Página 17 dos resultados de 33122 itens digitais encontrados em 0.034 segundos

## Baroclinic Instability in Stellar Radiation Zones

Kitchatinov, Leonid L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar radiation zones with baroclinic stratification can be unstable. Instabilities in radiation zones are of crucial importance for angular momentum transport, mixing of chemical species and, possibly, for magnetic field generation. This paper performs linear analysis of baroclinic instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation non-uniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of baroclinic instability. The instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic instability onsets at a very small differential rotation of below 1%. The characteristic time of instability growth is about one thousand rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from baroclinic instability in differentially rotating radiation zones is...

## Intrinsic Instability of Coronal Streamers

Chen, Y.; Li, X.; Song, H. Q.; Shi, Q. Q.; Feng, S. W.; Xia, L. D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
Plasma blobs are observed to be weak density enhancements as radially stretched structures emerging from the cusps of quiescent coronal streamers. In this paper, it is suggested that the formation of blobs is a consequence of an intrinsic instability of coronal streamers occurring at a very localized region around the cusp. The evolutionary process of the instability, as revealed in our calculations, can be described as follows: (1) through the localized cusp region where the field is too weak to sustain the confinement, plasmas expand and stretch the closed field lines radially outward as a result of the freezing-in effect of plasma-magnetic field coupling; the expansion brings a strong velocity gradient into the slow wind regime providing the free energy necessary for the onset of a subsequent magnetohydrodynamic instability; (2) the instability manifests itself mainly as mixed streaming sausage-kink modes, the former results in pinches of elongated magnetic loops to provoke reconnections at one or many locations to form blobs. Then, the streamer system returns to the configuration with a lower cusp point, subject to another cycle of streamer instability. Although the instability is intrinsic, it does not lead to the loss of the closed magnetic flux...

## The Gravitational instability of solids assisted by gas drag: slowing by turbulent mass diffusivity

Shariff, Karim; Cuzzi, Jeffrey N.
Tipo: Artigo de Revista Científica
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The Goldreich and Ward (1973) (axisymmetric) gravitational instability of a razor thin particle layer occurs when the Toomre parameter $Q_T \equiv c_p \Omega_0 / \pi G \Sigma_p < 1$ ($c_p$ being the particle dispersion velocity). Ward(1976,2000) extended this analysis by adding the effect of gas drag upon particles and found that even when $Q_T > 1$, sufficiently long waves were always unstable. Youdin (2005a,b) carried out a detailed analysis and showed that the instability allows chondrule-sized ($\sim 1$ mm) particles to undergo radial clumping with reasonable growth times even in the presence of a moderate amount of turbulent stirring. The analysis of Youdin includes the role of turbulence in setting the thickness of the dust layer and in creating a turbulent particle pressure in the momentum equation. However, he ignores the effect of turbulent mass diffusivity on the disturbance wave. Here we show that including this effect reduces the growth-rate significantly, by an amount that depends on the level of turbulence, and reduces the maximum intensity of turbulence the instability can withstand by 1 to 3 orders of magnitude. The instability is viable only when turbulence is extremely weak and the solid to gas surface density of the particle layer is considerably enhanced over minimum-mass-nebula values. A simple mechanistic explanation of the instability shows how the azimuthal component of drag promotes instability while the radial component hinders it. A gravito-diffusive overstability is also possible but never realized in the nebula models.; Comment: Accepted...

## Instability of bound states of a nonlinear Schr\"odinger equation with a Dirac potential

Le-Coz, Stefan; Fukuizumi, Reika; Fibich, Gadi; Ksherim, Baruch; Sivan, Yonatan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in $\hurad$ and unstable in $\hu$ under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a {\em finite-width instability}). In the non-radial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.

## Global Aspects of Elliptical Instability in Tidally Distorted Accretion Disks

Ryu, Dongsu; Goodman, Jeremy; Vishniac, Ethan T.
Tipo: Artigo de Revista Científica
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Tidally distorted accretion disks in binary star systems are subject to a local hydrodynamic instability which excites $m=1$ internal waves. This instability is three dimensional and approximately incompressible. We study the global aspects of this local instability using equations derived under the shearing sheet approximation, where the effects of the azimuthal variation along distorted orbital trajectories are included in source terms which oscillate with local orbital phase. Linear analyses show that the excitation of the instability is essentially local, i.e. insensitive to radial boundary conditions. The region of rapid growth feeds waves into the region of slow or negligible growth, allowing the instability to become global. The global growth rate depends the maximum local growth rate, the size of the rapid growth region, and the local group velocity. We present an empirical expression for the global growth rate. We note that the local nature of the instability allows the excitation of waves with $m\ne 1$ when the local growth rate is large.; Comment: ApJ submitted, 13 pages with 6 figures, uuencoded, gzipped, tarred postscript files, or available upon request to ryu@sirius.chungnam.ac.kr

## 3D Relativistic Magnetohydrodynamic Simulations of Current-Driven Instability. I. Instability of a static column

Mizuno, Yosuke; Lyubarsky, Yuri; Nishikawa, Ken-Ichi; Hardee, Philip E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the kink instability. The instability develops as predicted by linear theory. In the non-linear regime the kink amplitude continues to increase up to the terminal simulation time, albeit at different rates, for all but one simulation. The growth rate and nonlinear evolution of the CD kink instability depends moderately on the density profile and strongly on the magnetic pitch profile. The growth rate of the kink mode is reduced in the linear regime by an increase in the magnetic pitch with radius and the non-linear regime is reached at a later time than for constant helical pitch. On the other hand, the growth rate of the kink mode is increased in the linear regime by a decrease in the magnetic pitch with radius and reaches the non-linear regime sooner than the case with constant magnetic pitch. Kink amplitude growth in the non-linear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand...

## Eddy viscosity and turbulent Schmidt number by kink-type instability of strong toroidal magnetic fields

Ruediger, G.; Gellert, M.; Schultz, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
The potential of the nonaxisymmetric magnetic instability to transport angular momentum and to mix chemicals is probed considering the stability of a nearly uniform toroidal field between conducting cylinders with different rotation rates. The fluid between the cylinders is assumed as incompressible and to be of uniform density. With a linear theory the neutral-stability maps for m=1 are computed. Rigid rotation must be subAlfvenic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvenic rotation exists. The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm=1 and becomes much weaker for Pm unequal 1. The effective angular momentum transport by the instability is directed outwards(inwards) for subrotation(superrotation). The resulting magnetic-induced eddy viscosities exceed the microscopic values by factors of 10-100. This is only true for superAlfvenic flows; in the strong-field limit the values remain much smaller. The same instability also quenches concentration gradients of chemicals by its nonmagnetic fluctuations. The corresponding diffusion coefficient remains always smaller than the magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the ratio of the effective viscosity and the diffusion coefficient. The magnetic instability transports much more angular momentum than that it mixes chemicals.; Comment: 9 pages...

## Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars

Muhlberger, Curran D.; Nouri, Fatemeh Hossein; Duez, Matthew D.; Foucart, Francois; Kidder, Lawrence E.; Ott, Christian D.; Scheel, Mark A.; Szilágyi, Béla; Teukolsky, Saul A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the "low-T/|W| instability"), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magnetic fields on this instability. Though strong toroidal fields were predicted to suppress the low-T/|W| instability, we find that they do so only in a small range of field strengths. Below 4e13 G, poloidal seed fields do not wind up fast enough to have an effect before the instability saturates, while above 5e14 G, magnetic instabilities can actually amplify a global quadrupole mode (this threshold may be even lower in reality, as small-scale magnetic instabilities remain difficult to resolve numerically). Thus, the prospects for observing gravitational waves from such systems are not in fact diminished over most of the magnetic parameter space. Additionally...

## Kelvin-Helmholtz instability driven by coronal mass ejections in the turbulent corona

Gomez, Daniel O.; DeLuca, Edward E.; Mininni, Pablo D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
Recent high resolution AIA/SDO images show evidence of the development of the Kelvin-Helmholtz instability, as coronal mass ejections (CMEs) expand in the ambient corona. A large-scale magnetic field mostly tangential to the interface is observed, both on the CME and on the background sides. However, this magnetic field is not intense enough to quench the instability. There is also observational evidence that the ambient corona is in a turbulent regime, and therefore the development of the instability can differ significantly from the laminar case. To study the evolution of the Kelvin-Helmholtz instability with a turbulent background, we perform three-dimensional simulations of the magnetohydrodynamic equations. The instability is driven by a velocity profile tangential to the CME-corona interface, which we simulate through a hyperbolic tangent profile. The turbulent background is obtained by the application of a stationary stirring force. The main result from these simulations is the computation of the instability growth-rate for different values of the intensity of the turbulence.

## Screw instability of the magnetic field connecting a rotating black hole with its surrounding disk

Wang, D. X.; Ma, R. Y.; Lei, W. H.; Yao, G. Z.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
Screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disk is discussed based on the model of the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process (CEBZMC). A criterion for the screw instability with the state of CEBZMC is derived based on the calculations of the poloidal and toroidal components of the magnetic field on the disk. It is shown by the criterion that the screw instability will occur, if the BH spin and the power-law index for the variation of the magnetic field on the disk are greater than some critical values. It turns out that the instability occurs outside some critical radii on the disk. It is argued that the state of CEBZMC always accompanies the screw instability. In addtition, we show that the screw instability contributes only a small fraction of magnetic extraction of energy from a rotating BH.; Comment: 18 pages, 13 figures; Accepted by ApJ

## Instability criterion for oblique modes in stratified circular Couette flow

Normand, Christiane
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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An analytical approach is carried out that provides an inviscid stability criterion for the strato-rotational instability (in short SRI) occurring in a Taylor-Couette system. The control parameters of the problem are the rotation ratio $\mu$ and the radius ratio $\eta$. The study is motivated by recent experimental \cite{legal} and numerical \cite{rudi, rudi2} results reporting the existence of unstable modes beyond the Rayleigh line for centrifugal instability ($\mu =\eta^2$). The modified Rayleigh criterion for stably stratified flows provides the instability condition, $\mu<1$, while in experiments unstable modes were never found beyond the line $\mu=\eta$. Taking into account finite gap effects, we consider non axisymmetric perturbations with azimuthal wavenumber $l$ in the limit $l Fr<<1$, where $Fr$ is the Froude number. We derive a necessary condition for instability : $\mu < \mu^*$ where $\mu^*$, a function of $\eta$, takes the asymptotic values, $\mu^* \to 1$ in the narrow gap limit, and $\mu^* \to 2\eta^2(1+\eta)$ in the wide gap limit, in agreement with recent numerical findings. A stronger condition, $\mu<\eta$, is found when $\eta>0.38$, in agreement with experimental results obtained for $\eta=0.8$. Whatever the gap size...

## Current driven "plasmonic boom" instability in three-dimensional gated periodic ballistic nanostructures

Aizin, G. R.; Mikalopas, J.; Shur, M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
A new approach of using distributed transmission line analogy for solving transport equations for ballistic nanostructures is applied for solving the three dimensional problem of the electron transport in gated ballistic nanostructures with periodically changing width. The structures with the varying width allow for modulation of the electron drift velocity while keeping the plasma velocity constant. We predict that in such structures biased by a constant current, a periodic modulation of the electron drift velocity due the varying width results in the instability of the plasma waves if the electron drift velocity to plasma wave velocity ratio changes from below to above unity. The physics of such instability is similar to that of the sonic boom, but, in the periodically modulated structures, this analog of the sonic boom is repeated many times leading to a larger increment of the instability. The constant plasma velocity in the sections of different width leads to the resonant excitation of the unstable plasma modes with the varying bias current. This effect (that we refer to as the super plasmonic boom condition) results in a strong enhancement of the instability. The predicted instability involves the oscillating dipole charge carried by the plasma waves. The plasmons can be efficiently coupled to the terahertz (THz) electromagnetic radiation due to the periodic geometry of the gated structure. Our estimates show that the analyzed instability should enable powerful tunable terahertz electronic sources.; Comment: 12 pages...

## Energy Gradient Theory of Hydrodynamic Instability

Dou, Hua-Shu
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
A new universal theory for flow instability and turbulent transition is proposed in this study. Flow instability and turbulence transition have been challenging subjects for fluid dynamics for a century. The critical condition of turbulent transition from theory and experiments differs largely from each other for Poiseuille flows. In this paper, a new mechanism of flow instability and turbulence transition is presented for parallel shear flows and the energy gradient theory of hydrodynamic instability is proposed. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. A new dimensionless parameter K for characterizing flow instability is proposed for wall bounded shear flows, which is expressed as the ratio of the energy gradients in the two directions. It is thought that flow instability should first occur at the position of Kmax which may be the most dangerous position. This speculation is confirmed by Nishioka et al's experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of Kmax of about 385 for both plane Poiseuille flow and pipe Poiseuille flow...

## The magnetron instability in a pulsar's cylindrical electrosphere

Petri, Jerome
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
(abridged) The physics of the pulsar magnetosphere remains poorly constrained by observations. Little is known about their emission mechanism. Large vacuum gaps probably exist, and a non-neutral plasma partially fills the neutron star surroundings to form an electrosphere. We showed that the differentially rotating equatorial disk in the pulsar's electrosphere is diocotron unstable and that it tends to stabilise when relativistic effects are included. However, when approaching the light cylinder, particle inertia becomes significant and the electric drift approximation is violated. In this paper, we study the most general instability, i.e. by including particle inertia effects, as well as relativistic motions. This general non-neutral plasma instability is called the magnetron instability. We linearise the coupled relativistic cold-fluid and Maxwell equations. The non-linear eigenvalue problem for the perturbed azimuthal electric field component is solved numerically. The spectrum of the magnetron instability in a non-neutral plasma column confined between two cylindrically conducting walls is computed for several cylindrical configurations. For a pulsar electrosphere, no outer wall exists. In this case, we allow for electromagnetic wave emission propagating to infinity. When the self-field induced by the plasma becomes significant...

## Pair-Instability Supernovae in the Local Universe

Whalen, Daniel J.; Even, Wesley; Smidt, Joseph; Heger, Alexander; Hirschi, Raphael; Yusof, Norhasliza; Stiavelli, Massimo; Fryer, Chris L.; Chen, Ke-Jung; Joggerst, Candace C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
The discovery of 150 - 300 M$_{\odot}$ stars in the Local Group and pair-instability supernova candidates at low redshifts has excited interest in this exotic explosion mechanism. Realistic light curves for pair-instability supernovae at near-solar metallicities are key to identifying and properly interpreting these events as more are found. We have modeled pair-instability supernovae of 150 - 500 M$_{\odot}$ Z $\sim$ 0.1 - 0.4 Z$_{\odot}$ stars. These stars lose up to 80% of their mass to strong line-driven winds and explode as bare He cores. We find that their light curves and spectra are quite different from those of Population III pair-instability explosions, which therefore cannot be used as templates for low-redshift events. Although non-zero metallicity pair-instability supernovae are generally dimmer than their Population III counterparts, in some cases they will be bright enough to be detected at the earliest epochs at which they can occur, the formation of the first galaxies at $z \sim$ 10 - 15. Others can masquerade as dim, short duration supernovae that are only visible in the local universe and that under the right conditions could be hidden in a wide variety of supernova classes. We also report for the first time that some pair-instability explosions can create black holes with masses of $\sim$ 100 M$_{\odot}$.; Comment: 16 pages...

## Plasma effect in the longitudinal space charge induced microbunching instability for low energy electron beams

Huang, Dazhang; Ng, King Yuen; Gu, Qiang
Tipo: Artigo de Revista Científica
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The microbunching instability usually exists in the LINAC of a free electron laser (FEL) facility. In many cases, the longitudinal space charge (LSC) is a dominant factor that generates the instability. For the highly bright electron beams, the plasma effect is found to be non-trivial in the development of the instability. In this paper, starting from the Vlasov and Poisson equations in the multiple-dimensional phase space, we perform the straightforward analysis of the microbunching instability based on the explicit formula of the longitudinal electric field introduced by the density perturbation in the longitudinal direction, in such a way to be highly comparable to the well-developed method for higher energy beams. This method generally applies in both the cases with and without acceleration and independent of lattice components. The results show that for a electron beam with small transverse emittance at low energies, which is always the case in the injector of a free electron laser device, the plasma effect results in the oscillation of the longitudinal electric field in the modified plasma frequency that depends on the transverse size of the beam, and the Landau damping effect in the longitudinal electric field due to the uncorrelated longitudinal velocity spread during the beam transportation. These two effects both play important roles in the development of the instability. As the result...

## Constraints for the aperiodic O-mode streaming instability

Lazar, M.; Schlickeiser, R.; Poedts, S.; Stockem, A.; Vafin, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.47%
In plasmas where the thermal energy density exceeds the magnetic energy density ($\beta_\parallel > 1$), the aperiodic ordinary mode (O-mode) instability is driven by an excess of parallel temperature $A = T_\perp /T_\parallel < 1$ (where $\parallel$ and $\perp$ denote directions relative to the uniform magnetic field). When stimulated by parallel plasma streams the instability conditions extend to low beta states, i.e., $\beta_\parallel <1$, and recent studies have proven the existence of a new regime, where the anisotropy threshold decreases steeply with lowering $\beta_\parallel \to 0$ if the streaming velocity is sufficiently high. However, the occurrence of this instability is questionable especially in the low-beta plasmas, where the electrostatic two-stream instabilities are expected to develop much faster in the process of relaxation of the counterstreams. It is therefore proposed here to identify the instability conditions for the O-mode below those required for the onset of the electrostatic instability. An hierarchy of these two instabilities is established for both the low $\beta_\parallel <1$ and large $\beta_\parallel > 1$ plasmas. The conditions where the O-mode instability can operate efficiently are markedly constrained by the electrostatic instabilities especially in the low-beta plasmas.; Comment: 9 pages...

## The ballistic transport instability in Saturn's rings I: formalism and linear theory

Latter, Henrik; Ogilvie, Gordon; Chupeau, Marie
Tipo: Artigo de Revista Científica
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Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time scales of 10^5 - 10^7 years. The debris ejected from such impacts re-accretes on to the ring, though often at a slightly different orbital radius from the point of emission. This `ballistic transport' leads to a rearrangement of the disk's mass and angular momentum, and gives rise to a linear instability that generates structure on relatively large scales. It is likely that the 100-km undulations in Saturn's inner B-ring and the plateaus and 1000-km waves in Saturn's C-ring are connected to the nonlinear saturation of the instability. In this paper the physical problem is reformulated so as to apply to a local patch of disk (the shearing sheet). This new streamlined model helps facilitate our physical understanding of the instability, and also makes more tractable the analysis of its nonlinear dynamics. We concentrate on the linear theory in this paper, showing that the instability is restricted to a preferred range of intermediate wavenumbers and optical depths. We subsequently apply these general results to the inner B-ring and the C-ring and find that in both regions the ballistic transport instability should be near marginality...

## Effects of Rotation on the Minimum Mass of Primordial Progenitors of Pair Instability Supernovae

Chatzopoulos, Emmanouil; Wheeler, J. Craig
Tipo: Artigo de Revista Científica
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26.47%
The issue of which stars may reach the conditions of electron/positron pair formation instability is of importance to understand the final evolution both of the first stars and of contemporary stars. The criterion to enter the pair instability regime in density and temperature is basically controlled by the mass of the oxygen core. The main sequence masses that produce a given oxygen core mass are, in turn, dependent on metallicity, mass loss, and convective and rotationally-induced mixing. We examine the evolution of massive stars to determine the minimum main sequence mass that can encounter pair-instability effects, either a pulsational pair instability (PPISN) or a full-fledged pair-instability supernova (PISN). We concentrate on zero-metallicity stars with no mass loss subject to the Schwarzschild criterion for convective instability, but also explore solar metallicity and mass loss and the Ledoux criterion. As expected, for sufficiently strong rotationally-induced mixing, the minimum main sequence mass is encountered for conditions that induce effectively homogeneous evolution such that the original mass is converted almost entirely to helium and then to oxygen. For this case, we find that the minimum main sequence mass is ~40 Msun to encounter PPISN and ~65 Msun to encounter a PISN. When mass-loss is taken into account those mass limits become ~50 Msun for PPISN and ~80 Msun for PISN progenitors. The implications of these results for the first stars and for contemporary supernovae is discussed.; Comment: 23 pages...

## Is the Weibel instability enhanced by the suprathermal populations, or not?

Lazar, M.; Schlickeiser, R.; Poedts, S.
The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the anisotropic distribution function. In order to illustrate the distinguishing properties of this instability a \emph{product-bi-Kappa distribution} is introduced, with the advantage that this distribution function enables the use of different values of the spectral index in the two directions, $\kappa_{\parallel} \ne \kappa_{\perp}$. The growth rates and the instability threshold are derived and contrasted with those for a simple bi-Kappa and a bi-Maxwellian. Thus, while the maximum growth rates reached at the saturation are found to be higher, the threshold is drastically reduced making the anisotropic product-bi-Kappa (with small kappas) highly susceptible to the Weibel instability. This effect could also rise questions on the temperature or the temperature anisotropy that seems to be not an exclusive source of free energy for this instability...