No abstract available

[en] We have studied the stability of magnetosonic wave in a plasma, where the ions and electrons are described by anti-loss cone (ALC) distributions. Our studies indicate that the magnetosonic waves produced by ions and electrons with ALC distributions are in the higher frequency end within the range of frequencies, as observed by the Combined Release and Radiation Effects Satellite spacecraft. They are weakly damped and can, therefore, travel long distances. These waves are expected to play an important role in the acceleration of radiation belt electrons. (author)

[en] A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.

No abstract available

[en] Observation of the adiabatic behaviour of energetic particle pitch-angle distributions in the magnetosphere (Lyons, 1977, and others) in the past indicated the development of pronounced minima or drift-loss cones on the pitch-angle distributions centred at α approx.= 90⁰ in connection with storm-time changes in magnetospheric convection and magnetic field. Using a model of a drift-modified loss-cone distribution (MLCD) of the butterfly type, the linear stability of electromagnetic whistler or ion-cyclotron waves propagating parallel to the magnetic field has been investigated. The instability is shown to be quenched at high frequencies ω < ωsub(m) = A(A + 1), where A is the thermal anisotropy. This quenching becomes stronger the higher are the respective parallel hot particle thermal velocity Asub(h) and cold plasma density nsub(c). Particles around pitch-angles α approx. = 90⁰ are identified as generating electromagnetic cyclotron waves near the marginally stable frequency ωsub(m). It is concluded that the absence of electromagnetic VLF and ELF noise during times when MLCD develops is the result of the shift of the unstable spectrum to low frequencies. (orig.)

[en] It is shown that in electron beam injected mirror plasmas, the convective loss cone instability gets modified substantially and so reduces the critical lenght by at least an order of magnitude. This will seriously jeopardize the open ended confinement schemes employing electron beams. (orig.)

[en] Waves with frequencies near the harmonics of the proton-cyclotron frequency, and propagating almost transverse to the ambient magnetic field, can become unstable by hot protons having an anti-loss cone (ALC) distribution function. The maximum growth rates increase with an increase in anti-loss cone index, ratio of the temperatures of trapped to missing protons, and with a decrease in βHsub(H) (βsub(H) being the ratio of transverse thermal pressure of protons to magnetic field pressure). The growth rates are typically in the range 0.01-1.0 Ω, where Ω is the proton-cyclotron frequency. This instability may be relevant to the observations of EHC waves on auroral field lines (Kintner, 1979), ULF waves in the day-side magnetosphere (Perraut et al., 1978) and the low-frequency part of the electric field spectrum (from 5 Hz to 20 Hz) in the region upstream of the bow-shock (Gurnett et al., 1979). (orig.)

No abstract available

[en] The effects of adding warm plasmas on the kinetic DCLC mode in high β loss cone plasmas are investigated in detail. It is found that when the fluid DCLC mode is stabilized by a small amount of warm plasma, the kinetic excitation still remains due to two different mechanisms, namely, (1) magnetic drift resonance dissipation excites the negative energy wave; (2) a new type of positive energy wave can become unstable as the resonance condition is met. Comparing with fluid approximation theory, more warm plasmas are needed to suppress the kinetic DCLC instabilities

[en] We thoroughly analyse the method used by Pogorelov to construct piecewise-smooth tubular surfaces in R³ isometric to the surface of a right circular cylinder. The properties of the inverse images of edges of any tubular surface on its planar unfolding are investigated in detail. We find conditions on plane curves lying on the unfolding that enable them to be the inverse images of edges of some tubular surface. We make a refinement concerning the number of smooth pieces that form a piecewise-smooth tubular surface. We generalize Pogorelov's method from the surface of a right circular cylinder to that of a right circular cone