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Second breakdown and other thermal instabilities analyzed by heat flow equation, obtaining stability criteria predicting reduced power dissipation for transistor at low currents
The temporal evolution of density perturbations in an initially hydrostatic isothermal atmosphere consisting of an optically thin radiating compressible plasma is studied. Numerical techniques are used to describe the nonlinear evolution of the perturbations, and the relative equilibrium between dynamic and thermal instabilities as governed by three independent control parameters are examined, namely, the initial density contrast of the perturbation, the ratio of the local buoyancy oscillation period to the local radiative cooling time, and the ratio of the perturbation radius to the local scaleheight. Four orders of magnitude of initial density contrasts and ratios of buoyancy and cooling times, and one order of magnitude of the bubble dimensions are explored. Well-defined oscillations were found to occur in a limited parameter range, and thermal instability to occur even within secondary condensations deriving from the bubble fragmentation.
The nonlinear evolution and spatial propagation of the thermal instability in accretion disks in galactic nuclei are investigated. Integrations of the vertical structure of the disks are described for different alpha prescriptions, and the thermal stability is examined. Global time-dependent calculations of the unstable disks are performed which show that there are two distinct types of behavior according to the assumed prescription for the viscosity parameter: the 'purr' type and the 'roar' type. The roar type is analyzed in some detail.
Ways in which the radiation-driven thermal instability might affect the structure of the solar atmosphere are considered. It is found that the ultimate state of the medium is highly sensitive to the evolving modal content of the perturbation in that both the initial modal composition and the extent of mode coupling determine the final structure of the atmosphere. It is also found that the condensation process generates highly rotational flows during and after the transition to a new stable state.
The effects of heat conduction and magnetic fields on the growth of thermal instabilities in cooling flows are examined using a time-dependent hydrodynamics code. It is found that, for magnetic field strengths of roughly 1 micro-Gauss, magnetic pressure forces can completely suppress shocks from forming in thermally unstable entropy perturbations with initial length scales as large as 20 kpc, even for initial amplitudes as great as 60 percent. Perturbations with initial amplitudes of 50 percent and initial magnetic field strengths of 1 micro-Gauss cool to 10,000 K on a time scale which is only 22 percent of the initial instantaneous cooling time. Nonlinear perturbations can thus condense out of cooling flows on a time scale substantially less than the time required for linear perturbations and produce significant mass deposition of cold gas while the accreting intracluster gas is still at large radii.
The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.
This study reveals the role of thermal instability in hydrogen-substituted graphdiyne (HsGDY) and its impact on lithium–sulfur (Li–S) battery performance.
Nonlinear numerical calculations of stellar evolution at high mass show that thermal instability develops temporarily in the helium-burning shell, shortly after the ignition of shell helium. Manifestation of the instability is an irregular flickering of very small amplitude. There appear to be no observable consequences of the phenomenon.-
Previous studies of a thermal (radiative) instability in a sheared magnetic field have shown that, under solar coronal conditions, cool condensations can form in a small neighborhood about the shear layer. Such results have served to model the formation of solar filaments (or prominences) observed to occur above photospheric magnetic polarity-inversion lines. A surprising conclusion of these studies is that the width of the condensation does not depend on the thermal conductivity. By examining the mass-flow patterns of two-dimensional condensations in the absence of thermal conduction, it is demonstrated that local plasma dynamics and the constraints imposed by boundary conditions are together sufficient to explain the size of the condensation width. In addition the results of a series of numerical calculations are presented which illustrate the characteristic mode structure of sheared-field condensations.
Stability of dilute gas in mechanical and thermal equilibrium with application to nongravitational condensation phenomena in astronomy, particularly solar corona
The cooling of post-flare plasmas is discussed and the formation of loop prominences is explained as due to a thermal instability. A one-dimensional model was developed for active loop prominences. Only the motion and heat fluxes parallel to the existing magnetic fields are considered. The relevant size scales and time scales are such that single-fluid MHD equations are valid. The effects of gravity, the geometry of the field and conduction losses to the chromosphere are included. A computer code was constructed to solve the model equations. Basically, the system is treated as an initial value problem (with certain boundary conditions at the chromosphere-corona transition region), and a two-step time differencing scheme is used.
It is shown that radiatively driven, optically thin winds from active galactic nuclei are thermally unstable, provided that the mass loss rates are not smaller than about 50 solar masses/year. Clouds form at distances of less than about 1 pc, with electron densities greater than 100 million/cu cm, temperatures of more than 10,000 K, and radii between 3 x 10 to the 14th and 10 to the 15th cm. These values agree with the values deduced from observations. Since the clouds are formed in a high velocity wind, this model, as does the model by Eilek and Caroff (1979), avoids problems of disruption inherent in using radiation pressure to accelerate clouds from rest to velocities up to 0.1 c needed to explain the emission line widths. The thermal balance of the gas is discussed, the criteria for thermal instability are given, and a perturbation analysis is made. This analysis is restricted to objects with bolometric luminosities lower than approximately 2 x 10 to the 46th ergs/sec. For more luminous objects, only winds slightly optically thick to electron scattering can be unstable, provided one can extend this analysis to the optically thick case.
Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when pressure is instead treated as a dynamical quantity and allowed to evolve self-consistently, fundamentally different dynamics appear. Such a treatment is necessary in some laboratory plasmas, whose volume is constrained but whose pressure can vary. Here, solutions are derived for the evolution of clouds, accounting for pressure variation and interactions between conduction fronts. Additional stable configurations and secondary instabilities are derived, which may be relevant to fusion plasmas and to the study of photoionized plasma in the laboratory.
Significant quantities that affect the internal structure of the sun are examined for factors that reduce the temperature near the sun's center. The four factors discussed are: opacity, central black hole, thermal instability, and additional neutrino sources.
In this paper a scenario is proposed to explain the lack of young globular clusters in the Galaxy. It is argued that the formation of the Galactic disk would induce tidal compressions on protoglobular clouds during passage through the Galactic disk. Such a compression would trigger the onset of thermal instability in typical protoglobular cluster clouds, leading to rapid cooling and contraction and subsequent star formation. The clouds are thus unlikely to survive several passages through the Galactic disk following its formation. Instabilities preferentially occur in clouds with relatively high metallicity and with orbits lying more nearly in the plane of the Galaxy, possibly leading to the formation of a population of clusters with small orbital inclination, similar to the population of disk clusters observed in the Galaxy.
The metal abundances among the stars within a typical globular cluster are remarkably homogeneous. This indicates that star formation in these systems was a globally coordinated event which occurred over a time span less than or comparable to the collapse time scale of the cluster. This issue is addressed by assuming that the fragmentation of a proto-globular cluster cloud proceeded in two steps. In the first step, thermal instability led to the rapid growth of initial fluctuations. This led to a large contrast in the dynamical time scales between the perturbations and the parent cloud, and the perturbations then underwent gravitational instabilities on short time scales. This process is modeled using one-dimensional hydrodynamic simulations of clouds both with and without external heat sources and self-gravity. The models include the effects of a non-equilibrium H2 abundance. The results indicate that fragmentation can occur on time scales significantly less than the dynamical time scale of the parent cloud.
The thermal stability of confined solar coronal structures ('loops') is investigated, following both normal mode and a new, global instability analysis. It is demonstrated that: (1) normal mode analysis shows modes with size scales comparable to that of loops to be unstable, but to be strongly affected by the loop boundary conditions; (2) a global analysis, based upon variation of the total loop energy losses and gains, yields loop stability conditions for global modes dependent upon the coronal loop heating process, with magnetically coupled heating processes giving marginal stability. The connection between the present analysis and the minimum flux corona of Hearn is also discussed.
Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.