The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

Self-generated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that firehose and ordinary-mode instabilities can develop under the same conditions, which makes it challenging to separate the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron-temperature anisotropy T _∥>T _⊥, where ∥ and ⊥ denote directions with respect to the local mean magnetic field. In addition to the previously reported comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, with a focus on the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For stronger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding those of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the low β [<?1] regimes, here it is rigorously shown that only the high β [>?1] regimes are susceptible to these instabilities.     

Temperature anisotropy instabilities in a plasma containing cold and hot species in the magnetosphere

The nature of convective instability has been investigated for an electromagnetic wave, either right circularly polarised or left circularly polarised, propagating along a magnetic line of force in a plasma whose distribution function exhibits a temperature anisotropy in the hot species, a loss cone structure and a beam of cold electrons or ions travelling along the line of force with velocity V₁. Detailed numerical calculations have been made using a computer for the growth and decay of the wave for different values of the anisotropy ratio T_⊥/T_∥ = δ of the perpendicular and parallel temperatures, the McIlwain parameter L, the loss cone index j, velocity V₁ of the streaming particle and the particle density ratio ε. The ranges of values of ε and δ for which the wave becomes unstable have been studied in detail. It is found that wave propagation shows no dependence on the loss cone index but shows very strong dependence on the temperature anisotropy δ.     

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 stability of almost perpendicularly propagating ion cyclotron waves

The dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave, having a wavelength much larger than the ion Larmour radius r_L and a frequency $\text{ω ≈ Ω}{}^{\mathrm{+}}\text{(Ω}{}^{\mathrm{+}}$ is the ion cyclotron frequency), has been derived for a plasma consisting of a hot and a cold ion component. The hot ions and electrons have been described by loss-cone distribution functions; an ordering of the parameters was used to derive the cold ion contributions. Two modes, one with an increasing frequency and another with a constant frequency can propagate in the plasma. The two modes interact resulting in an instability of the former in the wavelength range k_⊥r_⊥ = 0.4?0.6 (for n_C/n_H = 0) and from k_⊥r_L = 0.5?0.8 (for n_C/n_H = 1.0) for a propagation angle of 70°. The instability of the mode is found to decrease with increasing cold ion densities and propagation angles.     

Role of anisotropy of the initial particle distribution in the acceleration in collapsing solar-flare traps

We consider the behavior of charged particles with an anisotropic initial velocity distribution in a magnetic trap with approaching mirrors in connection with the problem of particle acceleration in solar flares. We show that, irrespective of the charge sign, the efficiency of confinement and acceleration increases with increasing anisotropy factor of the initial distribution α = (T_⊥/T_∥)^1/2. For a positive electric potential of the trap plasma relative to the mirrors, the emerging additional effect of ion expulsion form the trap increases with α_i. The derived estimate of the electric potential suggests an amplification of the initial perturbation and the development of instability.     

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.     

The relationship of the boundary layer of the magnetosphere to IPRP events

A model is proposed in which a mixture of hot solar wind and cold atmospheric plasma flowing in the dayside equatorial boundary layer towards the dawn-dusk plane generates hydromagnetic waves near the frequency $\text{ω = ω}{}_{\mathrm{Bi}}\text{¦1 ? T}{}_{\mathrm{\parallel }}\text{¦T}{}_{\mathrm{\perp }}\text{¦}$ where ω_Bi is the ion gyrofrequency and T_∥, T_⊥ are the temperatures of the solar wind plasma, parallel and perpendicular respectively to the magnetic field B. The model accounts for the properties of IPRP events, i.e. intervals of geomagnetic pulsations of periods rising on average from about 2 s to about 7 s over an interval of about 5 min. The diagnostic potential of this phenomenon for study of the boundary layer is indicated.     

The electron-ion streaming instabilities driven by drift velocities of the order of electron thermal velocity in a nonmagnetized plasma

The kinetic Alfven waves are investigated using Maxwell-Boltzmann-Vlasov equation to evaluate the kinetic dispersion relation and growth/damping rate with magnetic field gradient, density gradient, temperature gradient and velocity gradient with inhomogeneous plasma. The effect of gradient terms is included in the analysis for both the regions k _⊥ ρ _i <1 and k _⊥ ρ _i >1, where k _⊥ is the perpendicular wave number and ρ _i is the ion gyroradius. This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. This model is able to explain many features observed in plasma sheet boundary layer as well as to evaluate the dispersion relation, growth rate, growth length and damping rate of kinetic Alfven wave. The applicability of this model is assumed for auroral acceleration region, plasma sheet boundary layer and cusp region.     

Quiet auroral arcs: Ionosphere effect of magnetospheric convection stratification

A detailed study of the mechanism of electromagnetic stratification of the large-scale stationary magnetospheric convection due to a friction of the convective flow in the ionosphere layer was performed. Magnetosphere-ionosphere interaction was taken into account by means of the effective boundary conditions on the ionosphere top and bottom boundaries including the actual height profile of charge particles velocity in the ionosphere. It has been shown that the magnetospheric convection is stratified into small-scale current sheets which are respective in the linear approximation to an oblique Alfvén wave. The dispersion equation was deduced for the Alfvén mode and its solution obtained determining the space-time scales and the increment of instability. The maximum increment is realized for the disturbances stretched along the convection velocity that is correspondent to the actual orientation of the auroral arcs. In the conditions of rapid growth of Alfvén velocity above the maximum of the ionosphere F layer, it was shown that small-scale disturbances with the transverse scales l_⊥ ? 1 km are localized at the altitudes up to several thousand kilometers whereas the large-scale stratification penetrate into the equatorial plane of the magnetosphere. A mechanism is proposed to intensify the parallel electric field acting at that stratification stage when the field-aligned currents in the Alfvén wave are sufficient to form abnormal resistance along geomagnetic lines of force.     

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.     

Evolution of the size of components of class D II radio sources

For 60 Class DII radio sources, I calculate the linear size of the radio components d in the direction perpendicular to the line joining the components. I find 1) d_⊥ has an upper limit of 150 kpc and a lower limit of 4～ 6 kpc, and 2) d_⊥, is correlated with the luminosity M_v of the central body, smaller components being associated with lower luminosities. This correlation is shown both by the regression of M_v on d_⊥, for 13 sources with redshifts between 0.35 and 0.60 and by an upper envelope in the M_v ? d_⊥ plot for the entire sample. This result is in conflict with the usual expanding models of radio lobes. An alternative model is proposed here: a radio lobe is taken to be a mass of turbulent plasmon formed with the intergalactic medium behind the shock front excited by an energy-carrying beam from the central body. The size of the lobe varies with the drilling velocity at the tip of the beam, which in turn depends on the energy transported within the beam. As the central body gets depleted, both its luminosity and the energy injected into the beam become less and the lobe gets smaller. An exponentially decaying central store can reproduce the observed statistical relation.     

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.     

Graphite grain formation in the atmospheres of R coronae borealis stars

The results of calculations of graphite grain formation in the atmospheres of R CrB stars are given. The parameters for the models wereM=1M _⊙,M _bol=?6 mag. The effective temperature ranged from 5300K to 8300K. The chemical composition corresponded to the hydrogen-deficient carbon rich mixture:X=0,Y=0.9,Z _c=0.1. The results obtained show the existence of a critical mass loss rate which is ranged fromM _*≈10^?6 M _⊙yr^?1 forT _eff=5300 K toM _*≈10^?5 M _⊙ yr^?1 forT _eff=8300 K. As soon as the rate of mass loss exceedsM _* by 3–5 times the degree of condensation of carbon changes from 0 to 0.7. The finite radii of grains are about from 0.01 μm to 0.6 μm depending on the density near the condensation point, the velocity of matter outflow, and the stellar effective temperature. The duration of grain growth should amount to some dozens of days. It is supposed that the most probable explanation of dust-shell formation around R CrB stars is graphite condensation behind a shock wave arising from nonlinear stellar pulsation.     

The effect of interplanetary acceleration on the propagation of energetic solar particles in prompt events

Crank-Nicholson solutions are obtained to the time-dependent Fokker-Planck equation for propagation in the interplanetary medium following a point in time injection of energetic solar particles and including the acceleration terms $$\frac{\partial }{{\partial T}}\left( {D_{TT} \frac{{\partial U}}{{\partial T}}} \right) - \frac{\partial }{{\partial T}}\left( {\frac{{D_{TT} U}}{{2T}}} \right)$$ . The diffusion coefficient in kinetic energyD _TT is allowed to be either independent of radial distance,R(AU), or follow the lawD _TT=D₀T²R ₀ ² /(A²+R²) in either case with the 1 AU value ofD _TT at 10 MeV ranging between 10^?4 (MeV)² s^?1 and zero. The spatial diffusion mean free path at the Earth's orbit is fixed at λ_‖ AU at 10 MeV according to numerical estimates made by Moussas and Quenby. However, a variety ofR dependences are allowed. Reasonable agreement with experimental data out to 4 AU is obtained with the above values ofD _TT and the spatial diffusion coefficientK _r=K₀R^?2 forR«1 andK _r=K₀R^0.4 forR»1 AU. It is only in the decay phases of prompt events as seen at 2–4 AU that significant differences in the temporal behaviour of the events can be distinguished, depending on the value ofD _TT chosen within the above range. Experimental determination of the decay constant is difficult.     

Temperature anisotropy of the Jovian sulfur nebula

We discuss the apparent paradox between the reported observation of a 3-eV gyration energy of Jupiter's ionized sulfur nebula and its observed thickness. We present an observation of the thickness of the cloud taken nearly edge on and show that this implies a large bounce-averaged anisotropy of the sulfur in temperature, T₆ ? T_⊥. From these observations, we construct a self-consistent model of the sulfur nebula in which the sulfur ions are injected by Io as ions and remain sufficiently collisionless in the magnetosphere to maintain the anisotropy for a time longer than a characteristic diffusion time. We also show that the proton-electron plasma is collisionally thermalized and provides an adequate means of tapping the rotational energy of the planet to provide the power radiated in the sulfur lines.     

Measurement of the longitudinal magnetic-field component for FU Ori

The Main Stellar Spectrograph of the 6-m Special Astrophysical Observatory telescope equipped with a polarimetric analyzer was used to measure the longitudinal magnetic-field component of FU Ori on January 24, 2002. The following (3σ) upper limits were obtained for the magnetic field B_‖: B_‖<350–400 G in the formation region of Fe I, Ni I, and Ca I absorption lines (disk + wind), and B_‖<200 G in the formation region of the absorption component of the Hα line with a P Cyg profile. We conclude that the strength of a large-scale magnetic field capable of collimating the disk wind does not exceed 300 G. For the region where the emission component of the Hα line is formed, we found that B_‖<100 G. Such a low value may have been obtained because the magnetic field lines in this region were almost perpendicular to the line of sight at the time of our observations.     

Radial pulsation of less-massive yellow supergiants

Linear and nonlinear pulsation computations for the modelsM=0.8M _⊙,L=10000 and 20000L _⊙ were carried out in order to understand FG Sge's pulsation. The results may be summarized as follows:

1. In the modelsL=10000L _⊙, the fundamental blue edge is nearT _e =5700 K. The models show that instability of the third overtone extends to 7400 K and still has large positive growth rates. A nonlinear model of 7000 K shows a small amplitude ΔV=10 km s^?1, ΔM _bol=0.03 with a period of around 18 days, nearly equal to that of the third overtone.
2. In the linear models ofL=20000L _⊙, the fundamental blue edge is shifted to 7000 K but the damping of this mode is so small that it is marginally stable to 7700 K. The third overtone has large positive growth rates of this region. The nonlinear model at 7700 K, however, shows no indication of third overtone pulsation.

We also examine the possibility, suggested by Whitney (1978), that the mass of FG Sge is 0.4M _⊙.     

Atmospheric parameters and mass distribution of DA-white dwarfs

The method of effective temperatureT _eff and logg determination for DA-white dwarfs by KSW model atmospheres is analyzed. The existence of systematic errors in logg determination, leading to lower mass values forT _eff>15000 K, is demonstrated. With due account to logg corrections, masses for 355 DA-dwarfs were evaluated. The influence of the effects of observational selection on mass distribution has been considered. These effects are connected with the fact that such selection on effects favour discovery of white dwarfs of low masses. The distribution obtained is characterized by the average mass of ～0.75M _⊙ and the distribution width of ～0.20M _⊙.     

Frost grain size metamorphism: Implications for remote sensing of planetary surfaces

An understanding of the rates of frost grain growth is essential to the goal of relating spectral data on surface mineralogy to the physical history of a planetary surface. Models of grain growth kinetics have been constructed for various frosts based on their individual thermodynamic properties and on the difference in binding energy between molecules on plane vs curved faces. A steady state situation can occur on planetary surfaces in which thermal elimination of small grains competes with their creation, usually by meteorite impact. We utilize predicted grain growth rates to explain telescopic spectral data on condensate surfaces throughout the solar system. On Pluto, predicted CH₄ ice grain growth rates are very high despite the low temperature, resulting in a multicentimeter optical path. This explains the strong CH₄ absorption band depths, which otherwise would require large amounts of CH₄ gas. On the Uranian and Saturnian satellites, extremely slow grain growth rates are predicted because of the low vapor pressure of H₂O at the existing average surface temperatures. This may explain evidence for fine grain size and peculiar microstructure. On Io, ordinary thermal exchange is more effective than sputtering in promoting grain growth because of the properties of SO₂. Over much of Io's disk, submicron size grains of SO₂ could plausibly reconfigure into a surface glaze on a timescale comparable to the resurfacing rate. This may explain the relatively strong SO₂ signature in Io's infrared absorption spectrum as opposed to its weaker manifestation in the visible spectrum. In spite of lower sputtering fluxes, sputtering plays a more important role in grain growth for Europa, Ganymede, and Callisto than on Io. This is a result of high rates of thermally activated grain growth and resurfacing on Io. The sequence of H₂O-ice absorption band depths (related to the mean grain size) is J₂(T) ～ J₃(T) > J₂(L) > J₃(L) ～ J₄(T) ～ J₄(L), where L = leading and T = trailing. This is to be expected if sputtering were dominant. The calculations show, however, that neither thermalized exchange fluxes nor sputtering exchange fluxes can produce the implied grain growth or the ordering by ice absorption band depths of the six satellite hemispheres. Only sputtering control by simple ejection of H₂O from the satellites, as the dominant cause of shorter mean lifetimes for smaller exposed grains, can satisfactorily explain the data. Some observations, which suggest that there are vertical grain size gradients, may result from a steady state balance between intense near surface production of fine frost by comminution, coupled with ongoing ubiquitous grain growth in the vertical column. In certain cases, e.g., Europa and Enceladus, the possibility exists that endogenic activity as well as comminution could affect grain size—at least locally. It is concluded that not only ice identification and mapping, but ice grain size mapping is an important experiment to be conducted on future missions.     

Instability of an area-preserving polynomial mapping

Fixed points and eigencurves have been studied for the Hénon-Heiles mapping:x′=x+a (y?y ³),y′=y(x′?x′ ³). Eigencurves of order 21 proceed rapidly to infinity fora=1.78, but as ‘a’ decreases, they spiral around the origin repeatedly before escaping to infinity. Fixed pointsx _f on thex-axis have been located for the range 1≤a≤2.4, for ordersn up to 100. Their locations vary continuously witha, as do the eigencurves, and hyperbolic points remain hyperbolic. Forn=3 and 2.4≥a≥2.37, a very detailed study has been made of how escape occurs, with segments of an eigencurve mapping to infinity through various escape channels. Further calculations with ‘a’ decreasing to 2.275 show that this instability is preserved and that the eigencurve will spiral many times around the origin before reaching an escape channel, there being more than 34 turns fora=2.28. The rapid increase of this number is associated with the rapid decrease of the intersection angle between forward and backward eigencurves (at the middle homoclinic point), with decreasing ‘a’, this angle governing the outward motion. By a semi-topological argument, it is shown that escape must occur if the above intersection angle is nonzero. In the absence of a theoretical expression for this angle, one is forced to rely on the numerical evidence. If the angle should attain zero for a valuea=a _c>a_m,wherea _m .is the minimum value for which the fixed points exist, then no escape would be possible fora _c However, on the basis of calculations by Jenkins and Bartlett (1972) forn=6, and the results of the present article forn=3, it appears highly probable thata _c=a_m,and that escape from the neighborhood of a hyperbolic point is always possible. If there is escape from the hyperbolic fixed point forn=4,a=1.6, located atx _f=0.268, then the eigencurve must cross the apparently closed invariant curve of Hénon-Heiles which intersects thex-axis atx?±0.4, so that this curve cannot in fact be closed.