Classification and stability of double water-bag plasma equilibria

Finzi, U.; Doremus, J. P.; Holec, Juraj; Feix, Marc

doi:10.1088/0032-1028/16/2/004

Cited by 10 publications

(2 citation statements)

References 7 publications

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“…where x is the characteristic length of the equilibrium and  , are averages in x . The criterion above has been compared with the results of numerical simulations in the case of selfconsistent inhomogeneous gravitational and electrostatic equilibria [32][33][34].…”

Section: The Electrostatic Entropy Conceptmentioning

confidence: 99%

Thermodynamics of High Temperature Plasmas

Minardi

2009

Entropy

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In this work we discuss how and to what extent the thermodynamic concepts and the thermodynamic formalism can be extended to the description of high temperature states of the plasma not necessarily associated with a Boltzmann distribution and with thermal equilibrium.The discussion is based on the “magnetic or electrostatic entropy concept”, an interpretative and predictive tool based on probability and information, defined in a suitably coarse-grained possibility space of all current density or of all electric charge density distributions under testable constraints, and whose variation properties are proven to be related under certain conditions to the equilibrium and the stability of the system. In the case of magnetic equilibrium the potentiality of the magnetic entropy concept is illustrated by comparing the predictions of the current density and pressure profiles with the observations in different tokamak machines and different tokamak regimes, as well as by showing how the equilibrium and the stability in devices as different as the reversed field pinch or the magnetic well are described by the variation properties of the same entropy functional applied to the different situations. In fact it emerges that the maximum of the entropy can be seen in these different cases as an optimization constraint for the minimum of the magnetic energy. The application of the entropy concept to the electrostatic processes shows in particular that the so-called reactive instabilities (non-dissipative, non-resonant instabilities with a marginal point) admit a neighboring state with higher entropy and are therefore of special relevance from the point of view of the physical evolution of the system. In this case the thermodynamic formalism allows the introduction of the concept of “thermodynamic fluctuations” of the macroscopic charge density and provides a method for the calculation of the “thermodynamic” fluctuation levels both on the stable as well as on the linearly unstable side of the marginal point. The paper discusses the relation between the variations of the entropy functional defined on statistical grounds and the motion of the underlying system of particles. It is found that the vanishing of the first variation of the entropy is connected, under certain assumptions, with the Hamilton’s principle, while the second variation is not directly related to the dynamics but is an expression of the fact that the entropy is a predictive tool based on probability and information

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Section: The Electrostatic Entropy Conceptmentioning

confidence: 99%

Thermodynamics of High Temperature Plasmas

Minardi

2009

Entropy

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“…and we can incorporate the physics that we need with a few degrees of freedom without having to take into account too many irrelevant details. We can recall the studies of Hohl [1969] and Finzi et al [1974] in the case of a plasma and those of Hohl and Feix [1967] and Doremus and Feix [ 1972] in the case of a self-gravitating gas.…”

Section: And Feix Velocity Space (Figure 1) We Can Write For the Projmentioning

confidence: 99%

Nonlinear steady state structures for inhomogeneous plasma

Trotignon¹,

Feix²

1977

Radio Science

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We study the nonlinear steady state structures created in a one-dimensional collisionless electron plasma by a transparent grid raised to a given potential. Moreover, natural structures, i.e., in the absence of a grid and consequently of any external charge, can also be obtained. For the electrons (here ions are supposed motionless and uniform), the structure must involve a hole in the trapped electron density distribution and is consequently attractive. A relationship between the depth of the potential and its possible length is obtained. These studies are preliminary to the problems of stability and waves propagating in strongly inhomogeneous plasma structures. FORMULATIONAND DISCUSSION OF PROBLEMS 2.1. Multiple Water Bag model. In this study we consider collisionless plasma, i.e., one in which the motion of a charged particle is due to the collective action of the other charged particles. In that way, we do not take individual effects into account, compared to the purely collective field, so that the plasma can be described by the V!asov equation. This nonlinear equation cannot be solved directly in most cases; consequently, plasma physicists have had to develop models which simplify the treatment at its beginning.An interesting model of that type is the Water Bag model. Its name, given by De Packh [1962], results from the analogy between a phase-space fluid and a real-space incompressible fluid. Let us consider in the phase space, at a given time t, a domain delineated by a closed surface with a space density constant inside it and equal to zero outside.

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References

1982

Handbook on Plasma Instabilities

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Classification and stability of double water-bag plasma equilibria

Cited by 10 publications

References 7 publications

Thermodynamics of High Temperature Plasmas

Thermodynamics of High Temperature Plasmas

Nonlinear steady state structures for inhomogeneous plasma

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