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3653 results in ebooks in fluid mechanics

Page 49 of 183

  • 6 - Magnetohydrodynamics

  • 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 186-220

  • Summary

    The field known as magnetohydrodynamics (MHD) dates to the earliest days of plasma physics and assumes that a plasma is a charged conducting fluid that responds to electromagnetic fields governed by Maxwell’s equations. Since this fluid approach ignores cyclotron motions, the MHD model is valid only at low frequencies, well below the lowest ion cyclotron frequency, and at large spatial scales, much larger than the largest ion cyclotron radius. In this chapter we show that, except for an Ohm’s law conductivity that relates the current to the electric field, all of the basic MHD equations can be derived from the moment equations given in Chapter 5. An approximate conductivity equation, called the “generalized Ohm’s law,” is derived that relates charges and current in the plasma to the large scale electric and magnetic fields. Equations are also derived showing that the magnetic field produces an anisotropic pressure that adds to the plasma pressure, and that the magnetic field lines cab be “frozen” into the plasma if the conductivity is sufficiently large.

  • 8 - Discontinuities and Shock Waves

  • 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 281-318

  • Summary

    Discontinuities are a common feature of plasmas, especially in space and astrophysical applications where large spatial scales are involved. These discontinuities arise from a process called “wave steepening,” wherein nonlinear effects cause a wave to steepen into a discontinuity, the thickness of which is controlled by some microscopic scale length of the plasma, such as an ion cyclotron radius. Several types of discontinuities are discussed, the most important of which is a shock wave. In a shock wave the flow velocity suddenly changes from supersonic to subsonic at the discontinuity, with a corresponding increase in the plasma density and magnetic field strength. A detailed derivation of the equations that determines the propagation speed of a MHD shock wave is given, including the limiting cases of weak and strong shocks. The mechanisms by which shocks can accelerate particles to very high energies are discussed. These include shocks from solar coronal mass ejections, which are known to accelerate charged particles to energies of many tens of MeV, and shocks produced by supernovae explosions, which are believed to be responsible for the acceleration of cosmic rays to extremely high energies, 1014 eV or more.

Introduction to Magnetohydrodynamics
  • 2nd edition
  • P. A. Davidson
  • Published online:
    09 February 2017
    Print publication:
    22 December 2016
  • Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite.

Page 49 of 183