An Efficient Computation of Coherent Synchrotron Radiation in a Rectangular Chamber, Applied to Resistive Wall Heating

We study coherent synchrotron radiation (CSR) in a perfectly conducting vacuum chamber of rectangular cross section, in a formalism allowing an arbitrary sequence of bends and straight sections. We apply the paraxial method in the frequency domain, with a Fourier development in the vertical coordinate but with no other mode expansions. A line charge source is handled numerically by a new method that rids the equations of singularities through a change of dependent variable. The resulting algorithm is fast compared to earlier methods, works for short bunches with complicated structure, and yields all six field components at any space-time point. As an example we compute the tangential magnetic field at the walls. From that one can make a perturbative treatment of the Poynting flux to estimate the energy deposited in resistive walls. The calculation was motivated by a design issue for LCLS-II, the question of how much wall heating from CSR occurs in the last bend of a bunch compressor and the following straight section. Working with a realistic longitudinal bunch form of r.m.s. length $10.4~\mu$m and a charge of 100 pC we conclude that the radiated power is quite small (28 W at a 1 MHz repetition rate), and all radiated energy is absorbed in the walls within 7 m along the straight section.Comment: 47 pages, 24 figure

Determination of U, V, and W from single station Doppler radar radial velocities

The ST/MST (stratosphere troposphere/mesosphere stratosphere troposphere) clear air Doppler radar, or wind profiler, is an important tool in observational meteorology because of its capability to remote observe dynamic parameters of the atmosphere. There are difficulties in transforming the observed radial velocities into meteorological wind components. How this problem has been treated in the past is reviewed, and some of the analysis is recast to a form more suited to the high diagnostic abilities of a number of fixed beam configurations with reference to a linear wind field. The results, in conjunction with other works which treats problems such as the effects of finite sample volumes in the presence of nonhomogeneous atmospheric reflectivity, have implications important to the design of both individual MST/ST radars and MST/ST radar networks. The key parameters to uncoupling terms in the scaling equations are w sub x and w sub y. Whenever the stratiform condition, which states that these two parameters are negligible, is satisfied, a five beam ST radar may determine unbiased values of u, v, and w for sample volumes directly above the radar. The divergence and partial deformation of the flow may also be determined. Three beam systems can determine w and w sub z, but are unable to obtain u and v wind components uncontaminated by vertical sheer terms, even when the stratiform condition is satisfied

Testing and optimizing MST coaxial collinear arrays, part 6.4A

Many clear-air VHF wind profiles use coaxial collinear (COCO) arrays for their antenna. A COCO array is composed of long lines of half-wave dipoles spaced one-half wavelength apart. An inexpensive method of checking a COCO array is described and its performance is optimized by measuring and then correcting the relative rf phase among its lines at their feed point. This method also gives an estimate of the rf current amplitude among the lines. The strength and location of the sidelobes in the H-plane of the array can be estimated

Recent results at the Sunset radar

The Sunset radar is a VHF, pulsed Doppler radar located in a narrow canyon near the Sunset townsite 15 km west of Boulder, CO. This facility is operated by the Aeronomy Laboratory, ERL, NOAA, exclusively for meteorological research and the development of the mesosphere-stratosphere-troposphere (MST) and stratosphere-troposphere (ST) radar technique. Recent results include a measurement of all three components of wind velocity for the Federal Administration

A comparison of vertical velocities measured from specular and nonspecular echoes by a VHF radar

For a number of years, there have been doubts about the accuracy of vertical wind velocities measured with quasi-specular reflections from mesosphere-stratosphere-troposphere (MST) radar. The concern has been that the layers producing the quasi-specular reflection process this hypothetical tilt. Because of the quasi-specular reflection process, this hypothetical tilt would control the effective zenith angle of the radar antenna beam so that a small component of the horizontal velocity would be included in what was assumed to be a truly vertical beam. The purpose here is to test the hypothesis that there is an effect on the wind velocities measured on a vertical antenna beam due to a long-term tilting of the stable atmospheric layers that cause quasi-specular reflection. Gravity waves have been observed to cause short-term tilting of turbulent layers and specularly reflecting layers. In both cases, the effect was a wave-like deformation atmospheric layers with a period of a few minutes. This geometry is shown. Because of this influence of gravity waves, it was expected that there would be short-term variations in the vertical velocity

One Work, Three Infringers: Calculating the Correct Number of Separate Awards of Statutory Damages in a Copyright Infringement Action

Columbia Pictures provides the most persuasive analysis of the correct number of separate awards of statutory damages available to a plaintiff. Lime Group recognized that the question was a particularly close one, and the court erred in reaching the opposite result from Columbia Pictures. The Lime Group analysis is based on a fundamentally flawed earlier decision and relies, in the end, on an approach as likely to reward infringers rather than defend the rights of copyright holders: determining whether the potential result in any given case is absurd. Regarding the hypothetical case provided at the beginning of this Essay, Warren should be entitled to sue only One Stop and recover three separate awards of statutory damages for each different recording of Ode. Nothing in the legislative history nor the plain language of the Copyright Act suggests that a high number of awards should vary the way that a court interprets 17 U.S.C. § 504(c)(1). To the contrary, both the statute and the legislative history look to the number of separately liable infringers rather than the number of infringements. In the hypothetical, three separately liable infringers infringed Warren\u27s work. If One Shop sells all three versions, then the only rationale supporting one award rather than three is the presence or absence of other defendants, namely the three separately liable manufacturers. Nothing in the Copyright Act, however, supports either an analysis or a result based on a question of joinder. In fact, the overarching question is which result better supports the policies underlying the Copyright Act; the better view will always defend the rights of the copyright owner rather than reward an infringer

The U.S. system for measuring cross-border investment in securities: a primer with a discussion of recent developments

The tremendous growth in cross-border securities investment in recent years has called attention to the systems used by the United States and other countries to measure international securities flows and holdings. Ideally, the data gathered by the United States could tell us the extent to which foreign investors hold U.S. securities, the types of securities held, and the countries in which the securities are held, for example, and could identify trends in investment. This article looks at how well the data shed light on these topics. Special attention is given to the system's design and the implications of the design for data analysis. Also discussed are anticipated changes to the system and international efforts to improve data collection systems worldwide.International finance ; Securities

Measurement of vertical velocity using clear-air Doppler radars

A new clear air Doppler radar was constructed, called the Flatland radar, in very flat terrain near Champaign-Urbana, Illinois. The radar wavelength is 6.02 m. The radar has been measuring vertical velocity every 153 s with a range resolution of 750 m almost continuously since March 2, 1987. The variance of vertical velocity at Flatland is usually quite small, comparable to the variance at radars located near rough terrain during periods of small background wind. The absence of orographic effects over very flat terrain suggests that clear air Doppler radars can be used to study vertical velocities due to other processes, including synoptic scale motions and propagating gravity waves. For example, near rough terrain the shape of frequency spectra changes drastically as the background wind increases. But at Flatland the shape at periods shorter than a few hours changes only slowly, consistent with the changes predicted by Doppler shifting of gravity wave spectra. Thus it appears that the short period fluctuations of vertical velocity at Flatland are alsmost entirely due to the propagating gravity waves