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Bunched beam instability with frequency spread

Description: In this paper, the eigenvalue type solution to the bunched beam instability with frequency spread is studied. The approach provides a comprehensive solution to the problem by including all necessary modes. The synchrotron frequency spread is represented by a mode decomposition, the decomposed modes have different inherent frequencies from each other and the corresponding radial functions are different from the ones without frequency spread. The environmental impedance induced feedback applied to these modes and then creates Landau damping effect. The radial modes and therefore the line densities can be solved throughout the Landau damping, thus to provide some insight into the process. Several conceptual and computational problems are discussed, and the method is compared with the conventional Landau damping treatment. Finally, the case of mode coupling is also discussed.
Date: September 1, 1994
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

On solutions of Sacherer integral equation

Description: There are basically two approaches in solving the Sacherer integral equation, one uses the orthogonal polynomial expansion for radial functions, and another uses the Hankel harmonic samplings, both have extensive application. In this article, we discuss these approaches and present the corresponding solutions. If the azimuthal modes are not coupled, the Sacherer integral equation can be treated as an eigenvalue problem. It is shown that the information provided by the eigenvalue alone are insufficient in determining the system response. The initial perturbation pattern with respect to the radial modes must be considered. Several particle distributions are used as examples to show the solutions to the equation, and the physical implication of the radial modes is illustrated by using the examples.
Date: June 17, 1994
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

The operational status of the Booster injector for the AGS accelerator complex at BNL

Description: The Booster synchrotron at Brookhaven National Laboratory has been incorporated into the accelerator chain at the Alternating Gradient Synchrotron (AGS) complex. After a successful first commissioning effort in the spring of 1991, the Booster has been part of this year`s silicon, gold and proton physics runs. After a brief review of the Booster design goals, and of the early commissioning, this paper will summarize this year`s activities.
Date: September 1, 1992
Creator: Ahrens, L.; Bleser, E.; Brennan, J. M.; Gardner, C.; Gill, E.; Glenn, J. W. et al.
Partner: UNT Libraries Government Documents Department

A new formulation of longitudinal coherent instabilities

Description: The quadrature response of longitudinal impedance is shown to be the effective impedance for the beam instability. The results of the application of this formulation are compared with that obtained using the Robinson-Pedersen approach and the Sacherer integral equation. 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.
Date: June 1, 1993
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Observation and correction of resonance stopbands in the AGS Booster

Description: At the design intensity of 1.5 {times} 10{sup 13} ppp, the space charge tune shift in the AGS Booster at injection has been estimated to be about 0.35. Therefore, the beam is spread over may lower order resonance lines and the stopbands have to be corrected to minimize the amplitude growth by proper compensation of the driving harmonics resulting from random errors. The observation and correction of second and third order resonance stopbands in the AGS Booster, and the establishment of a favorable operating point at high intensity are discussed.
Date: June 1, 1993
Creator: Gardner, C.; Shoji, Y.; Ahrens, L.; Glenn, J. W.; Lee, Y. Y.; Roser, T. et al.
Partner: UNT Libraries Government Documents Department

Evaluating impedances in a Sacherer integral equation

Description: In Sacherer integral equation, the beam line density is expanded on the phase deviation {phi}, generating a Hankel spectrum, rather than on the time, which generates a Fourier spectrum. This is a natural choice to deal with the particle evolution in phase space, it however causes complications whenever the impedance corresponding to the spectrum has to be evaluated. In this article, the line density expansion on {phi} is shown to be equivalent to a beam time modulation under an acceptable condition. Therefore for a Hankel spectrum, a number of sidebands, and the corresponding impedance as well, will be involved. For wideband resonators, it is shown that the original Sacherer solution is adequate. For narrowband resonators, the solution had been compromised, therefore a modification may be needed.
Date: August 1, 1994
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Effects of the second harmonic cavity on rf capture and transition crossing

Description: Presented is an analysis of longitudinal beam dynamics and results of numerical simulations showing that the addition of a second harmonic cavity to the fundamental one during rf capture helps to increase the bunching factor by 23--28%, and hence reduces the space charge tune spread by an equal amount. The addition of a second harmonic cavity also helps to prevent particle losses during transition crossing by confinement of the energy spread within the bunch. A numerical simulation study shows that the reduction of emittance blowup is about 20%.
Date: August 1, 1992
Creator: Kats, J. M. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Effect of space charge tune shift on transverse instabilities

Description: Transverse instabilities in synchrotrons with large space charge tune shift are considered. In particular the variation of the incoherent tune with longitudinal position in the bunch is included. Expansion in an appropriate basis set results in an eigenvalue problem which reduces to previously derived expressions when the space charge tune spread is ignored. The regime where the synchrotron tune is negligible compared to the space charge tune shift is also considered. Under appropriate conditions this results in a significantly smaller growth rate than the ones obtained using the weak coupling formalism. Finally, the effect of octupole induced betatron tune spread is included, resulting in a technique for estimating the maximum stable current.
Date: August 1, 1994
Creator: Blaskiewicz, M. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Analysis of Periodic Transient Beam Loading of the AGS

Description: In this note, we discuss the multi-batch bunched ;beam loading during the injection from the Booster to the AGS. The full intensity beam injection to the upgraded AGS RF system with beam phase and radial feedbacks will be studied. It is shown that a beam phase feed-back is necessary in order to guarantee a predictable beam behavior after the first batch injection, otherwise the initial phase deviation for the following batch injections cannot be controlled. However, the effectiveness of the phase feedback control of the transient beam loading is limited by the associated emittance blow-up in the process. It is shown that a fast power amplifier feedback with a moderate gain can significantly reduce the transient effect of the bunched beam injection.
Date: July 13, 1992
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Topics on RF beam control of a synchrotron

Description: In this paper, several typical situations of longitudinal motion in synchrotron design and operation are studied. The study is based on a unified beam dynamic model of synchrotron oscillation under phase and radial feedbacks. Cases studied include frequency error, lock-in range, bunch excursion, phase manipulation, injection and field errors.
Date: July 13, 1992
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Rf beam loading in the Brookhaven AGS with booster injection

Description: Multi-batch bunched beam loading during injection from the Booster to the AGS will be discussed. The full intensity beam injection to the upgraded AGS rf system with beam phase and radial feedbacks will be studied. It is shown that a beam phase feedback is necessary in order to guarantee a predictable hewn behavior after the first batch injection, otherwise the initial phase deviation for the following batch injections cannot be controlled. However, the effectiveness of the phase feedback control of the transient beam loading may be limited by an emittance blow up in the process. It is shown that a fast power amplifier feedback with a moderate gain can significantly reduce the transient effect of the bunched beam injection.
Date: September 1, 1992
Creator: Zhang, S. Y.; Raka, E. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

On the high intensity aspects of AGS Booster proton operation

Description: Observations of high intensity effects on the proton performance of the AGS Booster are presented, including present operational limits and correction methods. The transverse emittances, optimum tune working points, damping of coherent transverse oscillations and correction of stopband resonances through third-order are discussed in addition to the observed tune spread due to space charge forces. The initial longitudinal phase space distribution, capture and acceleration parameters and measurements are also given. Operational tools and strategies relevant to the high intensity setup are mentioned.
Date: June 1, 1993
Creator: Reece, R. K.; Ahrens, L. A.; Bleser, E. J.; Brennan, J. M.; Gardner, C.; Glenn, J. W. et al.
Partner: UNT Libraries Government Documents Department

Static and transient beam loading of a synchrotron

Description: In a synchrotron, when the beam induced current is comparable to the driver current, the RF cavity is subjected to beam loading perturbation and corrective steps have to be implemented to regain beam stability. In this paper, the static and transient beam loading will be studied. We first discuss the static beam loading, which includes the cavity detuning condition, the stability condition, and the generator power dissipation. The beam current induced beam phase deviation is used as criterion to study the transient beam loading. The upgraded and the old AGS RF system parameters are used as an example to demonstrate how to choose cavity and generator parameters to satisfy the stability requirements under the beam loading. The dynamic models for the beam loading with beam control, and the beam loading with fast power amplifier feedback are presented and analyzed. It is shown that the beam phase and radial feedbacks alone are insufficient for the transient beam loading compensation, but the fast power amplifier feedback can provide effective correction on the beam loading. The limitation of the fast feedback and the beam loading with tuning and AVC loops are also discussed.
Date: July 13, 1992
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Operation of the Brookhaven AGS with the Booster

Description: The Brookhaven Alternating Gradient Synchrotron (AGS) received protons directly from a Linac and heavy ions directly from a Tandem Van de Graaff before 1992. The newly constructed Booster has been brought on line to serve as an injector for the AGS. The operational status of the acceleration of proton and heavy ions through the Booster and the AGS is reviewed. Accelerator improvement programs to increase proton intensity for physics research and to prepare heavy ion beams for RHIC injection are discussed.
Date: June 1, 1993
Creator: Weng, W. T.
Partner: UNT Libraries Government Documents Department

Spectrum analysis in beam diagnostics

Description: 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.
Date: April 23, 1993
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

The method of minimal normal forms

Description: Normal form methods for solving nonlinear differential equations are reviewed and the comparative merits of three methods are evaluated. The concept of the minimal normal form is explained and is shown to be superior to other choices. The method is then extended to apply to the evaluation of discrete maps of an accelerator or storage ring. Such an extension, as suggested in this paper, is more suited for accelerator-based applications than a formulation utilizing continuous differential equations. A computer code has been generated to systematically implement various normal form formulations for maps in two-dimensional phase space. Specific examples of quadratic and cubic nonlinear fields were used and solved by the method developed. The minimal normal form method shown here gives good results using relatively low order expansions.
Date: December 31, 1992
Creator: Mane, S. R. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

Bunched beam longitudinal instability: Coherent dipole motion

Description: 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.
Date: April 23, 1993
Creator: Zhang, S. Y. & Weng, W. T.
Partner: UNT Libraries Government Documents Department

A new formulation of longitudinal coherent instabilities

Description: The quadrature response of longitudinal impedance is shown to be the effective impedance for the beam instability. The results of the application of this formulation are compared with that obtained using the Robinson-Pedersen approach and the Sacherer integral equation. 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.
Date: January 1, 1993
Creator: Zhang, S.Y. & Weng, W.T.
Partner: UNT Libraries Government Documents Department

Analysis of orbit perturbations of the SLC arcs

Description: The generation and correction of orbit errors are analyzed. A general stability criterion for the orbit correction is established and the rms orbit errors and corrector strengths are calculated. The formulation is then applied to the design of the Stanford Linear Collider to obtain estimates for residual orbit distortion after correction. (LEW)
Date: January 1, 1987
Creator: Weng, W.T.; Murray, J. & Chao, A.
Partner: UNT Libraries Government Documents Department

On the high intensity aspects of AGS Booster proton operation

Description: Observations of high intensity effects on the proton performance of the AGS Booster are presented, including present operational limits and correction methods. The transverse emittances, optimum tune working points, damping of coherent transverse oscillations and correction of stopband resonances through third-order are discussed in addition to the observed tune spread due to space charge forces. The initial longitudinal phase space distribution, capture and acceleration parameters and measurements are also given. Operational tools and strategies relevant to the high intensity setup are mentioned.
Date: January 1, 1993
Creator: Reece, R.K.; Ahrens, L.A.; Bleser, E.J.; Brennan, J.M.; Gardner, C.; Glenn, J.W. et al.
Partner: UNT Libraries Government Documents Department

Beam transfer from the AGS to ISABELLE

Description: The ISABELLE design current is built up by repetitive transfer of charge from the AGS. To do this, a momentum stacking method similar to the one used at the ISR has been chosen. The AGS beam bunches are synchronously transferred from the AGS into waiting rf buckets on the injection orbit at the ISA, and then slowly accelerated into the previously established debunched beam stack. This process is repeated until all the available momentum aperture in the ISA is filled up, whereupon the beam stack is rebunched and accelerated to the desired operating energy.
Date: January 1, 1979
Creator: Weng, W.T.; Brown, H.; Claus, J.; Foelsche, H.; Lee, Y.Y. & Raka, E.
Partner: UNT Libraries Government Documents Department

Multiwire secondary-emission monitor and the emittance measurement of the AGS beam

Description: For CBA injection the transverse emittances and the Twiss parameters of the AGS beam have to be well defined to minimize the phase space dilution in CBA. Althoug there exists a profile monitor device at U165, there are three reasons why construction of multiwire profile monitor system at three locations from U500 to U168 is required: (1) the dispersion function is not zero at U165 which makes it harder to interpret the measurement; (2) the original single wire device takes five minutes to traverse the whole beam; (3) a three station multiwire system can provide the profile information at all locations in one pulse which makes on-line analysis possible. In summary, a set of three stations of Multiwire Secondary Emission Monitor (MSEM) has been built and installed in the fast external beam line for the measurement of beam profiles. Each unit consists of two planes each with 30 nickel wires having a diameter of 5 mils. The signal is linear within the range of 10/sup 10/ to 10/sup 13/ incident protons on the wire and the resolution of the signal is well within a few percent. A least-square fitting routine has been used to extract the emittance and phase space parameters of the beam. The emittances obtained at various intensities will help us to understand the AGS acceleration process and to choose the optimal injection scheme for CBA.
Date: January 1, 1983
Creator: Weng, W.T.; Chiang, I.H.; Smith, G.A. & Soukas, A.
Partner: UNT Libraries Government Documents Department

Fundamentals: Longitudinal motion

Description: This paper discusses the following topics on synchrotrons: Dynamics of Synchrotron; Acceleration Cavity; Beam Manipulation and Beam Control; and High Intensity Effects. 21 refs., 26 figs. (LSP)
Date: November 7, 1988
Creator: Weng, W.T.
Partner: UNT Libraries Government Documents Department

AGS new fast extraction system and the single bunch extraction test

Description: For the neutrino physics program and for the CBA injection, a new fast extraction system has been implemented to improve the extraction efficiency and the quality of the extracted beam. Central to the new system is a new fast kicker, placed at the H5 straight section, capable of rising between bunches, t/sub r/ < 170 nsec, and staying constant for 2.6 ..mu..sec with flat top ripple less than +-1.5%. So far, the system has been operated for longer than 3000 hours and routinely extracts 10/sup 13/ ppp at 99% efficiency. Experiment 745 on QCD test requires a single AGS bunch of 40 nsec. For this purpose another fast kicker was placed at the E5 straight section and powered by a new pulser to produce a half sinusoidal pulse with both a rise and fall time of 200 nsec. A single AGS bunch was extracted through the slow beam channel at 22 GeV/c leaving the remaining 11 bunches undisturbed which continued to be accelerated to 29.4 GeV/c and extracted by the H5 kicker through the fast beam channel. Because the ring circumference ratio of CBA to the AGS is 4-3/4, some of the injected beam from the AGS has to contain 11 bunches instead of 12; consequently, this single bunch extraction mode will also be used for CBA injection.
Date: January 1, 1983
Creator: Weng, W.T.
Partner: UNT Libraries Government Documents Department