In this paper, the authors present a new formulation for the longitudinal coherent dipole motion, where a quadrature response of the environmental impedance is shown to be the effective longitudinal impedance for the beam instability. The Robinson-Pedersen formulation for the longitudinal dipole motion is also presented, the difference of the two approaches is discussed in the comparison. The results by using the Sacherer integral equation for the coherent dipole motion can generate the same results as by using the other two approaches, except for a scaling difference. The formulation is further generalized to the rigid bunch motion using signal analysis method, where a form factor shows up naturally. Finally, the formulation is applied to solve the coupled bunch instabilities. Examples of the AGS Booster and the AGS coupled bunch instabilities are used to illustrate the applications of the formulation.

In this paper, the authors present a new formulation for the longitudinal coherent dipole motion, where a quadrature response of the environmental impedance is shown to be the effective longitudinal impedance for the beam instability. The Robinson-Pedersen formulation for the longitudinal dipole motion is also presented, the difference of the two approaches is discussed in the comparison. The results by using the Sacherer integral equation for the coherent dipole motion can generate the same results as by using the other two approaches, except for a scaling difference. The formulation is further generalized to the rigid bunch motion using signal analysis method, where a form factor shows up naturally. Finally, the formulation is applied to solve the coupled bunch instabilities. Examples of the AGS Booster and the AGS coupled bunch instabilities are used to illustrate the applications of the formulation.

In the standard Richtmyer-Meshkov instability, perturbations at a shocked interface grow after the passage of a shock. Freeze-out refers to the phenomenon whereby the perturbations do not grow, i.e., freeze-out, after the passage of a shock. This is fairly straightforward, at least theoretically (no experiments have been done so far) in a doubly shocked system. The first shock induces a growth which can be completely neutralized by a second shock, provided that the direction and the strength and timing of the second shock are properly chosen. This type of double-shock freeze-out occurs in compressible as well as incompressible fluids, and is easy to understand. Somewhat more subtle is single-shock freeze-out; in the pursuit of this phenomenon, the author found that in certain cases Richtmyer`s prescription fails to give the correct growth rate.

AGS beam losses at transition are now tolerable ([lt]5%), but as the present improvement plans are implemented and the intensity is increased, new mechanisms will become important and the losses will increase. This Note describes studies directed towards minimizing these losses. Werner Hardt has studied these losses at the CERN PS. In particular, he found that by sharply reducing the time spent going through transition he could reduce the losses. Hardt visited Brookhaven in early June, 1986, in order to help us better understand the AGS. As a result of work inspired by his visit, we now believe that intensities of [approximately]5x10[sup 13] circulating protons are attainable in the AGS without significant losses at transition.

AGS beam losses at transition are now tolerable ({lt}5%), but as the present improvement plans are implemented and the intensity is increased, new mechanisms will become important and the losses will increase. This Note describes studies directed towards minimizing these losses. Werner Hardt has studied these losses at the CERN PS. In particular, he found that by sharply reducing the time spent going through transition he could reduce the losses. Hardt visited Brookhaven in early June, 1986, in order to help us better understand the AGS. As a result of work inspired by his visit, we now believe that intensities of {approximately}5x10{sup 13} circulating protons are attainable in the AGS without significant losses at transition.

In this article, we discuss fundamentals of the spectrum analysis in beam diagnostics, where several important particle motions in a circular accelerator are considered. The properties of the Fourier transform are presented. Then the coasting and the bunched beam motion in both longitudinal and transverse are studied. The discussions are separated for the signal particle, multiple particle, and the Schottky noise cases. To demonstrate the interesting properties of the beam motion spectrum, time domain functions are generated, and then the associated spectra are calculated and plotted. In order to show the whole picture in a single plot, some data have been scaled, therefore they may not be realistic in an accelerator.

In this article, we discuss fundamentals of the spectrum analysis in beam diagnostics, where several important particle motions in a circular accelerator are considered. The properties of the Fourier transform are presented. Then the coasting and the bunched beam motion in both longitudinal and transverse are studied. The discussions are separated for the signal particle, multiple particle, and the Schottky noise cases. To demonstrate the interesting properties of the beam motion spectrum, time domain functions are generated, and then the associated spectra are calculated and plotted. In order to show the whole picture in a single plot, some data have been scaled, therefore they may not be realistic in an accelerator.

On Wednesday, July 24, 1991, we studied the effectiveness of constant amplitude'' transverse damping at the Fermilab Tevatron. In this mode of damping, whenever a bunch's displacement exceeds a specified threshold, a constant (usually maximum) aplitude correction pulse is applied to the damper kicker. This is in contrast to the linear'' mode, where the kick is proportional to the displacement.

On Wednesday, July 24, 1991, we studied the effectiveness of ``constant amplitude`` transverse damping at the Fermilab Tevatron. In this mode of damping, whenever a bunch`s displacement exceeds a specified threshold, a constant (usually maximum) aplitude correction pulse is applied to the damper kicker. This is in contrast to the ``linear`` mode, where the kick is proportional to the displacement.

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A weekly publication, the Texas Register serves as the journal of state agency rulemaking for Texas. Information published in the Texas Register includes proposed, adopted, withdrawn and emergency rule actions, notices of state agency review of agency rules, governor's appointments, attorney general opinions, and miscellaneous documents such as requests for proposals. After adoption, these rulemaking actions are codified into the Texas Administrative Code.

A weekly publication, the Texas Register serves as the journal of state agency rulemaking for Texas. Information published in the Texas Register includes proposed, adopted, withdrawn and emergency rule actions, notices of state agency review of agency rules, governor's appointments, attorney general opinions, and miscellaneous documents such as requests for proposals. After adoption, these rulemaking actions are codified into the Texas Administrative Code.

Data taken from tests of annulus shield flow versus Christmas tree temperature show that the temperature of the tree is controlled by the annulus flow and the LHe level in the reservoir. Graphs indicating this are shown in Figures 1 and 2. An equation determined from the data taken on 4/19 to model the flow and LHe level dependence of tree temperature is as follows: T = AL + BF + C; T = tree temperature (K); A = -0.0055 (K/%); L = LHe Level (%) - 10% (0.6-inch) < L < 65% (3.9-inch); B = -1.166 (K/scfh air); F = annulus flow (scfh air) - 0.5 < F < 1.0 scfh; and C = 7.889 (K). From the above equation it is evident that shield flow has a significant effect on tree temperature while the percent of LHe in the reservoir is much less significant. The following illustrates the temperature's relative sensitivity to the two variables: {Delta}flow = 0.5 scfh gives {Delta}T = 0.58 K and {Delta}level = 40% LHe gives {Delta}T = 0.22 K. A graph of Temperature Calculated vs. Temperature Measured in Figure 3 shows the degree to which the equation conforms to the data taken on …