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Extreme Physics

Book Description

Most matter in the Universe, from the deep interior of planets to the core of stars, is at high temperature or high pressure compared to the matter of our ordinary experience. This book offers a comprehensive introduction to the basic physical theory on matter at such extreme conditions and the mathematical modeling techniques involved in numerical simulations of its properties and behavior. Focusing on computational modeling, the book discusses topics such as the basic properties of dense plasmas; ionization physics; the physical mechanisms by which laser light is absorbed in matter; radiation transport in matter; the basics of hydrodynamics and shock-wave formation and propagation; and numerical simulation of radiation-hydrodynamics phenomenology. End-of-chapter exercises allow the reader to test their understanding of the material and introduce additional physics, making this an invaluable resource for researchers and graduate students in this broad and interdisciplinary area of physics.

Table of Contents

  1. Coverpage
  2. Extreme physics
  3. Title page
  4. Copyright page
  5. Contents
  6. Acknowledgments
  7. 1 Extreme environments: What, where, how
    1. 1.1 Background, definitions, and assumptions
      1. 1.1.1 Background
      2. 1.1.2 Definitions
      3. 1.1.3 Assumptions
    2. 1.2 Elements of the extreme physics environment
      1. 1.2.1 Classifications
      2. 1.2.2 Environments
    3. 1.3 Scope of the physics
    4. 1.4 How to achieve extreme conditions
      1. 1.4.1 Lasers and accelerators
      2. 1.4.2 Z-pinches, flyers, rail guns, and gas guns
    5. 1.5 Example problems and exercises
  8. 2 Properties of dense and classical plasma
    1. 2.1 Kinetic theory
      1. 2.1.1 The distribution function
      2. 2.1.2 The Maxwell–Boltzmann distribution function
      3. 2.1.3 Electron degeneracy and the Fermi–Dirac distribution function
    2. 2.2 Electron–ion collisions
      1. 2.2.1 Coulomb collisions
      2. 2.2.2 Relaxation times
    3. 2.3 Collective plasma effects
      1. 2.3.1 Debye shielding and quasi-neutrality
      2. 2.3.2 Electron plasma frequency and plasma waves
    4. 2.4 Example problems and exercises
  9. 3 Laser energy absorption in matter
    1. 3.1 Maxwell's equations and electromagnetic wave propagation
    2. 3.2 Laser energy deposition at high laser intensities
      1. 3.2.1 Inverse bremsstrahlung absorption
      2. 3.2.2 Resonance absorption
      3. 3.2.3 Ponderomotive force and ablation pressure
    3. 3.3 Laser energy deposition at low laser intensities
    4. 3.4 Laser energy deposition at very low laser intensities
      1. 3.4.1 Conductivity and skin depth
      2. 3.4.2 Electromagnetic wave absorption in metals
      3. 3.4.3 Absorption in dielectrics and tamped ablation
    5. 3.5 Example problems and exercises
  10. 4 Hydrodynamic motion
    1. 4.1 Derivation of Navier–Stokes equations
      1. 4.1.1 Continuum flux
      2. 4.1.2 Conservation relations
      3. 4.1.3 Lagrangian derivative
      4. 4.1.4 Scaling and self-similarity
    2. 4.2 Compression and rarefaction waves
      1. 4.2.1 Acoustic waves, sound speed
      2. 4.2.2 Characteristics of the flow
      3. 4.2.3 Compression waves and shock fronts
      4. 4.2.4 Rarefaction waves and rarefaction shocks
    3. 4.3 Hydrodynamic instabilities
      1. 4.3.1 Rayleigh–Taylor instability
      2. 4.3.2 Stabilization mechanisms
      3. 4.3.3 Kelvin–Helmholtz and Bell–Plesset
      4. 4.3.4 Non-linear growth and turbulence
    4. 4.4 Example problems and exercises
  11. 5 Shocks
    1. 5.1 Rankine–Hugoniot equations
      1. 5.1.1 Jump conditions
      2. 5.1.2 Shocks in an ideal gas
    2. 5.2 Shocks at boundaries and interfaces
      1. 5.2.1 Reflected shocks and Mach stems
      2. 5.2.2 Shocks at interfaces and the Richtmyer–Meshkov instability
      3. 5.2.3 Emergence of shocks at a free surface
    3. 5.3 Structure of the shock front
      1. 5.3.1 Entropy and adiabaticity
      2. 5.3.2 Viscosity and heat conduction
    4. 5.4 Blast waves
    5. 5.5 Shocks in solids
      1. 5.5.1 Elastic–plastic behavior and material strength
      2. 5.5.2 Material constitutive models
      3. 5.5.3 Solid-state Rayleigh–Taylor instability
    6. 5.6 Example problems and exercises
  12. 6 Equation of state
    1. 6.1 Basic thermodynamic relations
    2. 6.2 EOS for gases and plasmas
      1. 6.2.1 EOS for monatomic gases
      2. 6.2.2 Two-temperature EOS for plasmas
      3. 6.2.3 Thomas–Fermi model
    3. 6.3 EOS for solids and liquids
      1. 6.3.1 Grüneisen EOS
      2. 6.3.2 EOS for porous solids
      3. 6.3.3 Phase transitions
    4. 6.4 Example problems and exercises
  13. 7 Ionization
    1. 7.1 Electron structure of atoms
      1. 7.1.1 The Bohr atom
      2. 7.1.2 Quantum electronic energy levels
    2. 7.2 Ionization models
      1. 7.2.1 Saha
      2. 7.2.2 Pressure ionization and continuum lowering
      3. 7.2.3 Thomas–Fermi
      4. 7.2.4 Hydrogenic average-atom
    3. 7.3 Example problems and exercises
  14. 8 Thermal energy transport
    1. 8.1 Thermal energy transport equation
      1. 8.1.1 Linear heat conduction
      2. 8.1.2 Non-linear heat conduction
    2. 8.2 Conductivity coefficients
    3. 8.3 Inhibited thermal transport
    4. 8.4 Electron–ion energy exchange
    5. 8.5 Electron degeneracy effects
    6. 8.6 Coulomb logarithms
    7. 8.7 Example problems and exercises
  15. 9 Radiation energy transport
    1. 9.1 Radiation as a fluid and the Planck distribution function
    2. 9.2 Radiation flux
      1. 9.2.1 The equations of motion with radiation flux
      2. 9.2.2 Absorption and emission
      3. 9.2.3 Principle of detailed balance
      4. 9.2.4 The radiation transfer equation
    3. 9.3 Solutions of the radiation transfer equation
      1. 9.3.1 Pn and SN
      2. 9.3.2 The diffusion approximation
      3. 9.3.3 Marshak waves and hohlraums
    4. 9.4 Material opacity
      1. 9.4.1 Models for material opacity
      2. 9.4.2 Averaging over photon frequencies
    5. 9.5 Non-LTE radiation transport
    6. 9.6 Radiation-dominated hydrodynamics
    7. 9.7 Example problems and exercises
  16. 10 Magnetohydrodynamics
    1. 10.1 Plasma electrodynamics
    2. 10.2 Equations of magnetohydrodynamics
      1. 10.2.1 Induction equation
      2. 10.2.2 Momentum equation
      3. 10.2.3 Thermal conduction equations
      4. 10.2.4 1D cylindrically symmetric equations
      5. 10.2.5 Magnetic energy
    3. 10.3 Generalized Ohm's law
    4. 10.4 Magnetic reconnection
    5. 10.5 Magnetic confinement
      1. 10.5.1 The Z-pinch
      2. 10.5.2 The θ-pinch
      3. 10.5.3 The screw pinch
    6. 10.6 Example problems and exercises
  17. 11 Considerations for constructing radiation-hydrodynamics computer codes
    1. 11.1 Radiation-hydrodynamics computer codes
    2. 11.2 Code development philosophy and architecture
    3. 11.3 Structure of PDEs
      1. 11.3.1 Hyperbolic equations
      2. 11.3.2 Parabolic equations
      3. 11.3.3 Elliptic equations
    4. 11.4 Finite-difference approximation
      1. 11.4.1 Computational grid
      2. 11.4.2 Partial derivatives
      3. 11.4.3 Partial differential equations
      4. 11.4.4 Solution of tridiagonal systems
      5. 11.4.5 Accuracy, convergence, consistency, and stability
      6. 11.4.6 Operator splitting
    5. 11.5 Example problems and exercises
  18. 12 Numerical simulations
    1. 12.1 Lagrangian hydrodynamics
      1. 12.1.1 Momentum equation
      2. 12.1.2 Stability of the momentum equation
      3. 12.1.3 Shocks and artificial viscosity
      4. 12.1.4 The energy equation and thermal transport
    2. 12.2 Code verification
      1. 12.2.1 Non-linear electron thermal transport
      2. 12.2.2 Shock propagation
    3. 12.3 Code validation
  19. Appendix I Units and constants, glossary of symbols
  20. Appendix II The elements
  21. Appendix III Physical properties of select materials
  22. References
  23. Further reading
  24. Index