By S. Chandrasekhar, Space
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Additional info for An introduction to the study of stellar structure
27) Note that the presence of a background flow not only enlarges the set of equilibrium solutions with an additional function v(r), but it also enlarges the freedom of choice for the functions ρ(r), p(r) and B(r). Paradoxically, though more equations are to be satisfied, more solutions are permitted. To convince yourself of this basic fact, consider a variant of Fig. 1  with two balls on opposite sides of the top of a hill: not an equilibrium. However, if the two balls are constrained by a wire connecting them, all of a sudden infinitely many equilibrium positions are obtained.
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. Can this be generalized for plasmas with background flow? perturbed flow ξ (r 0 , t ) stationary flow r r 0, t r0 ,t = 0 Fig.
93)  with the “shooting” method. Clearly, the consideration of magnetic shear is essential for the analysis of local stability criteria, as usual in tokamak stability studies, but not so important for the Parker instability. In conclusion, a full spectral analysis of gravitational instabilities exhibits the existence of a large class of instabilities, called quasi-Parker instabilities, that smoothly connect the Parker instability (operating at k B) of astrophysical plasmas to the quasi-interchanges and interchanges of laboratory plasmas (operating at k ⊥ B).