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767 results in Plasma Physics and Fusion Physics

Page 15 of 39

An Introduction to Space Plasma Complexity
  • Tom Tien Sun Chang
  • Published online:
    05 March 2015
    Print publication:
    09 March 2015
  • An Introduction to Space Plasma Complexity considers select examples of complexity phenomena related to observed plasma processes in the space environment, such as those pertaining to the solar corona, the interplanetary medium, and Earth's magnetosphere and ionosphere. This book provides a guided tour of the ideas behind forced and/or self-organized criticality, intermittency, multifractals, and the theory of the dynamic renormalization group, with applications to space plasma complexity. There is much to be explored and studied in this relatively new and developing field. Readers will be able to apply the concepts and methodologies espoused in this introduction to their own research interests and activities.

Ideal MHD
  • Jeffrey P. Freidberg
  • Published online:
    05 July 2014
    Print publication:
    26 June 2014
  • Comprehensive, self-contained, and clearly written, this successor to Ideal Magnetohydrodynamics (1987) describes the macroscopic equilibrium and stability of high temperature plasmas - the basic fuel for the development of fusion power. Now fully updated, this book discusses the underlying physical assumptions for three basic MHD models: ideal, kinetic, and double-adiabatic MHD. Included are detailed analyses of MHD equilibrium and stability, with a particular focus on three key configurations at the cutting-edge of fusion research: the tokamak, stellarator, and reversed field pinch. Other new topics include continuum damping, MHD stability comparison theorems, neoclassical transport in stellarators, and how quasi-omnigeneity, quasi-symmetry, and quasi-isodynamic constraints impact the design of optimized stellarators. Including full derivations of almost every important result, in-depth physical explanations throughout, and a large number of problem sets to help master the material, this is an exceptional resource for graduate students and researchers in plasma and fusion physics.

  • 2 - The ideal MHD model

  • Jeffrey P. Freidberg, Massachusetts Institute of Technology
  • Book:
    Ideal MHD
    Published online:
    05 July 2014
    Print publication:
    26 June 2014, pp 7-38

  • Summary

    Introduction

    The goal of Chapter 2 is to provide a physical understanding of the ideal MHD model. Included in the discussion are (1) a basic description of the model, (2) a derivation starting from a more fundamental kinetic model, and, most importantly, (3) an examination of its range of validity.

    In particular, it is shown that ideal MHD is the simplest fluid model that describes the macroscopic equilibrium and stability properties of a plasma. The claim of “simplest” is justified by a discussion of the large number of important plasma phenomena not covered by the model. However, in spite of its simplicity it is still a difficult model to solve analytically or even computationally because of the geometrical complexities associated with the two and three dimensionality of the configurations of fusion interest.

    The derivation of the MHD model follows from the standard procedure of starting with a more fundamental and inclusive kinetic description of the plasma which describes the behavior of the electron and ion distribution functions. The mass, momentum, and energy moments of the kinetic equations are then evaluated. By introducing the characteristic length and time scales of ideal MHD, and making several corresponding ordering approximations, one is then able to close the system. The end result is the set of ideal MHD fluid equations.

  • 6 - Equilibrium: two-dimensional configurations

  • Jeffrey P. Freidberg, Massachusetts Institute of Technology
  • Book:
    Ideal MHD
    Published online:
    05 July 2014
    Print publication:
    26 June 2014, pp 123-222

  • Summary

    Introduction

    In Chapter 5 it was shown that a one-dimensional, cylindrically symmetric magnetic geometry accurately describes radial pressure balance in many fusion configurations. The primary goal of Chapter 6 is to address the problem of toroidal force balance in a two-dimensional axisymmetric toroidal geometry. A secondary goal analyzes straight systems with two-dimensional helical symmetry.

    The discussion starts with a derivation of the Grad–Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. For configurations possessing such symmetry, the solutions to this equation provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium β limits, rotational transform, and kink safety factor. A wide number of configurations are well described by the Grad–Shafranov equation. Included among them are all types of tokamaks, the reversed field pinch, the levitated dipole, the spheromak, and the field reversed configuration.

Page 15 of 39