The propagation and stability of waves in relativistic astrophysical plasmas is presented. Our investigation, using a relativistic two-fluid model, is different from previous relativistic fluid studies in that the plasma is treated fully relativistically, both in temperature and in directed speed. Much of this study is devoted to relativistic linear waves in pulsar pair plasmas, with a view to elucidating a possible mechanism for pulsar radio wave emission. We also study interesting nonlinear exact solutions in both relativistic and non-relativistic plasmas. Pulsar pair plasmas can support four transverse modes for parallel propagation. Two of these are electromagnetic plasma modes, which at high temperature become light waves. The remaining two are Alfvénic modes, split into a fast and a slow mode. The slow mode, always sub-luminous, is cyclotron (Alfvén) two-stream unstable at large wavelengths. We find that temperature effects, within the fluid model used, do not suppress the instability in the limit of large (finite) magnetic field. The fast Alfvén mode can be super-luminous only at large wavelengths; however, it is always sub-luminous at high temperatures. In this incompressible approximation, only the ordinary mode is present for perpendicular propagation. We discuss the implications of the unstable mode for radio emission mechanisms. For typical values, the instability is quite fast, and the waves can grow to sizable levels, such that, the magnetic modulation could act as a wiggler. The pulsar primary beam interacting with this wiggler, could drive a free electron laser (FEL) effect, yielding coherent radiation. Investigation of the FEL in this setting and demonstrating that the frequency spectral range, and luminosities, predicted by this mechanism is well within the observed range of radio frequency (and luminosity) emissions, is one of the principal results of this dissertation. It is tempting to speculate, then, that an FEL-like radiation effect could be responsible for the highly coherent radio wave emissions from pulsars. In the study of nonlinear exact solutions we have generalized the results to the incompressible Hall Magnetohydrodynamics (HMHD). We find that for cases when the plasma is weakly magnetized the frequencies of the modes decrease as the wave amplitude (effective mass) increases. For very strongly magnetized plasmas the light-like modes tend to be asymptotically linear; the frequency is unaffected by wave amplitude. / text

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This thesis has two parts: In the first part, we study the dispersion characteristics of structural-acoustic waveguides by obtaining closed-form solutions for the coupled wave numbers. Two representative systems are considered for the above study: an infinite two-dimensional rectangular waveguide and an infinite fluid- filled orthotropic circular cylindrical shell. In the second part, these asymptotic expressions are used to study the nonlinear wave propagation in the same two systems. The first part involves obtaining asymptotic expansions for the fluid-structure coupled wave numbers in both the systems. Certain expansions are already available in the literature. Hence, the gaps in the literature are filled. Thus, for cylindrical shells even in vacuo wavenumbers are obtained as part of the objective. Here, singular and regular perturbation methods are used by taking the thickness parameter as the asymptotic parameter. Valid wavenumber expressions are obtained at all the frequencies. A transition in the behavior of the flexural wavenumbers occurs in the neighborhood of the ring frequency. This frequency of transition is identified for the orthotropic shells also. The closed-form expressions for the orthotropic shells are obtained in the limit of slight orthotropy for the circumferential orders n > 0 at all the frequency ranges. Following this, we derive the coupled wavenumber expressions for the two systems for an arbitrary fluid loading. Here, the two-dimensional rectangular waveguide is considered first. This rectangular waveguide has a one-dimensional plate and a rigid surface as its lateral boundaries. The effects due to the structural boundary are studied by analyzing the phase change due to the structure on an incident plane wave. The complications due to the cross-sectional modes are eliminated by ignoring the presence of the other rigid boundary. Dispersion characteristics are predicted at various regions of the dispersion diagram based on the phase change. Moreover, the also identified. Next, the rigid boundary is considered and the coupled dispersion relation for the waveguide is solved for the wavenumber expressions. The coupled wavenumbers are obtained as the coupled rigid-duct, the coupled structural and the coupled pressure-release wavenumbers. Next, based on the above asymptotic analysis on a two-dimensional rectangular waveguide, the asymptotic expansions are obtained for the coupled wavenumbers in isotropic and orthotropic fluid- filled cylindrical shells. The asymptotic expansions of the wavenumbers are obtained without any restriction on the fluid loading. They are compared with the numerical solutions and a good match is obtained. In the second part or the nonlinear section of the thesis, the coupled wavenumber expressions are used to study the propagation of small but a finite amplitude acoustic potential in the above structural-acoustic waveguides. It must be mentioned here that for the rst time in the literature, for a structural-acoustic system having a contained fluid, both the structure and the acoustic fluid are nonlinear. Standard nonlinear equations are used. The focus is restricted to non-planar modes. The study of the cylindrical shell parallels that of the 2-D rectangular waveguide, except in that the former is more practical and complicated due to the curvature. Thus, with regard to both systems, a narrow-band wavepacket of the acoustic potential centered around a frequency is considered. The approximate solution of the acoustic velocity potential is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that the amplitude modulation is governed by the Nonlinear Schr•odinger equation (NLSE). The nonlinear term in the NLSE is analyzed, since the sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. This sign change is predicted using the coupled wavenumber expressions. Secondly, at specific frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonic. This happens when the phase speeds of the waves match. The frequencies of such interactions are identified, again using the coupled wavenumber expressions. The novelty of this work lies firstly in considering nonlinear acoustic wave prop-agation in nonlinear structural waveguides. Secondly, in deriving the asymptotic expansions for the coupled wavenumbers for both the two-dimensional rectangular waveguide and the fluid- filled circular cylindrical shell. Then in using the same to study the behavior of the nonlinear term in NLSE. And lastly in identifying the frequencies of nonlinear interactions in the respective waveguides.

Denna rapport ämnar undersöka de vanligast förekommande typerna av teknologier för vågkraftverk (eng. Wave Energy Converter, WEC) teknologier för att jämföra de olika konceptens förmåga att absorbera vågenergi. Koncept som undersöks är punktabsorbatorer och oscillerande vattenkolumner. I denna rapport används de vanligt använda engelska översättningarna point absorber och oscillating water column (OWC). Beräkningar görs för de olika koncepten i liknande vågförhållanden för att kunna jämföra den energi som kan utvinnas. I rapporten sker beräkningar under optimala vågförhållanden. Vågorna antas vara linjära och vågkraftverken antas vara i fas med vågens svängningsrörelse. Den vågdata som använts är uppmätt utanför Belmullet i Irland. Beräkningar görs på vågor med en signifikant våghöjd på 1,25 m och en periodtid på 7,5 s. Det görs även beräkningar på den största uppmätta förekommande vågen. I huvudsak används effektberäkningar enligt en modell som Kjell Budal. Syftet är att grafiskt och numeriskt jämföra den teoretiska och faktiska maxeffekt som kan utvinnas ur respektive våg. Resultatet från undersökningen visar att den största bidragande faktorn till en hög energiutvinning beror på bojens volym. Volymen måste anpassas för de vågförhållanden som finns där bojen ska placeras.Vid beräkningar av en OWC med tvärsnittsarea på 19 m2 visar det sig att den effekt som kan utvinnas av en luftkammare med tillhörande turbin är ungefär 10 kW, 1/30 av de 300kW som kan utvinnas av en point absorber. En OWC består dock sällan utav en ensam luftkammare utan ofta i en array med ett flertal luftkammare med separata turbiner för att öka effekten. / This report intends to examine the most common types of wave energy converter technologies to compare the different concepts' ability to absorb wave energy. Concepts being investigated are point absorbers and oscillating water columns (OWC). Calculations are made for the different concepts in the same wave conditions to be able to compare the energy that can be extracted. In the report, calculations are made under optimal wave conditions. The waves are assumed to be linear and the wave energy converter is assumed to be in phase with the oscillating motion of the wave. The wave data used is measured outside Belmullet in Ireland. Calculations are made on waves with a significant wave height of 1.25 m and a period time of 7.5 s. Calculations are also made on the largest measured wave present. In essence, power calculations are used according to a model developed by Kjell Budal and with the help of this be able to graphically and numerically compare the theoretical and actual maximum power that can be extracted from each scale. The results from the survey show that the largest contributing factor to high energy recovery is due to the volume of the buoy. The volume must be adapted to the wave conditions that exist where the buoy is to be placed.When calculating an OWC with a cross sectional area of 19 m2, it turns out that the power that can be extracted from an air chamber with an associated turbine is approximately 10 kW, 1/30 of the 300 kW that can be extracted by one point absorber. However, an OWC rarely consists of a single air chamber but often in a construction with several air chambers with separate turbines to increase the power.