Development Of Thermal Instability Research Articles

The Flare Emission of the May 4, 2022 Event and Its Millimeter Component

Based on observations at the RT-7.5 radio telescope of the Bauman Moscow State Technical Universityat a wavelength of 3.2 mm (93 GHz), along with other ground-based and space instruments (Siberianradioheliograph, Solar Dynamics Observatory (SDO), Metsähovi radio observatory), the origin of millimeterradiation from a solar flare was investigated for the SOL2022-05-04T08:45 X-ray class M 5.7 flare. Ananalysis of the time profiles of radiation in the X-ray and centimeter ranges showed that the millimeter emissionsource is not associated with hot (5 × 105–107 K) coronal plasma. This is also evidenced by the estimateof the sub-THz flux of radiating hot plasma according to the AIA/SDO data, which turned out to be muchless than the observed values. Indications were obtained of the development of thermal instability in flareultraviolet loops. The relationship between the millimeter emission of the flare and the heat source in thesolar chromosphere has been substantiated.

Rapid microwave sintering of functional electroceramic materials

Rapid microwave sintering processes with heating rates of up to 300 °C/min and zero isothermal hold have been implemented using a 5 kW 24 GHz gyrotron system for high-temperature microwave processing of materials. ZnO-based varistor ceramics, BaTiO3/SrTiO3 dielectric ceramics and Gd:CeO2 ceramics for solid electrolyte applications have been sintered to densities of up to 96% of the theoretical value. Using in situ optical dilatometry, correlation between the development of thermal instability under intense volumetric microwave heating and the early onset of densification has been revealed. The influence of the absorbed microwave power on densification and grain growth has been studied by comparing direct and susceptor-assisted microwave heating processes. The possibility of tailoring the microstructure and functional properties of the obtained materials by choosing optimal regimes of rapid microwave sintering is discussed.

Influence of the Hall current on the convective and magnetorotational instability in a thin layer of an electrically conductive nanofluid

This study investigates the combined influence of the Hall current and the axial magnetic field on the criterion for the onset of convection in a nonuniformly rotating layer of electrically conductive nanofluids taking into account the effects of Brownian diffusion and thermophoresis. The analytical and numerical computations are presented for water-based nanofluids with alumina nanoparticles. In the absence of a temperature gradient, a new type of magnetorotational instability in an axial magnetic field in a thin layer of a nanofluid is considered. The growth rate and regions of development of this instability are numerically obtained depending on the angular velocity profile (the Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, the stationary regime of nonuniformly rotating magnetoconvection is studied. The exact analytical expression for critical Rayleigh number Rast is obtained in terms of various nondimensional parameters. The results indicate that the increase in the Lewis number, the modified diffusivity ratio, and the concentration Rayleigh number is to accelerate the onset of convection. The increase in the Hall current parameter can delay or enhance the onset of convective instability. Rotation profiles with negative Rossby numbers lower the threshold for the development of thermal instability and stimulate the onset of convection. The conditions for stabilization and destabilization of stationary convection in an axial magnetic field are determined. The results are represented graphically and verified numerically.

Thermal instability and multiphase gas in the simulated interstellar medium with conduction, viscosity, and magnetic fields

ABSTRACT Thermal instability plays a crucial role in the formation of multiphase structures and their dynamics in the interstellar medium, and is a leading theory for cold cloud creation in various astrophysical environments. In this paper, we use 2D simulations to investigate thermal instability under the influence of various initial conditions and physical processes. We experiment with Gaussian random field (GRF) density perturbations of different initial power spectra. We also enrol thermal conduction and physical viscosity in isotropic hydrodynamic and anisotropic magnetohydrodynamic (MHD) simulations. We find that the initial GRF spectral index α has a dramatic impact on the pure hydrodynamic development of thermal instability, influencing the size, number, and motions of clouds. Cloud fragmentation happens due to two mechanisms: tearing and contraction rebound. In the runs with isotropic conduction and viscosity, the structures and dynamics of the clouds are dominated by evaporation and condensation flows in the non-linear regime, and the flow speed is regulated by viscosity. Cloud disruptions happen as a result of the Darrieus–Landau instability. However, at very late times, all individual clouds merge into one cold structure in all hydrodynamic runs. In the MHD case, the cloud structure is determined by both the initial perturbations and the initial magnetic field strength. In high-β runs, anisotropic conduction causes dense filaments to align with the local magnetic fields and the field direction can become reoriented. Strong magnetic fields suppress cross-field contraction and cold filaments can form along or perpendicular to the initial fields.

Shatter or not: role of temperature and metallicity in the evolution of thermal instability

ABSTRACT We test how metallicity variation (a background gradient and fluctuations) affects the physics of local thermal instability using analytical calculations and idealized, high-resolution 1D hydrodynamic simulations. Although the cooling function (Λ[T, Z]) and the cooling time (tcool) depend on gas temperature and metallicity, we find that the growth rate of thermal instability is explicitly dependent only on the derivative of the cooling function relative to temperature (∂ln Λ/∂ln T) and not on the metallicity derivative (∂ln Λ/∂ln Z). For most of 104 K ≲ T ≲ 107 K, both the isobaric and isochoric modes (occurring at scales smaller and larger than the sonic length covered in a cooling time [cstcool], respectively) grow linearly, and at higher temperatures (≳107 K) the isochoric modes are stable. We show that even the non-linear evolution depends on whether the isochoric modes are linearly stable or unstable. For the stable isochoric modes, we observe the growth of small-scale isobaric modes but this is distinct from the non-linear fragmentation of a dense cooling region. For unstable isochoric perturbations we do not observe large density perturbations at small scales. While very small clouds (∼min[cstcool]) form in the transient state of non-linear evolution of the stable isochoric thermal instability, most of them merge eventually.

Rapid microwave sintering of alumina ceramics with an addition of carbon nanotubes

Compacted alumina samples with an addition of 1.0 and 2.5 wt % carbon nanotubes (CNT) have been microwave sintered at heating rates 50 and 100°С/min to a maximum temperature of 1550–1600°С with zero hold time. The densification kinetics has been studied using optical dilatometry. No noticeable influence of CNT on the development of thermal instability during rapid microwave sintering of alumina has been detected. The relative densities of the samples containing 1.0 and 2.5 wt % CNT sintered at a maximum temperature of 1550 °C and zero hold time were 93.8 and 87.5%, respectively. Microwave sintering with a repeated development of thermal instability has resulted in an increase in the final density to 95.0%.

Filamentation of Current-Carrying Plasma Shells

Magnetohydrodynamic instabilities of various types develop in the current-carrying plasma. One type of instability is the formation of filaments – individual current channels. In this paper, based on the methods of small perturbation theory, we analyze the development of thermal instabilities leading to the formation of filaments. Theoretical results are compared with experimental data on compression of plasma-puff liners obtained on an IMRI-5 generator.

Thermal filamentation instabilities developing in imploding plasma liners

Filamentation is a type of magnetohydrodynamic instability that may develop in a current-carrying plasma. It is supposed that filaments, individual current channels, are formed due to thermal instabilities. The growth of these instabilities is determined by the behavior of the electrical conductivity of the material depending on its thermodynamic parameters. If the conductivity increases with temperature, as is the case in a plasma, thermal instabilities should give rise to the formation of separate current channels. This paper presents an analysis of the development of thermal instabilities in imploding plasma liners performed in terms of small perturbation theory. The theoretical predictions are compared with the results of experiments conducted on the IMRI-5 facility at a current of amplitude up to 450 kA and rise time about 500 ns.

Thermal instability of superconducting composites at magnetic flux creep

The conditions of the onset and development of thermal instabilities occurring under the action of thermal disturbance in superconducting composites with voltage-current characteristic described by a power equation are discussed. The investigation is done in the framework of the quasi-linear model, as in the Stekly approximation. The critical energies, which lead to the transition of the superconducting state to the normal one, and the velocities of irreversible propagation of the thermal instability along the composite are determined. It is shown that the largest current stably flowing in a superconducting composite can be either lower or higher than a priori defined critical current of a superconductor with a real (continuously increasing) voltage-current characteristic. The condition of the complete thermal stabilization for the superconducting composites with a power voltage-current characteristic is formulated. It is shown that the commonly accepted Stekly condition of the complete thermal stabilization, according to which the superconducting composite is completely stable to the thermal perturbations with any energy, does not allow to determine correctly the conditions providing the complete thermal stabilization of superconducting composites with real voltage-current characteristics. The results of the numerical simulations express that the existing theory of the thermal stabilization in the framework of which a jump transition from a superconducting state to a normal one is supposed leads to a limitation of the currents, at which a stable superconducting state exists.

On the correlation between the thermal instability onset and the flash sintering event

In the experiments on microwave sintering of alumina ceramics at high levels of the volumetrically deposited power a long delay, on the order of 100 s, is observed between the development of thermal instability and the onset of rapid (“flash”) densification. The observed delay demonstrates the causal relationship between the thermal instability development, accompanied by liquid phase formation, and the occurrence of rapid densification resulting from a change in the sintering mechanism.

Cosmic-ray propagation in the bi-stable interstellar medium

Context. Cosmic rays propagate through the galactic scales down to the smaller scales at which stars form. Cosmic rays are close to energy equipartition with the other components of the interstellar medium and can provide a support against gravity if pressure gradients develop. Aims. We study the propagation of cosmic rays within the turbulent and magnetised bi-stable interstellar gas. The conditions necessary for cosmic-ray trapping and cosmic-ray pressure gradient development are investigated. Methods. We derived an analytical value of the critical diffusion coefficient for cosmic-ray trapping within a turbulent medium, which follows the observed scaling relations. We then presented a numerical study using 3D simulations of the evolution of a mixture of interstellar gas and cosmic rays, in which turbulence is driven at varying scales by stochastic forcing within a box of 40 pc. We explored a large parameter space in which the cosmic-ray diffusion coefficient, the magnetisation, the driving scale, and the amplitude of the turbulence forcing, as well as the initial cosmic-ray energy density, vary. Results. We identify a clear transition in the interstellar dynamics for cosmic-ray diffusion coefficients below a critical value deduced from observed scaling relations. This critical diffusion depends on the characteristic length scale L of Dcrit ≃ 3.1 × 1023 cm2 s−1(L/1 pc)q+1, where the exponent q relates the turbulent velocity dispersion σ to the length scale as σ ~ Lq. Hence, in our simulations this transition occurs around Dcrit ≃ 1024–1025 cm2 s−1. The transition is recovered in all cases of our parameter study and is in very good agreement with our simple analytical estimate. In the trapped cosmic-ray regime, the induced cosmic-ray pressure gradients can modify the gas flow and provide a support against the thermal instability development. We discuss possible mechanisms that can significantly reduce the cosmic-ray diffusion coefficients within the interstellar medium. Conclusions. Cosmic-ray pressure gradients can develop and modify the evolution of thermally bi-stable gas for diffusion coefficients D0 ≤ 1025 cm2 s−1 or in regions where the cosmic-ray pressure exceeds the thermal one by more than a factor of ten. This study provides the basis for further works including more realistic cosmic-ray diffusion coefficients, as well as local cosmic-ray sources.

AGN feedback and multiphase gas in giant elliptical galaxies

Recent observations have found extended multi-phase gas in a significant fraction of massive elliptical galaxies. We perform high-resolution three-dimensional hydrodynamical simulations of two idealized elliptical galaxies -- one representing a typical galaxy characterized by initial conditions conducive to the development of thermal instability and the other one less likely to develop thermal instability -- in order to study the development of thermal instability and the formation of multi-phase structures. We analyze the interplay between radiative cooling, momentum-driven AGN feedback, star formation, and stellar feedback from both young and old stars. We find that in one class of elliptical galaxies, the entropy of the hot halo gas rises sharply as a function of radius, and the hot halo is thermally stable and run-away cooling can only happen in the very center of the galaxy. In other class of ellipticals, the hot halo gas has a cooling to free-fall time ratio close to 10, and the non-linear perturbation driven by AGN feedback can cause the hot gas to frequently precipitate into extended multi-phase filaments. Both multi- and single-phase elliptical galaxies experience cooling-driven AGN feedback cycles. Interestingly, AGN feedback maintains the multi- or single-phase nature of the halo but does not turn multi-phase galaxies into single-phase ones or vice versa. Some of the extended cold gas in the multi-phase galaxy also forms young stars. The level of star formation and its spatial distribution are in excellent agreement with {\it Hubble} observations of nearby elliptical galaxies.

Thermal stabilization of the resistive states of superconducting composites: Quasilinear approximation

The conditions of the occurrence and development of thermal instabilities in the composite superconductor with a continuously increasing current-voltage characteristic, which is described by the power equation, have been studied. The conditions for thermal stabilization have been analyzed in the general form using dimensionless variables that keep their invariance when varying. For the local temperature disturbance, the critical energies and velocities of its irreversible propagation have been calculated. It has been proved that composites superconductors can have stable states, when the ultimate currents can be higher or lower of the conventionally preset critical current of the composite. Furthermore, superconductivity destruction at supercritical currents takes place not in the form of a stepwise transition from the superconducting to normal state, but due to the formation of thermal and electric switching waves that propagate along the composite superconductor with a constant speed. The condition for full thermal stabilization has been formulated for the superconducting composites with a power current–voltage characteristic. The results of the numerical experiments have proved that the existing theory of thermal stabilization, which assumes a stepwise superconducting–normal transition, leads to the considerable limitation of the range of the stable currents, at which a superconducting state can be kept.

MHD instabilities developing in a conductor exploding in the skin effect mode

The results of experiments with exploding copper conductors, performed on the MIG facility (providing currents of amplitude of about 2.5 MA and rise time of 100 ns), are analyzed. With an frame optical camera, large-scale instabilities of wavelength 0.2–0.5 mm were detected on the conductor surface. The instabilities show up as plasma “tongues” expanding with a sound velocity in the opposite direction to the magnetic field gradient. Analysis performed using a two-dimensional MHD code has shown that the structures observed in the experiments were formed most probably due to flute instabilities. The growth of flute instabilities is predetermined by the development of thermal instabilities near the conductor surface. The thermal instabilities arise behind the front of the nonlinear magnetic diffusion wave propagating through the conductor. The wavefront on its own is not subject to thermal instabilities.

Pre-Explosion Phenomena Beneath the Plasma of a Vacuum Arc Cathode Spot

A 2-D hydrodynamic model has been developed that describes the pre-explosion processes in a microprotrusion of a vacuum arc cathode based on a self-consistent calculation of the electric potential drop in the near-cathode region. The model includes a calculation of the cathode temperature in view of the surface heat fluxes carried by electrons and ions during the interaction of the cathode surface with the cathode spot plasma and the Joule heating of the cathode. The near-cathode space charge sheath is considered in the 1-D local Bohm approximation. It has been shown that the heat flux from a cathode plasma having parameters characteristic of low-current vacuum arcs can induce thermal instability (thermal runaway) in a cathode microprotrusion and heat it to a critical temperature within some tens of nanoseconds. Comparative analysis of the volumetric Joule mechanism and the surface electron-plasma mechanism underlying the development of thermal instabilities in a cathode has been performed in one numerical experiment. It has been shown that the instability induced by the surface mechanism can arise at lower densities of the cathode spot plasma and its growth rate is lower compared with the instability induced by the Joule mechanism.

Generation of hydrogen isotope ions in a vacuum arc discharge with a composite zirconium deuteride cathode

The mass and charge composition of the plasma of a vacuum arc with thick and film-type zirconium cathodes containing deuterium and hydrogen is investigated experimentally and theoretically. For a thick cathode, it is shown that such a system ensures effective generation of deuterium ions with an integral fraction per arc current pulse of approximately 60%; the maximal concentration of deuterium is observed at the initial stage of the arc operation. In the case of the film cathode, such a concentration of hydrogen isotopes can be attained for currents exceeding 400 A and for an arc duration at a level of a few tens of microseconds. Occlusion of deuterium in the cathode leads to additional energy expenditures for its ionization and, as a consequence, a decrease in the average charge of ions of the cathode material in the arc plasma. Deuterium in the cathode spot is ionized completely, and the drift velocity of its ions almost coincides with the velocity of ions of the cathode material due to the high frequency of ion-ion collisions in the cathode region. The interaction of a dense (∼1020 cm−3) cathode-spot plasma with microinhomogeneities of the cathode surface leads to the development of thermal instability in them over time intervals that do not exceed tens of nanoseconds.

THE DENSITY DISTRIBUTION IN TURBULENT BISTABLE FLOWS

We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function (Sigma-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50pc. At low densities (n <= 0.6cm^-3) the n-PDF, is well described by a lognormal distribution for average local Mach number ranging from ~0.2 to ~5.5. As a consequence of the non linear development of thermal instability (TI), the logarithmic variance of the distribution for the diffuse gas increases with M faster than in the well known isothermal case. The average local Mach number for the dense gas (n >= 7.1cm^-3) goes from ~1.1 to ~16.9 and the shape of the high density zone of the n-PDF changes from a power-law at low Mach numbers to a lognormal at high M values. In the latter case the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities the Sigma-PDF is well described by a lognormal for all the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different form those of the isothermal case.

Direct Numerical Simulation of the turbulent wake behind a heated cylinder

Direct Numerical Simulations were conducted to describe a well-known and widely studied configuration, i.e. flow field development downstream from a cylinder under the mixed convection regime, which has too rarely been considered. The Richardson number studied was equal to 2.77 and the Reynolds number equal to 1000; under such conditions, thermal instability development along the cylinder was found to interact with and pronouncedly disturb upper shear-layer development. Whole flow behavior in the back of the cylinder is consequently asymmetric. The resulting flow corresponds to complex features ranging from Kelvin–Helmholtz instabilities to pure buoyant diffusion process and Von Karman alley, the latter being significantly deviated upward.

Periodic thermomagnetic structures in solar plasma

Stationary solutions in the form of small-scale periodic cells in a plane perpendicular to the magnetic field are obtained in the framework of two-fluid magnetohydrodynamics. The solutions are established as a result of the development of thermal instability and represent a superposition of standing temperature waves. In solving the problem, an expression is used for a generalized heat source (including heating and radiative cooling) that forms a temperature transition region between the chromosphere and corona.

Thermal instability during an electrical wire explosion

The development of thermal instabilities during an electrical wire explosion is analyzed in the present work based on the methods of small perturbation theory. For two cases, with and without allowance for motion, the dispersion equations are derived that describe a relationship between the instantaneous buildup increment and the axial wave vector component. It is demonstrated that the thermal instabilities are always formed during electrical explosion, irrespective of the explosion mode. There are three destabilizing factors leading to the development of the thermal instabilities: a temperature rise, an increase in the specific resistance with increasing temperature, and an increase in the specific resistance with decreasing density. The critical value of current density below which the sausage instabilities grow faster than the thermal ones and above which, on the contrary, the thermal instabilities are dominant can be found for each metal.