On the nonlinear instability of a thermal field

Ibanez, M.; Parravano, S. A.; Mendoza, Carolina

doi:10.1086/172543

ApJ

1993

DOI: 10.1086/172543

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On the nonlinear instability of a thermal field

M. Ibanez¹,

S. A. Parravano²,

Carolina Mendoza³

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Cited by 7 publications

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Nonlinear thermal instability in optically thin plasmas

Steele

Sira

2000

Physics of Plasmas

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This paper contains a study of the stability of a slablike thermal structure constituted by an optically thin plasma with solar abundances in which there is generation and loss of energy, and a thermal diffusion of heat dependent on both density and temperature. The analysis is carried out by means of a second order approximation. A general expression for the Landau constant is obtained. Close to the first order marginal state, this constant is completely determined by the power of the heat diffusion law and the first and second order derivatives with respect to density and temperature of the heat/loss function. Normally, near the first-order marginal state, the second order is such that cooling perturbations are enhanced. However, it is possible to find circumstances where a finite perturbation may lead to the enhancement of heating. First and second order bifurcation points are determined when this function has a power dependence on density and temperature. The regions with a different kind of instability or stability have been determined on the plane defined by the ratios between the dynamical and the relaxation time scale (α) and between the dynamical and the heating time scale (ε). Additionally, the time evolution at the onset of the nonlinear regime is analyzed.

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Nonlinear thermal instability in optically thin plasmas

Steele

Sira

2000

Physics of Plasmas

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Propagation of sound and thermal waves in an ionizing-recombining hydrogen plasma: Revision of results

2002

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The propagation of acoustic and thermal waves in a heat conducting, hydrogen plasma, in which photoionization and photorecombination ͓H ϩ ϩe Ϫ Hϩh()͔ processes are progressing, is re-examined here using linear analysis. The resulting dispersion equation is solved analytically and the results are compared with previous solutions for the same plasma model. In particular, it is found that wave propagation in a slightly and highly ionized hydrogen plasma is affected by crossing between acoustic and thermal modes. At temperatures where the plasma is partially ionized, waves of all frequencies propagate without the occurrence of mode crossing. These results disagree with those reported in previous work, thereby leading to a different physical interpretation of the propagation of small linear disturbances in a conducting, ionizing-recombining, hydrogen plasma.

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Analytical criteria for nonlinear instability of thermal structures

Ibáñez

Rosenzweig

1995

Physics of Plasmas

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Analytical criteria for supercritical and asymptotic stability and for subcritical and superexponential instability are obtained for slab-like, spherical, and cylindrical thermal structures. It is assumed that both, the thermal conductivity κ(T) and the gain/loss function Q(T), can be written as continuous functions of the temperature and they have continuous derivatives. Conditions on κ and Q under which the symmetry of the structure determines the kind of instability (or stability) are obtained. Additionally, it is found that the response of the structure not only depends on the amplitude of the disturbance, but also on whether the disturbance increases or decreases the initial steady temperature. In particular, the threshold value for the amplitude of the disturbances beyond which a linearly stable configuration destabilizes, and explicit conditions for catastrophic heating or cooling are obtained. Applications to structures constituted by atomic and molecular gas are outlined.

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On the nonlinear instability of a thermal field

Cited by 7 publications

References 0 publications

Nonlinear thermal instability in optically thin plasmas

Nonlinear thermal instability in optically thin plasmas

Propagation of sound and thermal waves in an ionizing-recombining hydrogen plasma: Revision of results

Analytical criteria for nonlinear instability of thermal structures

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