**Preface XI**


Chapter 2 **Sub-Fluid Models in Dissipative Magneto-Hydrodynamics 35**  Massimo Materassi, Giuseppe Consolini and Emanuele Tassi


Preface

Magnetohydrodynamics (MHD) is concerned with the dynamic motion of electrically conducting medium (i.e., so-called plasma) in the presence of magnetic field, which is either applied externally or self-generated. MHD is traditionally interpreted as follows: "Magneto" has to do with electro-magnetic fields; "hydro" indicates to deal with fluid medium; while "dynamics" designates to study its time evolution of physical processes. Another kind of interpretation can, however, be as follows: "Magnetohydro" refers to the "magneto" type of fluids, in which particles are stuck together primarily by magnetic field, instead of by collisions. Due to the presentation of strong magnetic field, charged particles gyrate around magnetic field lines, so that the guiding center of charged particle's gyro-motion is primarily frozen in the magnetic field line. Therefore, even in the weak collision case charged particles can move collectively as if fluid in the perpendicular direction. The later interpretation

MHD theory has been used to study controlled nuclear fusion, space/astronomic plasma physics, such as solar physics, and low temperature plasma physics, such as plasma processing, MHD generator, etc. The collective motion of charged particles is an intrinsically complicated issue, due to the long-range correlation feature of Coulomb and Lorentz forces. Nevertheless, MHD theory is able to catch the leading behaviors in a clear and tractable manner. This has led to the success of MHD theory.

There are several excellent MHD books in the market. Also, MHD theory is described about in every plasma physics books. Nevertheless, as plasma physics science advances, the gap between cutting-edge researches and textbooks always develops. To fill in this gap, several MHD-related topics are reviewed by eight authors in this book,

In Chapter 1 an overview of MHD theory for toroidal plasma confinement in controlled nuclear fusion is given. Especially, the toroidal theories for four major types of MHD modes: interchange, ballooning, toroidal Alfven egenmodes, and kinetically driven modes (such as energetic particle modes) are reviewed. In Chapter 2 the recent development of sub-fluid models in dissipative MHD is reviewed. Especially, three models to approach "stochastic coherent structures theory" are described. In Chapter 3 the implicit numerical methods for resistive MHD is reviewed. Especially two broad

covers a broad scope in which MHD theory applies.

according to authors' expertise.
