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## Propagation and Generation of Electromagnetic Waves at Proton Gyrofrequencies in a Relativistic Electron-Positron Plasma. I. Low-Frequency Weakly Damped Electromagnetic Waves

We consider the dispersion characteristics of electromagnetic waves in a plasma with strong magnetic field and equal content of relativistic electrons and positrons, whose synchrotron radiation can be the source of optical radiation of a pulsar. It is shown that when a small fraction of nonrelativistic protons with a nonequilibrium distribution function is present in the plasma, an effective instability can develop at frequencies below the first harmonic of the relativistic gyrofrequency of electrons, namely, at the harmonics of the proton gyrofrequency. This instability leads to the excitation of the O- and X-mode electromagnetic waves, which can, in principle, be related with the observed pulsar radiation. In part I of this paper, we study dispersion characteristics of low-frequency electromagnetic waves (with frequencies below the relativistic gyrofrequency of electrons) in an ultrarelativistic electron-positron plasma with an isotropic momentum distribution function of the particles. Instabilities of the O- and X-mode waves and the conditions of escape of the radiation from the region of strong magnetic field into a rarefied isotropic plasma will be considered in paper II. The results can be used in the interpretation of known experimental data on the dynamic pulsar radiation spectra obtained with high temporal and frequency resolution.

This paper describes modeling of spacecraft charging dynamics which is used in COULOMB-2 code in the case of spacecraft surface complex shape. The modeling of spacecraft charging is carried out via numerically solving the system of differential equations for time variations of local electric charge on every discrete element of the spacecraft surface. The presented computation results are obtained for spacecraft charging in hot magnetosphere plasma for several spacecraft design elements in a time interval of 20–10 000 s. The results are compared with the similar ones obtained with the NASCAP-2k and MUSCAT codes, and a good consistency was found.

Increasing the temporal resolution and instant coverage of velocity space of space plasma measurements is one of the key issues for experimentalists. Today, the top‐hat plasma analyzer appears to be the favorite solution due to its relative simplicity and the possibility to extend its application by adding a mass‐analysis section and an electrostatic angular scanner. Similarly, great success has been achieved in MMS mission using such multiple top‐hat analyzers to achieve unprecedented temporal resolution. An instantaneous angular coverage of charged particles measurements is an alternative approach to pursuing the goal of high time resolution. This was done with 4‐D Fast Omnidirectional Nonscanning Energy Mass Analyzer and, to a lesser extent, by DYMIO instruments for Mars‐96 and with the Fast Imaging Plasma Spectrometer instrument for MErcury Surface, Space ENvironment, GEochemistry, and Ranging mission. In this paper we describe, along with precursors, a plasma analyzer with a 2*π* electrostatic mirror that was developed originally for the Phobos‐Soil mission with a follow‐up in the frame of the BepiColombo mission and is under development for future Russian missions. Different versions of instrument are discussed along with their advantages and drawbacks

It is proposed to consider the scalings of anomalous transport (superdiusion), determined experimentally in turbulent plasma of the Earth's magnetosphere and laboratory plasma of thermonuclear facilities and processed using modern statistical cascade models of strong turbulence with intermittency, also within the approach of physical kinetics to the theory of plasma turbulence.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.