By J. P. Goedbloed, Rony Keppens, Stefaan Poedts
Following on from the better half quantity rules of Magnetohydrodynamics, this textbook analyzes the functions of plasma physics to thermonuclear fusion and plasma astrophysics from the one standpoint of MHD. This strategy seems to be ever extra strong while utilized to streaming plasmas (the overwhelming majority of obvious topic within the Universe), toroidal plasmas (the so much promising method of fusion energy), and nonlinear dynamics (where all of it comes including glossy computational options and severe transonic and relativistic plasma flows). The textbook interweaves concept and specific calculations of waves and instabilities of streaming plasmas in complicated magnetic geometries. it truly is ultimate 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
6 . For model I (plasma inside a rigid wall), as well as for models II and II* (configurations with a plasma–plasma or plasma–vacuum interface), the last three terms of the surface integral vanish because the equilibrium requires vn = 0, Bn = 0, jn = 0 at a wall (model I), as well as at a stationary interface (models II and II*). The extra condition vn = 0 (compared to static plasmas) insures that equilibria have stationary interfaces. It remains to demonstrate symmetry of the remaining terms of the surface integral for the different models.
3. 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.
84) This proves that the generalized force operator G is indeed self-adjoint for model I perturbations, QED. Next, we extend the discussion to model II*, where two plasmas are separated by an interface S with a tangential discontinuity. We distinguish the quantities of the two plasmas by putting a hat on one of them, indicate the discontinuities at the interface by the notation [[f ]] ≡ fˆ − f , and let the normal n point into the plasma with the hat. The equilibrium pressure balance BC then reads [[ p + 12 B 2 ]] = 0 (on S) .
Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas by J. P. Goedbloed, Rony Keppens, Stefaan Poedts