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17002 results

Page 179 of 851

  • 1 - Introduction

  • Jon Larsen
  • Book:
    Foundations of High-Energy-Density Physics
    Published online:
    06 April 2017
    Print publication:
    10 March 2017, pp 1-8
    • Chapter
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Relativistic Kinetic Theory
  • With Applications in Astrophysics and Cosmology
  • Gregory V. Vereshchagin, Alexey G. Aksenov
  • Published online:
    09 March 2017
    Print publication:
    16 February 2017
  • Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neutrino emission during the gravitational collapse.

What Goes Up... Gravity and Scientific Method
  • Peter Kosso
  • Published online:
    02 March 2017
    Print publication:
    20 January 2017
  • The concept of gravity provides a natural phenomenon that is simultaneously obvious and obscure; we all know what it is, but rarely question why it is. The simple observation that 'what goes up must come down' contrasts starkly with our current scientific explanation of gravity, which involves challenging and sometimes counterintuitive concepts. With such extremes between the plain and the perplexing, gravity forces a sharp focus on scientific method. Following the history of gravity from Aristotle to Einstein, this clear account highlights the logic of scientific method for non-specialists. Successive theories of gravity and the evidence for each are presented clearly and rationally, focusing on the fundamental ideas behind them. Using only high-school level algebra and geometry, the author emphasizes what the equations mean rather than how they are derived, making this accessible for all those curious about gravity and how science really works.

Planetesimals
  • Early Differentiation and Consequences for Planets
  • Edited by Linda T. Elkins-Tanton, Benjamin P. Weiss
  • Published online:
    25 February 2017
    Print publication:
    26 January 2017
  • Processes governing the evolution of planetesimals are critical to understanding how rocky planets are formed, how water is delivered to them, the origin of planetary atmospheres, how cores and magnetic dynamos develop, and ultimately, which planets have the potential to be habitable. Theoretical advances and new data from asteroid and meteorite observations, coupled with spacecraft missions such as Rosetta and Dawn, have led to major advances in this field over the last decade. This transdisciplinary volume presents an authoritative overview of the latest in our understanding of the processes of planet formation. Combining meteorite, asteroid and icy body observations with theory and modelling of accretion and orbital dynamics, this text also provides insights into the exoplanetary system and the search for habitable worlds. This is an essential reference for those interested in planetary formation, solar system dynamics, exoplanets and planetary habitability.

  • 9 - Electrostatic Waves in a Hot Unmagnetized Plasma

  • Donald A. Gurnett, University of Iowa, Amitava Bhattacharjee, Princeton University, New Jersey
  • Book:
    Introduction to Plasma Physics
    Published online:
    16 March 2017
    Print publication:
    20 February 2017, pp 319-377

  • Summary

    An analysis of electrostatic waves in a hot unmagnetized plasma is presented. Two approaches are discussed. The first, based on the Vlasov equation and using the same Fourier normal-mode analysis presented in Chapter 4, fails because it does not adequately account for the interaction of the wave with particles moving at the phase velocity of the wave. This approach is replaced by an analysis that treats the problem as an initial-value problem using Laplace transforms. This method succeeds and shows that electrostatic waves decay via a completely new process called “Landau damping.” The existence of this damping is surprising because the Vlasov equation has no irreversible process that would lead to damping. The resolution of this paradox is discussed and involves a resonant transfer of the wave energy to particles with velocities near the phase velocity of the wave. Applications to various types of electrostatic instabilities are given, including waves driven by electron beams and other types of unstable velocity distribution functions.

  • 1 - Introduction

  • Donald A. Gurnett, University of Iowa, Amitava Bhattacharjee, Princeton University, New Jersey
  • Book:
    Introduction to Plasma Physics
    Published online:
    16 March 2017
    Print publication:
    20 February 2017, pp 1-3

  • Summary

    A plasma is an ionized gas consisting of positively and negatively charged particles with approximately equal charge densities. Plasmas can be produced by heating an ordinary gas to such a high temperature that the random kinetic energy of the molecules exceeds the ionization energy. Collisions then strip some of the electrons from the atoms, forming a mixture of electrons and ions. Because the ionization process starts at a fairly well-defined temperature, usually a few thousand K, a plasma is often referred to as the “fourth” state of matter. Plasmas can also be produced by exposing an ordinary gas to energetic photons, such as ultraviolet light or X-rays. The steady-state ionization density depends on a balance between ionization and recombination. In order to maintain a high degree of ionization, either the ionization source must be very strong, or the plasma must be very tenuous so that the recombination rate is low.

    The definition of a plasma requires that any deviation from charge neutrality must be very small. For simplicity, unless stated otherwise, we will assume that the ions are singly charged. The charge neutrality condition is then equivalent to requiring that the electron and ion number densities be approximately the same. In the absence of a loss mechanism, the overall charge neutrality assumption is usually satisfied because all ionization processes produce equal amounts of positive and negative charge. However, deviations from local charge neutrality can occur. Usually these deviations are small, since as soon as a charge imbalance develops, large electric fields are produced that act to restore charge neutrality. Systems that display large deviations from charge neutrality, such as vacuum tubes and various electronic devices, are not plasmas, even though some aspects of their physics are similar.

    In the most common type of plasma, the charged particles are in an unbound gaseous state. This requirement can be made more specific by requiring that the random kinetic energy be much greater than the average electrostatic energy, and is imposed to provide a distinction between a plasma, in which the particles move relatively freely, and condensed matter, such as metals, where electrostatic forces play a dominant role.

  • 10 - Waves in a Hot Magnetized Plasma

  • Donald A. Gurnett, University of Iowa, Amitava Bhattacharjee, Princeton University, New Jersey
  • Book:
    Introduction to Plasma Physics
    Published online:
    16 March 2017
    Print publication:
    20 February 2017, pp 378-427

  • Summary

    An extension of the Landau analysis method presented in Chapter 9 is given to waves propagating in hot magnetized plasmas. The analysis presented reveals an entirely new category of both electrostatic and electromagnetic waves that propagate near harmonics of the electron and ion cyclotron frequencies. These waves are called “Bernstein modes.” For certain types of velocity distribution functions these and other previously analyzed modes, such the whistler mode, can become unstable. Especially notable for being unstable are velocity distribution functions that are rotationally anisotropic with respect to the static magnetic field, such as the loss cone in a planetary radiation belt. Such waves often cause violations of the adiabatic invariants (as in Chapter 3), and cause pitch-angle scattering that leads to the loss of particles from planetary radiation belts. Similar processes also occur for magnetically confined laboratory plasmas.

  • 11 - Nonlinear Effects

  • Donald A. Gurnett, University of Iowa, Amitava Bhattacharjee, Princeton University, New Jersey
  • Book:
    Introduction to Plasma Physics
    Published online:
    16 March 2017
    Print publication:
    20 February 2017, pp 428-478

  • Summary

    An analysis is given of various types of nonlinear effects that can occur in plasmas. The topics covered are quasi-linear theory, wave-wave interactions, Langmuir wave solitons, and stationary nonlinear electrostatic potentials. Quasi-linear theory describes how an electrostatic wave driven by an unstable velocity distribution function causes the velocity distribution function to evolve in such a way that it eliminates the instability. The discussion of wave-wave interactions describes how a wave can nonlinearly interact with another wave to produce a third wave at either the sum or difference of the frequencies of the two interacting waves. The section on Langmuir wave solitons describes how a very intense single wave can alter the initial local plasma density in such a way as to form intense isolated wave structure known as a solitons. The section on stationary electrostatic potentials shows how highly nonlinear self-consistent electrostatic structures can form in otherwise time-stationary plasmas. Although there are many other nonlinear processes that can occur, these examples provide a good overview of the methods used to analyze these effects.

Page 179 of 851