By Jeffrey P. Freidberg
Accomplished, self-contained, and obviously written, this successor to perfect Magnetohydrodynamics (1987) describes the macroscopic equilibrium and balance of extreme temperature plasmas - the fundamental gasoline for the advance of fusion strength. Now totally up to date, this ebook discusses the underlying actual assumptions for 3 simple MHD versions: excellent, kinetic, and double-adiabatic MHD. incorporated are special analyses of MHD equilibrium and balance, with a specific specialise in 3 key configurations on the state-of-the-art of fusion study: the tokamak, stellarator, and reversed box pinch. different new themes contain continuum damping, MHD balance comparability theorems, neoclassical shipping in stellarators, and the way quasi-omnigeneity, quasi-symmetry, and quasi-isodynamic constraints effect the layout of optimized stellarators. together with complete derivations of virtually each vital consequence, in-depth actual motives all through, and a lot of challenge units to assist grasp the cloth, this can be a good source for graduate scholars and researchers in plasma and fusion physics.
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Extra resources for Ideal MHD
N α r Á uα ¼ 0 ! # α d 1 3 nα À Z α enα uα Á E þ r Á ðuα Á Pα þ qα Þ ¼ Qα þ uα Á Rα mα u2α þ T α dt 2 2 α α ð2:20Þ where d ∂ þ uα Á r dt α ∂t ð2:21Þ is the convective derivative for the species α. A further reduction can be made leading to a simpler form of the energy equation. ). Upon replacing the energy equation with the simpliﬁed form one obtains the ﬁnal set of two-ﬂuid equations given by ! dnα þ nα r Á uα ¼ 0 dt α ! duα À Z α enα ðE þ uα Â BÞ þ r Á Pα ¼ Rα mα nα dt α ! 3 dT α þ Pα : ruα þ r Á qα ¼ Qα nα 2 dt ð2:22Þ α rÂE¼À ∂B ∂t r Â B ¼ μ0 eðni ui À ne ue Þ þ 1 ∂E c2 ∂t e ðni À ne Þ ε0 rÁB ¼ 0 rÁE ¼ where, as stated, the ions are singly charged so that Zi ¼ ÀZe ¼ 1.
2004). Principles of Magnetohydrodynamics. Cambridge: Cambridge University Press. Grad, H. (1956). Notes on Magnetohydrodynamics. New York University Report NYO6486-I, New York. D. D. (2003). Plasma Conﬁnement. Redwood City, CA: Addison-Wesley. J. and Clark, M. (1961). Plasmas and Controlled Fusion. Cambridge, MA: MIT Press. Spitzer, L. (1962). Physics of Fully Ionized Gases New York: Interscience. J. H. (1995). Introduction to Plasma Physics. Bristol: Institute of Physics. Helander, P. J. (2002).
In summary, although many important plasma physics processes are neglected in the derivation of ideal MHD, the one critical phenomenon that remains is the self-consistent treatment of macroscopic equilibrium and stability in multidimensional magnetic geometries. 1 Starting equations In order to more fully appreciate the physics content of ideal MHD as well as the subtleties involved, a derivation of the model is presented starting from basic principles. A number of such derivations exist in the literature and each, including the one presented here, follows the same general procedure: ﬂuid moments are calculated from a general kinetic model, and then a number of assumptions are made to obtain closure of the system.