Microwave growth from the beam breakup instability in long‐pulse electron beam experiments

The beam breakup (BBU) instability has been investigated in high‐current, long‐pulse electron beams propagating through microwave cavities. Experiments are performed using a relativistic electron‐beam generator with diode parameters: 0.7–0.8 MV, 1–15 kA, and 0.5–1.5 μs. The magnitude of the solenoidal magnetic field places these experiments in an intermediate regime between strong focusing and weak focusing. The electron‐beam transport system consists of ten identical pillbox cavities each containing a small microwave loop antenna designed to detect the TM110 beam breakup mode. The TM110 microwave mode is primed in the first cavity by a magnetron tuned to the resonance frequency of 2.5 GHz. The BBU instability growth is measured through the amplification of the 2.5 GHz microwaves between the second and tenth cavities. Strong growth (25–38 dB) of the TM110 microwave signal is observed when the initial cavity is primed exactly on resonance, with a rapid decrease of the growth rate off‐resonance. The magnitude of microwave growth is consistent with the predictions of BBU theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69350/2/APPLAB-61-6-642-1.pd

The beam breakup instability in quadrupole and solenoidal electron‐beam transport systems

Dispersion relations are derived to determine the growth rate, dominant wavelength, and group velocity of disturbances caused by the beam breakup instability. Considerations include weak and strong focusing, x‐y coupling in solenoidal transport, the spacing of accelerator cavities, and periodically pulsed beams. Beam breakup growth is minimum when the cavity spacing equals an integral number of half‐betatron wavelengths for quadrupole focusing, and an integral number of betatron wavelengths for solenoidal focusing. Minimum growth is also found for periodic pulses separated by an integral number of half‐periods of the TM110 cavity mode. Expressions for beam breakup growth at the minima are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71286/2/JAPIAU-71-7-3091-1.pd

A biologically relevant rapid quantification of physical and biological stress profiles on rocky shores.

Different combinations and intensities of physical (e.g. thermal) and biological (e.g.competition or predation) stress operate on organisms in different locations. Variation in these stresses can occur over small to medium spatial scales (cm to 10s m) in heterogeneous environments such as rocky shores, due to differences in sun and wave exposure, shore topography and/or recruitment. In this study we demonstrate how simple measurements can be taken that represent physical and biological stresses (stress profiles)in a given location. Using a bootstrapped principal component analysis, we identified significantly different stress profiles at four sites separated by only 10s to 100s of metres on the Shek O peninsula in Hong Kong. We then measured response to thermal stress, as determined by detachment temperature, in the limpet Cellana grata (which is known to be a sensitive indicator species to thermal stress) from each location. Significant differences in stress profile between locations were also seen in thermal stress tolerance of limpets from those locations. At locations where the major stresses are likely to be more physical or less biological in nature (e.g. southerly facing aspect or lower density of grazers), the mean detachment temperature was higher, whereas detachment temperature was lower at sites with more biological or less physical stress. This method is, therefore, able to determine biologically meaningful differences in stress profiles over small to medium spatial scales, and demonstrates that localised adaptation (i.e. post planktonic settlement) or acclimation of species may occur in response to these different stress profiles. The technique can be adapted to different environments and smaller or larger spatial scales as long as the stress experienced by the study species is relevant to these scales

Arctic sea-ice melt in 2008 and the role of solar heating

There has been a marked decline in the summer extent of Arctic sea ice over the past few decades. Data from autonomous ice mass-balance buoys can enhance our understanding of this decline. These buoys monitor changes in snow deposition and ablation, ice growth, and ice surface and bottom melt. Results from the summer of 2008 showed considerable large-scale spatial variability in the amount of surface and bottom melt. Small amounts of melting were observed north of Greenland, while melting in the southern Beaufort Sea was quite large. Comparison of net solar heat input to the ice and heat required for surface ablation showed only modest correlation. However, there was a strong correlation between solar heat input to the ocean and bottom melting. As the ice concentration in the Beaufort Sea region decreased, there was an increase in solar heat to the ocean and an increase in bottom melting

Beam breakup growth and reduction experiments in long‐pulse electron beam transport

The results of an experimental program whose sole objective is to investigate the cumulative beam breakup instability (BBU) in electron beam accelerators are presented. The BBU growth rate scalings are examined with regard to beam current, focusing field, cavity Q, and propagation distance. A microwave cavity array was designed and fabricated to excite and measure the cumulative BBU resulting from beam interactions with the deflecting TM110 cavity mode. One phase of this experiment used high Q(≊1000) cavities with relatively large frequency spread (Δf/f0≊0.1%). The observed TM110 mode microwave growth between an upstream (second) and a downstream (tenth) cavity indicated BBU growth of 26 dB for an electron beam of kinetic energy of 750 keV, 45 A, and focused by a 1.1 kG solenoidal field. At beam currents of less than 100 A the experiments agreed well with a two‐dimensional continuum theory; the agreement was worse at higher beam currents (≳100 A) due to beam loading. The second‐phase experiments used lower Q(≊200) cavities with relatively low frequency spread (Δf/f0≊0.03%). Theory and experiment agreed well for beam currents up to 220 A. Distance scaling experiments were also performed by doubling the propagation length. Instability growth reduction experiments using the technique of external cavity coupling resulted in a factor of four decrease in energy in BBU growth when seven internal beam cavities were coupled by microwave cable to seven identical external dummy cavities. A theory invoking power sharing between the internal beam cavities and the external dummy cavities was used to explain the experimental reduction with excellent agreement using an equivalent circuit model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71080/2/JAPIAU-75-3-1258-1.pd

An Enhanced Perturbational Study on Spectral Properties of the Anderson Model

The infinite-$U$ single impurity Anderson model for rare earth alloys is examined with a new set of self-consistent coupled integral equations, which can be embedded in the large $N$ expansion scheme ($N$ is the local spin degeneracy). The finite temperature impurity density of states (DOS) and the spin-fluctuation spectra are calculated exactly up to the order $O(1/N^2)$. The presented conserving approximation goes well beyond the $1/N$-approximation ({\em NCA}) and maintains local Fermi-liquid properties down to very low temperatures. The position of the low lying Abrikosov-Suhl resonance (ASR) in the impurity DOS is in accordance with Friedel's sum rule. For $N=2$ its shift toward the chemical potential, compared to the {\em NCA}, can be traced back to the influence of the vertex corrections. The width and height of the ASR is governed by the universal low temperature energy scale $T_K$. Temperature and degeneracy $N$-dependence of the static magnetic susceptibility is found in excellent agreement with the Bethe-Ansatz results. Threshold exponents of the local propagators are discussed. Resonant level regime ($N=1$) and intermediate valence regime ($|\epsilon_f| <\Delta$) of the model are thoroughly investigated as a critical test of the quality of the approximation. Some applications to the Anderson lattice model are pointed out.Comment: 19 pages, ReVTeX, no figures. 17 Postscript figures available on the WWW at http://spy.fkp.physik.th-darmstadt.de/~frithjof