By Jeffrey P. Freidberg

Complete, self-contained, and obviously written, this successor to perfect Magnetohydrodynamics (1987) describes the macroscopic equilibrium and balance of extreme temperature plasmas - the elemental gasoline for the advance of fusion strength. Now totally up-to-date, this booklet discusses the underlying actual assumptions for 3 simple MHD types: perfect, kinetic, and double-adiabatic MHD. incorporated are exact analyses of MHD equilibrium and balance, with a specific specialize 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 delivery in stellarators, and the way quasi-omnigeneity, quasi-symmetry, and quasi-isodynamic constraints influence the layout of optimized stellarators. together with complete derivations of virtually each very important consequence, in-depth actual factors all through, and loads of challenge units to aid grasp the cloth, this is often a great source for graduate scholars and researchers in plasma and fusion physics.

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**Extra resources for Ideal MHD**

**Example text**

The full set of kinetic-Maxwell equations provides a detailed and complete description of plasma behavior. At one end of the spectrum, it contains microscopic information about the orbits of individual charged particles on the very short gyro time scale and gyro radius length scale. At the other end, it accurately describes the macroscopic behavior of large plasma experiments including MHD equilibrium and stability as well as very slow transport phenomena. Not surprisingly, the complexity arising from this breadth of information makes it virtually impossible to solve, even numerically, the kinetic-Maxwell system of equations in any non-trivial geometry.

Since the truncated system is by design focused on a speciﬁc regime of physics its total information content is much less than that of the original kinetic equation. Even so, the virtue of the ﬂuid equations is that they are enormously simpler to solve. To derive the ideal MHD model, the moments that are required correspond to mass, momentum, and energy; that is, starting with the kinetic equation one evaluates ! Z df α ∂f α À dv ¼ 0 ð2:8Þ gi dt ∂t c for i ¼ 1 À 3 with gi(v) given by g1 ¼ 1 g2 ¼ mα v g3 ¼ mα v2 =2 ðmassÞ ðmomentumÞ ðenergyÞ ð2:9Þ After a straightforward calculation the ﬂuid equations for each species can be written as ∂nα þ r Á ðnα uα Þ ¼ 0 ∂t Z ∂ ðmα nα uα Þ þ r Á ðmα nα hvviÞ À Z α enα ðE þ uα Â BÞ ¼ mα v C αβ dv ð2:10Þ ∂t !

The particular 18 The ideal MHD model prescription that leads to the ideal MHD equations consists of the following steps. First, certain asymptotic orderings are introduced that eliminate the very highfrequency, short-wavelength information in the model. , those involving the macroscopic behavior of fusion plasmas. Next, the equations are rewritten as a set of singleﬂuid equations by the introduction of appropriate single-ﬂuid variables. These equations still have more unknowns than equations. A crucial step follows.