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Microwave stability limits for the main ring and growth across transition

Description: The purpose of this paper is to estimate the phase space blowup across transition and give critical absolute value of Z/n limits at each stage of performance. It turns out that the most stringent limit is absolute value of Z/n approx.1.3 ..cap omega.. which occurs during the RF manipulation of the proton bunches at 120 GeV in preparation of anti p production.
Date: January 1, 1986
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Single bunch instabilities of the RHIC booster

Description: In this paper, we try to estimate the stability limits and impedances of the Brookhaven RHIC booster. Some important data on the booster are shown. From the stability limits and impedances, it is clear that the booster is safe against either fast microwave instabilities or slow mode-colliding single bunch instabilities. 4 figs., 5 tabs.
Date: February 1, 1986
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Comments on the impedances of the SSC shielded bellows at low frequencies due to the truncation of the wake fields

Description: The behavior of the longitudinal impedance of the SSC shielded bellow at low frequencies depends very much on the length of the wake field used in the Fourier transformation. We show analytically and numerically that, regardless of the difference, single-bunch effects are independent of the actual shape of the impedance when the length of the wake used is bigger than the bunch length.
Date: September 1, 1986
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Estimate of the longitudinal and transverse impedances of the main ring in the TeV I project

Description: To guarantee the successful performance of the Main Ring in Tevatron I, its stability limits and impedances have to be estimated and controlled. The impedances of the Main Ring are estimated, considering contributions from the bellows, beam position monitors, wall resistivity, kickers and Lambertsons. The estimations of the contributions to the longitudinal and transverse impedances are tabulated and plotted. The stability limits for the worst situation are also tabulated for comparison. The slow-growing single bunch instability caused by longitudinal mode coupling is found to be safe. The corresponding instability caused by transverse mode coupling is not. The fast-growing longitudinal microwave instability is found to be driven by the sharp resonances of the bellows and beam monitors and may be the broad resonances of the Lambertsons also. The fast-growing transverse microwave instability is found to be safe. It is found that, to have stability, the bellows have to be shielded and the beam monitors terminated at the ends instead of the center. The slow-growing transverse mode coupling is found to be curable by feedback. 6 tabs., 7 figs. (LEW)
Date: February 1, 1986
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Estimate of the longitudinal and transverse impedances for the superconducting super collider

Description: We try to estimate the longitudinal impedance per harmonic Z/sub L//n as well as the transverse impedance Z/sub T/ for the 20 TeV Superconducting Super Collider (SSC). Effects due to space charge, wall resistivity, bellows, monitor plates, synchrotron radiation are considered. The resulting Z/sub L//n and Z/sub T/ are plotted. Such a knowledge of Z/sub L//n and Z/sub T/ is necessary in computing the limits of many types of instabilities for the bunched beam. To be more specific, in our estimation, we consider the special case of an injection energy of 1 TeV and assume a maximum field of 5 Tesla in the SSC dipoles. In some cases, we also assume a 60/sup 0/ FODO cell structure consisting of 4 dipoles and 2 quadrupoles each with 2 long straight sections. The beampipe radius and beam radius are chosen as b = 1.0 in. and a = 0.05 cm respectively. Totally, the storage ring consists of 364 cells and has a mean radius of R = 17.38 km. Our results show that when monitor plates matched at both ends (such as the ones used in the Tevatron) are used, their effects dominate both Z/sub L//n and Z/sub T. 7 references, 5 figures.
Date: January 1, 1984
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Exact solutions for the longitudinal and transverse impedances of an off-centered beam in a rectangular beampipe

Description: In storage rings and accumulators, some sections of the beampipe may be rectangular in cross section and the beam may not be at the center of the beampipe. In this note, through conformal mapping, we try to compute exactly the longitudinal, vertical and horizontal transverse impedances for the beam under these circumstances. For simplicity, we restrict the beam to the horizontal symmetry axis of the beampipe. Both the effects due to the resistivity of the beampipe's wall and space-charge are considered.
Date: September 1, 1983
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Measurement of the main ring longitudinal impedance by debunching

Description: An experiment was carried out to observe microwave signals of the bunched beam in the Fermilab Main Ring. The purpose of this paper is to analyze the experiment and attempt a computation of the longitudinal impedance per unit harmonic Z/n of the Main Ring. The result of the analysis indicates Z/n = 8.6 ..cap omega.. if the driving impedance is a broad band at f/sub MW/ = 1.646 GHz. However, if the driving impedance is a high-Q resonance at 1.646 GHz with RMS width less than approx.0.13 GHz (or Q approx. 50), Z/sub sh//Q of the resonance is 5.2 k..cap omega... We demonstrate that the proton bunches are of Gaussian shape. The time at which the microwave amplitude starts to grow is determined. We find that this occurs when two adjacent bunches overlap each other. A stability criterion is derived for the overlapped bunches. Then Z/n and Z/sub sh//Q are computed. The source of the driving impedance is traced.
Date: February 1, 1986
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Investigation of the skin depth effect of a metallic coating on a ceramic beampipe inside a kicker

Description: Inside a kicker magnet, metallic beampipe cannot be used because it will screen off the rapid rising of the kicker's magnetic field. When a ceramic beampipe is used, one usually coats the inside with a thin layer of metal so as to carry at least part of the beam's image current and to prevent static charge buildup. The purpose of this article is to investigate whether such a coating will alter the risetime constant of the magnetic field significantly, whether such a coating can withstand the strong transient current induced by the fast rising magnetic field, and whether the back magnetic field generated by this transient current is strong enough to upset the designed risetime of the kicker.
Date: July 1, 1985
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Comparison of the second-order tune shift formulas due to sextupoles given by Collins and Ohnuma

Description: Recently, T. Collins put forth a theory of beam distortion and tune-shift due to sextupoles around the accelerator ring. He obtained formulas for the second-order tune shifts. In a contribution to the Conference on the Intersections between Particle and Nuclear Physics at Steamboat Springs, Ohnuma also computed the second-order tune-shifts due to sextupoles. He expanded the sextupole strength as harmonics around the ring and performed a canonical transformation so as to solve the equations of motion exactly up to first order in sextupole strength. These formulas appear to be quite different from those given by Collins. The purpose of this note is to show that they are in fact exactly the same.
Date: August 1, 1984
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Derivation of Collins' formulas for beam-shape distortion due to sextupoles using Hamiltonian method

Description: The introduction of sextupoles into a storage ring will distort the beam shape in both the horizontal and vertical phase space. The purpose of this note is to rederive the formulas for the lowest-order beam-shape distortion given by Collins using the Hamiltonian approach such as the one used by Ohnuma. Collins' formulas for the second-order tune-shift have been rederived by the Hamiltonian method in a recent note. We go over the Hamiltonian method briefly for two reasons: (1) to make this note more readable; and (2) to conform with the convention of Collins so that a comparison can be made.
Date: October 1, 1984
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Toroidal resonant impedances in RHIC

Description: In a toroidal beam pipe, a wave with a particular azimuthal variation travels with different speeds depending on the distance from the center of the toroidal ring. For example, if the beam travels with velocity ..beta..c at a toroidal radius R, the electromagnetic wave traveling with the beam will have a velocity r..beta..c/R at a radius r. If this velocity reaches c, this electromagnetic wave can also propagate. This wave will interact back with the beam and a resonance occurs. These resonances are positioned at azimuthal harmonics. For a perfectly conducting pipe wall, a beam at a particular radius r from the center of the toroidal ring may excite on infinitely sharp resonance at one azimuthal harmonic n/sub r/, which is an integer. The resonance at the next harmonic n/sub r'/ = n/sub r/ + 1 will be excited by the beam particles ar radius r' which is very close to r. However, for a beam pipe with wall resistivity, each of these resonances will have a azimuthal harmonic width of ..delta..n which is of the order of 100. What the beam particle sees will be a broad resonance which, in principle, can drive a ''microwave'' growth. For this reason, the study of toroidal resonances is meaningful and important. 5 refs., 1 tab.
Date: April 1, 1988
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Estimate of the contributions of bellows to the impedances and beam instabilities of the SSC

Description: Between sections of the vacuum chamber, bellows are needed to compensate for thermal expansion and transverse offsets. For beampipe made of stainless steel with a coefficient of linear expansion 19 x 10/sup -6///sup 0/C and a temperature variation of approx.316/sup 0/C, the allowance for bellows is approx.1.2% of the total length of the beampipe, if we assume that the bellows are 50% compressible. This implies 1.08 km of bellows for Design A of the SSC which has a circumference of 90 km. Such a length of bellows will certainly contribute to the longitudinal and transverse impedances of the accelerator and will therefore affect the stability of the beam. In the Reference Designs, the actual impedances of the bellows have not been calculated; only an allowance of Z/sub parallel//n = 0.05 ..cap omega.. and Z/sub perpendicular/ = 7 M..cap omega../m is made for miscellaneous discontinuities because all the bellows and pumping ports are assumed totally shielded. It is the purpose of this article to examine the actual contributions by the bellows to the longitudinal and transverse impedances assuming that they are not shielded.
Date: July 1, 1985
Creator: Bisognano, J. & Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Landau damping

Description: Section 2.5.8 of the Handbook of Accelerator Physics and Engineering on Landau damping is rewritten. An solvable example is first given to demonstrate the interplay between Landau damping and decoherence. This example is an actual one when the beam oscillatory motion is driven by a wake force. The dispersion relation is derived and its implication on Landau damping is illustrated. The rest of the article touches on the Landau damping of transverse and longitudinal beam oscillations. The stability criteria are given for a bunched beam and the changes of the criteria when the beam is lengthened and becomes unbunched.
Date: October 1, 2010
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Momentum compaction and phase slip factor

Description: Section 2.3.11 of the Handbook of Accelerator Physics and Engineering on Landau damping is updated. The slip factor and its higher orders are given in terms of the various orders of the momentum compaction. With the aid of a simplified FODO lattice, formulas are given for the alteration of the lower orders of the momentum compaction by various higher multipole magnets. The transition to isochronicity is next demonstrated. Formulas are given for the extraction of the first three orders of the slip factor from the measurement of the synchrotron tune while changing the rf frequency. Finally bunch-length compression experiments in semi-isochronous rings are reported.
Date: October 1, 2010
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Small-amplitude synchrotron tune near transition

Description: The separatrices of the rf buckets near transition are mapped when the synchronous phase is neither 0 or {pi}. The small-amplitude synchronous tune is derived when the rf frequency is changed. Synchrotron radiation is present in all electron storage ring. As a result, the synchronous phase is always offset from {phi}{sub s} = {pi} to compensate for the power loss. Even for proton storage rings with negligible synchrotron radiation, the synchronous phase is also required to be offset from {phi}{sub s} = 0 or {pi} slightly to compensate for beam loading. Thus for all storage rings operating near transition, beam particles reside in accelerating buckets instead of stationary bucket. It is of interest to map these buckets and see how they evolve near transition. When the rf frequency is varied, the closed orbit is pushed radially inward or outward. The momentum of the particle synchronous with the rf is thus changed. By measuring the small-amplitude synchrotron tune as a function of the rf frequency, the lowest first few orders of the slip factor can be inferred. Here, we derive this relationship up to the lowest first three orders of the slip factor when the particle velocity is not ultra-relativistic.
Date: May 1, 2010
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Comments on the slip factor and the relation Delta phi = -h Delta theta

Description: The definition of the slip factor can be obtained from the phase equation. However, a derivation using the relation {Delta}{phi} = -h{Delta}{theta} leads to a different slip-factor definition. This apparent paradox is examined in detail and resolved. Here {Delta}{phi} is the rf phase difference and {Delta}{theta} is the azimuthal phase difference around the accelerator ring between an off-momentum particle and the synchronous particle, while h is the rf harmonic.
Date: September 1, 2009
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Decoherence and Landau-Damping

Description: The terminologies, decoherence and Landau damping, are often used concerning the damping of a collective instability. This article revisits the difference and relation between decoherence and Landau damping. A model is given to demonstrate how Landau damping affects the rate of damping coming from decoherence.
Date: December 1, 2005
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

The equivalence of inverse Compton scattering and the undulator concept

Description: Inverse Compton scattering is a method to produce very high frequency photon beam. However, the production mechanism can also be viewed as a undulator emission. This is because the electron sees electric and magnetic fields of the incident laser beam and is driven into transverse oscillatory motion in exactly the same way when the electron passes through a undulator consisting of alternating magnetic field. This note gives a detailed examination of the similarity about the two views. Equivalent undulator parameters are derived for the incident laser beam, as well as the differential cross section of photon emission.
Date: August 1, 2009
Creator: Ng, K. Y,
Partner: UNT Libraries Government Documents Department

Electron cloud and space charge effects in the Fermilab Booster

Description: The stable region of the Fermilab Booster beam in the complex coherent-tune-shift plane appears to have been shifted far away from the origin by its intense space charge making Landau damping appear impossible. Simulations reveal a substantial buildup of electron cloud in the whole Booster ramping cycle, both inside the unshielded combined-function magnets and the beam pipes joining the magnets, whenever the secondary-emission yield (SEY) is larger than {approx}1.6. The implication of the electron-cloud effects on the space charge and collective instabilities of the beam is investigated.
Date: June 1, 2007
Creator: Ng, K. Y.
Partner: UNT Libraries Government Documents Department

Electron cloud in the Fermilab Booster

Description: Simulations of the Fermilab Booster reveal a substantial electron-cloud buildup both inside the unshielded combined-function magnets and the beam pipes joining the magnets, when the second-emission yield (SEY) is larger than {approx}1.6. The implication of the electron-cloud effects on space charge and collective instabilities of the beam is discussed.
Date: June 1, 2007
Creator: Ng, K. Y.
Partner: UNT Libraries Government Documents Department

The transverse space-charge force in tri-gaussian distribution

Description: In tracking, the transverse space-charge force can be represented by changes in the horizontal and vertical divergences, {Delta}x{prime} and {Delta}y{prime} at many locations around the accelerator ring. In this note, they are going to list some formulas for {Delta}x{prime} and {delta}y{prime} arising from space-charge kicks when the beam is tri-Gaussian distributed. They will discuss separately a flat beam and a round beam. they are not interested in the situation when the emittance growth arising from space charge becomes too large and the shape of the beam becomes weird. For this reason, they can assume the bunch still retains its tri-Gaussian distribution, with its rms sizes {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} increasing by certain factors. Thus after each turn, {sigma}{sub x}, {sigma}{sub y}, and {sigma}{sub z} can be re-calculated.
Date: December 1, 2005
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department