in MHD plasmas, magnetically confined plasma, and waves in magnetized hot and cold plasma. Written by an acknowledged expert with more than five decades’ active research experience in the field, this authoritative text:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIdentifies and emphasizes the similarities and differences between plasmas and fluids\u003c\/li\u003e \u003cli\u003eDescribes the different types of interparticle forces that influence the collective behavior of plasma\u003c\/li\u003e \u003cli\u003eDemonstrates and stresses the importance of coherent and collective effects in plasma\u003c\/li\u003e \u003cli\u003eContains an introduction to interactions between laser beams and plasma\u003c\/li\u003e \u003cli\u003eIncludes supplementary sections on the basic models of low temperature plasma and the theory of complex variables and Laplace transforms\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eFoundations of Plasma Physics for Physicists and Mathematicians\u003c\/i\u003e is the ideal textbook for advanced undergraduate and graduate students in plasma physics, and a valuable compendium for physicists working in plasma physics and fluid mechanics.\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Fundamental Plasma Parameters – Collective Behaviour 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 Cold Plasma Waves 2\u003c\/p\u003e \u003cp\u003e1.2.1 Wave Breaking 3\u003c\/p\u003e \u003cp\u003e1.3 Debye Shielding 4\u003c\/p\u003e \u003cp\u003e1.3.1 Weakly and Strongly Coupled Plasmas 6\u003c\/p\u003e \u003cp\u003e1.3.2 The Plasma Parameter 7\u003c\/p\u003e \u003cp\u003e1.4 Diffusion and Mobility 8\u003c\/p\u003e \u003cp\u003e1.4.1 Einstein–Smoluchowski Relation 8\u003c\/p\u003e \u003cp\u003e1.4.2 Ambipolar Diffusion 9\u003c\/p\u003e \u003cp\u003e1.5 Wall Sheath 9\u003c\/p\u003e \u003cp\u003e1.5.1 Positively Biased Wall 10\u003c\/p\u003e \u003cp\u003e1.5.2 Free Fall Sheath 10\u003c\/p\u003e \u003cp\u003e1.5.2.1 Pre-sheath 11\u003c\/p\u003e \u003cp\u003e1.5.3 Mobility Limited Sheath 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fundamental Plasma Parameters – Collisional Behaviour 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Electron Scattering by Ions 13\u003c\/p\u003e \u003cp\u003e2.1.1 Binary Collisions – Rutherford Cross Section 13\u003c\/p\u003e \u003cp\u003e2.1.2 Momentum Transfer Cross Section 15\u003c\/p\u003e \u003cp\u003e2.1.2.1 Dynamical Friction and Diffusion 16\u003c\/p\u003e \u003cp\u003e2.1.3 Many Body Collisions – Impulse Approximation 16\u003c\/p\u003e \u003cp\u003e2.1.4 Relaxation Times 20\u003c\/p\u003e \u003cp\u003e2.2 Collisional Transport Effects 21\u003c\/p\u003e \u003cp\u003e2.2.1 Random Walk Model for Transport Effects 22\u003c\/p\u003e \u003cp\u003e2.2.2 Maxwell’s Mean Free Path Model of Transport Phenomena 23\u003c\/p\u003e \u003cp\u003e2.2.2.1 Flux Limitation 25\u003c\/p\u003e \u003cp\u003e2.2.3 Drude Model of Electrical Conductivity 26\u003c\/p\u003e \u003cp\u003e2.2.3.1 Alternating Electric Field, No Magnetic Field 27\u003c\/p\u003e \u003cp\u003e2.2.3.2 Steady Electric Field, Finite Magnetic Field 27\u003c\/p\u003e \u003cp\u003e2.2.3.3 Oscillatory Electric Field, Finite Magnetic Field 28\u003c\/p\u003e \u003cp\u003e2.2.4 Diffusivity and Mobility in a Uniform Magnetic Field 29\u003c\/p\u003e \u003cp\u003e2.3 Plasma Permittivity 30\u003c\/p\u003e \u003cp\u003e2.3.1 Poynting’s Theorem – Energy Balance in an Electro-magnetic Field 31\u003c\/p\u003e \u003cp\u003e2.4 Plasma as a Fluid – Two Fluid Model 32\u003c\/p\u003e \u003cp\u003e2.4.1 Waves in Plasma 33\u003c\/p\u003e \u003cp\u003e2.4.2 Beam Instabilities 36\u003c\/p\u003e \u003cp\u003e2.4.2.1 Plasma Bunching 36\u003c\/p\u003e \u003cp\u003e2.4.2.2 Two Stream Instability 36\u003c\/p\u003e \u003cp\u003e2.4.3 Kinematics of Growing Waves 37\u003c\/p\u003e \u003cp\u003eAppendix 2.A Momentum Transfer Collision Rate 39\u003c\/p\u003e \u003cp\u003eAppendix 2.B The Central Limit Theorem 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Single Particle Motion – Guiding Centre Model 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 43\u003c\/p\u003e \u003cp\u003e3.2 Motion in Stationary and Uniform Fields 44\u003c\/p\u003e \u003cp\u003e3.2.1 Static Uniform Magnetic Field – Cyclotron Motion 44\u003c\/p\u003e \u003cp\u003e3.2.2 Uniform Static Electric and Magnetic Fields 45\u003c\/p\u003e \u003cp\u003e3.3 The Guiding Centre Approximation 45\u003c\/p\u003e \u003cp\u003e3.3.1 The Method of Averaging 46\u003c\/p\u003e \u003cp\u003e3.3.2 The Guiding Centre Model for Charged Particles 48\u003c\/p\u003e \u003cp\u003e3.4 Particle Kinetic Energy 51\u003c\/p\u003e \u003cp\u003e3.5 Motion in a Static Inhomogeneous Magnetic Field 52\u003c\/p\u003e \u003cp\u003e3.5.1 Field Gradient Drift 53\u003c\/p\u003e \u003cp\u003e3.5.2 Curvature Drift 53\u003c\/p\u003e \u003cp\u003e3.5.3 Divergent Field Lines 55\u003c\/p\u003e \u003cp\u003e3.5.4 Twisted Field Lines 55\u003c\/p\u003e \u003cp\u003e3.6 Motion in a Time Varying Magnetic Field 56\u003c\/p\u003e \u003cp\u003e3.7 Motion in a Time Varying Electric Field 56\u003c\/p\u003e \u003cp\u003e3.8 Collisional Drift 58\u003c\/p\u003e \u003cp\u003e3.9 Plasma Diamagnetism 58\u003c\/p\u003e \u003cp\u003e3.10 Particle Trapping and Magnetic Mirrors 59\u003c\/p\u003e \u003cp\u003e3.10.1 Fermi Acceleration 61\u003c\/p\u003e \u003cp\u003e3.11 Adiabatic Invariance 61\u003c\/p\u003e \u003cp\u003e3.12 Adiabatic Invariants of Charged Particle Motions 63\u003c\/p\u003e \u003cp\u003eAppendix 3.A Northrop’s Expansion Procedure 64\u003c\/p\u003e \u003cp\u003e3.A.1 Drift Velocity and Longitudinal Motion along the Field Lines 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Kinetic Theory of Gases 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 67\u003c\/p\u003e \u003cp\u003e4.2 Phase Space 68\u003c\/p\u003e \u003cp\u003e4.2.1 Γ Phase Space 68\u003c\/p\u003e \u003cp\u003e4.2.1.1 Liouville’s Equation 69\u003c\/p\u003e \u003cp\u003e4.2.2 \u003ci\u003e𝜇\u003c\/i\u003eSpace 70\u003c\/p\u003e \u003cp\u003e4.3 Relationship Between Γ Space and \u003ci\u003e𝜇\u003c\/i\u003eSpace 71\u003c\/p\u003e \u003cp\u003e4.3.1 Integrals of the Liouville Equation 72\u003c\/p\u003e \u003cp\u003e4.4 The BBGKY (Bogoliubov–Born–Green–Kirkwood–Yvon) Hierarchy 73\u003c\/p\u003e \u003cp\u003e4.5 Bogoliubov’s Hypothesis for Dilute Gases 74\u003c\/p\u003e \u003cp\u003e4.6 Derivation of the Boltzmann Collision Integral from the BBGKY Hierarchy 76\u003c\/p\u003e \u003cp\u003e4.7 Boltzmann Collision Operator 78\u003c\/p\u003e \u003cp\u003e4.7.1 Summation Invariants 79\u003c\/p\u003e \u003cp\u003e4.8 Boltzmann’s H Theorem 79\u003c\/p\u003e \u003cp\u003e4.9 The Equilibrium Maxwell–Boltzmann Distribution 80\u003c\/p\u003e \u003cp\u003e4.9.1 Entropy and the \u003ci\u003eH \u003c\/i\u003efunction 81\u003c\/p\u003e \u003cp\u003e4.10 Hydrodynamic Limit – Method of Moments 81\u003c\/p\u003e \u003cp\u003e4.10.1 Conservation of Mass 83\u003c\/p\u003e \u003cp\u003e4.10.2 Conservation of Momentum 83\u003c\/p\u003e \u003cp\u003e4.10.3 Conservation of Energy 84\u003c\/p\u003e \u003cp\u003e4.11 The Departure from Steady Homogeneous Flow: The Chapman–Enskog Approximation 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Wave Propagation in Inhomogeneous, Dispersive Media 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 89\u003c\/p\u003e \u003cp\u003e5.2 Basic Concepts of Wave Propagation – The Geometrical Optics Approximation 90\u003c\/p\u003e \u003cp\u003e5.3 The WKB Approximation 92\u003c\/p\u003e \u003cp\u003e5.3.1 Oblique Incidence 93\u003c\/p\u003e \u003cp\u003e5.4 Singularities in Waves 93\u003c\/p\u003e \u003cp\u003e5.4.1 Cut-off or Turning Point 94\u003c\/p\u003e \u003cp\u003e5.4.2 Resonance Point 96\u003c\/p\u003e \u003cp\u003e5.4.3 Resonance Layer and Collisional Damping 99\u003c\/p\u003e \u003cp\u003e5.5 The Propagation of Energy 100\u003c\/p\u003e \u003cp\u003e5.5.1 Group Velocity of Waves in Dispersive Media 100\u003c\/p\u003e \u003cp\u003e5.5.2 Waves in Dispersive Isotropic Media 101\u003c\/p\u003e \u003cp\u003e5.6 Group Velocity of Waves in Anisotropic Dispersive Media 102\u003c\/p\u003e \u003cp\u003e5.6.1 Equivalence of Energy Transport Velocity and Group Velocity 106\u003c\/p\u003e \u003cp\u003eAppendix 5.A Waves in Anisotropic Inhomogeneous Media 107\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Kinetic Theory of Plasmas – Collisionless Models 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 111\u003c\/p\u003e \u003cp\u003e6.2 Vlasov Equation 111\u003c\/p\u003e \u003cp\u003e6.3 Particle Trapping by a Potential Well 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Kinetic Theory of Plasmas 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 121\u003c\/p\u003e \u003cp\u003e7.2 The Fokker–Planck Equation – The Stochastic Approach 122\u003c\/p\u003e \u003cp\u003e7.2.1 The Scattering Integral for Coulomb Collisions 124\u003c\/p\u003e \u003cp\u003e7.3 The Fokker–Planck Equation – The Landau Equation 128\u003c\/p\u003e \u003cp\u003e7.3.1 Application to Collisions between Charged Particles 130\u003c\/p\u003e \u003cp\u003e7.4 The Fokker–Planck Equation – The Cluster Expansion 131\u003c\/p\u003e \u003cp\u003e7.4.1 The Balescu–Lenard Equation 132\u003c\/p\u003e \u003cp\u003e7.5 Relaxation of a Distribution to the Equilibrium Form 135\u003c\/p\u003e \u003cp\u003e7.5.1 Isotropic Distribution 135\u003c\/p\u003e \u003cp\u003e7.5.2 Anisotropic Distribution 137\u003c\/p\u003e \u003cp\u003e7.6 Ion–Electron Thermal Equilibration by Coulomb Collisions 139\u003c\/p\u003e \u003cp\u003e7.7 Dynamical Friction 140\u003c\/p\u003e \u003cp\u003eAppendix 7.A Reduction of the Boltzmann Equation to Fokker–Planck Form in the Weak Collision Limit 142\u003c\/p\u003e \u003cp\u003eAppendix 7.B Finite Difference Algorithm for Integrating the Isotropic Fokker–Planck Equation 144\u003c\/p\u003e \u003cp\u003eAppendix 7.C Monte Carlo Algorithm for Integrating the Fokker–Planck Equation 145\u003c\/p\u003e \u003cp\u003eAppendix 7.D Landau’s Calculation of the Electron–Ion Equilibration Rate 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Hydrodynamic Limit for Plasma 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction – Individual Particle Fluid Equations 149\u003c\/p\u003e \u003cp\u003e8.2 The Departure from Steady, Homogeneous Flow: The Transport Coefficients 150\u003c\/p\u003e \u003cp\u003e8.3 Magneto-hydrodynamic Equations 151\u003c\/p\u003e \u003cp\u003e8.3.1 Equation of Mass Conservation 151\u003c\/p\u003e \u003cp\u003e8.3.2 Equation of Momentum Conservation 152\u003c\/p\u003e \u003cp\u003e8.3.3 Virial Theorem 154\u003c\/p\u003e \u003cp\u003e8.3.4 Equation of Current Flow 154\u003c\/p\u003e \u003cp\u003e8.3.5 Equation of Energy Conservation 155\u003c\/p\u003e \u003cp\u003e8.4 Transport Equations 156\u003c\/p\u003e \u003cp\u003e8.4.1 Collision Times 157\u003c\/p\u003e \u003cp\u003e8.4.2 Symmetry of the Transport Equations 158\u003c\/p\u003e \u003cp\u003e8.5 Two Fluid MHD Equations – Braginskii Equations 161\u003c\/p\u003e \u003cp\u003e8.5.1 Magnetic Field Equations 162\u003c\/p\u003e \u003cp\u003e8.5.1.1 Energy Balance 164\u003c\/p\u003e \u003cp\u003e8.6 Transport Coefficients 165\u003c\/p\u003e \u003cp\u003e8.6.1 Collisional Dominated Plasma 165\u003c\/p\u003e \u003cp\u003e8.6.1.1 Force Terms F 165\u003c\/p\u003e \u003cp\u003e8.6.1.2 Energy Flux Terms 165\u003c\/p\u003e \u003cp\u003e8.6.1.3 Viscosity 166\u003c\/p\u003e \u003cp\u003e8.6.2 Field-Dominated Plasma 166\u003c\/p\u003e \u003cp\u003e8.6.2.1 Force Terms F 166\u003c\/p\u003e \u003cp\u003e8.6.2.2 Energy Flux Terms 167\u003c\/p\u003e \u003cp\u003e8.6.2.3 Viscosity 168\u003c\/p\u003e \u003cp\u003e8.7 Calculation of the Transport Coefficients 168\u003c\/p\u003e \u003cp\u003e8.8 Lorentz Approximation 170\u003c\/p\u003e \u003cp\u003e8.8.1 Electron–Electron Collisions 173\u003c\/p\u003e \u003cp\u003e8.8.2 Electron Runaway 174\u003c\/p\u003e \u003cp\u003e8.9 Deficiencies in the Spitzer\/Braginskii Model of Transport Coefficients 177\u003c\/p\u003e \u003cp\u003eAppendix 8.A BGK Model for the Calculation of Transport Coefficients 178\u003c\/p\u003e \u003cp\u003e8.A.1 BGK Conductivity Model 178\u003c\/p\u003e \u003cp\u003e8.A.2 BGK Viscosity Model 180\u003c\/p\u003e \u003cp\u003eAppendix 8.B The Relationship Between the Flux Equations Given By Shkarofsky and Braginskii 181\u003c\/p\u003e \u003cp\u003eAppendix 8.C Electrical Conductivity in a Weakly Ionised Gas and the Druyvesteyn Distribution 182\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Ideal Magnetohydrodynamics 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Infinite Conductivity MHD Flow 188\u003c\/p\u003e \u003cp\u003e9.1.1 Frozen Field Condition 189\u003c\/p\u003e \u003cp\u003e9.1.2 Adiabatic Equation of State 190\u003c\/p\u003e \u003cp\u003e9.1.3 Pressure Balance 191\u003c\/p\u003e \u003cp\u003e9.1.3.1 Virial Theorem 191\u003c\/p\u003e \u003cp\u003e9.2 Incompressible Approximation 192\u003c\/p\u003e \u003cp\u003e9.2.1 Bernoulli’s Equation – Steady Flow 192\u003c\/p\u003e \u003cp\u003e9.2.2 Kelvin’s Theorem – Circulation 193\u003c\/p\u003e \u003cp\u003e9.2.3 Alfvén Waves 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Waves in MHD Fluids 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 197\u003c\/p\u003e \u003cp\u003e10.2 Magneto-sonic Waves 198\u003c\/p\u003e \u003cp\u003e10.3 Discontinuities in Fluid Mechanics 203\u003c\/p\u003e \u003cp\u003e10.3.1 Classical Fluids 203\u003c\/p\u003e \u003cp\u003e10.3.2 Discontinuities in Magneto-hydrodynamic Fluids 204\u003c\/p\u003e \u003cp\u003e10.4 The Rankine–Hugoniot Relations for MHD Flows 205\u003c\/p\u003e \u003cp\u003e10.5 Discontinuities in MHD Flows 206\u003c\/p\u003e \u003cp\u003e10.6 MHD Shock Waves 207\u003c\/p\u003e \u003cp\u003e10.6.1 Simplifying Frame Transformations 207\u003c\/p\u003e \u003cp\u003e10.7 Properties of MHD Shocks 208\u003c\/p\u003e \u003cp\u003e10.7.1 Shock Hugoniot 208\u003c\/p\u003e \u003cp\u003e10.7.2 Shock Adiabat – General Solution for a Polytropic Gas 209\u003c\/p\u003e \u003cp\u003e10.8 Evolutionary Shocks 212\u003c\/p\u003e \u003cp\u003e10.8.1 Evolutionary MHD Shock Waves 213\u003c\/p\u003e \u003cp\u003e10.8.2 Parallel Shock – Magnetic Field Normal to the Shock Plane 214\u003c\/p\u003e \u003cp\u003e10.9 Switch-on and Switch-off Shocks 216\u003c\/p\u003e \u003cp\u003e10.10 Perpendicular Shock – Magnetic Field Lying in the Shock Plane 217\u003c\/p\u003e \u003cp\u003e10.11 Shock Structure and Stability 218\u003c\/p\u003e \u003cp\u003eAppendix 10.A Group Velocity of Magneto-sonic Waves 218\u003c\/p\u003e \u003cp\u003eAppendix 10.B Solution in de Hoffman–Teller Frame 220\u003c\/p\u003e \u003cp\u003e10.B.1 Parallel Shocks 222\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Waves in Cold Magnetised Plasma 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 223\u003c\/p\u003e \u003cp\u003e11.2 Waves in Cold Plasma 223\u003c\/p\u003e \u003cp\u003e11.2.1 Cut-off and Resonance 226\u003c\/p\u003e \u003cp\u003e11.2.2 Polarisation 227\u003c\/p\u003e \u003cp\u003e11.3 Cold Plasma Waves 227\u003c\/p\u003e \u003cp\u003e11.3.1 Zero Applied Magnetic Field 227\u003c\/p\u003e \u003cp\u003e11.3.2 Low Frequency Velocity Waves 228\u003c\/p\u003e \u003cp\u003e11.3.3 Propagation of Waves Parallel to the Magnetic Field 229\u003c\/p\u003e \u003cp\u003e11.3.4 Propagation of Waves Perpendicular to the Magnetic Field 232\u003c\/p\u003e \u003cp\u003e11.3.5 Resonance in Plasma Waves 234\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Waves in Magnetised Warm Plasma 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Dielectric Properties of Unmagnetised Warm Dilute Plasma 237\u003c\/p\u003e \u003cp\u003e12.1.1 Plasma Dispersion Relation 238\u003c\/p\u003e \u003cp\u003e12.1.1.1 Dispersion Relation for Transverse Waves 239\u003c\/p\u003e \u003cp\u003e12.1.1.2 Dispersion Relation for Longitudinal Waves 239\u003c\/p\u003e \u003cp\u003e12.1.2 Dielectric Constant of a Plasma 239\u003c\/p\u003e \u003cp\u003e12.1.2.1 The Landau Contour Integration Around the Singularity 241\u003c\/p\u003e \u003cp\u003e12.2 Transverse Waves 243\u003c\/p\u003e \u003cp\u003e12.3 Longitudinal Waves 244\u003c\/p\u003e \u003cp\u003e12.4 Linear Landau Damping 245\u003c\/p\u003e \u003cp\u003e12.4.1 Resonant Energy Absorption 245\u003c\/p\u003e \u003cp\u003e12.5 Non-linear Landau Damping 248\u003c\/p\u003e \u003cp\u003e12.5.1 Particle Trapping 248\u003c\/p\u003e \u003cp\u003e12.5.2 Plasma Wave Breaking 250\u003c\/p\u003e \u003cp\u003e12.6 The Plasma Dispersion Function 252\u003c\/p\u003e \u003cp\u003e12.7 Positive Ion Waves 256\u003c\/p\u003e \u003cp\u003e12.7.1 Transverse Waves 256\u003c\/p\u003e \u003cp\u003e12.7.2 Longitudinal Waves 256\u003c\/p\u003e \u003cp\u003e12.7.2.1 Plasma Waves, \u003ci\u003e𝜁\u003c\/i\u003e\u003ci\u003ee \u0026gt; \u003c\/i\u003e1 257\u003c\/p\u003e \u003cp\u003e12.7.2.2 Ion Waves \u003ci\u003e𝜁\u003c\/i\u003e\u003ci\u003ee \u0026lt; \u003c\/i\u003e1 257\u003c\/p\u003e \u003cp\u003e12.8 Microscopic Plasma Instability 258\u003c\/p\u003e \u003cp\u003e12.8.1 Nyquist Plot 259\u003c\/p\u003e \u003cp\u003e12.8.1.1 Penrose’s Criterion 260\u003c\/p\u003e \u003cp\u003e12.9 The Dielectric Properties of Warm Dilute Plasma in a Magnetic Field 262\u003c\/p\u003e \u003cp\u003e12.9.1 Propagation Parallel to the Magnetic Field 269\u003c\/p\u003e \u003cp\u003e12.9.2 Propagation Perpendicular to the Magnetic Field 270\u003c\/p\u003e \u003cp\u003eAppendix 12.A Landau’s Solution of the Vlasov Equation 274\u003c\/p\u003e \u003cp\u003eAppendix 12.B Electrostatic Waves 276\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Properties of Electro-magnetic Waves in Plasma 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Plasma Permittivity and the Dielectric Constant 281\u003c\/p\u003e \u003cp\u003e13.1.1 The Properties of the Permittivity Matrix 284\u003c\/p\u003e \u003cp\u003e13.2 Plane Waves in Homogeneous Plasma 286\u003c\/p\u003e \u003cp\u003e13.2.1 Waves in Collisional Cold Plasma 287\u003c\/p\u003e \u003cp\u003e13.2.1.1 Isotropic Unmagnetised Plasma 287\u003c\/p\u003e \u003cp\u003e13.2.1.2 Anisotropic Magnetised Plasma 289\u003c\/p\u003e \u003cp\u003e13.3 Plane Waves Incident Obliquely on a Refractive Index Gradient 290\u003c\/p\u003e \u003cp\u003e13.3.1 Oblique Incidence at a Cut-off Point – Resonance Absorption 293\u003c\/p\u003e \u003cp\u003e13.3.1.1 s Polarisation 293\u003c\/p\u003e \u003cp\u003e13.3.1.2 p Polarisation 293\u003c\/p\u003e \u003cp\u003e13.4 Single Particle Model of Electrons in an Electro-magnetic Field 295\u003c\/p\u003e \u003cp\u003e13.4.1 Quiver Motion 295\u003c\/p\u003e \u003cp\u003e13.4.2 Ponderomotive Force 297\u003c\/p\u003e \u003cp\u003e13.4.3 The Impact Model for Collisional Absorption 298\u003c\/p\u003e \u003cp\u003e13.4.3.1 Electron–Electron Collisions 301\u003c\/p\u003e \u003cp\u003e13.4.4 Distribution Function of Electrons Subject to Inverse Bremsstrahlung Heating 301\u003c\/p\u003e \u003cp\u003e13.5 Parametric Instabilities 305\u003c\/p\u003e \u003cp\u003e13.5.1 Coupled Wave Interactions 305\u003c\/p\u003e \u003cp\u003e13.5.1.1 Manley–Rowe Relations 306\u003c\/p\u003e \u003cp\u003e13.5.1.2 Parametric Instability 307\u003c\/p\u003e \u003cp\u003e13.5.2 Non-linear Laser-Plasma Absorption 308\u003c\/p\u003e \u003cp\u003e13.5.2.1 Absorption Instabilities 309\u003c\/p\u003e \u003cp\u003e13.5.2.2 Reflection Instabilities 310\u003c\/p\u003e \u003cp\u003eAppendix 13.A Ponderomotive Force 310\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Laser–Plasma Interaction 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 313\u003c\/p\u003e \u003cp\u003e14.2 The Classical Hydrodynamic Model of Laser-Solid Breakdown 314\u003c\/p\u003e \u003cp\u003e14.2.1 Basic Parameters of Laser Breakdown 315\u003c\/p\u003e \u003cp\u003e14.2.2 The General Theory of the Interaction of Lasers with Solid Targets 316\u003c\/p\u003e \u003cp\u003e14.2.3 Distributed Heating – Low Intensity, Self-regulating Flow 318\u003c\/p\u003e \u003cp\u003e14.2.3.1 Early Time Self-similar Solution 319\u003c\/p\u003e \u003cp\u003e14.2.3.2 Late Time Steady-State Solution 319\u003c\/p\u003e \u003cp\u003e14.2.4 Local Heating – High Intensity, Deflagration Flow 321\u003c\/p\u003e \u003cp\u003e14.2.4.1 Early Time Thermal Front 321\u003c\/p\u003e \u003cp\u003e14.2.4.2 Late Time Steady-State Flow 323\u003c\/p\u003e \u003cp\u003e14.2.5 Additional Simple Analytic Models 324\u003c\/p\u003e \u003cp\u003e14.2.5.1 Short Pulse Heating 324\u003c\/p\u003e \u003cp\u003e14.2.5.2 Heating of Small Pellets – Homogeneous Self-similar Model 325\u003c\/p\u003e \u003cp\u003e14.3 Simulation of Laser-Solid Target Interaction 325\u003c\/p\u003e \u003cp\u003eAppendix 14.A Non-linear Diffusion 327\u003c\/p\u003e \u003cp\u003eAppendix 14.B Self-similar Flows with Uniform Velocity Gradient 329\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Magnetically Confined Plasma 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 337\u003c\/p\u003e \u003cp\u003e15.2 Equilibrium Plasma Configurations 337\u003c\/p\u003e \u003cp\u003e15.3 Linear Devices 338\u003c\/p\u003e \u003cp\u003e15.4 Toroidal Devices 340\u003c\/p\u003e \u003cp\u003e15.4.1 Pressure Balance 341\u003c\/p\u003e \u003cp\u003e15.4.1.1 Pressure Imbalance Mitigation 342\u003c\/p\u003e \u003cp\u003e15.4.2 Guiding Centre Drift 343\u003c\/p\u003e \u003cp\u003e15.5 The General Problem: The Grad–Shafranov Equation 344\u003c\/p\u003e \u003cp\u003e15.6 Boundary Conditions 345\u003c\/p\u003e \u003cp\u003e15.7 Equilibrium Plasma Configurations 347\u003c\/p\u003e \u003cp\u003e15.7.1 Perturbation Methods 348\u003c\/p\u003e \u003cp\u003e15.7.2 Analytical Solutions of the Grad–Shafranov Equation 349\u003c\/p\u003e \u003cp\u003e15.7.3 Numerical Solutions of the Grad–Shafranov Equation 350\u003c\/p\u003e \u003cp\u003e15.8 Classical Magnetic Cross Field Diffusion 351\u003c\/p\u003e \u003cp\u003e15.9 Trapped Particles and Banana Orbits 352\u003c\/p\u003e \u003cp\u003e15.9.1 Collisionless Banana Regime (\u003ci\u003e𝜈\u003c\/i\u003e∗ \u003ci\u003e≪\u003c\/i\u003e1) 354\u003c\/p\u003e \u003cp\u003e15.9.1.1 Diffusion in the Banana Regime 355\u003c\/p\u003e \u003cp\u003e15.9.1.2 Bootstrap Current (\u003ci\u003e𝜈\u003c\/i\u003e∗ \u003ci\u003e≪\u003c\/i\u003e1) 355\u003c\/p\u003e \u003cp\u003e15.9.2 Resistive Plasma Diffusion – Collisional Pfirsch–Schlüter Regime 356\u003c\/p\u003e \u003cp\u003e15.9.2.1 Pfirsch–Schlüter Current (\u003ci\u003e𝜈\u003c\/i\u003e∗ \u003ci\u003e≫\u003c\/i\u003e1) 357\u003c\/p\u003e \u003cp\u003e15.9.2.2 Diffusion in the Pfirsch–Sclüter Regime 357\u003c\/p\u003e \u003cp\u003e15.9.3 Plateau Regime 357\u003c\/p\u003e \u003cp\u003e15.9.4 Diffusion in Tokamak Plasmas 358\u003c\/p\u003e \u003cp\u003eAppendix 15.A Equilibrium Maintaining ‘Vertical’ Field 359\u003c\/p\u003e \u003cp\u003eAppendix 15.B Perturbation Solution of the Grad–Shafranov Equation 360\u003c\/p\u003e \u003cp\u003eAppendix 15.C Analytic Solutions of the Homogeneous Grad–Shafranov Equation 363\u003c\/p\u003e \u003cp\u003eAppendix 15.D Guiding Centre Motion in a Twisted Circular Toroidal Plasma 364\u003c\/p\u003e \u003cp\u003eAppendix 15.E The Pfirsch–Schlüter Regime 368\u003c\/p\u003e \u003cp\u003e15.E.1 Diffusion in the Pfirsch–Schlüter Regime 369\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Instability of an Equilibrium Confined Plasma 371\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 371\u003c\/p\u003e \u003cp\u003e16.2 Ideal MHD Instability 371\u003c\/p\u003e \u003cp\u003e16.2.1 Linearised Stability Equations 371\u003c\/p\u003e \u003cp\u003e16.2.2 Normal Mode Analysis – The Stability of a Cylindrical Plasma Column 375\u003c\/p\u003e \u003cp\u003e16.2.3 \u003ci\u003em \u003c\/i\u003e= 0 Sausage Instability 379\u003c\/p\u003e \u003cp\u003e16.2.4 \u003ci\u003em \u003c\/i\u003e= 1 Kink Instability 380\u003c\/p\u003e \u003cp\u003e16.3 Potential Energy 381\u003c\/p\u003e \u003cp\u003e16.4 Interchange Instabilities 382\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSupplementary Material 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eM.1 Breakdown and Discharges in d.c. Electric Fields 387\u003c\/p\u003e \u003cp\u003eM.1.1 Gas Breakdown and Paschen’s Law 387\u003c\/p\u003e \u003cp\u003eM.1.2 Similarity and Proper Variables 388\u003c\/p\u003e \u003cp\u003eM.1.3 Townsend’s First Coefficient 388\u003c\/p\u003e \u003cp\u003eM.1.4 Townsend’s Breakdown Criterion 389\u003c\/p\u003e \u003cp\u003eM.1.5 Paschen Curve and Paschen Minimum 389\u003c\/p\u003e \u003cp\u003eM.1.6 Radial Profile of Glow Discharge 390\u003c\/p\u003e \u003cp\u003eM.1.7 Collisional Ionisation Rate for Low Temperature Electrons 391\u003c\/p\u003e \u003cp\u003eM.1.8 Radio Frequency and Microwave Discharges 392\u003c\/p\u003e \u003cp\u003eM.2 Key Facts Governing Nuclear Fusion 393\u003c\/p\u003e \u003cp\u003eM.2.1 Fusion Rate 393\u003c\/p\u003e \u003cp\u003eM.2.2 Lawson’s Criterion 396\u003c\/p\u003e \u003cp\u003eM.2.3 Triple Product 398\u003c\/p\u003e \u003cp\u003eM.3 A Short Introduction to Functions of a Complex Variable 400\u003c\/p\u003e \u003cp\u003eM.3.1 Cauchy–Riemann Relations 401\u003c\/p\u003e \u003cp\u003eM.3.2 Harmonic Functions 402\u003c\/p\u003e \u003cp\u003eM.3.3 Area Rule 402\u003c\/p\u003e \u003cp\u003eM.3.4 Cauchy Integral Theorem 402\u003c\/p\u003e \u003cp\u003eM.3.5 Morera’s Theorem 403\u003c\/p\u003e \u003cp\u003eM.3.6 Analytic Continuation 403\u003c\/p\u003e \u003cp\u003eM.3.7 Extension or Contraction of a Contour 404\u003c\/p\u003e \u003cp\u003eM.3.8 Inclusion of Isolated Singularities 404\u003c\/p\u003e \u003cp\u003eM.3.9 Cauchy Formula 404\u003c\/p\u003e \u003cp\u003eM.3.9.1 Interior Domain 404\u003c\/p\u003e \u003cp\u003eM.3.9.2 Exterior Domain 405\u003c\/p\u003e \u003cp\u003eM.3.10 Treatment of Improper Integrals 405\u003c\/p\u003e \u003cp\u003eM.3.11 Sokhotski–Plemelj Theorem 406\u003c\/p\u003e \u003cp\u003eM.3.12 Improper Integral Along a Real Line 407\u003c\/p\u003e \u003cp\u003eM.3.13 Taylor and Laurent Series 407\u003c\/p\u003e \u003cp\u003eM.3.14 The Argument Principle 408\u003c\/p\u003e \u003cp\u003eM.3.15 Estimation Lemma 408\u003c\/p\u003e \u003cp\u003eM.3.16 Jordan’s Lemma 409\u003c\/p\u003e \u003cp\u003eM.3.17 Conformal Mapping 409\u003c\/p\u003e \u003cp\u003eM.4 Laplace Transform 410\u003c\/p\u003e \u003cp\u003eM.4.1 Bromwich Contour 410\u003c\/p\u003e \u003cp\u003eProblems 413\u003c\/p\u003e \u003cp\u003eBibliography 427\u003c\/p\u003e \u003cp\u003eIndex 437\u003c\/p\u003e \u003cp\u003e\u003cb\u003eGeoffrey J. Pert\u003c\/b\u003e is Emeritus Professor, Department of Physics, University of York, UK. He has continuously been involved in research in plasma physics, primarily the interaction of high-power lasers with materials, since first studying the subject as a research student in the 1960’s. Professor Pert is a Fellow of the Royal Society and has published more than 200 papers in scientific research journals. He is the author of \u003ci\u003eIntroduction to Fluid Mechanics\u003c\/i\u003e and the co-author of \u003ci\u003eAn Introduction to Computer Simulation\u003c\/i\u003e.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eA comprehensive textbook on the foundational principles of plasmas, including material on advanced topics and related disciplines such as optics, fluid dynamics, and astrophysics\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eFoundations of Plasma Physics for Physicists and Mathematicians\u003c\/i\u003e covers the basic physics underlying plasmas and describes the methodology and techniques used in both plasma research and other disciplines such as optics and fluid mechanics. Designed to help readers develop physical understanding and mathematical competence in the subject, this rigorous textbook discusses the underlying theoretical foundations of plasma physics as well as a range of specific problems, focused on those principally associated with fusion.\u003c\/p\u003e\u003cp\u003eReflective of the development of plasma physics, the text first introduces readers to the collective and collisional behaviors of plasma, the single particle model, wave propagation, the kinetic effects of gases and plasma, and other foundational concepts and principles. Subsequent chapters cover topics including the hydrodynamic limit of plasma, ideal magneto-hydrodynamics, waves in MHD plasmas, magnetically confined plasma, and waves in magnetized hot and cold plasma. Written by an acknowledged expert with more than five decades’ active research experience in the field, this authoritative text:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eIdentifies and emphasizes the similarities and differences between plasmas and fluids\u003c\/li\u003e\n\u003cli\u003eDescribes the different types of interparticle forces that influence the collective behavior of plasma\u003c\/li\u003e\n\u003cli\u003eDemonstrates and stresses the importance of coherent and collective effects in plasma\u003c\/li\u003e\n\u003cli\u003eContains an introduction to interactions between laser beams and plasma\u003c\/li\u003e\n\u003cli\u003eIncludes supplementary sections on the basic models of low temperature plasma and the theory of complex variables and Laplace transforms\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003ci\u003eFoundations of Plasma Physics for Physicists and Mathematicians\u003c\/i\u003e is the ideal textbook for advanced undergraduate and graduate students in plasma physics, and a valuable compendium for physicists working in plasma physics and fluid mechanics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989238726885,"sku":"NP9781119774259","price":117.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119774259.jpg?v=1761783330","url":"https:\/\/k12savings.com\/products\/foundations-of-plasma-physics-for-physicists-and-mathematicians-isbn-9781119774259","provider":"K12savings","version":"1.0","type":"link"}