KEYWORDS: Systems modeling, Motion models, Mathematical modeling, Computer simulations, Process modeling, Lab on a chip, Systems engineering, Software engineering, Performance modeling, Modeling and simulation
A tractable scientific basis is needed for M&S modeling, specification, abstraction, refinement, composition, and decomposition. While the component composition, abstraction, and refinement work of others will provide valuable insights, M&S fundamentals for physical systems must be applicable to the lowest level of knowledge about those systems. Starting with objects, components, or systems (such as the approaches from the software engineering and systems engineering literature) is too high a level. In addition, none of the published theory addresses the situational requirements issues of M&S in conjunction with the fundamental composition, abstraction, and refinement issues. As a result, M&S development, integration, and evolution are often ad hoc, based on ambiguous specifications. Additional theoretical and practical work is needed to support M&S. This paper provides an overview description of several fundamental M&S issues and outlines a recommended M&S foundations research agenda to address these issues.
Previous studies of crossed-field electron vacuum devices, such as magnetrons and crossed-field amplifiers (CFA), have centered on their initial growth, as an indication of their operating modes. In such an analysis, one assumes a growth rate, and solves the equations for the density profile, the operating frequency, and the growth rate. What one obtains here are the conditions for the initial operation of the device. However, eventually the RF fields will have saturated, and the device then will enter into either a stationary operating regime, or some other mode, which could in general be some non-operating mode. To study this regime of operation, we return to the classical planar magnetron equations and study what the form of the solution will be for these stationary solutions. What we find is that upon saturation, as the growth rate vanishes, its effect is replaced by second-order velocity terms, and in particular, the second-order vertical velocity. What we will do here is to derive and present the magnetron equations when the growth rate vanishes, and discuss the solutions of the RF equations about the resonance points. Lastly, we shall consider what implications these results may have for relativistic and nonrelativistic crossed-field devices.
We present preliminary results for a model of a relativistic planar magnetron. Similar to our treatment of the non- relativistic case, we start with the cold-fluid relativistic equations and Fourier decomposition the equations, separating the physical quantities into a background mode and a pump mode. We use our previous techniques to determine the background mode and the RF pump mode.
Crossed-field electron vacuum devices are resonant devices. When properly tuned, they operate at a single frequency and have an average background distribution. Thus one can use the cold-fluid equations and a Fourier decomposition to separate the physical quantities into a background (DC) mode and a pump (RF) mode. We have improved our previous calculations on these devices and can now understand how the background plasma density varies and evolves as the RF wave travels down the slow-wave structure. We study the evolution of an RF pump wave through the device and find that in general, chaotic (period-2) instabilities can occur if the device is too long. We also present results for the high magnetic field case, (typical CFA/magnetron regime), for the moderate magnetic field case (ultra-low noise regime), and discuss how these solutions correspond to device operation. Lastly, we discuss our results and point out future work in need of study.
The purpose of this work is to theoretically understand what are the possible noise levels in a magnetron or a crossed- field amplifier, due to parametric three-wave interactions in the electron plasma, at various operating parameters. Our approach is to use the cold-fluid equations and their Fourier decomposition, into a background mode, a pump (RF) mode, and two other noise (RF) modes. The two RF noise modes are assumed to interact parametrically with the large RF pump mode, and to satisfy the standard resonance conditions for the sum of the wave vectors and sum of the frequencies.
We develop a perturbation theory to analytically calculate effects of interchannel collisions on Gaussian pulses in a wavelength-division-multiplexed system with strong dispersion management. We show that, for complete collisions, the collision-induced frequency shift of a Gaussian pulse is negligible, while for incomplete collisions, this shift is significant. We also show that, as the dispersion management strength increases, the collision- induced position shift becomes more important than the frequency shift. An interesting result of our analysis is that the collision-induced frequency and position shifts depend on the dispersion management strength and the path- average dispersion, but not on the lengths of the two opposite-dispersion fiber segments in the dispersion map. We check the analytical predictions against direct PDE simulations, finding satisfactory agreement between them. We also give an estimate of the limit imposed on the transmission distance by such collisions.
We use the cold-fluid plasma equations to consider the nonlinear effects of a strong, relativistic RF electric field (with a frequency, w, and a wavevector, k) which is propagating on the background electron density profile in a relativistic crossed-field, electron vacuum device. Earlier, we had shown that in the nonrelativistic case, when k and w are such that a wave-particle resonance, w equals vdk, can occur at the edge of a Brillouin sheath, then the Brillouin sheath becomes strongly unstable to a Rayleigh instability, with the instability being driven by the strong negative density gradient at the edge of the Brillouin sheath. As a consequence of this instability, the average DC density profile becomes strongly modified and is driven away from the classical Brillouin flow by the RF field, and is driven toward stationary solutions of a nonlinear diffusion equation. From this nonlinear diffusion equation, one can predict the DC current flow through a device and also can predict the shape of the stationary DC electron density profile. Also we have demonstrated that such stationary solutions do exist and can be calculated. Further, we showed that when one combined these stationary solutions with the RF field solutions, then the total solution would generate the standard spoke structure, long seen in numerical simulations. Here, we shall extend these calculations into the relativistic regime and discuss their form.
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