A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay

Optimizing the antenna system of a microwave space power station: Implications for the selection of operating power, frequency and antenna size

A design for a space power station that is to transmit power to the surface of a planet via high powered microwaves should commence with the optimum design of the transmitting and receiving antenna combination to be employed. Once one has assured that the desired amount of power has been transferred (which, after all, is the prupose of any power transmission system), one can, from the constraints imposed by such a design, taylor other parameters of the system such as antenna sizes and weights, power density in the planet's atmosphere (e.g., to avoid electrical breakdown), and frequency of operation. It is the purpose of this brief analysis to provide the working equations of such an optimized antenna system, and to give examples of their use. Related problems that should be analyzed in the future will then be discussed and a flow chart of the indicated order of priority presented. The analysis given here differs from previous work on this subject in that the development given will allow analytical expressions to be obtained for the relevant parameters. This is made possible by employing an approximation procedure to be given during the exposition

The theory of an auto-resonant field emission cathode relativistic electron accelerator for high efficiency microwave to direct current power conversion

A novel method of microwave power conversion to direct current is discussed that relies on a modification of well known resonant linear relativistic electron accelerator techniques. An analysis is presented that shows how, by establishing a 'slow' electromagnetic field in a waveguide, electrons liberated from an array of field emission cathodes, are resonantly accelerated to several times their rest energy, thus establishing an electric current over a large potential difference. Such an approach is not limited to the relatively low frequencies that characterize the operation of rectennas, and can, with appropriate waveguide and slow wave structure design, be employed in the 300 to 600 GHz range where much smaller transmitting and receiving antennas are needed

A random matrix definition of the boson peak

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling $\omega^*\sim p^{-1/2}$ . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of $\omega^{*}$ with coordination number that is observed near the jamming transition.Comment: 6 pages, 4 figures, Supplementary Figures available at https://mmanning.expressions.syr.edu/epl2015