Instabilities and Feedback

Impedances, Instability Theory, and Experiment

Paper Title Page
MPPP020 RF Phase Modulation at the LNLS Electron Storage Ring 1686
  • N.P. Abreu, N.P. Abreu
    UNICAMP, Campinas, São Paulo
  • R.H.A. Farias, P.F. Tavares
    LNLS, Campinas
  Funding: FAPESP

In the Brazilian Electron Storage Ring, we observed that modulating the phase of accelerating fields at twice the synchrotron frequency suppressed remarkably well a longitudinal coupled-bunch mode of the beam driven by one of the RF cavities. We present results of a set of systematic measurements, in single and multi-bunch mode, aimed at characterizing the effects of the modulation on the beam. We also compare those experiments with the results of tracking simulations.

MPPP021 Evolution of the Machine Impedance following the ESRF Upgrade to Low-Gap NEG Coated Aluminium Chambers 1712
  • T.F. Günzel, L. Farvacque, T. Perron, J.-L. Revol
    ESRF, Grenoble
  The installation of 5 meter-long, 8 mm vertical aperture insertion device (ID) aluminum chambers coated in house with non evaporable getter material is progressing at a rate of one chamber per shutdown. The evolution of the impedance with associated consequences on instability thresholds, following the installation of a number of low aperture insertion device chambers will be reported. In particular the impedance measurement using the local bump method allowed the identification and the replacement of the chambers of highest impedance. Correlation with the evolution of the single bunch instability thresholds and the theoretical prediction will be discussed. It could be observed that change in vertical aperture has a sensible effect on the single bunch horizontal threshold.  
MPPP022 The Impedance of Selected Components of the Synchrotron Light Source Petra III 1751
  • R. Wanzenberg, K. Balewski
    DESY, Hamburg
  At DESY it is planned to convert the PETRA ring into a synchrotron radiation facility, called PETRA III, in 2007. Since the impedance of the machine determines its performance with respect to coupled and single bunch instabilities it is important to know the wakefields and higher order modes (HOMs) of the different components of the vacuum system. Numerical calculations of wakefields and HOMs are presented for several components of PETRA III, including the rf-cavities, shielded bellows and tapered vacuum chamber transitions. The impedance of these components is presented in terms of the loss and kick parameters.  
MPPP023 Numerical Calculation of Coupling Impedances for Kicker Modules 1820
  • B. Doliwa, H. De Gersem, T. Weiland
    TEMF, Darmstadt
  Funding: Work supported in part by DFG under contract GraKo 410 and GSI, Darmstadt.

Maintaining the impedance budget is an important task in the planning of any new accelerator facility. While estimates from analytical computations and measurements play a central role in doing so, numerical calculations have become an important alternative today. On the basis of Finite Integration Theory, we have developed a simulation tool for the direct computation of coupling impedances in the frequency domain. After discussing the special features of our code as compared to commercial programs, we present our results for cases where coupling impedances have been obtained from another source, e.g. experiment. In particular, we consider the longitudinal and transverse impedances of the SNS extraction kicker and present investigations related to the injection/extraction system of the future heavy-ion synchrotron at GSI.

MPPP024 Recent Observations on a Horizontal Instability in the DAFNE Positron Ring 1841
  • A. Drago, M. Zobov
    INFN/LNF, Frascati (Roma)
  • D. Teytelman
    SLAC, Menlo Park, California
  A strong horizontal instability limits the maximum positron current storable in the DAFNE Phi-Factory. A powerful feedback system makes it possible to store and collide up to 1250 mA of positron current in 105 bunches. Nevertheless, a much higher current (> 2.4A) has been successfully stored in the twin electron ring. Measurements have been carried out to understand the positron current limit and to characterize the behavior of the horizontal instability at high current with different bunch patterns. Grow/damp turn-by-turn data obtained by turning off the horizontal feedback have been acquired and analyzed. Spectral analysis and grow rates of the instability are shown. In particular, the -1 mode has strong evidence and fast grow rate. Its grow rate behavior is analyzed at different beam currents and bunch patterns.  
MPPP025 The Impedance of the Ceramic Chamber in J-PARC 1898
  • Y. Shobuda
    JAERI/J-PARC, Tokai-Mura, Naka-Gun, Ibaraki-Ken
  • Y.H. Chin, K. Ohmi, T. Toyama
    KEK, Ibaraki
  The ceramic chamber is adopted at the RCS (rapid cycling synchrotron) in J-PARC. The copper stripes are on the outer surface of the chamber in order to shield the electro-magnetic field produced by the beam. The inner surface of the chamber is coated by TiN to suppress the secondary electron emission. In this paper, we calculate the strength of electro-magnetic field produced by the beam and evaluate the impedance of this ceramic chamber.  
MPPP026 Development of Longitudinal Coupling Impedance Measurement Platform for BEPCII 1940
  • G. Huang, W.-H. Huang, S. Zheng
    Tsinghua University, Beijing
  • J.Q. Wang, D.M. Zhou
    IHEP Beijing, Beijing
  Funding: Supported by NSFC 10375035.

A coaxial line impedance measurement platform is developed for BEPCII. A pair of gradual change impedance matching section is designed and fabricated by numerical control milling machine. The special designed RF connector is applied to strengthen the inner conductor. The algorithm of TRL calibration is applied in the system to avoid the usage of a reference pipe for each device under test. The measurement is accomplished by a VNA under the control of the software written in LabView.

MPPP027 Suppression of the Longitudinal Coupled-Bunch Instabilities by the RF Phase Modulation in the Pohang Light Source 1970
  • I. Hwang, M. Yoon
    POSTECH, Pohang, Kyungbuk
  • Y.J. Han, E.-S. Kim, J.S. Yang
    PAL, Pohang, Kyungbuk
  In the 2.5 GeV Pohang Light Source, we have investigated the suppression of the longitudinal coupled instabilities (CBI) caused by higher order modes (HOMs) of RF cavities. At higher beam current than 170 mA the 758 MHz or 1300 MHz HOMs occurred and the beam could be unstable. The longitudinal CBI could be suppressed by modulating the phase of an RF accelerating voltage at a frequency of 2 times the synchrotron oscillation frequency and by adjusting the water temperatures of the RF cavities. The longitudinal beam oscillations measured by streak camera in synchro-scan mode were shown. The experiment results were compared with the macro particle tracking simulation.  
MPPP028 The Code MBIM1 for the Calculation of the Multibunch Beams Coherent Oscillations Stability (in Approach of Short Bunches) 2009
  • N. Mityanina
    BINP SB RAS, Novosibirsk
  The code MBIM1 for the calculation of the coherent oscillations stability for multibunch beams in storage rings is presented. The multibunch beams with arbitrary charges of bunches are considered, including counterrotating bunches (in approach of short bunches in comparison with minimal wavelength of considered environment RF spectrum), with the account of beams coupling with the environment (i.e. RF cavities or/and smooth vacuum chamber with walls of finite conductivity). The code uses the approach of small shifts of coherent frequencies, when different multipole types of synchrotron oscillations can be treated as independent from each other.  
MPPP029 The Code MBIM2 for the Calculation of the Arbitrary Multibunch Beams Longitudinal Coherent Oscillations Stability (in the Case of Long Bunches) 2110
  • N. Mityanina
    BINP SB RAS, Novosibirsk
  The presented code is an advanced version of the code MBIM1 also presented at this conference and dealing with short bunches. The code MBIM2 analyses the stability of longitudinal coherent motion for arbitrary multibunch beams in storage rings without limitations on the bunch length or RF cavities wavelength, which is especially important for higher types of multipole synchrotron oscillations. The code implies also the possibility to consider coupling between different types of multipole synchrotron oscillations and Landau damping. In considered approach, the problem reduces to the eigenvalue problem for the linear algebraic equation system. The order of this system is equal to the number of bunches times number of multipole types times approximation order wich appears to be small (a few units) in most cases.  
MPPP030 Analytic Evaluation of the Series over Azimuthal Harmonics at the Analysis of the Stability of Bunched Beams Coherent Oscillations 2149
  • N. Mityanina
    BINP SB RAS, Novosibirsk
  At the analysis of the stability of coherent motion of multibunch beams including counterrotating beams) one should deal with expressions analogous to the effective impedance - the serieses over harmonics of revolution frequency of the RF structure impedance at the side frequencies to these harmonics, with certain factors depending on the harmonic number, such as the bunch line density spectrum, the phase factor and the factor describing the order of multipole synchrotron oscillations. In this paper, we present the method for analytic summation of these serieses for resonant impedance, which seems not to be made before in the common case including all mentioned factors. Comparison of obtained expressions with formulae used in previous papers shows the limits of validity of simpler approaches. The obtained expressions are used in the computer codes MBIM1 and MBIM2 presented at this conference, which calculate coherent oscillations stability for arbitrary multibunch beams.  
MPPP031 The CERN-SPS Experiment on Microwave Transmission Through the Beam Pipe 2212
  • T. Kroyer, T. Kroyer
    TU Vienna, Vienna
  • F. Caspers, E. Mahner
    CERN, Geneva
  Funding: Ministry for Education, Science and Culture, Austria.

In the CERN SPS microwave transmission measurements through beampipe sections with a length of 30 m and 7 m meter respectively have been carried out in the frequency range 2-4 GHz since spring 2003. Here we report on new results obtained with improved measurement techniques during the 2004 run. Observation techniques include a fast real time scope, spectrum analyser IF and video output signal registration and baseband signal observation using a PC soundcard. The unexpected beam induced amplitude modulation has been confirmed on all kinds of available beams including single bunches. It was found that there is a correlation between the amount of beam induced signal attenuation and the beam losses registered by external scintillators. Potential theoretical models are discussed.

MPPP033 Beam Transfer Functions and Beam Stabilisation in a Double RF System 2300
  • E.N. Shaposhnikova, T. Bohl, T.P.R. Linnecar
    CERN, Geneva
  The high intensity proton beam for LHC accelerated in the CERN SPS is stabilised against coupled-bunch instabilities by a 4th harmonic RF system in bunch-shortening mode. Bunch-lengthening mode, which could also be useful to reduce peak line density and alleviate problems from e-cloud and kicker heating does not give desirable results for beam stability. In this paper an analysis of the limitations of these two different modes of operation is presented together with measurements of the Beam Transfer Function for the double RF system. As predicted by theory, for sufficiently long bunches with the same noise excitation, the measured amplitude of the beam response in bunch-lengthening mode is an order of magnitude higher than that for bunch-shortening mode or for a single RF system.  
MPPP034 Collective Effects in the TLS Storage Ring after the Installation of Superconducting RF Cavity 2360
  • P.J. Chou, J. Chen, K.-T. Hsu, C.-C. Kuo, C. Wang, M.-H. Wang
    NSRRC, Hsinchu
  A superconducting rf cavity designed by Cornell University was installed in the storage ring at Taiwan Light Source in December of 2004. The purpose of rf system upgrade is to achieve a stored beam current of 400 mA without collective instabilities caused by high-order-modes of rf cavities. Beam measurements related to collective effects are performed. Results are compared with those measured prior to the rf system upgrade. Theoretical studies on collective effects after the rf upgrade are also presented.  
MPPP035 Investigation of APS PAR Vertical Beam Instability 2393
  • C. Yao, Y.-C. Chae, N. Sereno, B.X. Yang
    ANL, Argonne, Illinois
  Funding: This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.

The Advanced Photon Source (APS) particle accumulator ring (PAR) is a 325-MeV storage ring that collects and compresses linac pulse trains into a single bunch for booster injection. A vertical beam instability has been observed when only a single linac bunch is injected and the total beam charge is from 0.15 to 0.7 nC. The instability starts about 80 ms after the injection, lasts about 160 ms, and is highly reproducible. We performed spectral measurement and time-resolved imaging with both a gated-intensified camera and a streak camera in order to characterize this instability. Initial analysis of the data indicates that the instability is due to ion trapping. A stable lattice was established as result of the investigation. This report summarizes the experimental results and gives some preliminary analysis.

MPPP036 Collective Effects for NSLS-II
  • A. Blednykh, S. Krinsky, B. Podobedov, J. Rose, N.A. Towne, J.-M. Wang
    BNL, Upton, Long Island, New York
  NSLS-II is a 3 GeV ultra high brightness storage ring that is planned to succeed the present NSLS rings at Brookhaven. NSLS-II will provide hard X-ray photons from ~20 mini-gap undulators that may significantly contribute to the machine impedance. This, in combination with very high beam phase space density, and low momentum compaction drives a number of coherent instabilities. This paper reviews the most important collective effects for NSLS-II and their implications on the machine design.  
MPPP037 A Model Study of Transverse Mode Coupling Instability at NSLS-II. 2500
  • A. Blednykh, J.-M. Wang
    BNL, Upton, Long Island, New York
  The vertical impedances of the preliminary designs of NSLS-II MGUs are calculated by means of GdfidL code. The TMCI thresholds corresponding to these impedances are estimated using an analytically solvable model.  
MPPP038 Harmonic Cavity Performance for NSLS-II 2544
  • A. Blednykh, S. Krinsky, B. Podobedov, J. Rose, N.A. Towne, J.-M. Wang
    BNL, Upton, Long Island, New York
  NSLS-II is a 3 GeV ultra-high brightness storage ring that is planned to succeed the present NSLS rings at Brookhaven. Ultra-low emittance bunch combined with a short bunch length results in the Touschek lifetime of only a few hours, which strongly advocates including harmonic RF in the baseline design of NSLS-II. This paper describes the required harmonic RF parameters, trade-offs between the possible choices and the expected system performance, including the implications on lifetime and instabilities.  
MPPP039 Impedance of Finite Length Resistor 2595
  • S. Krinsky, B. Podobedov
    BNL, Upton, Long Island, New York
  • R.L. Gluckstern
    University of Maryland, College Park, Maryland
  Funding: Department of Energy contract DE-AC02-98CH10886.

We determine the impedance of a cylindrical metal tube (resistor) of radius a and length g, attached at each end to perfect conductors of semi-infinite length. Our main interest is in the behavior of the impedance at high frequency (k>>1/a). In the equilibrium regime, ka2<<g, the impedance per unit length is accurately described by the well-known result for an infinite length resistive tube. In the transient regime, ka2>>g, we derive an analytic expression for the impedance and compute the short-range wakefield.

MPPP041 Transverse Instability of a Rectangular Bunch 2657
  • V. Balbekov
    Fermilab, Batavia, Illinois
  Funding: Work supported by the U.S. Department of Energy under contract No. DE-AC02-76CH03000.

Some results of theoretical investigations of transverse dipole instability of a rectangular bunch are reported in this paper. Such a form is characteristic of the bunch in a rectangular potential wall which is created by a barrier-shaped acceleration field. Similar regime is a major one for accumulating and cooling of antiproton beams in the Fermilab Recycler Ring. In this case, the known theory of transverse instability of a bunched beam is inapplicable directly both because of "unusual" form of phase trajectories and strong dependence of synchrotron frequency on energy. A series of equations, adequately describing the instability is derived in the paper. Exact analytical solution is obtained for space charge dominated impedance, and some approximate methods are proposed for arbitrary impedance. The theory is applied to the Fermilab Recycler Ring including a numerical simulation.

MPPP042 Landau Damping of the Weak Head-Tail Instability at Tevatron 2714
  • P.M. Ivanov, Y. Alexahin, J. Annala, V. Lebedev, V.D. Shiltsev
    Fermilab, Batavia, Illinois
  Landau damping of the head-tail modes in Tevatron beam with the help of octupole-generated betatron tune spreads permits to reduce chromaticity from 15-20 units to zero thus significantly improving the beam lifetime. The octupole strengths have been experimentally optimized at different stages of the Tevatron operation, from proton injection to collision. Predictions of the analytical Landau damping model are compared with the experimental results.  
MPPP043 Betatron Tune Spread Generation and Differential Chromaticity Control by Octupole at Tevatron 2756
  • P.M. Ivanov, Y. Alexahin, J. Annala, V. Lebedev
    Fermilab, Batavia, Illinois
  Application of octupoles for Landau damping of the unstable head-tail modes requires careful consideration at their combination into separate families to insure maximum effectiveness and avoid degradation of the dynamic aperture due to the non-linear magnetic fields. Existing octupolar magnets around the machine have been arranged into four functional families with individual power supplies. Two of these families generate betatron tune spreads in the vertical and horizontal planes whereas the other two control the differential chromaticity between the proton and antiproton helices. The calculated effect on tunes and chromaticity is compared with direct measurements. Analytical formulas for betatron tune spectral density functions are presented.  
MPPP044 Impedance Calculation for Ferrite Inserts 2818
  • S.-Y. Lee, S. Breitzmann
    IUCF, Bloomington, Indiana
  • K.Y. Ng
    Fermilab, Batavia, Illinois
  Funding: NSF PHY-0244793; DOE DE-FG02-92ER40747.

Passive ferrite inserts were used to compensate the space charge impedance in high intensity space charge dominated accelerators. We study the narrowband longitudinal impedance of these ferrite inserts. We find that the shunt impedance and the quality factor for ferrite inserts are inversely proportional to the imaginary part of the permeability of ferrite materials. We also provide a receipe for truly passive space charge impedance compensation and, at the same time, avoiding the narrowband microwave instabilities.

MPPP045 Two Dimensional Aspects of the Regenerative BBU in Two-Pass Recirculating Accelerators 2872
  • E.P. Pozdeyev
    Jefferson Lab, Newport News, Virginia
  Funding: Work supported by DOE Contract DE-AC05-84ER40150.

In this paper, I present the formula, describing a threshold of the regenerative multi-pass Beam Breakup (BBU) for a single dipole higher order mode with arbitrary polarization in a two-pass accelerator with a general-form, 4x4 recirculation matrix. To illustrate specifics of the BBU in two dimensions, the formula is used to calculate the threshold for the reflecting and rotating optics of the recirculator that can lead to higher threshold currents. Then, I present a mathematical relation between transfer matrices between cavities of the accelerating structure and recirculation matrices for each cavity, which must be satisfied in order to successfully suppress the BBU by reflection or rotation in several cavities. At the end of the paper, a fast, two-dimensional BBU code developed at the Jefferson Lab is described.

MPPP046 Transient Resistive Wall Wake for Very Short Bunches 2926
  • G.V. Stupakov
    SLAC, Menlo Park, California
  Funding: Work supported by U.S. Department of Energy, contract DE-AC03-76SF00515.

The catch up distance for the resistive wall wake in a round pipe is approximately equal to the square of the pipe radius divided by the bunch length. The standard formulae for this wake are applicable at distances much larger than the catch up distance. For extremely short bunches, considered recently by Zholents and Fawley in application for SASE (PRL, vol. 92, p. 224801), this formation length can be tens of meters. In this paper, we calculate the resistive wall wake for such a beam at distances compared with the catch up distance assuming a constant wall conductivity. We also discuss how the derivation can be modified to include the frequency dependence of the conductivity characteristic for very short wavelength.

MPPP049 Observations and Measurements of Anomalous Hollow Electron Beams in a Storage Ring 3082
  • Y.K. Wu, J. Li
    DU/FEL, Durham, North Carolina
  • J. Wu
    SLAC, Menlo Park, California
  Funding: This work is supported by the U.S. AFOSR MFEL grant F49620-001-0370 and by U.S. DOE grant DE-FG05-91ER40665 (YW and JL). This work is also supported by U.S. DOE contract DE-AC02-76SF00515 (JW).

This paper reports first observations and measurements of anomalous hollow electron beams in a storage ring. In a lattice with a negative chromaticity, hollow electron beams consisting of a solid core beam inside and a large ring beam outside have been created and studied in the Duke storage ring. We report the detailed measurements of the hollow beam phenomenon, including its distinct image pattern, spectrum signature, and its evolution with time. By capturing the post-instability bursting beam, the hollow beam is a unique model system for studying the transverse instabilities, in particular, the interplay of the wake field and the lattice nonlinearity. In addition, the hollow beam can be used as a powerful tool to study the linear and nonlinear particle dynamics in the storage ring.

MPPP051 Transverse Impedance of Two-Layer Tube 3138
  • M. Ivanyan, A.V. Tsakanian
    CANDLE, Yerevan
  The exact analytical expressions for the multipole longitudinaland transverse impedances of two-layer tube with finite wall thickness areobtained. The numerical examples for the impedances of the vacuum chamberwith laminated walls are given.  
MPPP052 Longitudinal Impedance Measurements of the Components for the BEPCII 3212
  • D.M. Zhou, W. Kang, J.Q. Wang, L.J. Zhou
    IHEP Beijing, Beijing
  • G. Huang
    TUB, Beijing
  Funding: Work supported by the National Natural Science Foundation of China (NSFC) under contract No.10375076.

A longitudinal impedance measurement system was established for the BEPCII. The measurements, done in the frequency domain, are based on the coaxial wire method using HP/Agilent 8720ES network analyzer. The applications of the TRL calibration technique and absorbers were investigated to find a good approach for impedance measurements. The impedance, larger than 20 Ohm and below 6 GHz, can be measured using the TRL calibration technique in the experiment. And better measurement results were got using the reference pipes with the absorbers. So, this system satisfies the requirements of the BEPCII. This paper gives a review on this impedance measurements system for the BEPCII. The measurements results show that there are no serious impedance problems for BEPCII bellows and injection kickers, agreeing well with the numerical simulations. More improvements on this system are in progress.