Longitudinal Coupling Impedance Research Articles

Beam coupling impedance of the main extraction kickers in the CERN PS

In view of the High Luminosity (HL) upgrade of the LHC, the beam intensity must be doubled in the injector chain. To perform reliable beam dynamics simulations, the beam coupling impedance in the injectors, such as the Proton Synchrotron (PS), must be followed closely by including all contributing elements into the impedance model. The existing kicker magnets of the PS had been optimized for large kick strength and short rise/fall times, but not necessarily to minimise beam coupling impedance. Hence, unwanted beam induced voltage can build up in their electrical circuits, with an impact on the beam. The beam coupling impedances of the two main kicker magnets used for the fast extraction from PS, the KFA71 and KFA79, are extensively characterized in this study. In particular, electromagnetic simulation results for the longitudinal and transverse coupling impedance are shown. The critical impedance contributions are identified, and their effect on beam stability with a possible mitigation solution is discussed. Moreover, the impact of the cable terminations on the electromagnetic field pattern and possible mitigation techniques are presented, providing a complete impedance evaluation of the entire kicker installation.

Beam coupling impedance measurement based on Goubau line method

The Goubau line method has been recently proposed and used for the longitudinal beam coupling impedance measurement of vacuum components. To extend the application of this method, the measurement of transverse impedance using the Goubau line method is proposed in this work. The feasibility of measuring the transverse impedance using the Goubau line method has been tested using a pillbox cavity. Additionally, the frequency shift induced by the dielectric-coated wire in the Goubau line measurements has been investigated analytically. The contribution of the dielectric coating to the frequency shift has been studied. Finally, the Goubau line setup has been optimized and used to evaluate the longitudinal and transverse beam coupling impedance of key vacuum components in the High Energy Photon Source.

Characterization of the longitudinal beam coupling impedance and mitigation strategy for the fast extraction kicker KFA79 in the CERN PS

In the framework of the High Luminosity Upgrade of the LHC (HL-LHC) the beam intensity from the injectors must be doubled while keeping longitudinal beam parameters unchanged. As such, high-quality beams with high intensities are required also from the Proton Synchrotron (PS). The beam coupling impedance plays a crucial role and mitigation measures must be taken to remain within a stringent impedance budget. Kicker magnets are important contributors to the overall broadband impedance of the PS. Moreover, the detailed study of kicker impedances revealed additional resonant modes which may be critical for the beam stability. The longitudinal beam coupling impedance for the fast extraction kicker KFA79 is presented in this study, and a solution to reduce the impedance of the critical resonant modes is introduced. Electromagnetic (EM) simulations have been performed to determine the impedance behaviour. Finally, the insertion of transition pieces between magnet modules is presented as a measure for mitigating the low frequency resonant impedance contributions.

Design and thermal analysis of the BPM-bellows assembly front-end photon block for Hefei Advanced Light Facility

The BPM-bellows front-end photon block with ellipse cross-sections has been designed for Hefei Advanced Light Facility (HALF). Such structure has lower longitudinal coupling impedances than the photon block with commonly-used circle cross-sections. In addition, two types of cooling structures have been designed, which are shared water-cooling pipe (cooling structure 1, CS1) and independent water-cooling tank (cooling structure 1, CS2), respectively. The CS1 is simple and space-saving, while the CS2 has better heat dissipation capability. In order to calculate power density on complex light-receiving surfaces, the Monte Carlo simulation tool, Synrad, was applied. By building finite element models and importing power density data from Syrand, the temperature and thermal stress distributions of photon blocks with two different cooling structures were calculated. The thermal analysis indicates that the maximum temperature (37.73°C) is located at CS1, but the maximum stress (16.28 MPa) is on CS2 due to the difference in structure and heat dissipation capability. Moreover, the maximum temperature and thermal stress values are far below the material criteria of CuCrZr. Therefore, the simple and space-saving CS1 is more suitable for HALF, which can reduce manufacturing costs and better satisfy the compact layout in the storage ring.

Longitudinal parameters measurement at BEPC II storage rings

A new upgrade to BEPC II has been deployed to improve the luminosity and maximum energy. After the upgrade, the maximum beam energy will reach to 2.8 GeV, and the optimized luminosity at 2.35 GeV will be tripled through squeezing the bunch length and the vertical beta function at the interaction point β y *. Therefore, one more RF cavity will be added to each ring to increase the RF voltage to 3.3 MV. In order to study the feasibility of this upgrade and the longitudinal beam characteristics after the upgrade, some beam-based experiments were carried out at the electron and positron rings of BEPC II. Bunch length and its variation with RF gap voltage are measured, shows that it can be squeezed by approximately 30% at 3.3 MV compared to the normal 1.65 MV operation voltage. Bunch synchronous phases at different RF voltages are also obtained by fitting the variation of bunch centroid with RF voltage at low current. The longitudinal broadband coupling impedance is measured with streak camera, real part impedance is obtained from synchronous phase shift with current, and the imaginary part from bunch lengthening with current. Energy loss per turn at 2.474 GeV is 363.2 ± 14.5 keV by measuring synchrotron tune varies with RF voltages.

Experimental research on the longitudinal coupling impedance of RF-shielded BPM-bellows assemblies designed for the Hefei Advanced Light Facility

A compact beam position monitor bellows (BPM-bellows) assembly using the finger-type shield has been designed and manufactured for Hefei Advanced Light Facility (HALF). This RF shield is applied to screen the high resonance in the bellows volume. The coaxial wire method was chosen for the measurement of longitudinal coupling impedance, and the experimental setup was placed vertically to eliminate the sag effect. In order to overcome the precision limitation of the setup when measuring the small-aperture shielded bellows assembly, 5 bellows assemblies have been connected together as one device under test (DUT). The impedance of this long DUT can be conveniently tested. This 5-bellows DUT method has better repeatability than measuring one shielded bellows DUT. In addition, the 5-bellows method can detect the small impedance of bellows assembly generated from the RF shield structure and CF flange cavities. The measurement results also reveal that the shielded bellows assembly has a low impedance close to that of a vacuum tube compared with the unshielded one, so the finger-type structure can achieve the demand of RF shielding.

Impedance minimization of the CERN Super Proton Synchrotron cavities using the generalized coupled S -parameter method

In the context of the Large Hadron Collider (LHC) injector upgrade, components with high contribution to the beam coupling impedance of the injector chain have to be identified and optimized to ensure the delivery of high-intensity proton beams to the LHC. The Super Proton Synchrotron (SPS) is the last accelerator in the LHC injector chain. In the existing design, the longitudinal beam coupling impedance of the SPS cavities limits the increase of the beam intensity in the SPS ring. Since the 200 MHz traveling wave cavities are one of the main contributors to the overall beam coupling budget of the SPS machine, different types of higher-order mode (HOM) couplers are used in the long 33-cell and 44-cell cavities for the damping of various HOMs. The location of the HOM couplers in the cavity, as well as their shape, affects the damping of HOMs. Finding a suitable arrangement of the HOM couplers requires solving a discrete optimization problem. The repetitive calculation of the beam coupling impedance by the conventional time-domain wakefield solvers in the optimization is hindered by the large size of the SPS cavities. The generalized coupled $S$-parameter method is a domain decomposition method for the calculation of the $S$ parameters and beam coupling impedance of large structures. In this paper, this method is employed to calculate the beam coupling impedance of the SPS cavities. Then, an optimization method is proposed to find an optimal arrangement of the HOM couplers in the cavities. The article presents the geometrical details of the SPS cavities, a short description of the generalized coupled $S$-parameter method, and a discrete optimization method applied to the SPS cavities.

Characterizations of the longitudinal beam behaviors and impedances measurements at HLS-II

In this article, the longitudinal beam bunch behaviors of the Hefei Light source-II (HLS-II) are effectively investigated and analyzed based on the beam multi-parameter measurement system. Simultaneously, the temporal beam characteristic parameter extraction (T-BCPE) method is developed for measuring the longitudinal impedances of machine. In the case of 100.4 kV radio-frequency (RF) voltage, the inductance and resistance in the longitudinal coupling impedance of HLS-II are obtained as 115 ± 13 nH and 1320 ± 310 Ω by extracting bunch lengthening factor and asymmetry factor, respectively. In addition, the longitudinal beam dynamical characteristics and potential-well distortion are also in-depth analyzed above the threshold current of the microwave instability. As a result, the longitudinal broadband impedance of HLS-II is measured to be 8.94 ± 0.44 Ω while 0.339 ± 0.004 of the scaling factor in combination with the theoretical analysis.

Combined Effect of Beam-Beam Interaction and Beam Coupling Impedance in Future Circular Colliders

The future large scale electron-positron colliders, such as FCC-ee in Europe and CEPC in China, will rely on the crab waist collision scheme with a large Piwinski angle. Differently from the past generation colliders both luminosity and beam-beam tune shifts depend on the bunch length in such a collision scheme. In addition, for the future circular colliders with extreme beam parameters in collision several new effects become important such as beamstrahlung, coherent X-Z instability and 3D flip-flop. For all these effects the longitudinal beam dynamics plays an essential role and should be taken into account for the collider luminosity optimization. In this paper we discuss an impact of the longitudinal beam coupling impedance on the collider performance.

Coupling impedance of a PEC angular strip in a vacuum pipe

This study deals with the evaluation of the longitudinal and transverse coupling impedance of a charge travelling in a drift tube with a perfectly electric conductive angular strip. The problem is formulated in the particle frame as dual series equations, and efficiently solved through the representation of the unknown in terms of Neumann series. Then, the electric parameters are obtained in the pipe frame through the Lorentz transforms. The presented solution can be adopted as the general methodology in case of angular discontinuities in particle accelerators.

Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Longitudinal coupling impedance of a particle traveling in PEC rings: A regularised analysis

Impedance optimization and measurements of the injection stripline kicker

Stripline kickers are commonly used for on-axis injection in the low emittance rings. The beam coupling impedances of the kickers normally show large contributions to the total impedance budget. In the High Energy Photon Source, the necessity of the short pulse bottom width (less than 10 ns) and strong deflection field requires the kicker to have a short length and a small gap between the electrodes, respectively. A new five-cell stripline kicker is proposed in order to save longitudinal space as well as to reduce the beam coupling impedance. Comprehensive studies have been undertaken to characterize the impedance of the stripline kicker. The beam coupling impedance and heat load dissipation on the kicker due to the beam passage are studied numerically. Strategies to further reduce the impedance are discussed. In addition, impedance bench measurements are launched to identify the impedance of the kicker experimentally. The longitudinal beam coupling impedance is measured with different terminations by using coaxial wire method. A satisfactory agreement has been reached between the numerical predictions and the measurements. A novel fasten block design with ceramic is proposed for the wire stretching and the center holding of the inner conductor in a small beam pipe.

Self-consistent simulations of beam-beam interaction in future e+e− circular colliders including beamstrahlung and longitudinal coupling impedance

For the past generation ${e}^{+}{e}^{\ensuremath{-}}$ storage ring colliders, we usually used natural bunch length or its impedance lengthened value in beam-beam simulations instead of considering the impedance directly. In the future colliders, such as FCC-ee and CEPC, the beam-beam interaction becomes essentially three dimensional. In order to increase the luminosity, the future accelerators will collide very intense beams of high energy with low emittances and small beta functions at the collision points exploiting the crab waist collision scheme with a large Piwinski angle. For these extreme parameters several new effects become important for the collider performance such as beamstrahlung, coherent X-Z instability, 3D flip-flop so that the longitudinal beam dynamics should be also treated in a self-consistent manner. In this paper we describe the numerical code for the self-consistent 3D beam-beam simulations including beamstrahlung and the longitudinal beam coupling impedance and study interplay of different effects arising in beam-beam collisions of the future colliders.

Helical beam screen for the Future Circular Collider for hadrons injection kicker magnets

The Future Circular Collider for hadrons (FCC-hh) is the proposed high-energy frontier particle collider, which is expected to enable proton-proton collisions at a center-of-mass energy of 100 TeV. The specifications for the FCC-hh injection kicker system are very challenging. To provide fast magnetic field rise and fall times, and low ripple during the flat-top, ferrite loaded transmission line type magnets will be used. To limit the beam coupling impedance, a suitable beam screen will be placed in the aperture of each kicker magnet. Due to issues associated with the ``conventional'' beam screen design, used in the injection kickers magnets of the Large Hadron Collider (LHC), such as high voltage (HV) breakdowns and yoke heating problems, we have developed a novel concept of a helical beam screen. The fundamental advantage of the new design, in comparison to the conventional beam screen, is a significant reduction of the maximum voltage induced on the screen conductors, thus a greatly reduced probability of an electrical breakdown of the beam screen. In addition, the longitudinal beam coupling impedance of the helical beam screen is optimized to reduce power deposition in the kicker magnet. Furthermore, the helical beam screen allows a reduction of the maximum transverse beam coupling impedance of the kicker system. Detailed numerical simulations, theoretical studies and experimental results demonstrate that a new design is a promising solution not only for the FCC-hh, but also for existing machines.

New spiral beam screen design for the FCC-hh injection kicker magnet

The injection kicker system for the Future Circular Collider (FCC-hh) must satisfy demanding requirements. To achieve low pulse ripple and fast field rise and fall times, the injection system will use ferrite loaded transmission line type magnets. The beam coupling impedance of the kicker magnets is crucial, as this can be a dominant contribution to beam instabilities. In addition, interaction of the high intensity beam with the real part of the longitudinal beam coupling impedance can result in high power deposition in the ferrite yoke. This gives a significant risk that the ferrite yoke will exceed its Curie temperature: hence, a suitable beam screen will be a critical feature. In this paper, we present a novel concept - a spiral beam screen. The fundamental advantage of the new design is a significant reduction of the maximum voltage induced on the screen conductors, thus decreased probability of electrical breakdown. In addition, the longitudinal beam coupling impedance is optimized to minimize power deposition in the magnet.

Model for the Evaluation of an Angular Slot’s Coupling Impedance

In high energy particle accelerators, a careful modeling of the electromagnetic interaction between the particle beam and the structure is essential to ensure the performance of the experiments. Particular interest arises in the presence of angular discontinuities of the structure, due to the asymmetrical behavior. In this case, semi-analytical models allow one to reduce the computational effort and to better understand the physics of the phenomena, with respect to purely numerical models. In the paper, a model for analyzing the electromagnetic interaction between a traveling charge particle and a perfectly conducting angular slot of a negligible thickness is discussed. The particle travels at a constant velocity along a straight line parallel to the axis of symmetry of the strip. The longitudinal and transverse coupling impedances are therefore evaluated for a wide range of parameters.

Measurements of electromagnetic properties of ferrites as a function of frequency and temperature

Fast kicker magnets are used to inject beam into and extract beam out of the CERN accelerator rings. These kickers are often ferrite loaded transmission line type magnets with a rectangular shaped aperture through which the beam passes. The interaction of the beam with the resistive part of the longitudinal beam coupling impedance leads to power dissipation and heating of different elements in the accelerator ring. In particular, power deposition in the kicker magnets can be a limitation: if the temperature of the ferrite yoke exceeds the Curie temperature, the beam will not be properly deflected. In addition, the imaginary portion of the beam coupling impedance contributes to beam instabilities. A good knowledge of electromagnetic properties of materials up to GHz frequency range is essential for a correct impedance evaluation. This paper presents the results of transmission line measurements of complex initial permeability and permittivity for different ferrite types. We present an approach for deriving electromagnetic properties as a function of both frequency and temperature; this information is required for simulating ferrite behaviour under realistic operating conditions.

Measurements of Electromagnetic Properties of Ferrites as a Function of Frequency and Temperature

Fast kicker magnets are used to inject beam into and extract beam out of the CERN accelerator rings. These kickers are often ferrite loaded transmission line type magnets with a rectangular shaped aperture through which the beam passes. The interaction of the beam with the resistive part of the longitudinal beam coupling impedance leads to power dissipation and heating of different elements in the accelerator ring. In particular, power deposition in the kicker magnets can be a limitation: if the temperature of the ferrite yoke exceeds the Curie temperature, the beam will not be properly deflected. In addition, the imaginary portion of the beam coupling impedance contributes to beam instabilities. A good knowledge of electromagnetic properties of materials up to GHz frequency range is essential for a correct impedance evaluation. This paper presents the results of transmission line measurements of complex initial permeability and permittivity for different ferrite types. We present an approach for deriving electromagnetic properties as a function of both frequency and temperature; this information is required for simulating ferrite behaviour under realistic operating conditions.

LONGITUDINAL COUPLING IMPEDANCE FOR PARTICLE BEAMS OF PARABOLIC TRANSVERSE CHARGE ISTRIBUTION MOVING IN A RESISTIVE CULINDRICAL BEAM-PIPE OF FINITE WALL THICKENS

The longitudinal coupling impedance for particle beams of parabolic transverse charge distribution moving in aresistive cylindrical beam-pipe of finite wall thicken studied theoretically. The particle beam is moving at constant speeddown a resistive cylindrical pipe of fintie wall thickness. The wave equations for the lectromagnetic fields induced by thebeam motion inside the cylindrical pipe have been derived and solved. The space charge and the wall impedances have been obtained analyticaaly and then analyzed numberically for diferent beam energies, diferent wall conductivities and diferent wave mode frequencies. The real part for the wall impedance is found to be a positive resistance while the imaginary part is a positive reacetance (inductive). At low beam energies we observed no differences between the impedances of quadratic and uniform beams. At high beam energies and for all wave mode frequencies, differences between the two impedance are observed frow all thickness bellow the skin penetration depth s. The impedance converges for large wall thicknetowared a small value of the order of the sufface impedance of a thick conducting wall.

Mode error analysis of impedance measurement using twin wires**Supported by Natural Science Foundation of China (11175193, 11275221)

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.