Limits for the Firehose Instability in Space Plasmas

Electromagnetic instabilities in high-β plasmas, where β is the ratio of the kinetic plasma energy to the magnetic energy, have a broad range of astrophysical applications. The presence of temperature anisotropies T _∥ /T _⊥ >1 (where ∥ and ⊥ denote directions relative to the background magnetic field) in solar flares and the solar wind is sustained by the observations and robust acceleration mechanisms that heat plasma particles in the parallel direction. The surplus of parallel kinetic energy can excite either the Weibel-like instability (WI) of the ordinary mode perpendicular to the magnetic field or the firehose instability (FHI) of the circularly polarized waves at parallel propagation. The interplay of these two instabilities is examined. The growth rates and the thresholds provided by the kinetic Vlasov – Maxwell theory are compared. The WI is the fastest growing one with a growth rate that is several orders of magnitude larger than that of the FHI. These instabilities are however inhibited by the ambient magnetic field by introducing a temperature anisotropy threshold. The WI admits a larger anisotropy threshold, so that, under this threshold, the FHI remains the principal mechanism of relaxation. The criteria provided here by describing the interplay of the WI and FHI are relevant for the existence of these two instabilities in any space plasma system characterized by an excess of parallel kinetic energy.     

High-latitude Pc1–2 geomagnetic pulsations and their connection with location of the dayside polar cusp

The result of investigating high-latitude Pc1–2 pulsations are presented in this paper. They show that these unstructured oscillations are typical in intervals of low magnetic activity for regions of projections of the dayside cusp on the Earth's surface. The morphological properties of these pulsations, namely the character of their diurnal variations and dependence of their amplitude and frequency of occurrence on magnetic activity on different latitudes, suggest methods of utilization for tracing the location of the equatorial boundary of the dayside cusp. It is suggested that Pc1–2 pulsations are generated mainly in the dayside magnetosheath on field lines, crossing the magnetopause and entering in the dayside cusp. The possible mechanism of generation is the ion-cyclotron instability of plasma of finite pressure (β_⊥ ? 1) and with anisotropic temperature (T_⊥ > T_∥).     

On the distribution of By in the geomagnetic tail

The distribution of B_y in the geomagnetic tail associated with a net cross-tail magnetic flux, recently experimentally discovered, is here investigated within the framework of two-dimensional but non-planar field adiabatic time-independent equilbria. It is found that the flux distribution is controlled by the pressure anisotropy of the plasma, B_y being enhanced at the current sheet centre relative to that in the lobes for P_∥>P_⊥ and vice-versa for P_⊥>P_∥. For P_⊥>P_∥ a broad region of depressed field strength is found across the centre plane of the current sheet, terminated at its outer boundaries by spikes in the perpendicular current, across which B_y and B_x are “switched on” and rapidly increase towards their values in the low-β lobes. For P_∥>P_⊥ a thin high-current density layer forms at the sheet centre if the marginal firehose condition is approached, across which the B_x field reverses by rotation at nearly constant magnitude about the z-axis. The field magnitude in this thin layer depends upon the pressure anisotropy, such that the plasma remains just firehose stable within it, and may approach an appreciable fraction of the lobe field strength even for moderate anisotropies. Such structures have been observed in the geomagnetic tail, but do not appear to be a common feature of the quiet-time plasmasheet, where the field strength at the centre plane can reach small values with little obvious enhancement of B_y. In terms of the present model these observations require that either P_⊥>P_∥ in the quiet-time tail or that the plasma is within one or two per cent of isotropy if P_∥>P_⊥. These results then indicate that the production of plasma pressure anisotropy during adiabatic inward transport towards the Earth, which is generally expected to lead to P_∥>P_⊥ and its destruction by either macroscopic or microscopic processes, requires further study.     

On the role of plasma parameters and the Kelvin-Helmholtz instability in a viscous interaction of solar wind streams

We examine a mechanism for breaking down solar wind (SW) speed shears within 1 astronomical unit (a.u.), initiated by the development of the Kelvin-Helmholtz (K-H) instability for typical parameters of the plasma and magnetic field in the interplanetary medium. A semi-empirical SW model has been invoked to derive a distribution of the plasma parameters β = 8πP/B² and M_A² = (ρν²/2)/(B²/8π) between the Sun and 1 a.u. It is shown that in the vicinity of the Sun, up to heliocentric distances r ≈ 0.1 a.u., the parameters β ? 1, and M²_A ? 1 and therefore the magnetic field here may be considered a very strong one. Because of the stabilizing effect of the magnetic field the K-H instability in this region does not develop and a presence of great shears in SW speed with large velocity gradients is possible here.At distances r > 0.1 a.u. the parameters β ? 1, and M²_A > 1. Examination of a variety of SW speed profiles showed that the presence of plasma flow velocity shears in this region leads to an excitation of the K-H instability. Numerical analysis results indicate that a principal role in the excitation of this instability is played by oblique waves that propagate at an angle α ≈ 45° to the stream velocity vector.The question of the evolution of the leading front of a high speed SW streams within 1 a.u. is discussed, with a proper account of the influence of competing effects of kinematic steepening and turbulent viscosity, the latter being due to the development of the K-H instability. It is shown that the turbulent viscosity effect in this region is substantial and is capable of ensuring an expansion of the leading front of the high speed SW stream as this moves from 0.3 to 1 a.u., in agreement with experimental evidence reported by Rosenbauer et al. (1977).     

Stability of zonal flows on Jupiter

Jupiter's troposphere is bounded below by a deep layer of fluid which is probably extremely close to adiabatic. This paper explores the effect of this new boundary condition on the stability of atmospheric jets. The three parameters of the problem are the Rossby number Ro = U/fl, the ratio of the deformation radius l to the horizontal scale of jets y₀, and the nondimensional value of $\text{β,}\text{β}\text{= βl}{}^2\text{/U}$. The tropospheric deformation radius is unknown; all other quantities are constrained by observation. If the deformation radius is small, then nongeostrophic instabilities are of interest, and the regime is given by $\text{Ro = O(1), l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Using an Eady model, it is found for this case that the new boundary condition suppresses baroclinic instabilities but that if Ro > 1 (corresponding to a Richardson number less than unity) then inertial instabilities exist as usual. If the deformation radius is somewhat larger, the regime of interest if $\text{Ro ? 1, l/y}{}_0\text{? 1,}\text{β}\text{? 1}$. Horizontal shear can be neglected but β cannot. In this case, it is found that Eady-type baroclinic modes $\text{(}\text{β}\text{= 0)}$ again do not grow, but that the Charney modes $\text{(}\text{β}\text{≠ 0)}$ can exist. Finally, if l/y₀ = O(1) it is found that mixed barotropic-baroclinic instability can exist. Its stability boundaries and energetics approach those of pure barotropic instability when l/y₀ exceeds unity. Observations are discussed: the l/y₀ ? 1 regime appears most relevant. The mixed barotropic-baroclinic modes in this regime display upgradient momentum fluxes.     

On the interaction between the URCA process and convection

The influence of the URCA process (β-decay, electron capture) on convective stability is investigated and a stability criterion is derived. The criterion contains the Schwarzschild criterion and the thermohaline convection. It is found that URCA may cause convective instability to an otherwise stable medium, but it cannot stabilize an unstable medium, only the growth rate is affected. A numerical example for the Na²³?Ne²³ URCA pair shows the regions in the ?-T plane where instability is caused (assuming given abundances of the isotopes). The evolution of C-O core of an evolved 3.5M _⊙–8M _⊙ star may be affected by formation of convective regions even prior to C¹² ignition.     

Drift instabilities associated with the particles in ring current and inner edge of plasma sheet

Electromagnetic waves propagating transverse to the magnetic field, containing inhomogenous and loss cone plasma, may become unstable due to the excitation of resonant proton, resonant electron and drift cyclotron instabilities. Resonant proton instability gets excited in inhomogenous plasma, irrespective of the presence of temperature anisotropy, loss cone or temperature gradient. However, the growth rate of this instability is much smaller than the other two instabilities. The maximum growth rates of resonant electron instability are enhanced with the increase of loss cone index, gradients in transverse temperature and magnetic field, and with the decrease of temperature anisotropy and gradients in density and parallel temperature. The drift cyclotron instability exists in a bounded range of wave numbers and its growth rate increases with the increase of electron temperature, density and magnetic field gradient, and with the decrease of proton temperature and temperature anisotropy. In the region of ring current for beyond plasmapause the resonant proton and resonant electron instabilities have the characterstic frequencies around 0.1Ω_p and growth rates ~10^?6Ω_p and 10^?3Ω_p, respectively. In the ring current region the drift cyclotron instability is not excited whereas in the plasma sheet region the frequency and growth rate of this instability are around Ω_p and 10^?2Ω_p, respectively. These instabilities can accelerate the ring current particles along the magnetic field lines and dump them into the auroral region.     

Stability of a class of non-static axial self-gravitating systems in f(R) gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider f(R)=R+?R ² model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, Γ ₁, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the f(R) model affect the instability ranges.     

Electromagnetic instability in collisionless anisotropic plasma contrastreams

The electromagnetic instability in collisionless, anisotropic magnetized plasma contrastreams for perturbations propagating normally to the ambient magnetic field is investigated. It is found that the parallel temperature stabilizes the configuration forT _‖≤T _⊥ while it shows destabilizing effect forT _‖>T _⊥. A comparative study of the growth rates associated with various coexisting modes reveals that the electromagnetic instability may, under certain conditions, be associated with larger growth rates than the electrostatic instability.     

Numerical solution of the time-dependent heat energy equations for the magnetosphere

A new solution of the magnetospheric heat equations capable of covering the whole region from 300 km along a field line to the equatorial plane has been achieved by adapting the searching procedure of Murphy (1974). It has been found that the protonospheric heat reservoir is sufficient to maintain T_e >T_n down to the height of the F2-peak electron density all through the night at mid-latitudes. Full solution of the equations has also shown that T_i >T_e in the protonosphere at night and the ions constitute a significant source of heat for the electrons.     

Cosmological evolution of agegraphic dark energy with the sign-changeable interaction

In this paper, we study a cosmological model with the sign-changeable interaction between agegraphic dark energy (ADE) and dark matter. For the accelerated expansion of the universe, the model parameters n and β should satisfy the condition n>1 and $-\frac{2}{3}<\beta<0$ . We also investigate the effect of the parameters n and β on the evolutive behavior of our universe. Furthermore, by analysis it is shown that the equation of state of ADE with the sign-changeable interaction can cross the phantom divide from w _d >?1 to w _d <?1 for the appropriate n and β. This is different from that of ADE with usual interaction, whose equation of state changes from w _d <?1 to w _d >?1.     

Pulsational instability of yellow hypergiants

Instability of population I (X = 0.7, Z = 0.02) massive stars against radial oscillations during the post-main-sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range 65M _⊙ ≤ M _ZAMS ≤ 90M _⊙. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is T _eff > 6700 K for M _ZAMS = 65M _⊙ and T _eff > 7200 K for M _ZAMS = 90M _⊙. Pulsational instability is due to the κ-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed ≈200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is T _eff > 7300 K for M _ZAMS = 65M _⊙ and T _eff > 7600 K for M _ZAMS = 90M _⊙. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (T _eff > 7700 K for M _ZAMS = 65M _⊙ and T _eff > 8200 K for M _ZAMS = 90M _⊙). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed ≈130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.     

MHD waves and instabilities of a temperature-anisotropic plasma in the solar corona as a source of its heating

The MHD instabilities of a temperature-anisotropic coronal plasma are considered. We show that aperiodic mirror instabilities of slow MHD waves can develop under solar coronal conditions for weak magnetic fields (B < 1 G) and periodic ion-acoustic instabilities can develop for strong magnetic fields (B > 10 G). We have found the instability growth rates and estimated the temporal and spatial scales of development and decay of the periodic instability. We show that the instabilities under consideration can play a prominent role in the energy balance of the corona and may be considered as a large-scale energy source of the wave coronal heating mechanism.     

Study of inertial kinetic Alfven waves around cusp region

The effect of electron inertia on kinetic Alfven wave has been studied. The expressions for the dispersion relation, growth/damping rate and growth/damping length of the inertial kinetic Alfven wave (IKAW) are derived using the kinetic approach in cusp region. The Vlasov-kinetic theory has been adopted to evaluate the dispersion relation, growth/damping rate and growth/damping length with respect to the perpendicular wave number k_⊥ρ_i (ρ_i is the ion gyroradius) at different plasma densities. The growth/damping rate and growth/damping length are evaluated for different m_e/βm_i, where β is the ratio of electron pressure to the magnetic field pressure, m_{i, e} are the mass of ion and electron, respectively, as I=m_e/βm_i represent boundary between the kinetic and inertial regimes. It is observed that frequency of inertial kinetic Alfven wave (IKAW) ω is decreasing with k_⊥ρ_i and plasma density. The polar cusp is an ideal laboratory for studies of nonlinear plasma processes important for understanding the basic plasma physics, as well as the magnetospheric and astrophysical applications of these processes.     

Microscopic filamentation due to electrothermal instability and plasma heating in time-dependent solar transition layer

We have investigated nonlinear equilibrium states of a microscopic current filamentation (electrothermal instability) in solar atmosphere. The microscopic filamentation instability will develop for transition zone ion temperature plasmas, provided T _e/T_i > 1, where T _e and T _i are the electron and ion temperatures, respectively. Since the temperature radio for a steady-state solar atmosphere is approximately unity, the electrothermal instability will develop only in a time-dependent solar atmosphere. Indeed, such a condition is provided by time-dependent currents, which seem to exist in many magnetic loops as recent analysis by Porter et al. (1987) indicates. When the onset condition for the electrothermal instability is satisfied, the instability drives a current filamentation to a nonlinear equilibrium state with a spatially periodic electron temperature variation with the wavelength comparable to several ion-Larmor radii. The amplitude of the periodic temperature variation may be so large that the transition layer temperature and coronal temperature plasmas may exist within several Larmor radii — coexistence of the transition zone and corona within the same macro-volume.     

On the peak level of tearing instability in an ion-scale current sheet: The effects of ion temperature anisotropy

We have systematically surveyed the effects of the ion temperature anisotropy on the peak reconnected flux level of the tearing instability excited in a thick current sheet (its half-thickness D equal to the ion inertial length). A series of two- and three-dimensional (2-D and 3-D) simulations have been performed for a magnetotail-like situation, where the ion perpendicular temperature is fixed to balance the magnetic pressure of the lobe while the ion parallel temperature can be varied to give rise to the temperature anisotropy α_i=T_i,perp/T_i,para. Focusing on the behavior of the fastest growing mode (wavelength λ=12D), the results are summarized as follows: (1) The peak levels are larger when the initial α_i is larger and lobe reconnection is obtained only when α_i>1.5. (2) 3-D effects do speed-up the reconnection process but do not change the peak level substantially. (3) The time-scale of gas pressure build-up at the center of magnetic islands relative to the time-scale of reconnected flux growth is identified to be the key issue in determining the peak level. Based on these results for the fastest growing mode with λ=12D, discussion is given on the larger-scale development, that is, what happens when longer wavelength modes are allowed to develop.     

The Long-term Light Variation of BL Lac Object 1ES 1959+650

According to the data of optical observations of the Tuorla Observatory in Finland, using the power spectrum method, DCF (Discrete Correlation Function) method, and Jurkevich method, respectively, we analyzed the periodicity of the long-term light variation of the BL Lac object 1ES 1959+650, and obtained its light period to be P =1.4±0.3 yr. Assuming that the origin of the periodicity is concerned with the accretion disk, we obtained the region where the instability of this source occurs being R =9.65 R_g, here R_g represents the Schwarzschild radius.     

Suppression of the firehose instability by hard energy spectra

The growth rate of the relativistic firehose instability is an order of magnitude smaller, near marginal instability, for plasmas with particle energy spectraN(E)dEE ^–2.5dE than for those withN(E)dEE ^–3dE. If cosmic rays are accelerated impulsively in limited regions, with initially flat spectra, the sudden increase in the firehose growth rate could lead to release of the particles when the spectrum has steepened beyond exponent 2.5.     

Kinetic Alfven waves in plasma sheet boundary layer—particle aspect analysis

The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of kinetic Alfven wave. Expressions are found for the dispersion relation, damping rate and associated currents in homogenous plasma. Kinetic effects of electrons and ions are included to study kinetic Alfven wave because both are important in the transition region. It is found that the ratio β of electron thermal energy density to magnetic field energy density and the ratio of ion to electron thermal temperature (T_i/T_e) affect the dispersion relation, damping-rate and associated currents in both cases (warm and cold electron limits). The treatment of kinetic Alfven wave instability is based on the assumption that the plasma consists of resonant and non-resonant particles. The resonant particles participate in an energy exchange process, whereas the non-resonant particles support the oscillatory motion of the wave.