In this paper we present several techniques for characterizing longitudinal impedances based on transient measurements of the growth rates and tune shifts of unstable coupled-bunch modes. These techniques are applicable to measurement of both fundamental and higher-order mode impedances and allow characterization of shunt impedances and quality factors of the HOMs. Methods presented here are complementary to lab bench measurements of RF cavities, in that the beam based measurements directly sense the physical impedance in the installed configuration. In contrast to a single-bunch integrated impedance measurement these techniques resolve the impedances in the frequency domain. These methods allow determination of the impedance's unaliased frequency by analyzing synchronous phase transients. Experimental results from ALS and BESSY-II are presented showing the use of these techniques to measure complex impedances.
This paper analyzes the longitudinal space charge (LSC) impedances of a round uniform beam inside a rectangular and parallel plate chambers using the image charge method. This analysis is valid for arbitrary wavelengths and the calculation converges fast. The research shows that only a few of the image beams are needed to obtain a relative error less than 0.1%. The beam offset effect is also discussed in the analysis.
This paper studies the space charge impedances of a rectangular beam inside a rectangular chamber, and the limiting case, e.g., a rectangular beam between parallel plates, respectively. The charged beam has uniform density in vertical direction and arbitrary distribution in horizontal direction. The method of separation of variables is used to calculate the space charge potentials, fields, and impedances which are valid in the whole perturbation wavelength spectrum. Comparisons between the theoretical calculations and the numerical simulations are also provided and they match quite well. It is…
This paper presents the approximate analytical solutions to the longitudinal space charge (LSC) impedances of a round beam with uniform transverse distribution and sinusoidal line density modulations under two boundary conditions: (a) between parallel plates (b) inside a rectangular chamber, respectively. When the ratio of beam diameter to chamber height is small, the image charge fields of the round beam can be approximated by those of a line charge, the approximate analytical LSC impedances can be obtained by image method. The derived theoretical LSC impedances are valid at any perturbation …
In carrying out calculations of the effect of longitudinal space charge on longitudinal motion, the transverse beam size appears in a form factor which is usually written as $g=1+2\ln (b/a)$. In fact, this expression applies to particles with vanishing betatron amplitude in a beam with uniform transverse distribution. It is argued that an average over the transverse distribution should be used instead of the value on axis. It is shown that for the realistic `binomial' family of distributions the 1 in the above expression for $g$ should be replaced by a value near 0.5 if $a$ is interpreted as t…
Both longitudinal and transverse coupling impedance for some critical components need to be measured for accelerator design. The twin wires method is widely used to measure longitudinal and transverse impedance on the bench. A mode error is induced when the twin wires method is used with a two-port network analyzer. Here, the mode error is analyzed theoretically and an example analysis is given. Moreover, the mode error in the measurement is a few percent when a hybrid with no less than 25 dB isolation and a splitter with no less than 20 dB magnitude error are used.
The FCC-ee impedance model is being constantly updated closely following the vacuum chamber design and parameters evolution. In particular, at present, a thicker NEG coating of 150 nm (instead of previous 100 nm) has been suggested by the vacuum experts, and a more realistic impedance model of the bellows has been investigated. Moreover, also the transverse impedance has been updated by considering the same sources as for the longitudinal case. Therefore, the FCC-ee impedance database is getting more complete and the impedance model is being refined. In this paper we describe the presently ava…
In this paper a review of some important impedance-induced instabilities are briefly described for both the longitudinal and transverse planes. The main tools used nowadays to predict these instabilities and some considerations about possible mitigation techniques are also presented.
The method of the optical approximation is used to estimate the high frequency impedances of different vacuum chamber transitions of the European XFEL beam line. The approximations of the longitudinal impedances are obtained in terms of simple one-dimensional integrals. The transverse impedances are written in analytical closed form. The analytical results are compared with the results obtained by numerical solution of Maxwell's equations.
In the framework of the "LHC Injectors Upgrade" (LIU) project, the CERN Proton Synchrotron (PS) is being prepared as a pre-injector for the Large Hadron Collider at high luminosity (HL-LHC). RF systems at 20 MHz, 40 MHz and 80 MHz are required for longitudinal beam manipulations to provide 25 ns bunch spacing and short bunches at transfer to the Super Proton Synchrotron (SPS). Beam induced voltage in these cavities causes transient beam-loading and uncontrolled longitudinal emittance blow-up. To reduce the impedance beyond the reach of the wide-band feedback around the power amplifier, a new m…
In this article we derive longitudinal impedance and wake function for an undulator setup with arbitrary undulator parameter, taking into account a finite transverse size of the electron bunch. Earlier studies considered a line density-distribution of electrons instead. We focus our attention on the long-wavelength asymptote (compared with resonance wavelength), at large distance of the electron bunch from the undulator entrance compared to the overtaking length, and for large vacuum-chamber size compared to the typical transverse size of the field. These restrictions define a parameter region…
In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In pa…
Coaxial wire measurements have provided a simple and effective way to measure the beam coupling impedance of accelerator structures for a number of years. It has been known how to measure the longitudinal and dipolar transverse impedance using one and two wires for some time. Recently the ability to measure the quadrupolar impedance of structures exhibiting top/bottom and left/right symmetry has been demonstrated. A method for measuring the beam coupling impedance of asymmetric structures using displaced single wires and two wire measurements is proposed. Simulations of the measurement system …
The upgrade project of Hefei Light Source storage ring is under way. In this paper, the broadband impedances of resistive wall and coated ceramic vacuum chamber were calculated using the analytic formula, the wake fields and impedances of other designed vacuum chambers have been simulated by the CST code, and then the broadband impedances model was obtained. Using the theoretical formula, longitudinal and transverse single bunch instabilities were discussed. With the carefully-designed vacuum chamber, we find that the thresholds of the beam instabilities are higher than the beam current goal.
An analytical method is developed for calculating the geometric wakefield and impedances of an ultrarelativistic beam propagating on- and off-axis through an axially symmetric geometry with slowly varying circular cross-section, such as a transition. Unlike previous analytical methods, our approach considers a beam of arbitrary longitudinal profile and permits detailed perturbative investigation of impedance as a function of frequency. We compare the accuracy of the results of our approach with numerical simulations performed using the code ECHO and determine parameters in which there is good …
We have estimated contributions from the lossy and inductive vacuum chamber omponents to the broadband impedance of the NESTOR storage ring by using analytical formulas. As was expected considering the small ring circumference (15.44m), the main contributions both to the longitudinal impedance Z/n and the loss factor k come from the RF-cavity. Cavity impedance was also estimated with CST Microwave Studio (CST Studio Suite{TM} 2006) by simulating coaxial wire method commonly used for impedance measurements. Both estimates agree well. The upper limit of impedance of elliptic holes in the vacuum …
A new powerful longitudinal diagnostics is being developed for the two CERN's antiproton machines, the Antiproton Decelerator (AD) and the Extra Low ENergy ANtiproton (ELENA) ring. The longitudinal diagnostics receives data from the Low-Level Radiofrequency (LLRF) system via optical fiber. Real time processing of gigabit data-streams is enabled by its computational resources and real-time operating system. Measurement of intensity, bunch length and turn-by-turn bunch profiles are available for bunched beams. Intensity, momentum spread and average frequency will soon be measured for debunched b…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameter-less integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the RF bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny c…
Shanghai Institute of Applied Physics（上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；Zhangjiang Laboratory（张江实验室）；Shanghai Advanced Research Institute（上海高等研究院）
The longitudinal and transverse coupling impedances produced by the long slots in the Low Energy Ring of KEK B-factory are calculated. The power dissipated inside the vacuum chamber due to the fields scattered by the slots is evaluated using results for the real part of the coupling impedance. Estimates are made for the power flow through the slots to the pumping chamber.
Dipole modes are the main cause of transverse emittance dilution in the Japanese Linear Collider / Next Linear Collider (JLC/NLC). A diagnostic setup has been built in order to investigate them. The method is based on using a coaxial wire to excite and measure electromagnetic modes of accelerating structures. This method can offer a more efficient and less expensive procedure than the ASSET facility. Initial measurements have been made and are presented in this paper.
The successful operation of X-ray free-electron lasers (FELs), like the Linac Coherent Light Source or the Free-Electron Laser in Hamburg (FLASH), makes unprecedented research on matter at atomic length and ultrafast time scales possible. However, in order to take advantage of these unique light sources and to meet the strict requirements of many experiments in photon science, FEL photon pulse durations need to be known and tunable. This can be achieved by controlling the FEL driving electron beams, and high-resolution longitudinal electron beam diagnostics can be utilized to provide constrain…
The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated [e.g., S.S. Kurennoy, R.L. Gluckstern, and G.V. Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using the Bethe diffraction theory. Here we extend the results to an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along the beam path, cross section. The longitudinal and transverse coupling impedances are derived in terms of series over cross-section eigenfunctions, while the discontinuity shape enters via its polarizabilities. S…
Fast kicker magnets are used to inject beam into and eject beam out of the CERN accelerator rings. These kickers are generally transmission line type magnets with a rectangular shaped aperture through which the beam passes. Unless special precautions are taken the impedance of the yoke can provoke significant beam induced heating, especially for high intensities. In addition the impedance may contribute to beam instabilities. The results of longitudinal and transverse impedance measurements, for various kicker magnets, are presented and compared with analytical calculations: in addition predic…
Landau damping mechanism plays a crucial role in providing single-bunch stability in LHC, High-Luminosity LHC, other existing as well as previous and future (like FCC) circular hadron accelerators. In this paper, the thresholds for the loss of Landau damping (LLD) in the longitudinal plane are derived analytically using the Lebedev matrix equation (1968) and the concept of the emerged van Kampen modes (1983). We have found that for the commonly-used particle distribution functions from a binomial family, the LLD threshold vanishes in the presence of the constant inductive impedance Im$Z/k$ abo…
Coherent Synchrotron Radiation (CSR) can play an important role by not only increasing the energy spread and emittance of a beam, but also leading to a potential instability. Previous studies of the CSR induced longitudinal instability were carried out for the CSR impedance due to dipole magnets. However, many storage rings include long wigglers where a large fraction of the synchrotron radiation is emitted. This includes high-luminosity factories such as DAPHNE, PEP-II, KEK-B, and CESR-C as well as the damping rings of future linear colliders. In this paper, the instability due to the CSR imp…
Longitudinal properties of electron bunches are critical for the performance of a wide range of scientific facilities. In a free-electron laser, for example, the existing diagnostics only provide very limited longitudinal information of the electron bunch during online tuning and optimization. We leverage the power of artificial intelligence to build a neural network model using experimental data, in order to bring the destructive longitudinal phase space (LPS) diagnostics online virtually and improve the existing current profile online diagnostics which uses a coherent transition radiation (C…
The longitudinal and transverse beam coupling impedance of the first final TOTEM Roman Pot unit has been measured in the laboratory with the wire method. For the evaluation of transverse impedance the wire position has been kept constant, and the insertions of the RP were moved asymmetrically. With the original configuration of the RP, resonances with fairly high Q values were observed. In order to mitigate this problem, RF-absorbing ferrite plates were mounted in appropriate locations. As a result, all resonances were sufficiently damped to meet the stringent LHC beam coupling impedance requi…
Conditions for existence, uniqueness and stability of bunch steady states are considered. For the existence uniqueness problem, simple algebraic equations are derived, showing the result both for the action and Hamiltonian domain distributions. For the stability problem, van Kampen theory is used. Emerging of discrete van Kampen modes show either loss of Landau damping, or instability. This method can be applied for an arbitrary impedance, RF shape and beam distribution function Available areas on intensity-emittance plane are shown for resistive wall wake and single harmonic, bunch shortening…
The longitudinal and transverse coupling impedances of a small discontinuity on the accelerator chamber wall can be expressed in terms of the electric and magnetic polarizabilities of the discontinuity. The polarizabilities are geometrical factors and can be found by solving a static (electric or magnetic) problem. However, they are known in the explicit analytical form only for a few simple-shaped discontinuities, for example, for an elliptic hole in a thin wall. In the present paper the polarizabilities of a ring-shaped cut in the wall are obtained. The results are applied to calculate the c…
The piece of NESTOR vacuum chamber with the ceramic insertion for DC-monitor and RF-shields was simulated by using both transient and wake field solvers of CST Studio Suite. For a 6 mm gap between two RF-shields the contributions of the assembly considered to the longitudinal broadband (BB) impedance Z/n and the loss factor kloss are 0.71 Ohm and 0.21 V/pC, correspondingly. These estimates are the second largest after those of the RF-cavity that were obtained till now for the NESTOR ring components. Contributions from a beam position monitor (BPM) are also obtained by simulation and compared w…
SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Longitudinal phase space (LPS) provides a critical information about electron beam dynamics for various scientific applications. For example, it can give insight into the high-brightness X-ray radiation from a free electron laser. Existing diagnostics are invasive, and often times cannot operate at the required resolution. In this work we present a machine learning-based Virtual Diagnostic (VD) tool to accurately predict the LPS for every shot using spectral information collected non-destructively from the radiation of relativistic electron beam. We demonstrate the tool's accuracy for three di…
The generation and properties of transition radiation (TR) are thoroughly treated. The spectral energy density, as described by the Ginzburg-Frank formula, is computed analytically, and the modifications caused by the finite size of the TR screen and by near-field diffraction effects are carefully analyzed. The principles of electron bunch shape reconstruction using coherent transition radiation are outlined. Spectroscopic measure- ments yield only the magnitude of the longitudinal form factor but not its phase. Two phase retrieval methods are investigated and illustrated with model calculatio…
In the upgrade project of Hefei Light Source (HLS II), a new digital longitudinal bunch-by-bunch feedback system will be developed to suppress the coupled bunch instabilities in the storage ring effectively. We design a new waveguide overloaded cavity longitudinal feedback kicker as the feedback actuator. The beam pipe of the kicker is racetrack shape so as to avoid a transition part to the octagonal vacuum chamber. The central frequency and the bandwidth of the kicker have been simulated and optimized to achieve design goals by the HFSS code. The higher shunt impedance can be obtained by usin…
The first mention of the impedance concept appeared on November 1966 in the CERN internal report "Longitudinal instability of a coasting beam above transition, due to the action of lumped discontinuities" by V.G. Vaccaro. This was the beginning of many studies, which took place over the last five decades, and today, impedances and wake fields continue to be an important field of activity, as concerns theory, simulation, bench and beam-based measurements. Building a reliable impedance or wake field model of a machine is the first necessary step to be able to evaluate the machine performance lim…
Knowledge of the electromagnetic interaction between a beam and the surrounding vacuum chamber is necessary in order to optimize the accelerator performance in terms of stored current. Many instability phenomena may occur in the machine because of the fields produced by the beam and acting back on itself as in a feedback device. Basically, these fields produce an extra voltage and energy gain, affecting the longitudinal dynamics, and a transverse momentum kick which deflects the beam. In this paper we describe the main features of this interaction with typical machine components.
In modern high-gain free-electron lasers, ultra-fast photon pulses designed for studying chemical, atomic and biological systems are generated from a serial of behaviors of high-brightness electron beam at the time-scale ranging from several hundred femtoseconds to sub-femtosecond. Currently, radiofrequency transverse deflectors are widely used to provide reliable, single-shot electron beam phase space diagnostics, with a temporal resolution of femtosecond. Here, we show that the time resolution limitations caused by the intrinsic beam size in transverse deflectors, can be compensated with spe…
The use of Smith-Purcell radiation to measure electrons longitudinal profiles has been demonstrated at several facilities in the picosecond and sub-picosecond range. There is a strong interest for the development of non intercepting longitudinal profile diagnostics for high current proton beams. We present here results of simulations on the expected yield of longitudinal profile monitors using Smith-Purcell radiation for such proton beams.
The possibility of using electron beam phase space manipulations to support a free-electron laser accelerator design optimization has motivated our research. An on-going program demonstrating the exchange of transverse horizontal and longitudinal emittances at the Fermilab A0 photoinjector has benefited recently from the upgrade of several of the key diagnostics stations. Accurate measurements of these properties upstream and downstream of the exchanger beamline are needed. Improvements in the screen resolution term and reduced impact of the optical system's depth-of-focus by using YAG:Ce sing…
A technique using RF bucket reduction for acquiring information about the particle distribution in longitudinal phase space has been applied in the Fermilab Booster. Data sets were obtained at six important time intervals of a Booster cycle for three different beam intensities. Controlled RF bucket reduction also provides other opportunities for beam manipulation.
We have considered the possibility of using coherent Smith-Purcell radiation for the single-shot determination of the longitudinal profile of 50 fs (FWHM) long electron bunches. This length is typical for the bunches currently produced by Laser Wakefield Acceleration and is at the limit of what is achievable by alternative techniques, such as Electro-Optic sampling. It is concluded that there are no obstacles, either theoretical or experimental, in the implementation of this technique. A set of three gratings, with periods of 15, 85 and 500 micrometres, will produce detectable energy in the wa…
The Fermilab Linac delivers 400 MeV H- beam to the rest of the accelerator chain. Providing stable intensity, energy, and emittance is key since it directly affects downstream machines. To counter fluctuations of Linac output due to various effects to be described below we are working on implementing dynamic longitudinal parameter optimization based on Machine Learning (ML). As inputs for the ML model, signals from beam diagnostics have to be well understood and reliable. In this paper we discuss the status and plans for ML-based optimization as well as preliminary results of diagnostics studi…
As soon as the first particles emerge from an ion source, the source characteristics need to be determined. The total beam intensity, the transverse particle distributions, the beam divergence and emittance as well as the longitudinal parameters of the beam must be measured. This chapter provides an overview of typical measurement methods and the instruments used, and shows the results obtained.
