Magnetothermal Instability Research Articles

The effect of cosmic rays on the stability of hot dilute plasmas

Many factors are considered in instability analysis, such as self-gravity, differential rotation, and magnetic field. Cosmic rays (CRs) are another factor that have been recently considered and shown to play a dynamic role. However, the effect of CRs on the stability of hot dilute plasma systems has not yet been considered. This type of plasma is believed to be found in the intracluster medium of galaxy clusters and inefficient radiation accretion flows around black holes. Here, we study the dynamic effects of CRs on instability modes in such systems. We discuss analytically some special cases and work out general cases numerically. We show that the growth rate of some unstable modes such as magnetothermal instability (MTI), gyroviscous magnetorotational instability, and convective instability which depend on the ratio of CR pressure to gas pressure (βcr), the ratio of the radial gradient of CR pressure to the radial gradient of gas pressure (Φ), and CR diffusion coefficient. CRs can alter MTI criterion. In this paper, we show that a plasma which is stable in ideal MTI criterion, i.e. dT/dR > 0, such as cooling flow clusters, can be unstable in the presence of CRs if |Φ| > 1.

Characterization of $\hbox{Nb}_{3}\hbox{Sn}$ Rutherford Cables for the LHC 11-T Dipole Magnet

The so-called CERN-LHC DS upgrade relies on the use of 11-T dipole magnets. For these magnets, 40 strands Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn type Rutherford cables based on 0.7-mm wires are being developed. Recently, four samples of the cables were characterized in the CERN FRESCA cable test station. The critical current and the premature quench current due to magneto-thermal instability were measured at 1.9 and 4.3 K in a background magnetic field between 0 and 9.6 T (the peak magnetic field on the conductor, including the self-field of the cable, ranges from ~ 2 T to ~ 12 T). Two cable samples were based on Powder-In-Tube (PIT) wire and two on Restacked-Rod-Process (RRP) wire. The PIT samples were identical and without a core in the cable while one of the RRP samples features a 25- μm-thick stainless steel core. All cables samples tested have a width and a thickness of about 14.7 and 1.25 mm, respectively. Cables and sample holders were manufactured at CERN. In this paper, we report and discuss the cable test results and compare them to the performance of witness strands, heat treated and measured on ITER-VAMAS type sample holders.

THE COLLISIONLESS MAGNETOVISCOUS-THERMAL INSTABILITY

It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outwards. A class of new magnetohydrodynamical fluid instabilities -- the magnetoviscous-thermal instability (MVTI) (Islam12) -- was found to transport angular momentum and energy along magnetic field lines through large (fluid) viscosities and thermal conductivities. This paper describes the collisionless and mildly collisional analogue to the MVTI, the collisional magnetothermal instability (CMTI), that similarly transports energy and angular momentum outwards, expected to be important in describing the flow properties of hot, dilute, and radiatively inefficient accretion flows around black holes. In this paper we derive a form of the collisionless drift-kinetic equation appropriate for accretion physics. We construct a local equilibrium for MHD stability analysis in this differentially rotating disk. We then find and characterize specific instabilities expected to be important in describing the flow properties of hot, dilute, and radiatively inefficient accretion flows around black holes, and show their qualitative similarities to instabilities derived using a fluid formalism (Islam12). We conclude with further work needed in modeling this class of accretion flow.

Instability-driven electromagnetic fields in coronal plasmas

Filamentary electromagnetic fields previously observed in the coronae of laser-driven spherical targets [F. H. Séguin et al., Phys. Plasma. 19, 012701 (2012)] have been further investigated in laser-irradiated plastic foils. Face-on proton-radiography provides an axial view of these filaments and shows coherent cellular structure regardless of initial foil-surface conditions. The observed cellular fields are shown to have an approximately constant scale size of ∼210 μm throughout the plasma evolution. A discussion of possible field-generation mechanisms is provided and it is demonstrated that the likely source of the cellular field structure is the magnetothermal instability. Using predicted temperature and density profiles, the fastest growing modes of this instability were found to be slowly varying in time and consistent with the observed cellular size.

What sets temperature gradients in galaxy clusters? Implications for non-thermal pressure support and mass-observable scaling relations

We present a spherically symmetric model for the origin and evolution of the temperature profiles in the hot plasma filling galaxy groups and clusters. We find that the gas in clusters is generically not isothermal, and that the temperature declines with radius at large distances from the cluster center (outside the core- and scale radii). This temperature profile is determined by the accretion history of the halo, and is not quantitatively well-described by a polytropic model. We explain quantitatively how the large-scale temperature gradient persists in spite of thermal conduction and convection. These results are a consequence of the cosmological assembly of clusters and cannot be reproduced with non-cosmological simulations of isolated halos. We show that the variation in halo assembly histories produces a ~10% scatter in temperature at fixed mass. On top of this scatter, conduction decreases the temperature of the gas near the scale radius in massive clusters, which may bias hydrostatic mass estimates inferred from x-ray and SZ observations. As an example application of our model profiles, we use mixing-length theory to estimate the turbulent pressure support created by the magnetothermal instability (MTI): in agreement with our earlier MHD simulations, we find that the convection produced by the MTI can provide ~5% non-thermal pressure support near r_500. The magnitude of this turbulent pressure support is likely to be non-monotonic in halo mass, peaking in ~10^14.5 M_sun halos.

THE STABILITY OF WEAKLY COLLISIONAL PLASMAS WITH THERMAL AND COMPOSITION GRADIENTS

Over the last decade, substantial efforts have been devoted to understanding the stability properties, transport phenomena, and long-term evolution of weakly-collisional, magnetized plasmas which are stratified in temperature. These studies have improved our understanding of the physics governing the intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This, however, might not be a good approximation if heavy elements sediment in the inner region of the galaxy cluster. In this paper, we analyze the stability of a weakly-collisional, magnetized plane-parallel atmosphere which is stratified in both temperature and composition. This allows us to discuss for the first time the dynamics of weakly-collisional environments where heat conduction, momentum transport, and ion-diffusion are anisotropic with respect to the direction of the magnetic field. We show that, depending on the relative signs and magnitudes of the gradients in the temperature and the mean molecular weight, the plasma can be subject to a wide variety of unstable modes which include modifications to the magnetothermal instability (MTI), the heat-flux-driven buoyancy instability (HBI), and overstable gravity modes previously studied in homogeneous media. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented. Our findings suggest that the core insulation that results from the magnetic field configurations that arise as a natural consequence of the HBI, which would be MTI stable in a homogeneous medium, could be alleviated if the mean molecular weight gradient is steep enough, i.e., $(\nabla \mu)/\mu > (\nabla T)/T$. This study constitutes a first step toward understanding the interaction between magnetic turbulence and the diffusion of heavy elements in the ICM. (abridged)

Perturbation Sensitivity of Magnetothermal Instability

The magnetothermal instability (MTI) is an issue in the high-Jc Nb3Sn superconducting strands for accelerator magnets. The first kind of MTI is magnetization instability, which may be significantly reduced by using small filaments and with a high copper residual resistivity ratio (RRR) ≥ 100. However, theoretical and experimental evidence suggests that there is a second kind of MTI, which is self-field instability, which seems to be highly sensitive to external perturbations and less sensitive to RRRs. Recently at the European Organization for Nuclear Research (CERN), for studying this effect, a new measurement setup based on a Q-switched laser has been developed. By using the setup, it is possible to provide a local and controlled perturbation in nanosecond timescale from 0.5 to 26 μJ , which is absorbed by the strand at cryogenic temperature. In this paper, we report the results obtained by testing high-Jc Nb3Sn strands with different RRRs. It is shown that the self-field instability is sensitive to the trigger energy in moderately high magnetic fields. Therefore, the stability is highly dependent on the perturbation spectrum, i.e., the conventional stability measurements might not be fully representative of the strand stability in magnets wound with high-Jc Nb3Sn strands.

Improving Magnetothermal Stability in High-$J_{c}\ \hbox{Nb}_{3}\hbox{Sn}$ Superconducting Strands via the Filament Cut Technique

Magnetothermal instability may affect the performance of high critical current density Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strands by quenching the superconductor at current values lower than its critical current. This phenomenon has important implications in the design of next-generation superconducting magnets for accelerators. According to the theory, the strand magnetothermal stability can be improved by changing the current distribution within the strand. In this paper, a technique to improve the conductor stability is presented. It consists in partially cutting the strand's outer superconducting subelements in the region where the wire is soldered to the copper block that feeds the current. The special cut forces the current to enter into the inner subelements without degrading the current capacity. As a consequence, the stability is increased, which avoids changing the strand critical current or its residual resistivity ratio because current redistribution during an external perturbation is strongly reduced. The experimental results obtained by applying this technique on a 0.8-mm restacked-rod process strand are presented and discussed.

BUOYANCY INSTABILITIES IN A WEAKLY COLLISIONAL INTRACLUSTER MEDIUM

The intracluster medium of galaxy clusters is a weakly collisional, high-beta plasma in which the transport of heat and momentum occurs primarily along magnetic-field lines. Anisotropic heat conduction allows convective instabilities to be driven by temperature gradients of either sign, the magnetothermal instability (MTI) in the outskirts of non-isothermal clusters and the heat-flux buoyancy-driven instability (HBI) in their cooling cores. We employ the Athena MHD code to investigate the nonlinear evolution of these instabilities, self-consistently including the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy), anisotropic conduction, and radiative cooling. We highlight the importance of the microscale instabilities that inevitably accompany and regulate the pressure anisotropies generated by the HBI and MTI. We find that, in all but the innermost regions of cool-core clusters, anisotropic viscosity significantly impairs the ability of the HBI to reorient magnetic-field lines orthogonal to the temperature gradient. Thus, while radio-mode feedback appears necessary in the central few tens of kpc, conduction may be capable of offsetting radiative losses throughout most of a cool core over a significant fraction of the Hubble time. Magnetically-aligned cold filaments are then able to form by local thermal instability. Viscous dissipation during the formation of a cold filament produces accompanying hot filaments, which can be searched for in deep Chandra observations of nearby cool-core clusters. In the case of the MTI, anisotropic viscosity maintains the coherence of magnetic-field lines over larger distances than in the inviscid case, providing a natural lower limit for the scale on which the field can fluctuate freely. In the nonlinear state, the magnetic field exhibits a folded structure in which the field-line curvature and field strength are anti-correlated.

An Experimental Setup to Measure the Minimum Trigger Energy for Magnetothermal Instability in $\hbox{Nb}_{3}\hbox{Sn}$ Strands

Magnetothermal instability may affect high critical current density superconducting strands that can quench even though the transport current is low compared to the critical current with important implications in the design of next generation superconducting magnets. The instability is initiated by a small perturbation energy which is considerably lower than the minimum quench energy (MQE). At CERN, a new experimental setup was developed to measure the smallest perturbation energy [minimum trigger energy (MTE)] which is able to trigger the magnetothermal instability in superconducting -strands. The setup is based on Q-switched laser technology which is able to provide a localized perturbation in nanosecond time scale. Using this technique the energy deposition into the strand is well defined and reliable. The laser is located outside the cryostat at room temperature. The beam is guided from room temperature on to the superconducting strand by using a UV-enhanced fused silica fiber. The strand is mounted on a VAMAS barrel. A part of the beam's energy is absorbed into the strand acting as the trigger energy for the magnetothermal instability. In this paper the experimental setup and the calibration of the absorbed energy is presented.

Magnetothermal instability in laser plasmas including hydrodynamic effects

The impact of both density gradients and hydrodynamics on the evolution of the field compressing magnetothermal instability is considered [J. J. Bissell et al., Phys. Rev. Lett. 105, 175001 (2010)]. Hydrodynamic motion is found to have a limited effect on overall growth-rates; however, density gradients are shown to introduce an additional source term corresponding to a generalised description of the field generating thermal instability [D. Tidman and R. Shanny, Phys. Fluids 17, 1207 (1974)]. The field compressing and field generating source terms are contrasted, and the former is found to represent either the primary or sole instability mechanism for a range of conditions, especially those with Hall parameter χ&amp;gt;10-1. The generalised theory is compared to numerical simulation in the context of a recent nano-second gas-jet experiment [D. H. Froula et al., Phys. Rev. Lett. 98, 135001 (2007)] and shown to be in good agreement: exhibiting peak growth-rates and wavelengths of order 10 ns1 and 50 μm, respectively. The instability’s relevance to other experimental conditions, including those in inertial confinement fusion (I.C.F.) hohlraums, is also discussed.

The effects of anisotropic viscosity on turbulence and heat transport in the intracluster medium

In the intracluster medium (ICM) of galaxy clusters, heat and momentum are transported almost entirely along (but not across) magnetic field lines. We perform the first fully self-consistent Braginskii magnetohydrodynamics (MHD) simulations of galaxy clusters including both of these effects. Specifically, we perform local and global simulations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability (HBI) and assess the effects of viscosity on their saturation and astrophysical implications. We find that viscosity has only a modest effect on the saturation of the MTI. As in previous calculations, we find that the MTI can generate nearly sonic turbulent velocities in the outer parts of galaxy clusters, although viscosity somewhat suppresses the magnetic field amplification. At smaller radii in cool-core clusters, viscosity can decrease the linear growth rates of the HBI. However, it has less of an effect on the HBI’s non-linear saturation, in part because three-dimensional interchange motions (magnetic flux tubes slipping past each other) are not damped by anisotropic viscosity. In global simulations of cool-core clusters, we show that the HBI robustly inhibits radial thermal conduction and thus precipitates a cooling catastrophe. The effects of viscosity are, however, more important for higher entropy clusters. We argue that viscosity can contribute to the global transition of cluster cores from cool-core to non-cool-core states: additional sources of intracluster turbulence, such as can be produced by active galactic nuclei feedback or galactic wakes, suppress the HBI, heating the cluster core by thermal conduction; this makes the ICM more viscous, which slows the growth of the HBI, allowing further conductive heating of the cluster core and a transition to a non-cool-core state.

Turbulent pressure support in the outer parts of galaxy clusters

Abstract We use 3D magnetohydrodynamics simulations with anisotropic thermal conduction to study turbulence due to the magnetothermal instability (MTI) in the intracluster medium (ICM) of galaxy clusters. The MTI grows on time-scales of ≲1 Gyr and is capable of driving vigorous, sustained turbulence in the outer parts of galaxy clusters if the temperature gradient is maintained in spite of the rapid thermal conduction. If this is the case, turbulence due to the MTI can provide up to 5–30 per cent of the pressure support beyond r500 in galaxy clusters, an effect that is strongest for hot, massive clusters. The turbulence driven by the MTI is generally additive to other sources of turbulence in the ICM, such as that produced by structure formation. This new source of non-thermal pressure support reduces the observed Sunyaev–Zel'dovich (SZ) signal and X-ray pressure gradient for a given cluster mass and introduces a cluster mass and temperature-gradient-dependent bias in SZ and X-ray mass estimates of clusters. This additional physics may also need to be taken into account when estimating the matter power spectrum normalization, σ8, through simulation templates from the observed amplitude of the SZ power spectrum.

COSMOLOGICAL MAGNETOHYDRODYNAMIC SIMULATIONS OF CLUSTER FORMATION WITH ANISOTROPIC THERMAL CONDUCTION

(abridged) The ICM has been suggested to be buoyantly unstable in the presence of magnetic field and anisotropic thermal conduction. We perform first cosmological simulations of galaxy cluster formation that simultaneously include magnetic fields, radiative cooling and anisotropic thermal conduction. In isolated and idealized cluster models, the magnetothermal instability (MTI) tends to reorient the magnetic fields radially. Using cosmological simulations of the Santa Barbara cluster we detect radial bias in the velocity and magnetic fields. Such radial bias is consistent with either the inhomogeneous radial gas flows due to substructures or residual MTI-driven field rearangements that are expected even in the presence of turbulence. Although disentangling the two scenarios is challenging, we do not detect excess bias in the runs that include anisotropic thermal conduction. The anisotropy effect is potentially detectable via radio polarization measurements with LOFAR and SKA and future X-ray spectroscopic studies with the IXO. We demonstrate that radiative cooling boosts the amplification of the magnetic field by about two orders of magnitude beyond what is expected in the non-radiative cases. At z=0 the field is amplified by a factor of about 10^6 compared to the uniform magnetic field evolved due to the universal expansion alone. Interestingly, the runs that include both radiative cooling and anisotropic thermal conduction exhibit stronger magnetic field amplification than purely radiative runs at the off-center locations. In these runs, shallow temperature gradients away from the cluster center make the ICM neutrally buoyant. The ICM is more easily mixed in these regions and the winding up of the frozen-in magnetic field is more efficient resulting in stronger magnetic field amplification.

Dynamical stability of a thermally stratified intracluster medium with anisotropic momentum and heat transport

In weakly-collisional plasmas such as the intracluster medium (ICM), heat and momentum transport become anisotropic with respect to the local magnetic field direction. Anisotropic heat conduction causes the slow magnetosonic wave to become buoyantly unstable to the magnetothermal instability (MTI) when the temperature increases in the direction of gravity and to the heat-flux--driven buoyancy instability (HBI) when the temperature decreases in the direction of gravity. The local changes in magnetic field strength that attend these instabilities cause pressure anisotropies that viscously damp motions parallel to the magnetic field. In this paper we employ a linear stability analysis to elucidate the effects of anisotropic viscosity (i.e. Braginskii pressure anisotropy) on the MTI and HBI. By stifling the convergence/divergence of magnetic field lines, pressure anisotropy significantly affects how the ICM interacts with the temperature gradient. Instabilities which depend upon the convergence/divergence of magnetic field lines to generate unstable buoyant motions (the HBI) are suppressed over much of the wavenumber space, whereas those which are otherwise impeded by field-line convergence/divergence (the MTI) are strengthened. As a result, the wavenumbers at which the HBI survives largely unsuppressed in the ICM have parallel components too small to rigorously be considered local. This is particularly true as the magnetic field becomes more and more orthogonal to the temperature gradient. In contrast, the fastest-growing MTI modes are unaffected by anisotropic viscosity. However, we find that anisotropic viscosity couples slow and Alfven waves in such a way as to buoyantly destabilise Alfvenic fluctuations when the temperature increases in the direction of gravity. Consequently, many wavenumbers previously considered MTI-stable or slow-growing are in fact maximally unstable. (abridged)

THE ANISOTROPIC TRANSPORT EFFECTS ON DILUTE PLASMAS

We examine the linear stability analysis of a hot, dilute and differentially rotating plasma by considering anisotropic transport effects. In the dilute plasmas, the ion Larmor radius is small compared with its collisional mean free path. In this case, the transport of heat and momentum along the magnetic field lines become important. This paper presents a novel linear instability that may more powerful and greater than ideal magnetothermal instability (MTI) and ideal magnetorotational instability (MRI) in the dilute astrophysical plasmas. This type of plasma is believed to be found in the intracluster medium of galaxy clusters and radiatively ineffective accretion flows around black holes. We derive the dispersion relation of this instability and obtain the instability condition. There is at least one unstable mode that is independent of the temperature gradient direction for a helical magnetic field geometry. This novel instability is driven by the gyroviscosity coupled with differential rotation. Therefore we call it as gyroviscous modified magnetorotational instability (GvMRI). We examine how the instability depends on signs of the temperature gradient and the gyroviscosity, and also on the magnitude of the thermal frequency and on the values of the pitch angle. We provide a detailed physical interpretation of obtained results. The GvMRI is applicable not only to the accretion flows and intracluster medium but also to the transition region between cool dense gas and the hot low-density plasma in stellar coronae, accretion disks, and the multiphase interstellar medium because of being independent of the temperature gradient direction.

Magnetothermal and magnetorotational instabilities in hot accretion flows

In a hot, dilute, magnetized accretion flow, the electron mean-free path can be much greater than the Larmor radius, thus thermal conduction is anisotropic and along magnetic field lines. In this case, if the temperature decreases outward, the flow may be subject to a buoyancy instability (the magnetothermal instability, or MTI). The MTI amplifies the magnetic field, and aligns field lines with the radial direction. If the accretion flow is differentially rotating, the magnetorotational instability (MRI) may also be present. Using two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate the interaction between these two instabilities. We use global simulations that span over two orders of magnitude in radius, centered on the region around the Bondi radius where the infall time of gas is longer than the growth time of both the MTI and MRI. Significant amplification of the magnetic field is produced by both instabilities, although we find that the MTI primarily amplifies the radial component, and the MRI primarily the toroidal component, of the field, respectively. Most importantly, we find that if the MTI can amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$, then when the MTI and MRI are both present, the magnetic energy can be amplified by a factor of $F_t \cdot F_r$. We therefore conclude that amplification of the magnetic energy by the MTI and MRI operates independently. We also find that the MTI contributes to the transport of angular momentum, because radial motions induced by the MTI increase the Maxwell (by amplifying the magnetic field) and Reynolds stresses. Finally, we find that thermal conduction decreases the slope of the radial temperature profile. The increased temperature near the Bondi radius decreases the mass accretion rate.

Anisotropic dissipative effects on the buoyancy instability with background heat flux

The linear buoyancy instability in magnetized plasmas is investigated in the presence of anisotropic resistivity and viscosity by taking into account the background heat flux. The magnetic field is assumed to be homogeneous and has both horizontal and vertical components. The heat is primarily transported along the magnetic force lines when the gyro radius is much less than the mean collision free path. The Hall term is examined first and shows a damping effect on the magnetothermal instability. The heat-flux-driven buoyancy instability (HBI) is then investigated by taking into account the parallel resistivity (PR), cross-field resistivity (CR), and the anisotropic viscosity. The general dispersion relation (DR) is derived and discussed in several special cases. We show that only the CR and viscosity exert effects on the DR in the first case. The critical condition for the occurrence of HBI is modified by the CR coupled with the viscosity and the value of the instability growth rate is diminished by them. The effects due to the PR (resp. viscosity) on the HBI are examined next. The PR (resp. viscosity) is shown to alter not only the growth rate but also the instability criterion. There exists an unstable mode when the temperature decreases in the direction of gravity while this case is proven to be magnetothermally stable in the ideal magnetohydrodynamic limit. A new unstable mode is solely induced by the presence of PR (resp. viscosity). When the PR and CR are both taken into account, the resistivity is shown to induce a damping mode rather than an instability. Finally, considering the PR and viscosity simultaneously, it is found that a new unstable mode is excited when the PR is not equal to the viscosity, or else, dissipation effects do not alter the instability criterion and just cut down the growth rate.

Can conduction induce convection? On the non-linear saturation of buoyancy instabilities in dilute plasmas

We study the effects of anisotropic thermal conduction on low-collisionality, astrophysical plasmas using two and three-dimensional magnetohydrodynamic simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable for either sign of the temperature gradient: the heat-flux-driven buoyancy instability (HBI) operates when the temperature increases with radius while the magnetothermal instability (MTI) operates in the opposite limit. In contrast to previous results, we show that, in the presence of a sustained temperature gradient, the MTI drives strong turbulence and operates as an efficient magnetic dynamo (akin to standard, adiabatic convection). Together, the turbulent and magnetic energies contribute up to ~10% of the pressure support in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5% of rho c_s^3. These findings are robust even in the presence of an external source of strong turbulence. Our results on the nonlinear saturation of the HBI are consistent with previous studies but we explain physically why the HBI saturates quiescently by re-orienting the magnetic field (suppressing the conductive heat flux through the plasma), while the MTI saturates by generating sustained turbulence. We also systematically study how an external source of turbulence affects the saturation of the HBI: such turbulence can disrupt the HBI only on scales where the shearing rate of the turbulence is faster than the growth rate of the HBI. In particular, our results provide a simple mapping between the level of turbulence in a plasma and the effective isotropic thermal conductivity. We discuss the astrophysical implications of these findings, with a particular focus on the intracluster medium of galaxy clusters.

Coupling of Kelvin–Helmholtz instability and buoyancy instability in a thermally laminar plasma

Thermal convective instability is investigated in a thermally stratified plasma in the presence of shear flow, which is known to give rise to the Kelvin–Helmholtz (KH) instability. We examine how the KH instability and magnetothermal instability (MTI) affect each other. Based on the sharp boundary model, the KH instability coupled with the MTI is studied. We present the growth rate and instability criteria. The shear flow is shown to significantly alter the critical condition for the occurrence of thermal convective instability.