ОДНОРОДНАЯ КРАЕВАЯ ЗАДАЧА РИМАНА С МЕРОМОРФНЫМИ КОЭФФИЦИЕНТАМИ ДЛЯ БЕСКОНЕЧНО СВЯЗНЫХ ОБЛАСТЕЙ

Homogeneous Riemann boundary value problem with meromorphic coefficients for infinitely connected domains is considered. In the closed form the problem is solved in the class of piece-wise analytic functions, possessing meromorphic continuation to the whole complex plane. Special attention is paid to the existence of doubly periodic solutions to the problem with elliptic coefficients. The example of the problem having a unique solution up to an arbitrary constant multiplier is presented, as well as of the problem with a solution depending on a number of arbitrary parameters. The obtained results can be used for solving of an inhomogeneous Riemann boundary value problem with meromorphic coefficients in an infinitely connected domain in the general statement.В исследованиях эффективных свойств двумерных композиционных материалов наиболее изученным является случай материалов с периодической микроструктурой. Это связано с возможностью представления решений соответствующих краевых задач через значения некоторых эллиптических функций. В данной работе рассматривается однородная краевая задача Римана для бесконечно связных областей и мероморфных коэффициентов. В замкнутой форме дается решение задачи в классе кусочно-аналитических функций, допускающих мероморфное продолжение на всю комплексную плоскость. Как частный случай решается вопрос существования и единственности двоякопериодических решений задачи с эллиптическим коэффициентом. Приводится пример задачи, имеющей единственное, с точностью до произвольного числового множителя, решение, и пример задачи, решение которой зависит от произвольных независимых параметров. Полученные результаты могут служить базой для исследования случая, когда коэффициенты задачи являются различными для каждого из контуров, а также при решении неоднородной задачи Римана с мероморфными коэффициентами и свободными членами в бесконечно связных областях.

Nonlinear whistler wave scattering in space plasmas

In this paper the evolution of nonlinear scattering of whistler mode waves by kinetic Alfven waves (KAW) in time and two spatial dimensions is studied analytically. The authors suggest this nonlinear process as a mechanism of kinetic Alfven wave generation in space plasmas. This mechanism can explain the dependence of Alfven wave generation on whistler waves observed in magnetospheric and ionospheric plasmas. The observational data show a dependence for the generation of long periodic pulsations Pc5 on whistler wave excitation in the auroral and subauroral zone of the magnetosphere. This dependence was first observed by Ondoh T.I. For 79 cases of VLF wave excitation registered by Ondoh at College Observatory (L=64.6 N), 52 of them were followed by Pc5 geomagnetic pulsation generation. Similar results were obtained at the Loparskaia Observatory (L=64 N) for auroral and subauroral zone of the magnetosphere. Thus, in 95% of the cases when VLF wave excitation occurred the generation of long periodic geomagnetic pulsations Pc5 were observed. The observations also show that geomagnetic pulsations Pc5 are excited simultaneously or insignificantly later than VLF waves. In fact these two phenomena are associated genetically: the excitation of VLF waves leads to the generation of geomagnetic pulsations Pc5. The observations show intensive generation of geomagnetic pulsations during thunderstorms. Using an electromagnetic noise monitoring system covering the ULF range (0.01-10 Hz) A.S. Fraser-Smith observed intensive ULF electromagnetic wave during a large thunderstorm near the San-Francisco Bay area on September 23, 1990. According to this data the most significant amplification in ULF wave activity was observed for waves with a frequency of 0.01 Hz and it is entirely possible that stronger enhancements would have been measured at lower frequencies

Nonliner mechanism of electromagnetic waves generations in space dust plasma

We consider a parametric excitation of electromagnetic waves induced by inertial Alfvén wave (IAW) in space dust plasma. The nonlinear dispersion equations describing decay of upper-hybrid wave (UHW) into the IAW and the ordinary electromagnetic wave as well as decay of UNW into the IAW and the left-hand circularly polarized (LHCP) wave are obtained using the three-fluid magnetohydrodynamics. The instability growth rates which depend on dust plasma parameters are found. It is shown that the LPCH wave is preferably excited by the UH pump wave for the parameters of the Saturn's F-ring.Розглянуто параметричне збудження електромагнітних хвиль інерційними альфвенівськими хвилями (ІАХ) в пиловій космічній плазмі. На основі рівнянь трирідинної магнітної гідродинаміки отримано нелінійне дисперсійне рівняння, що описує як розпад верхньогібридної хвилі на ІАХ та звичайну електромагнітну хвилю, так і розпад верхньогібридної хвилі на ІАХ та на лівополяризовану електромагнітну хвилю. Знайдено інкремент розвитку нестійкості, який залежить від параметрів пилової плазми. Показано, що лівополяризована електромагнітна хвиля переважно збуджується верхньогібридною хвилею накачки для параметрів F-кільця Сатурна.Рассмотрено параметрическое возбуждение электромагнитных волн инерциальными альфвеновскими волнами (ИАВ) в пылевой космической плазме. На основе уравнений трехжидкостной магнитной гидродинамики получено нелинейное дисперсионное уравнение, описывающее как распад верхнегибридной волны на ИАВ и обыкновенную электромагнитную волну, так и распад верхнегибридной волны на ИАВ и левополяризованную электромагнитную волну. Найден инкремент развития неустойчивости, зависящий от параметров пылевой плазмы. Показано, что левополяризованная электромагнитная волна преимущественно возбуждается верхнегибридной волной накачки для параметров F-кольца Сатурна

The transformation of long scale Alfven waves in space dusty plasma

A nonlinear mechanism of the generation of kinetic Alfv´en waves (KAW) on dust plasma with small plasma parameter β is proposed. As the generation mechanism, the parametric instability where a pumping wave is the MHD Alfv´en wave is considered. On the basis of the three-fluid MHD, the nonlinear dispersion equation describing the three-wave interaction is deduced and its solution is derived. Obtained instability growth rate is determined by parameters of dust plasma particles. The nonlinear process under consideration can take place both in laboratory and in space plasma with small plasma parameter β. As an application of theoretical results, we consider Saturn’s F-ring

Nonlinear excitation of kinetic Alfven waves and whistler waves by electron beam-driven Langmuir waves in the solar corona

© ESO 2003We study a new nonlinear excitation mechanism of kinetic Alfvén waves (KAWs) and whistler waves (Ws) by electron beam-driven Langmuir waves (Ls). The generation conditions for the parametric decay instability L W + KAW are determined and the growth rate is calculated. We show that the resonant pairs of KAWs and whistler waves are nonlinearly coupled to the pump Langmuir waves and their amplitudes undergo exponential growth from the thermal level. The perpendicular dispersion of KAWs strongly increases the coupling due to the nonlinear current parallel to the ambient magnetic field. Our study suggests that the nonlinear coupling of Langmuir wave energy into KAWs and whistlers can provide an efficient sink for weakly dispersive Langmuir waves excited by fast electron beams in the solar corona when the electron plasma frequency is lower than the electron gyrofrequency. This condition can be satisfied in the low-density magnetic filaments that are rooted in the depleted patches at the coronal base and extend to the high corona. At the same time, the Langmuir-driven KAWs and whistlers give rise to scattering and/or thin structures of radio emission penetrating through, or generated in these regions. Since the decay into sunward propagating KAWs is strongest, the nonlinearly driven KAWs can be easily distinguished from the waves generated at the coronal base and propagating away from the Sun. Our results may be used in the analysis of solar radio data and for remote probing of the coronal plasma, magnetic fields, and waves.Yu. Voitenko, M. Goossens, O. Sirenko and A. C.-L. Chia

Optical, radio and x-ray radiation of red sprites produced by runaway air breakdown

The authors use the runaway air breakdown model of upward discharges to calculate optical, radio, and X-ray radiation generated by red sprites. Red sprites are high altitude (up to 90 km) lightning discharges. Aircraft based observations show that sprites are predominantly red in color at altitudes above {approximately}55 km with faint blue tendrils, which extend downward to an altitude of 40 km; the duration of a single sprite is less than 17 ms, their maximum brightness is about 600 kR, and estimated total optical energy is about 1--5 kJ per event. The ground based observations show similar results, and provide some additional information on spatial and temporal structure of sprites, and on sprite locations. One difference between aircraft and ground-based observations is that blue tendrils are rarely observed from the ground. Sprites usually occur above the anvils of large mesoscale convective systems and correlate with strong positive cloud to ground discharge. Upward discharges are the most probable source of X-ray emission observed above large thunderstorm complexes by the Compton Gamma-ray Observatory. To escape the atmosphere these {gamma}-rays must originate above 25 km altitude. Red sprites are usually observed at altitudes higher than 50 km, and are therefore a likely source of this x-ray emission

Generation of elves by sprites and jets

Recent years of observations of the upper atmosphere and the lower ionosphere brought a fascinating collection of new phenomena including optical, radio, and gamma-ray emissions originating in the 20 to 90 km altitude range. Up to now, the most diverse phenomenology has emerged from the optical observations which have led to the identification of red sprites, blue jets, blue starts, and elves. Most of the studies have concentrated on relating such phenomena in the upper atmosphere to regular lightning discharges in the troposphere. The sprite/jet discharge itself can be caused by the runaway air breakdown, or regular air breakdown. The standard theory for optical airglow transients in the lower ionosphere above the thunderstorms also known as elves suggests that they are produced during interaction of electromagnetic pulses (EMP) from lightning with the lower ionosphere. Heating of the ambient electrons by the EMP in the D region can result in excitation of optical emissions once the optical excitation thresholds are reached. In this paper the authors suggest that in addition to this mechanism elves can be caused by an EMP generated by sprites and jets

High altitude atmospheric discharges according to the runaway air breakdown mechanism

High altitude optical transients - red sprites, blue jets, and elves - are modeled in the context of the relativistic electron runaway air breakdown mechanism. These emissions are usually associated with large mesoscale convective systems (hereafter MCS). In thunderstorms cloud electrification proceeds over a time scale long enough to permit the conducting atmosphere above the cloud to polarize and short out the thunderstorm electric field. When a lightning strike rapidly neutralizes a cloud charge layer runaway driving fields can develop in the stratosphere and mesosphere. According to present simulations of the full runaway process the variety of observed optical emissions are due to the nature of the normal lightning event in the MCS that kick starts the runaway avalanche. In this paper the authors describe some details of the model, present the results of the evolution of the primary electron population, and summarize the initial conditions necessary for different types of discharges. Two companion papers present (a) the predicted optical, gamma ray, and radio emissions caused by these electrical discharges, and (b) the time evolution of the secondary electron population and its implications in terms of observables

Search for Primordial Black Holes with SGARFACE

The Short GAmma Ray Front Air Cherenkov Experiment (SGARFACE) uses the Whipple 10 m telescope to search for bursts of $\gamma$ rays. SGARFACE is sensitive to bursts with duration from a few ns to $\sim$20 $\mu$s and with $\gamma$-ray energy above 100 MeV. SGARFACE began operating in March 2003 and has collected 2.2 million events during an exposure time of 2267 hours. A search for bursts of $\gamma$ rays from explosions of primordial black holes (PBH) was carried out. A Hagedorn-type PBH explosion is predicted to be visible within 60 pc of Earth. Background events were caused by cosmic rays and by atmospheric phenomena and their rejection was accomplished to a large extent using the time-resolved images. No unambiguous detection of bursts of $\gamma$ rays could be made as the remaining background events mimic the expected shape and time development of bursts. Upper limits on the PBH explosion rate were derived from the SGARFACE data and are compared to previous and future experiments. We note that a future array of large wide-field air-Cherenkov telescopes equipped with a SGARFACE-like trigger would be able to operate background-free with a 20 to 30 times higher sensitivity for PBH explosions.Comment: 18 pages, 30 figures, accepted by Astroparticle Physics, corrected author list and Section 2.

Long term time variability of cosmic rays and possible relevance to the development of life on Earth

An analysis is made of the manner in which the cosmic ray intensity at Earth has varied over its existence and its possible relevance to both the origin and the evolution of life. Much of the analysis relates to the 'high energy' cosmic rays ($E>10^{14}eV;=0.1PeV$) and their variability due to the changing proximity of the solar system to supernova remnants which are generally believed to be responsible for most cosmic rays up to PeV energies. It is pointed out that, on a statistical basis, there will have been considerable variations in the likely 100 My between the Earth's biosphere reaching reasonable stability and the onset of very elementary life. Interestingly, there is the increasingly strong possibility that PeV cosmic rays are responsible for the initiation of terrestrial lightning strokes and the possibility arises of considerable increases in the frequency of lightnings and thereby the formation of some of the complex molecules which are the 'building blocks of life'. Attention is also given to the well known generation of the oxides of nitrogen by lightning strokes which are poisonous to animal life but helpful to plant growth; here, too, the violent swings of cosmic ray intensities may have had relevance to evolutionary changes. A particular variant of the cosmic ray acceleration model, put forward by us, predicts an increase in lightning rate in the past and this has been sought in Korean historical records. Finally, the time dependence of the overall cosmic ray intensity, which manifests itself mainly at sub-10 GeV energies, has been examined. The relevance of cosmic rays to the 'global electrical circuit' points to the importance of this concept.Comment: 18 pages, 5 figures, accepted by 'Surveys in Geophysics