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Notes: Abstract The schemes for division of holohedral simple forms of crystals into conjugated simple forms are derived by decomposition of the symmetry group of the primitive sublattice into double cosets. The number of equivalently oriented simple forms in the intergrowth of crystals, whose primitive space sublattices are parallel to one another, is equal to the number of holohedral permutational conjugated simple forms, which has the value 992 for all the 32 symmetry classes.

Notes: The poloidal rotation of tokamak plasmas is studied in the plateau regime. It is shown that the relaxation rate is given by vT/(qR)νˆ1/3O(1), while the inertia enhancement in this regime is 1+q2νˆ−1/3O(1), resulting from the time-dependent parallel viscosity, where q is the safety factor, νˆ=ε3/2ν* is the plateau collisionality parameter (ε3/2〈νˆ〈1), ε is the inverse aspect ratio, and ν* is the standard neoclassical collisionality parameter. An evolutionary equation for the radial electric field is derived. © 1995 American Institute of Physics.

Notes: [Auszug] The spacecraft Vega 1 and Vega 2 encountered comet Halley on 6 and 9 March 1986. Their scientific payload comprised 14 instruments, which collected data concerning the comet's optical characteristics, dust emission, and neutral gas, plasma and electromagnetic field environment. The main ...

Notes: Abstract The author expounds a nonlinear theory of the instability of a weakly inhomogeneous plasma with hot ions when a”loss cone” is present in their velocity distribution. Flute-type instabilities (kZ= 0) are considered, which for a strong enough irregularity may build up even in short traps with”magnetic mirrors.” It is shown that the total ion flux through the magnetic mirrors, which is caused by turbulent diffusion into the loss cone, exceeds by a factor of (2n/RH ∇n)1/2 the ion flux across the magnetic field as a result of diffusion in coordinate space (here n, ∇n, are the density and its gradient, RH is the ion Larmor radius). The diffusion time of ions into the “loss cone” is of the order τ=10Ωϰ ϰ (2n/R ϰ∇n)3/2 (ΩH is the ion Larmor frequency). A plasma contained in magnetic traps is always in a nonequilibrium thermodynamic state. The nature of the nonequilibrium is connected with the specific geometry of the containing magnetic field. Here we will consider open traps with magnetic mirrors in which the nonequilibrium of the plasma is caused by: 1) the curvature of the magnetic field force lines and its associated effective gravity field; 2) the localization of the plasma in a small volume, which brings about its inhomogeneity; 3) the presence of the so-called “loss cone” in the velocity distribution of the particles, in which the relation of the longitudinal and transverse velocities is such that they cannot be contained in the trap. Under the influence of particle collisions the plasma tends to pass to a state of thermodynamic equilibrium. Here there is diffusion of the particles in velocity space and after virtually only one collision the particle falls into the “loss cone” and escapes from the trap. The time of particle containment within the trap could be increased if collisions were made less frequent. However, in such a rarefied plasma various types of oscillation may arise spontaneously. The relaxation of the plasma state to one of thermodynamic equilibrium comes about much faster under the influence of these oscillations than relaxation due to collisions. Consideration of transport processes in a turbulent plasma enables us to estimate the real life time of particles in the trap, and this turns out to be less than would be expected from rare collisions. Suitable choice of magnetic field geometry enables us to stifle the hydrodynamic instabilities associated with curvature of the force lines, and the weak kinetic instabilities arising from the excitation of low-frequency “drift waves.” Thus instabilities associated with the presence of a “loss cone” are more important. Such an instability was first detected by Rosenbluth and Post [1]. Development of this instability leads to a state of affairs where under conditions close to optimal for thermonuclear reactions to take a normal course, anomalous diffusion of ions into the “loss cone” causes them to pass through the magnetic mirrors very rapidly [2]. However, the perturbations considered in [1] have the form of a wave exp(−iωt+ +ikZZ) running along the magnetic field H0Z, and as shown in the same paper, perturbations of this type are strong damped in the region of the “magnetic mirrors,” where the phase velocity of the perturbations becomes comparable with the thermal velocity of the electrons. This imposes a lower limit on the length of the systems in which instabilities of this type can develop L〉Lc [1]. On the other hand, in short systems of length L〈Lc flute-type oscillations exist (kZ≡O) in the same region of frequency and wavelength, associated with density inhomogeneity [3]. Calculations similar to those in [1] have shown that the presence of a “loss cone” also suffices for the development of these oscillations [4]. The critical radius rc of the plasma volume, below which the instability develops, turns out to be, under conditions necessary for thermonuclear reactions to take place, of the same order as the critical length rc≈ lc≈102 rh (RH is the ion Larmor radius) [4]. Thus, in view of the requirement R〈 L it is impossible to obtain a stable plasma in which R〉rc and L〈LC. Instabilities of the latter type, which we will call drift-anisotropic instabilities, clearly limit the density of the plasma stably contained in existing devices [7]. Accordingly, §1 gives equations describing the state of a weakly turbulent plasma of this type. In §2 the energy distribution over turbulent pulsations with different scales is examined. The fluxes of ions through the “magnetic mirrors” and across the magnetic field are determined on the basis of the results of §2 and §3.

Notes: Abstract Axford and McKenzie [1992] suggested that the energy released in impulsive reconnection events generates high frequency Alfvén waves. The kinetic equation for spectral energy density of waves is derived in the random phase approximation. Solving this equation we find the wave spectrum with the power law "−1" in the low frequency range which is matched to the spectrum above the spectral brake with the power low "−1.6." The heating rate of solar wind protons due to the dissipation of Alfvén waves is obtained.

Notes: Abstract The quasilinear relaxation of pickup interstellar helium ions is described in the diffusion shell approximation. It is shown that the Cherenkov damping of Alfvén waves due to their refraction in the nonuniform solar wind could inhibit the complete relaxation of pickup helium ions over the bispherical shell.

Notes: Abstract A brief summary is presented of recent progress in estimating the rates of energy, momentum and mass transport of the solar wind through the magnetopause in terms of an analysis of the non-linear stage of various plasma instabilities. It is shown that the energy supply to the Earth's magnetosphere is due to reconnection on the dayside magnetopause and its dissipation during magnetospheric substorms, being controlled by both the interplanetary field parameters and by the dynamic pressure of the solar wind.

Notes: Abstract The ion tearing mode is considered as the only mechanism capable of initiating reconnection processes in the equilibrium plasma sheet whose scale considerably exceeds the ion Larmor radius. The paper gives a brief review of linear theory of the tearing mode instability that allows the onset of its development to be determined. It is shown that the explosive growth of the tearing mode in a nonlinear stage is consistent with the dynamics of charged particle acceleration and the behaviour of the magnetic field variations and plasma flow in the magnetotail. The tail structure formed, as a result of the development of the tearing mode, is also discussed.

Notes: Abstract This review is devoted to the problem of the internal fine structure of the Earth's magnetopause. A number of theoretical and experimental papers dealing with this subject is discussed from a unified viewpoint. The Vlasov kinetic approach is used to study the stability of magnetopause magnetic surfaces that can be destructed by the growth and overlapping of magnetic islands. The stochastic wandering of magnetic field lines between the destructed surfaces can result in magnetic percolation, i.e. the appearance of a topological connection of interplanetary and geomagnetic field lines. Such a process may be considered as a mechanism of the macroscopic (but spatially localized) reconnection. We discuss this in relation with the phenomena of spontaneous ‘patchy’ reconnection, recently observed at ISEE satellites and now known as flux transfer events. Drift tearing mode, which is responsible for the growth of magnetic islands can be stabilized due to its coupling with ion sound waves, and the process of percolation will be interrupted if even a thin region with smooth stable magnetic surfaces exists within the magnetopause. Accordingly, we obtain a magnetopause stability threshold for localized reconnection. It is represented in the form of dependence of marginal dimensionless thickness of the magnetopause on the angle of magnetic field rotation within it. Further, we discuss the possible role of lower hybrid turbulence permanently observed within the. magnetopause and speeding up the process of reconnection. Nonlinear calculations supporting the developed model are given in the appendices. We consider briefly the motion of reconnecting flux tubes and evaluate the time necessary for the accomplishment of percolation. The calculations show that the appearance of reconnection ‘patchies’ at the dayside magnetopause cannot occur too far from the stagnation region. The latter agrees with experimental indications on the most probable site of the formation of flux transfer events. In the concluding part of the review we discuss the necessary limitations on the theory, possible lines of its future advance and comparison with the experimental data.