Longitudinal Impedance Research Articles

Coherent synchrotron radiation instability in low-emittance electron storage rings

High-frequency longitudinal impedances, particularly at wavenumbers k≫1/σz (where σz is the bunch length), can drive microwave instability and potentially limit the performance of modern low-emittance electron storage rings. In such rings, the coherent synchrotron radiation (CSR) emerges as a prominent contributor to these high-frequency impedances. This paper undertakes a systematic investigation into the effects of CSR on electron rings, utilizing the fourth-generation storage ring light source Elettra 2.0 and the low-energy ring of the SuperKEKB e+e− circular collider as illustrative examples. Our work revisits theories of microwave instability driven by CSR impedance, extending the analysis to encompass other high-frequency impedances, such as resistive wall and coherent wiggler radiation. Through instability analysis and numerical simulations conducted on the two aforementioned rings, the study explored the impact of high-frequency impedances and their combined effects with broadband impedances caused by discontinuities in vacuum chambers. Published by the American Physical Society 2024

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.

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, in particular beam-coupling impedance, can significantly affect Schottky spectra when large bunch charges are involved. In such conditions, the available interpretation methods are difficult to apply directly to the measured spectra, thus preventing the extraction of beam and machine parameters, which is possible for lower bunch charges. To study the impact of impedance on such spectra, we introduce a method for building Schottky spectra from macro-particle simulations performed with the PyHEADTAIL code, applied to LHC beam conditions. In this case, the use of a standard Fast Fourier Transform (FFT) algorithm to recover the spectral content of the beam becomes computationally intractable memory-wise, because of the relatively short bunch length compared to the large revolution period. To circumvent this difficulty, a semi-analytical method was developed to efficiently compute the Fourier transform. The simulated Schottky spectrum is then compared against theoretical formulas and measurements of Schottky signals previously obtained with lead ion beams in the LHC where impedance effects are expected to be limited. Furthermore, this study provides preliminary interpretations of the impact of beam-coupling impedance on proton Schottky spectra by incorporating longitudinal and transverse resonator-like impedance models into the simulations. A theoretical framework is also introduced for the case of the longitudinal impedance, allowing the extension of the existing theoretical formalism.

Study of beam-beam interaction in FCC-ee including updated transverse and longitudinal Impedances

Beam-beam interaction in FCC-ee can be seriously affected by the vacuum chamber coupling impedance resulting in a safe tune areas reduction, tune shifts and spread, bunch length and energy spread variation. The interplay of the two effects has a drastic impact on the stability of colliding bunches and respectively on the achievable luminosity. In this paper, beam-beam collisions in FCC-ee with 4 interaction points are studied including the updated transverse and longitudinal impedances.

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.

Higher-order mode analysis for SOLEIL-type superconducting cavity

A 499.8 MHz SOLEIL-type superconducting cavity was simulated and designed for the first time in this paper. The higher-order mode (HOM) properties of the cavity were investigated. Two kinds of coaxial HOM couplers were designed. Using 4 L-type and 4 T-type HOM couplers, the longitudinal impedance was suppressed to 3 kΩ, and the transverse impedance below 30 kΩ/m. The HOM damping requirements of Hefei Advanced Light Facility (HALF) were satisfied. This paper conducts an in-depth study on the radio frequency (RF) design, multipacting optimization, and thermal analysis of these coaxial couplers. Simulation results indicated that under operating acceleration voltage, the optimized couplers does not exhibit multiplicating or thermal breakdown phenomena. The cavity has the potential to reach a higher acceleration gradient.

Microbunching of thermionic cathode rf gun beams in the Advanced Photon Source s-band linac

We report on measurements of beams from thermionic cathode (TC) rf guns in the Advanced Photon Source S-Band Linac. These measurements include the macropulse out of both new and existing TC guns as well as the observation of microbunching within the micropulses of these beams. A gun chopper limits the macropulse FWHM duration to the 10-ns range. Our objectives were to analyse the new TC gun and investigate microbunching within a TC-rf-gun-generated beam. Our diagnostics elucidated longitudinal beam structures from the ns to the fs time scales. Coherent transition radiation (CTR) interferometers responding to far-infrared wavelengths were employed after each compression stage to provide the autocorrelations of the sub-ps micropulse durations. The first compression stage is an alpha magnet and the second a chicane. A CCD camera was used to image the beam via optical transition radiation from an Al screen at the end of the linac and also employed to measure coherent optical transition radiation (COTR) in the visible range. The COTR diagnostic observations, implying microbunching on a fs time scale, are presented and compared with a longitudinal space-charge impedance model.

A low-frequency normal conducting cavity with higher-order mode damping for fourth-generation synchrotron radiation sources.

The utilization of a low-frequency (<200MHz) RF system in storage facilitates the attainment of ultra-low emittances in synchrotron light sources through on-axis injection. This paper focuses on the development of a low-frequency normal conducting (NC) cavity with higher-order mode (HOM) damping for fourth-generation synchrotron light sources. We propose a novel approach to achieve efficient HOM damping in a NC cavity by optimizing the lowest frequency HOM and implementing a beam-line absorber. Notably, unlike conventional NC cavities, the presence of a large beam tube for the beam-line absorber does not compromise the accelerating performance in a coaxial resonant cavity, enabling effective HOM damping while maintaining a high shunt impedance. Through simulations, the prototype design of a 166.6MHz HOM-damped cavity demonstrates a fundamental mode impedance of ∼8 MΩ, with longitudinal and transverse HOM impedances below 2.0 and 50 kΩ/m, respectively.

Measurement and optimization of the beam coupling impedance of a novel 3D-printed titanium alloy cage inside the thin-wall vacuum chamber.

Dipole magnet vacuum chambers are among the most critical and costly components of rapid-cycling accelerator facilities. Alternative approaches to traditional ceramic chambers have been explored for the implementation of fast-ramping dipole-magnet vacuum chambers, including thin-wall metallic beam pipe chambers strengthened with transverse ribs and ceramic rings inside thin-walled chambers. Here, we report a novel 3D-printed titanium alloy cage inside the thin-wall vacuum chamber, which is designed for high-intensity heavy ion accelerator facility (HIAF) to reduce manufacturing difficulty and cost, shorten the production cycle, and improve the quality. Comprehensive studies were undertaken to characterize the impedance of the 3D-printed titanium alloy cage inside the thin-wall vacuum chamber. The beam-coupling impedance and eddy currents of the new thin-wall vacuum chamber were studied mostly numerically. Strategies for further reducing the beam-coupling impedance were explored. In addition, impedance bench measurements using the "half wavelength" resonant method were conducted to identify the longitudinal and transverse impedances of the 3D-printed titanium alloy cage inside the thin-wall vacuum chamber prototype experimentally. The simulated and measured results for the impedance were consistent. Furthermore, a campaign for resonance-check measurements on the 3D-printed titanium alloy ring loaded inside a thin-wall vacuum chamber prototype was launched. This novel thin-wall vacuum chamber structure is now entering the fabrication stage and will soon be ready for installation in the Booster Ring (BRing).

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.

On the longitudinal wave pumping in fluid-filled compliant tubes

This study investigates the physics of the longitudinal stretching-based wave pumping mechanism, a novel extension of the traditional impedance pump. In its simplest form, an impedance pump consists of a fluid-filled elastic tube connected to rigid tubes with a wave generator. These valveless pumps operate based on the principles of wave propagation in a fluid-filled compliant tube. Cardiovascular magnetic resonance imaging of the human circulatory system has shown substantial stretching of the aorta (the largest compliant artery of the body carrying blood) during the heart contraction and recoil of the aorta during the relaxation. Inspired by this dynamic mechanism, a comprehensive analysis of a longitudinal impedance pump is conducted in this study where waves are generated by stretching of the elastic wall and its recoil. We developed a fully coupled fluid–structure interaction computational model consisting of a straight fluid-filled elastic tube with longitudinal stretch at one end and a fixed reflection site at the other end. The pump's behavior is quantified as a function of stretching frequency and tube wall characteristics. Our results indicate that stretch-related wave propagation and reflection can induce frequency-dependent pumping. Findings suggest a non-linear pattern for the mean flow–frequency relationship. Based on the analysis of the propagated waveforms, the underlying physical mechanism in the longitudinal impedance pump is discussed. It is shown that both the direction and magnitude of the net flow strongly depend on the wave characteristics. These findings provide a fundamental understanding of stretch-related wave pumping and can inform the future design of such pumps.

1256 Fabricating Artificial Kidney Stones of Different Physical Properties for Ex Vivo Experimentation

Abstract Introduction There have been several new technologies introduced recently for lithotripsy. The optimal settings of these devices are unknown for different kidney stone densities. This study aims to develop artificial kidney stones for ex vivo studies. Method BegoStone was prepared with a powder to water ratio (by weight) ranging from 15:3 to 15:6. The phantoms' acoustic properties were characterised by using an ultrasound transmission technique, from which the corresponding mechanical properties can calculated based on elastic wave theory. Results The measured parameters for BegoStone phantoms of different water contents were assessed with regard to longitudinal wave speed &amp; density. If transverse wave speeds were measured then longitudinal acoustic impedance, transverse acoustic impedance, Young's modulus, bulk modulus, and shear modulus can be derived. Longitudinal (CL (m/s)) and density (ρ (Kg/m3)) of BegoStone phantoms with different powder to water ratios corresponded to the known properties reported in natural kidney stones (Calcium Oxalate Monohydrate, Brushite, Uric acid and Struvite). A BegoStone water ratio of 15:3 had similar properties to Calcium Oxalate Monohydrate, 15:4 to be similar to Brushite, 15:5 was similar to Uric acid, and 15:6 was similar to Struvite. Conclusions This BegoStone preparation method can be used to fabricate artificial stones with physical properties matched with those of natural kidney stones of various chemical compositions.

Association between resistance to cerebrospinal fluid flow and cardiac-induced brain tissue motion for Chiari malformation type I.

Chiari malformation type I (CMI) patients have been independently shown to have both increased resistance to cerebrospinal fluid (CSF) flow in the cervical spinal canal and greater cardiac-induced neural tissue motion compared to healthy controls. The goal of this paper is to determine if a relationship exists between CSF flow resistance and brain tissue motion in CMI subjects. Computational fluid dynamics (CFD) techniques were employed to compute integrated longitudinal impedance (ILI) as a measure of unsteady resistance to CSF flow in the cervical spinal canal in thirty-two CMI subjects and eighteen healthy controls. Neural tissue motion during the cardiac cycle was assessed using displacement encoding with stimulated echoes (DENSE) magnetic resonance imaging (MRI) technique. The results demonstrate a positive correlation between resistance to CSF flow and the maximum displacement of the cerebellum for CMI subjects (r = 0.75, p = 6.77 × 10-10) but not for healthy controls. No correlation was found between CSF flow resistance and maximum displacement in the brainstem for CMI or healthy subjects. The magnitude of resistance to CSF flow and maximum cardiac-induced brain tissue motion were not statistically different for CMI subjects with and without the presence of five CMI symptoms: imbalance, vertigo, swallowing difficulties, nausea or vomiting, and hoarseness. This study establishes a relationship between CSF flow resistance in the cervical spinal canal and cardiac-induced brain tissue motion in the cerebellum for CMI subjects. Further research is necessary to understand the importance of resistance and brain tissue motion in the symptomatology of CMI.

Dynamic Interaction Factor of Pipe Group Piles Considering the Scattering Effect of Passive Piles

Based on the plane–strain assumption, a calculation model of pile–soil–pile vertical coupling vibration response considering the scattering effect of passive piles is established in this paper. Using this model, the vertical displacement expressions of pile core soil and pile surrounding soil, soil displacement attenuation function, and longitudinal complex impedance are obtained. Then, based on the strict pile–soil coupling effect, the displacement of the active pile under vertical load and scattering effect, as well as the displacement of the passive pile under incident waves, are solved separately. A new type of dynamic interaction factor for pipe group piles is derived by introducing scattering effect factors. A numerical example shows that the degenerate solution in this paper is in good agreement with the existing solution, which verifies the rationality of the solution. Considering the scattering effect is helpful in improving the accuracy of vibration response analysis of pile groups. The variation in parameters such as slenderness ratio, pile spacing, and outer diameter has significant effects on the interaction factor, and compared with the solid pile, the influence of parameter change on the pipe pile is smaller.

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.

Physical, optical, mechanical, and radiation shielding properties for the B2O3–Li2O glasses

After starting of using ionizing radiation in many different fields, the scientists focused on to develop protection methods as it is dangers for the human body. Besides time and distance the most important way is shielding of radiation by using effective materials. With this motivation, the present study analyzes the physical, optical, mechanical, and Radiation shielding properties for the B2O3–Li2O glasses. Four different glasses coded as G-1 to G-4 are simulated via MCNPX Monte Carlo code by varying the concentration of the B2O3 + Li2O at 0–15 MeV gamma ray energies. The obtained results reveal that Li2O has a favorable influence on the radiation shielding characteristics of the preferred glass sample. To assess the relation between Li2O concentration in glass and corresponding structural and mechanical changes in candidate glasses, Makishima–Mackenzie theory is applied and mechanical moduli are extracted. The structure and dimensionality of the preferred samples are derived based on the Bergman and Kantor model for fluid and compositions with the help of the fractal bond connectivity. In addition, the longitudinal velocity (VL), transverse velocity (VS), mean velocity (V mean), and acoustic impedance (Zi) related to the glasses are evaluated.

Longitudinal impedance measurements and simulations of a three-metal-strip kicker

Longitudinal impedance measurements and simulations of a three-metal-strip kicker

Characterization of the electrical properties of mammalian peripheral nerve laminae.

The intrinsic electrical material properties of the laminar components of the mammalian peripheral nerve bundle are important parameters necessary for the accurate simulation of the electrical interaction between nerve fibers and neural interfaces. Improvements in the accuracy of these parameters improve the realism of the simulation and enables realistic screening of novel devices used for extracellular recording and stimulation of mammalian peripheral nerves. This work aims to characterize these properties for mammalian peripheral nerves to build upon the resistive parameter set established by Weerasuriya et al. in 1984 for amphibian somatic peripheral nerves (frog sciatic nerve) that is currently used ubiquitously in the in-silico peripheral nerve modeling community. A custom designed characterization chamber was implemented and used to measure the radial and longitudinal impedance between 10 mHz and 50 kHz of freshly excised canine vagus nerves using four-point impedance spectroscopy. The impedance spectra were parametrically fitted to an equivalent circuit model to decompose and estimate the components of the various laminae. Histological sections of the electrically characterized nerves were then made to quantify the geometry and laminae thicknesses of the perineurium and epineurium. These measured values were then used to calculate the estimated intrinsic electrical properties, resistivity and permittivity, from the decomposed resistances and reactances. Finally, the estimated intrinsic electrical properties were used in a finite element method (FEM) model of the nerve characterization setup to evaluate the realism of the model. The geometric measurements were as follows: nerve bundle (1.6 ± 0.6 mm), major nerve fascicle diameter (1.3 ± 0.23 mm), and perineurium thickness (13.8 ± 2.1 μm). The longitudinal resistivity of the endoneurium was estimated to be 0.97 ± 0.05 Ωm. The relative permittivity and resistivity of the perineurium were estimated to be 2018 ± 391 and 3.75 kΩm ± 981 Ωm, respectively. The relative permittivity and resistivity of the epineurium were found to be 9.4 × 106 ± 8.2 × 106 and 55.0 ± 24.4 Ωm, respectively. The root mean squared (RMS) error of the experimentally obtained values when used in the equivalent circuit model to determine goodness of fit against the measured impedance spectra was found to be 13.0 ± 10.7 Ω, 2.4° ± 1.3°. The corner frequency of the perineurium and epineurium were found to be 2.6 ± 1.0 kHz and 368.5 ± 761.9 Hz, respectively. A comparison between the FEM model in-silico impedance experiment against the ex-vivo methods had a RMS error of 159.0 ± 95.4 Ω, 20.7° ± 9.8°. Although the resistive values measured in the mammalian nerve are similar to those of the amphibian model, the relative permittivity of the laminae bring new information about the reactance and the corner frequency (frequency at peak reactance) of the peripheral nerve. The measured and estimated corner frequency are well within the range of most bioelectric signals, and are important to take into account when modeling the nerve and neural interfaces.

Longitudinal mode-coupling instabilities of proton bunches in the CERN Super Proton Synchrotron

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 particular, we see that the uncontrolled longitudinal emittance blowup of single bunches observed before the recent impedance reduction campaign (2018--2021) is due to the radial mode-coupling instability. Unexpectedly, this instability is as strong as the azimuthal mode-coupling instability, which is possible in the SPS for other combinations of bunch length and intensity. We also demonstrate the significant role of rf nonlinearity and potential-well distortion in determining these instability thresholds. Finally, we discuss the effect of the recent impedance reduction campaign on beam stability in single- and double-rf configurations.