By J. P. Goedbloed, Rony Keppens, Stefaan Poedts
Following on from the spouse quantity ideas of Magnetohydrodynamics, this textbook analyzes the purposes of plasma physics to thermonuclear fusion and plasma astrophysics from the only point of view of MHD. This method seems to be ever extra strong whilst utilized to streaming plasmas (the overwhelming majority of noticeable topic within the Universe), toroidal plasmas (the so much promising method of fusion energy), and nonlinear dynamics (where all of it comes including sleek computational innovations and severe transonic and relativistic plasma flows). The textbook interweaves thought and particular calculations of waves and instabilities of streaming plasmas in advanced magnetic geometries. it's splendid to complicated undergraduate and graduate classes in plasma physics and astrophysics.
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Additional info for Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas
104)). For cylindrical plasmas in the absence of gravity, according to Eqs. 30), this term cancels with the rotational contribution so that only the magnetic curvature −Bθ2 /r remains. For toroidal equilibria, the second term of Eq. 3 for the similar definitions for magnetic field lines). 97) becomes much clearer when the latter is subjected to a similar operation as above (in the derivation of Eq. 91)), dotting it with ξ ∗ and integrating over the volume. 107) are real because of the proved self-adjointness of the operators ρ−1 U and ρ−1 G.
1 Basic equations To describe the dynamics of plasmas with stationary flow, we start from the set of nonlinear ideal MHD equations (see Volume , Chapter 4) for the density ρ, the velocity v, the pressure p and the magnetic field B: ∂ρ + ∇ · (ρv) = 0 , ∂t ∂v ρ + v · ∇v + ∇p − j × B − ρg = 0 , ∂t ∂p + v · ∇p + γp∇ · v = 0 , ∂t ∂B − ∇ × (v × B) = 0 , ∇ · B = 0. g. 1 . The gravitational acceleration g = −∇Φ is considered to be caused by a fixed external gravitational field Φ. 2 ) and drop factors μ0 .
2 Frieman–Rotenberg formulation Recall the discussion of MHD spectral theory in Volume , Chapter 6. 2 Spectral theory of stationary plasmas 17 in terms of the primitive, Eulerian, variables ρ1 , v1 , p1 and B1 to a representation in terms of the plasma displacement vector ξ alone. This led to the powerful force operator formalism, with spectral representations in complete analogy with the mathematics of quantum mechanics and, hence, the possible transfer of methods and insights from that part of physics.