Paper  Title  Page 

MPPP001  A Vertical MultiBunch Feedback System for ANKA  761 


ANKA is a synchrotron light source with a top energy of 2.5 GeV. The maximum electron current at ANKA is presently limited by multibunch instabilities to 200 mA. In order to overcome this barrier a transverse analog multibunch feedback system is presently being commissioned. A BPM is used for beam detection. The vertical position signal passes a notch filter, is amplified, and subsequently fed to a vertical beam kicker. The present paper shows the layout of ANKA feedback system and discusses the first results of its operation.  
MPPP002  Stochastic Cooling Electrodes for a Wide Velocity Range in the CR  799 


The CR storage ring is part of the FAIR project at GSI. It serves as a first stage of stochastic cooling for secondary rare isotopes at v/c=0.83 as well as for antiprotons at v/c=0.97. To avoid the installation of dedicated structures for each kind of beam, electrodes have been developed which are usable for both beams. They are based on slotline structures mounted perpendicular to the beam. They are shorted at the ends, and their signal is extracted by two striplines on the rear side, placed a quarter wavelength away from the open ends. The width of the structures can be adjusted to the initial betatron oscillation amplitudes. Their length is 24 mm, and the signal from many of these structures mounted in a row can be combined. The signal combination can be matched to the different beam velocities. The paper shows results from field calculations, prototype tests, and estimates of the signal combination efficiency. The beam impedance of the novel structures is compared with the superelectrodes applied in the former CERN AC and with the slowwave structures currently installed in the FNAL Debuncher.  
MPPP003  FALSE BPM READINGS AFFECTING ORBIT FEEDBACK  847 


Funding: Ministry of Science and Technology, Korea. A slow global orbit feedback (SOFB) is routinely operating in the usual user service operation at PLS. The orbit feedback uses 22 correctors in each plane which have 20bit capability for the vertical plane and 16bit capability for the horizontal plane, and the feedback speed is 4 seconds. The orbit stability in RMS was maintained below 1 mm in both planes for one hour and 3 mm for a 12hour operation. The BPM chamber movement due to the change of synchrotron radiation heat load mainly limits the SOFB performance. The intensity dependence of BPM electronics is well compensated by a lookup table of BPM. 

MPPP004  LHC Orbit Stablisation Tests at the SPS  886 


The LHC presently build at CERN is the first proton collider that requires a continuous orbit control for safe and reliable machine operation. A realistic test of the orbit feedback system has been performed in 2004 using already present LHC instrumentation and infrastructure on a 270 GeV coasting beam in the SPS. It has been demonstrated that the chosen feedback architecture can stabilise the beam better than 10 micrometre and is essentially limited by the noise of the beam position monitor and the bandwidth of the corrector magnets. The achieved orbit stability is comparable to those found at modern light sources and gives enough operational margin with respect to the requirements of the LHC Cleaning System (70 micrometre). Estimates for the long term drifts and achievable stability will be presented based on the experimental results.  
MPPP005  A New Kicker for the TLS Longitudinal Feedback System  949 


A new longitudinal kicker that is modified from the Swiss Light Source (SLS) design to fit into the TLS storage ring. It will be served as the actuator in the longitudinal multibunch feedback control loop. Beam coupling impedance has been calculated by Gdfidl with a PC cluster. Previous to the installation of this new kicker, bench measurement has been performed in the laboratory to characterize this new kicker. The experimental setups for bandwidth and coaxial wire measurement of longitudinal coupling impedance and their corresponding test results will be reported. As a cross check, beadpull measurement has also been done to verify the beam coupling measurement by coaxial wire method at the kicker center frequency. Longitudinal field profile of the accelerating mode along the beam path has also been mapped. High order cavity modes of the kicker have also been observed and their effects on the beam are evaluated.  
MPPP006  Performance Calculation on Orbit Feedback for NSLSII  1036 


We discuss the preliminary calculation on the performance of closed orbit feedback system for NSLSII, its relation to the requirement on BPM, floor and girder stability, power supply stability, etc.  
MPPP007  Operating Performance of the Low Group Delay Woofer Channel in PEPII  1069 


Funding: Work supported by U.S. Department of Energy contract DEAC0276SF00515. In PEPII collider a dedicated low groupdelay processing channel has been developed in order to provide high damping rates necessary to control the fastgrowing longitudinal eigenmodes driven by the fundamental impedances of the RF cavities. A description of the digital processing channel operating at 9.81 MHz and capable of supporting finite impulse response (FIR) controllers with up to 32 taps will be presented. A prototype system has been successfully commissioned in the HighEnergy Ring (HER) in May 2004. Operating experiences with the prototype and the newly determined limits on achievable longitudinal damping will be discussed and illustrated with experimental data. 

MPPP008  Equilibrium Beam Invariants of an Electron Storage Ring with Linear xy Coupling  1111 


Funding: Work is supported by the U.S. Department of Energy under contract DEAC0276SF00515.
In accelerator systems, it is very common that the motion of the horizontal plane is coupled to that of the vertical plane. Such coupling will induce tune shifts and can cause instabilities. The damping and diffusion rates are also changed, which in turn will lead to a change in the equilibrium invariants. Following the perturbative approach which we developed for synchrobetatron coupling,* we study the xy coupled case in this paper. Starting from the one turn map, we give explicit formulae for the tune shifts, damping and diffusion rates, and the equilibrium invariants. We focus on the cases where the system is near the integer or half integer, and sum or difference resonances where small coupling can cause a large change in the beam distribution.
*B. Nash, J. Wu, and A. Chao, work in progress. 

MPPP009  Linac Coherent Light Source Longitudinal Feedback Model  1156 


Funding: Work is supported by the US Department of Energy under contract DEAC0276SF00515. The Linac Coherent Light Source (LCLS) will be the world's first xray freeelectron laser (FEL). To ensure the vitality of FEL lasing, it is critical to preserve the high quality of the electron beam during acceleration and compression. The peak current and final energy are very sensitive to system jitter. To minimize this sensitivity, a longitudinal feedback system on the bunch length and energy is required, together with other diagnostics and feedback systems (e.g., on transverse phase space). In this paper, we describe a simulation framework, which includes a realistic jitter model for the LCLS accelerator system, the RF acceleration, structure wakefield, and second order optics. Simulation results show that to meet the tight requirements set by the FEL, such a longitudinal feedback system is mandatory. 

MPPP010  Feedback to Suppress Phase Noise at Aladdin  1180 


The performance of the Aladdin infrared beamline is adversely affected by a Robinson mode in which all bunches move in unison with a frequency of 3 kHz. To decrease these oscillations, feedback has been installed in the radiofrequency system to damp longitudinal motion of the bunch centroids. Simulations indicate that at frequencies around 3 kHz, the phase noise generated by Robinson modes may be reduced 20 dB by feedback with a damping time of 0.3 ms. This agrees with the measured performance of feedback circuitry. Since the feedback greatly improves operation of the infrared beamline, it is now incorporated into the standard operation of Aladdin.  
MPPP011  Fermilab Recycler Damper Requirements and Design  1239 


The design of transverse dampers for the Fermilab Recycler storage ring is described. An observed instability and analysis of subsequent measurements are used to identify the requirements. The digital approach being mplemented is presented.  
MPPP012  FirstPrinciples Simulation and Comparison with Beam Tests for Transverse Instabilities and Damper Performance in the Fermilab Main Injector  1300 


An endtoend performance calculation and comparison with beam tests was performed for the bunchbybunch digital transverse damper in the Fermilab Main Injector. Time dependent magnetic wakefields responsible for "Resistive Wall" transverse instabilities in the Main Injector were calculated with OPERA2D using the actual beam pipe and dipole magnet lamination geometry. The leading order dipole component was parameterized and used as input to a bunchbybunch simulation which included the filling pattern and injection errors experienced in highintensity operation of the Main Injector. The instability growth times, and the spreading of the disturbance due to newly misinjected batches was compared between simulations and beam data collected by the damper system. Further simulation models the effects of the damper system on the beam.  
MPPP013  Stabilizing Low Frequency Beam Motion in the Tevatron  1353 


Funding: Operated by Universities Research Association Inc. under Contract No. DEAC0276CH03000 with the United States Department of Energy. A feed back orbit stabilization system has been developed using a set of BPMS and existing Tevatron corrector magnets to stabilize beam motion up to 50 microns below 25 Hz. The construction of this system is described and the stability limits and magnitude of beam motion reduction is explored. 

MPPP015  Operational Performance of a Bunch by Bunch Digital Damper in the Fermilab Main Injector  1440 


We have implemented a transverse and longitudinal bunch by bunch digital damper system in the Fermilab Main Injector, using a single digital board for all 3 coordinates. The system has been commissioned over the last year, and is now operational in all MI cycles, damping beam bunched at both 53MHz and 2.5MHz. We describe the performance of this system both for collider operations and highintensity running for the NuMI project.  
MPPP016  Adaptive Feed Forward Beam Loading Compensation Experience at the Spallation Neutron Source Linac  1467 


Funding: SNS is managed by UTBattelle, LLC, under contract DEAC0500OR22725 for the U.S. Department of Energy. When initial beam studies at the Spallation Neutron Source (SNS) indicated a need for better compensation of the effects of beam loading, a succession of rapidprototyping and experimentation lead to the development of a simple yet successful adaptive feed forward technique within a few weeks. We describe the process and first results. 

MPPP017  User Operation and Upgrades of the Fast Orbit Feedback at the SLS  1538 


A report on the performance of the fast orbit feedback (FOFB) in its 2nd year of user operation is given. Photon beam position monitors (XBPM) have been included by means of a slow feedback which changes the reference settings of the FOFB. Users are permitted to change the XBPM references within certain limits while the feedback is running. A fast synchronous readout of the XBPMs allows their integration into the FOFB loop. The FOFB will be extended by an additional beam position monitor (BPM) in order to satisfy the requirements of the upcoming FEMTO project.  
MPPP018  Correction of Insertion Device Induced Orbit Distortions at the SLS  1584 


Corrections of insertion device (ID) induced orbit distortions at the SLS are performed by means of feed forward schemes down to the micron level at the corresponding photon beam position monitors (XBPMs). The remaining orbit fluctuations are suppressed by XBPM feedbacks which are an integral part of the fast orbit feedback system. As a result, subum RMS stability at the XBPMs is achieved while the ID settings are varied.  
MPPP019  Beam Orbit Diagnostics and Control in CANDLE Storage Ring  1655 


Stability requirements for the CANDLE light source are the consequence of a small electron beam size and a tolerable photon beam parameters. In a real machine, the components of the storage ring have static and dynamic imperfections, which cause disturbance of the electron beam and consequently photon beams parameters. In the present paper the basic approaches to the beam diagnostics, control and correction issues for the CANDLE facility are given. The algorithms, electronics and processing hardware are described.  
MPPP020  RF Phase Modulation at the LNLS Electron Storage Ring  1686 


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 coupledbunch mode of the beam driven by one of the RF cavities. We present results of a set of systematic measurements, in single and multibunch 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 LowGap NEG Coated Aluminium Chambers  1712 


The installation of 5 meterlong, 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 


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 rfcavities, 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 


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 heavyion synchrotron at GSI. 

MPPP024  Recent Observations on a Horizontal Instability in the DAFNE Positron Ring  1841 


A strong horizontal instability limits the maximum positron current storable in the DAFNE PhiFactory. 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 turnbyturn 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 JPARC  1898 


The ceramic chamber is adopted at the RCS (rapid cycling synchrotron) in JPARC. The copper stripes are on the outer surface of the chamber in order to shield the electromagnetic 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 electromagnetic field produced by the beam and evaluate the impedance of this ceramic chamber.  
MPPP026  Development of Longitudinal Coupling Impedance Measurement Platform for BEPCII  1940 


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 CoupledBunch Instabilities by the RF Phase Modulation in the Pohang Light Source  1970 


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 synchroscan 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 


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 


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 


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 CERNSPS Experiment on Microwave Transmission Through the Beam Pipe  2212 


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 24 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 


The high intensity proton beam for LHC accelerated in the CERN SPS is stabilised against coupledbunch instabilities by a 4th harmonic RF system in bunchshortening mode. Bunchlengthening mode, which could also be useful to reduce peak line density and alleviate problems from ecloud 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 bunchlengthening mode is an order of magnitude higher than that for bunchshortening mode or for a single RF system.  
MPPP034  Collective Effects in the TLS Storage Ring after the Installation of Superconducting RF Cavity  2360 


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 highordermodes 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 


Funding: This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. W31109ENG38. The Advanced Photon Source (APS) particle accumulator ring (PAR) is a 325MeV 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 timeresolved imaging with both a gatedintensified 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 NSLSII  


NSLSII is a 3 GeV ultra high brightness storage ring that is planned to succeed the present NSLS rings at Brookhaven. NSLSII will provide hard Xray photons from ~20 minigap 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 NSLSII and their implications on the machine design.  
MPPP037  A Model Study of Transverse Mode Coupling Instability at NSLSII.  2500 


The vertical impedances of the preliminary designs of NSLSII 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 NSLSII  2544 


NSLSII is a 3 GeV ultrahigh brightness storage ring that is planned to succeed the present NSLS rings at Brookhaven. Ultralow 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 NSLSII. This paper describes the required harmonic RF parameters, tradeoffs between the possible choices and the expected system performance, including the implications on lifetime and instabilities.  
MPPP039  Impedance of Finite Length Resistor  2595 


Funding: Department of Energy contract DEAC0298CH10886. We determine the impedance of a cylindrical metal tube (resistor) of radius a and length g, attached at each end to perfect conductors of semiinfinite length. Our main interest is in the behavior of the impedance at high frequency (k>>1/a). In the equilibrium regime, ka^{2}<<g, the impedance per unit length is accurately described by the wellknown result for an infinite length resistive tube. In the transient regime, ka^{2}>>g, we derive an analytic expression for the impedance and compute the shortrange wakefield. 

MPPP041  Transverse Instability of a Rectangular Bunch  2657 


Funding: Work supported by the U.S. Department of Energy under contract No. DEAC0276CH03000. 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 barriershaped 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 HeadTail Instability at Tevatron  2714 


Landau damping of the headtail modes in Tevatron beam with the help of octupolegenerated betatron tune spreads permits to reduce chromaticity from 1520 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 


Application of octupoles for Landau damping of the unstable headtail modes requires careful consideration at their combination into separate families to insure maximum effectiveness and avoid degradation of the dynamic aperture due to the nonlinear 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 


Funding: NSF PHY0244793; DOE DEFG0292ER40747. 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 TwoPass Recirculating Accelerators  2872 


Funding: Work supported by DOE Contract DEAC0584ER40150. In this paper, I present the formula, describing a threshold of the regenerative multipass Beam Breakup (BBU) for a single dipole higher order mode with arbitrary polarization in a twopass accelerator with a generalform, 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, twodimensional BBU code developed at the Jefferson Lab is described. 

MPPP046  Transient Resistive Wall Wake for Very Short Bunches  2926 


Funding: Work supported by U.S. Department of Energy, contract DEAC0376SF00515. 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 


Funding: This work is supported by the U.S. AFOSR MFEL grant F496200010370 and by U.S. DOE grant DEFG0591ER40665 (YW and JL). This work is also supported by U.S. DOE contract DEAC0276SF00515 (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 postinstability 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 TwoLayer Tube  3138 


The exact analytical expressions for the multipole longitudinaland transverse impedances of twolayer 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 


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. 