and let α1, . . . , αn be its roots, which are assumed to be distinct. By definition, the Galois Group G of this equation consists of those permutations of the roots which preserve all relations between them. Equivalently, G is the set of all those permutations σ of the symbols {1, 2, . . . , n} such that φ(ασ(1), . . . , ασ(n)) = 0 for every n-variable polynomial φ for which φ(α1, . . . , αn) ...

We have counted the number of references in 1179 papers published in Astronomy and Astrophysics over twenty years. The number of references has increased by 60% between 1975 and 1995, reflecting the increase (by the same amount) of the literature which must be cited, and of the number of pages per paper. There are 1.5 timesmore references in predominantly observational fields than in others. Re...

We report the rst studies of bunch length in collision in an operating linear collider, making use of a new rf bunch length monitor installed in the South Final Focus of the Stanford Linear Collider (SLC) prior to the 1997/98 luminosity run. The theoretical and measured monitor responses to linac injection phase and bunch compressor voltage are described. Correlations with beamstrahlung and lum...

At CesrTA, we have developed the capability to make automated measurements of the self-excited frequency spectra of individual bunches, to look for signals for singlebunch instabilities. We can also drive single bunches and measure the rate of decay of selected lines in their frequency spectra. We have used these capabilities to explore the dynamics of the interaction of a multi-bunch beam with...

Bunch lengths as short as 84 fs (rms) have been measured at Jefferson Lab using a zero-phasing RF technique. To the best of our knowledge, this is the first accurate bunch length measurement in this regime. In this letter, an analytical approach for computing the longitudinal distribution function and bunch length is described for . arbitrary longitudinal and transverse distributions. The measu...

Micro-bunching instabilities limit the longitudinal compression of bunches in an electron storage ring. They create substructures on the bunch profile of some hundred micrometer size leading to coherently emitted synchrotron radiation in the THz range. To detect the changing THz spectrum, single-shot bunch-by-bunch and turn-by-turn measurements are necessary. We present recent experiments at AN...

Streak camera measurements were made at SPEAR3 to characterize longitudinal coupling impedance. For the nominal optics, data was taken at three rf voltages and a single-bunch current range of 0-20mA. Both bunchcentroid phase shift and bunch lengthening were recorded to extract values for resistive and reactive impedance. An (R+L) and a Q=1 model were then back-substituted into the Haissinski eq...

The effects of amplitude modulation of RF cavity voltage on the longitudinal beam dynamics were studied experimentally at SRRC by using a streak camera system. The characteristics of parametric resonance in single bunch beam was investigated both by simulation and measurement. The formation of beamlets in the bunch helps to damp the coherent bunch oscillation. This property is employed to provi...

* The work is supported by DOE SBIR No. DE-FG03-96ER82213. Abstract Synchronous wakefields in a dispersive waveguide are formulated in a general form. The fundamental role of group velocity in wakefield propagation, calculation of attenuation, amplitudes, form-factors and loss-factors is demonstrated for single-bunch and multi-bunch train. Waveguide adiabatic tapering and bunch density variatio...