Circular Electron Positron Collider Research Articles

High-precision spatial measurement method of accelerator pre-alignment based on multiple total stations

Abstract With the development of accelerator technology, the scale of accelerators is becoming larger, ranging from hundreds of meters to several kilometers. For stable operation of accelerators, high-precision alignment, positioning, and installation are crucial. Installing all equipment inside the tunnel poses safety risks as personnel would be in a closed environment with potential radiation exposure for prolonged periods. To address the challenges of long adjustment and maintenance periods inside the tunnel due to the installation of equipment for large-scale accelerators, most accelerator devices under construction or in research have pre-alignment assemblies. Each assembly consists of a certain number of magnets distributed on girders. The magnets in one unit are pre-aligned with high precision in the laboratory and then transported to the tunnel. Aligning the entire magnet girder can significantly improve installation efficiency inside the tunnel. To meet the pre-alignment accuracy requirement of 10 μm in the horizontal and vertical directions for the magnet units in the high energy photon source (HEPS) storage ring, a system for high-precision pre-alignment of accelerator units using four total stations for angle observation has been designed in this paper. By employing different instrument layout configurations and incorporating reliable distance benchmarks, high-precision pre-alignment of the magnet are achieved. By arranging targets and utilizing recognition for automatic targeting, real-time point calculations during pre-alignment enhance efficiency. Subsequently, based on this system, pre-alignment simulation calculations and experimental verification of eight magnet focusing–defocusing units in the HEPS storage ring are conducted and ultimately realizing the 10 μm transverse and vertical pre-alignment measuring error within the units. This method, based on high-precision measurements in a small-scale space, reduces the period required for personnel on-site and improves pre-alignment efficiency. It also provides a reference for pre-alignment of multiple magnet units in large accelerators such as the Southern Advanced Photon Source and Circular Electron Positron Collider.

Prospects for detecting the couplings of axion-like particle with neutrinos at the CEPC

AbstractWe explore the possibility of detecting the couplings of axion-like particle (ALP) with leptons from their loop-level impact on the ALP couplings to electroweak (EW) gauge bosons via the signal process "Equation missing" at the circular electron positron collider (CEPC) and obtain prospective sensitivities to the ALP-lepton couplings. Our numerical results show that the CEPC with the center of mass energy $$\sqrt{s}=240~(91)$$ s = 240 ( 91 ) GeV and the integrated luminosity $$\mathcal {L}=5.6~(16)$$ L = 5.6 ( 16 ) $$\hbox {ab}^{-1}$$ ab - 1 might be sensitive for probing the ALP-lepton couplings in the ALP mass range from 10 GeV to 130 (50) GeV, where the prospective sensitivities to the ALP-neutrino coupling $$Tr(g_{a\nu \nu })/f_a$$ T r ( g a ν ν ) / f a can be as low as 0.016 (0.012) $$\hbox {GeV}^{-1}$$ GeV - 1 and $$0.0031~(2.8 \times 10^{-4})$$ 0.0031 ( 2.8 × 10 - 4 ) $$\hbox {GeV}^{-1}$$ GeV - 1 for $$c_{R}=0$$ c R = 0 and $$c_{R}=c_{L}$$ c R = c L , and to the ALP-charged lepton coupling $$Tr(g_{a\ell \ell })/f_a$$ T r ( g a ℓ ℓ ) / f a can be as low as 0.035 (0.07) $$\hbox {GeV}^{-1}$$ GeV - 1 for $$c_{L}=0$$ c L = 0 . We find that the prospective sensitivities given by the CEPC are not covered by the current and expected exclusion regions in some ALP mass intervals. The CEPC has the potential for exploring the ALP-neutrino couplings via some promising processes induced by the ALP-EW gauge boson couplings in the future.

High Q and high gradient performance of the first medium-temperature baking 1.3 GHz cryomodule

The world’s first 1.3 GHz cryomodule containing eight 9-cell superconducting radio-frequency (rf) cavities treated by medium-temperature furnace baking (mid-T bake) was developed at the Institute of High Energy Physics, Chinese Academy of Sciences. The 9-cell cavities in the cryomodule achieved an unprecedented high average intrinsic quality factor (Q0) of 3.8×1010 at 16 MV/m and 3.6×1010 at 21 MV/m in the horizontal test. The cryomodule can operate stably up to a total continuous wave rf voltage greater than 193 MV, with an average cavity usable accelerating gradient of more than 23 MV/m. The results significantly exceed the specifications of Circular Electron Positron Collider and Dalian advanced light source and the other high repetition rate free electron laser facilities [Linac Coherent Light Source II (LCLS-II), LCLS-II-high energy, Shanghai High Repetition Rate X-ray FEL and Extreme Light Facility, Shenzhen Superconducting Soft X-Ray Free Electron Laser, etc.]. There is evidence that the mid-T bake cavity may not require fast cooldown or long processing time in the cryomodule. This paper reviews the cryomodule performance and discusses some important issues in cryomodule assembly and testing. Published by the American Physical Society 2024

Exposing a dual-readout fibre calorimeter to electron beams, in preparation for HiDRa: High-resolution calorimeter for [formula omitted] colliders

Among the proposed accelerators for the post-LHC era are the Future Circular Collider (FCC) and the Circular Electron–Positron Collider (CEPC). Both projects would take advantage of the clean environment and low radiation damage of electron–positron collisions, providing the highest precision studies of electroweak and Higgs physics. The relatively high branching fraction of W, Z and Higgs bosons into hadronic jets makes the precise measurements of these objects an essential aspect on detector development for experiments at future collider facilities. One of the most promising calorimetry techniques for improved hadron energy reconstruction is the dual-readout method, which exploits signals from two different physics processes to correct for the fem of hadron showers, therefore boosting the standalone calorimeter performance. The usage of compact photosensors (e.g. Silicon PhotoMultipliers) for the readout enables a very fine segmentation, opening to particle-flow and advanced neural networks software reconstruction of events. In this contribution, the results of testing a small-scale dual-readout calorimeter prototype, characterised by a mixed PMT and SiPM readout solution, with an electron beam at the CERN SPS facility in the energy range [10, 120] GeV are presented. It follows the description of a larger prototype of the same type, currently under construction in the context of the INFN HiDRa project, that will be large enough to fully contain hadron showers. The design, construction technique and expected performance, as estimated through a Geant4 simulation parameterised on the previous prototype, are presented.

Prediction of the treatment effect of FLASH radiotherapy with synchrotron radiation from theCircular Electron-Positron Collider (CEPC).

The Circular Electron-Positron Collider (CEPC) in China can also work as an excellent powerful synchrotron light source, which can generate high-quality synchrotron radiation. This synchrotron radiation has potential advantages in the medical field as it has a broad spectrum, with energies ranging from visible light to X-rays used in conventional radiotherapy, up to several megaelectronvolts. FLASH radiotherapy is one of the most advanced radiotherapy modalities. It is a radiotherapy method that uses ultra-high dose rate irradiation to achieve the treatment dose in an instant; the ultra-high dose rate used is generally greater than 40 Gy s-1, and this type of radiotherapy can protect normal tissues well. In this paper, the treatment effect of CEPC synchrotron radiation for FLASH radiotherapy was evaluated by simulation. First, a Geant4 simulation was used to build a synchrotron radiation radiotherapy beamline station, and then the dose rate that the CEPC can produce was calculated. A physicochemical model of radiotherapy response kinetics was then established, and a large number of radiotherapy experimental data were comprehensively used to fit and determine the functional relationship between the treatment effect, dose rate and dose. Finally, the macroscopic treatment effect of FLASH radiotherapy was predicted using CEPC synchrotron radiation through the dose rate and the above-mentioned functional relationship. The results show that the synchrotron radiation beam from the CEPC is one of the best beams for FLASH radiotherapy.

Cryogenic system of the high performance 1.3 GHz 9-cell superconducting radio frequency prototype cryomodule

High quality factor 1.3 GHz 9-cell superconducting radio frequency (SRF) cavity cryomodule is the core technology of the international advanced accelerator. China’s first high-quality factor 1.3 GHz 9-cell SRF cavity cryomodule was developed, assembled and tested at the Institute of High Energy Physics (IHEP), Chinese Academy of Sciences for the Dalian Advanced Light Source (DALS) and Circular Electron Positron Collider (CEPC) R&D. The 9-cell cavities in the cryomodule achieved a high average intrinsic quality factor (Q0) of 3.8 × 1010 at 16 MV/m and 3.6 × 1010 at 21 MV/m in the horizontal test. With such high specifications, the SRF cavity system has corresponding requirements for the cryogenic system. Key criteria for stable and reliable operation include a dependable cryogenic refrigeration system and process design, good thermal insulation, pressure control, temperature uniformity, and quench protection, etc. IHEP has successfully completed cryogenic testing development of the first 1.3 GHz 9-cell SRF prototype cryomodule. The whole cooldown period was 74 h, and the automatic cooldown was completed. The successful development and implementation of the 1.3 GHz superconducting cryomodule cryogenic system will provide a stable and reliable test environment for advanced superconducting cavity cryogenic testing, which will be critical in promoting the further development of the Free Electron Laser (FEL) and CEPC projects.

Production of hidden-heavy and double-heavy hadronic molecules at the Z factory of CEPC

With a clean environment and high collision energy, the Circular Electron Positron Collider (CEPC) would be an excellent facility for heavy flavor physics. Using the Monte Carlo event generator ythia, we simulate the production of the charmed (bottom) hadron pairs in the electron-positron collisions at the Z factory of CEPC, and the inclusive production rates for typical candidates of the hidden/double-charm and hidden/double-bottom S-wave hadronic molecules are estimated at an order-of-magnitude level with the final state interactions after the hadron pair production. The predicted cross sections for the hidden-charm meson-meson molecules X(3872) and Zc(3900) are at pb level, which are about two to three orders of magnitude larger than the production cross sections for the double-charm meson-meson molecules Tcc and Tcc*, as the double-charmed ones require the production of two pairs of cc¯ from the Z boson decay. The production cross sections for the hidden-charm pentaquark states Pc and Pcs as meson-baryon molecules are a few to tens of fb, which are about one magnitude larger than those of the possible hidden-charm baryon-antibaryon and double-charm meson-baryon molecules. In the bottom sector, the production cross sections for the Zb states as B(*)B¯* molecules are about tens to hundreds of fb, indicating 106–107 events from a two-year operation of CEPC, and the expected events from the double-bottom molecules are about 2–5 orders of magnitude smaller than the Zb states. Our results shows great prospects of probing heavy exotic hadrons at CEPC. Published by the American Physical Society 2024

Simulation and reconstruction of particle trajectories in the CEPC drift chamber

The circular electron-positron collider (CEPC) is designed to precisely measure the properties of the Higgs boson, study electroweak interactions at the Z-boson peak, and search for new physics beyond the Standard Model. As a component of the 4th\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4^{\ ext {th}}$$\\end{document} conceptual CEPC detector, the drift chamber facilitates the measurement of charged particles. This study implemented a Geant4-based simulation and track reconstruction for the drift chamber. For the simulation, detector construction and response were implemented and added to the CEPC simulation chain. The development of track reconstruction involves track finding using the combinatorial Kalman filter method and track fitting using the tool of GenFit. Using the simulated data, the tracking performance was studied. The results showed that both the reconstruction resolution and tracking efficiency satisfied the requirements of the CEPC experiment.

Testing Bell inequality through at CEPC* *Tong Li is Supported by the National Natural Science Foundation of China (12375096, 12035008, 11975129), and "the Fundamental Research Funds for the Central Universities", Nankai University (63196013). Kai Ma was supported by the Natural Science Basic Research Program of Shaanxi Province, China (2023-JC-YB-041) and the Innovation Capability Support Program of Shaanxi Province, China (2021KJXX-47)

The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we consider the detector effects of CEPC including uncertainties for tracks and jets from Z boson in the production of . Necessary reconstruction approaches are described to measure quantum entanglement between and . Finally, we show the sensitivity of CEPC to Bell inequality violation for the two methods.

Right-handed slepton bulk region for dark matter in generalized no-scale F -SU(5) with effective supernatural supersymmetry

We propose generalized no-scale supergravity, the simplest scenario for effective supernatural supersymmetry, naturally solving the supersymmetry electroweak fine-tuning problem and including natural dark matter. A light right-handed slepton bulk region is realized in F-SU(5) and the phenomenological minimal supersymmetric standard model. The bulk may be beyond the LHC reach, although it can be probed at the 1000-day LUX-ZEPLIN, Future Circular Collider at CERN, Circular Electron-Positron Collider, and Hyper-Kamiokande. Published by the American Physical Society 2024

Study and analysis of high-power coupler failure due to asymmetric electric field distribution

Microwave vacuum electronics play a vital role in numerous applications, and high-power couplers are a critical component. However, coupler failure is a common problem in high-energy accelerators, especially in situations involving high continuous wave (CW) power operation, leading to costly downtime and reduced performance. This paper focuses on addressing the issue of coupler failure in high-power scenarios by studying the specific case of the Circular Electron-Positron Collider (CEPC) 650 MHz high-efficiency klystron, designed for a power of 800 kW and tested up to 700 kW. The failure was attributed to the cracking of the coupler ceramics due to asymmetric electric field distribution, a previously unnoticed issue. Consequently, this study describes the coupler testing process, analyzes the problem, and proposes corresponding solutions to achieve symmetrical electric field distribution and reduce thermal stress. After evaluating three approaches, we recommend the T-bar coupler with water cooling and forced air cooling as the most viable option. This research is significant for the future development of high-power couplers, as it offers references for overcoming technical challenges and optimizing structural designs. As a result, other high-power coupler designers may find inspiration in the suggested solutions as they strive for increased dependability and performance.

Design and test for the CEPC muon subdetector based on extruded scintillator and SiPM

The integration of a scintillator, wavelength-shifting fiber, and silicon photomultiplier (SiPM) has demonstrated superior performance in the K-long and Muon detector (KLM) of the Belle II experiment. This study outlines our research and development (R&D) initiatives aimed at harnessing similar detection technologies, incorporating a novel scintillator and SiPM, for potential use in a muon detector for the proposed Circular Electron Positron Collider (CEPC) experiment. Our R&D activities have been focused on evaluating the efficacy of a newly developed 150 cm-long scintillator, alongside the NDL SiPM featuring a sensitive area of 3 mm×3 mm, or the Hamamatsu MPPC with a 1.3 mm× 1.3 mm sensitive surface. The project also includes the fabrication of a detector strip and the implementation of techniques designed to optimize light collection efficiency. Cosmic ray testing has shown that both NDL SiPMs and MPPCs are capable of highly efficient photon collection, achieving efficiencies significantly exceeding 90% when employing a threshold of 8 photoelectrons. Additionally, the time resolution for detecting events at the distant end of a scintillator strip has been measured to be better than 1.7 ns. The remarkable performance observed lays the foundation for advancing R&D including prototype modules aiming for reference Technical Design Report of CEPC detector recently.

Jet-Origin Identification and Its Application at an Electron-Positron Higgs Factory.

To enhance the scientific discovery power of high-energy collider experiments, we propose and realize the concept of jet-origin identification that categorizes jets into five quark species (b,c,s,u,d), five antiquarks (b[over ¯],c[over ¯],s[over ¯],u[over ¯],d[over ¯]), and the gluon. Using state-of-the-art algorithms and simulated νν[over ¯]H,H→jj events at 240GeV center-of-mass energy at the electron-positron Higgs factory, the jet-origin identification simultaneously reaches jet flavor tagging efficiencies ranging from 67% to 92% for bottom, charm, and strange quarks and jet charge flip rates of 7%-24% for all quark species. We apply the jet-origin identification to Higgs rare and exotic decay measurements at the nominal luminosity of the Circular Electron Positron Collider and conclude that the upper limits on the branching ratios of H→ss[over ¯],uu[over ¯],dd[over ¯] and H→sb,db,uc,ds can be determined to 2×10^{-4} to 1×10^{-3} at 95%confidence level. The derived upper limit for H→ss[over ¯] decay is approximately 3 times the prediction of the standard model.

Testing lepton flavor universality at future Z factories

As one of the hypothetical principles in the Standard Model (SM), lepton flavor universality (LFU) should be tested with a precision as high as possible such that the physics violating this principle can be fully examined. The run of a Z factory at a future e+e− collider, such as the Circular Electron-Positron Collider or Future Circular Collider (electron/positron), provides a great opportunity to perform this task because of the large statistics and high reconstruction efficiencies for b hadrons at the Z pole. In this paper, we present a systematic study on the LFU test in future Z factories. The goal is threefold. First, we study the sensitivities of measuring the LFU-violating observables of b→cτν, i.e., RJ/ψ, RDs, RDs*, and RΛc, where τ decays muonically. For this purpose, we develop the strategies for event reconstruction, based on the track information significantly. Second, we explore the sensitivity robustness against detector performance and its potential improvement with the message of event shape or beyond the b-hadron decays. A picture is drawn on the variation of analysis sensitivities with the detector tracking resolution and soft photon detectability, and the impact of Fox-Wolfram moments is studied on the measurement of relevant flavor events. Finally, we interpret the projected sensitivities in the SM effective field theory, by combining the LFU tests of b→cτν and the measurements of b→sτ+τ− and b→sν¯ν. We show that the limits on the LFU-violating energy scale can be pushed up to ∼O(10) TeV for ≲O(1) Wilson coefficients at Tera-Z. Published by the American Physical Society 2024

Right-handed slepton bulk regions for dark matter in a generalized minimal supergravity

We study the light right-handed slepton bulk regions for dark matter from the generalized minimal supergravity (GmSUGRA) in the minimal supersymmetric Standard Model. In our comprehensive numerical studies, we show that Rϕ˜≳10% is a conservative criterion to formulate bulk region, where Rϕ˜≡(mϕ˜−mχ˜10)/mχ˜10. For right-handed stau as the next-to-the-lightest supersymmetric particle (NLSP), we find a large viable parameter space, consistent with the current LHC constraints, Planck2018 dark matter relic density bounds, and direct bounds on neutralino-nucleons scattering cross section that naturally supports the right-handed stau bulk regions for dark matter. In particular, the upper bounds on the masses of the lightest supersymmetric particle neutralino and right-handed stau are about 120.4 and 138 GeV, respectively. This bulk region may be beyond the current LHC reach and could be probed at LUX-ZEPLIN, a next-generation dark matter direct-detection experiment, the Future Circular Collider at CERN, and the Circular Electron Positron Collider. However, the scenario with the right-handed selectron as the NLSP is excluded by the LHC supersymmetry searches. Published by the American Physical Society 2024

Next-to-leading-order relativistic and QCD corrections to prompt pair photoproduction at future colliders* *Supported in part by the German Research Foundation DFG through Research Unit FOR 2926 "Next Generation Perturbative QCD for Hadron Structure: Preparing for the Electron-Ion Collider" (409651613). The work of X.B.J. was supported in part by National Natural Science Foundation of China (12061131006). The work of R.L. was

Within the framework of nonrelativistic-QCD factorization, we calculate both the next-to-leading-order relativistic and QCD corrections to prompt pair production, with feed-down from mesons, via photon-photon collisions at future colliders, including the Future Circular Lepton Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), and the Compact Linear Collider (CLIC). We present total cross sections and distributions in single transverse momentum and rapidity, as well as in pair invariant mass. The relativistic and QCD corrections both turn out to be large and negative. However, the production rates are large enough for useful experimental studies.

4 Gbps serializer circuits in a 180 nm technology for monolithic pixel sensor prototypes developed for the CEPC vertex detector

Monolithic Active Pixel Sensor is one of the promising candidates for the Circular Electron Positron Collider Vertex detector, due to its good performance and trade-off of granularity, readout speed, material budgets and power consumption. A full-scale TaichuPix chip, including a matrix of 512 × 1024 pixels with a size of 25 × 25 μm2 is developed to provide a spatial resolution better than 5 μm. It requires a raw data rate up to 3.84 Gbps and power consumption less than 100 mA for the serializer circuit. Based on one of the small-scale prototypes, the highest serial data rate is tested to be 3.36 Gbps with a peak-to-peak jitter of about 150 ps and large current consumption. Moreover, the 32-bit parallel data width of the serializer isn't suitable for the 8B10B encoder. Therefore, two 4 Gbps serializers have been designed and optimized to meet these requirements based on the same process node of 180 nm as the TaichuPix, considering the funding and time costs. The serializer consists of a phase locked loop (PLL), several 5:1 sub-multiplexers based on a shift-register chain, a 4:1 or 8:1 sub-multiplexer based on the binary-tree structure, a clock distributor and a high-speed driver. Both ring-oscillating PLL and LC-tank PLL were integrated for performance evaluation. The preliminary tests showed low-jitter characteristics of the two PLLs despite this version's biasing problem, and both serializer circuits functioned correctly. A revision corrected the error and was submitted in October 2023.

ParticleNet and its application on CEPC jet flavor tagging

Quarks (except top quarks) and gluons produced in collider experiments hadronize and fragment into sprays of stable particles, called jets. Identification of quark flavor is desired for collider experiments in high-energy physics, relying on flavor tagging algorithms. In this study, using a full simulation of the Circular Electron Positron Collider (CEPC), we investigate the flavor tagging performance of two different algorithms: ParticleNet, based on a Graph Neural Network, and LCFIPlus, based on the Gradient Booted Decision Tree. Compared to LCFIPlus, ParticleNet significantly enhances flavor tagging performance, resulting in a significant improvement in benchmark measurement accuracy, i.e., a 36% improvement for σ(ZH)·Br(Z→νν¯,H→cc¯)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma (ZH)\\cdot Br(Z\\rightarrow \ u \\bar{\ u }, H\\rightarrow c\\bar{c})$$\\end{document} measurement and a 75% improvement for |Vcb|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|V_{cb}|$$\\end{document} measurement via W boson decay, respectively, when the CEPC operates as a Higgs factory at the center-of-mass energy of 240 GeV and collects an integrated luminosity of 5.6 ab-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}. We compare the performance of ParticleNet and LCFIPlus at different vertex detector configurations, observing that the inner radius is the most sensitive parameter, followed by material budget and spatial resolution.

Searching for the light leptophilic gauge boson Z x via four-lepton final states at the CEPC* *Supported by the National Natural Science Foundation of China (11875157, 12147214)

We investigate the possibility of detecting the leptophilic gauge boson predicted by the model via the processes and at the Circular Electron Positron Collider (CEPC) with a center of mass energy GeV and luminosity . We provide the expected sensitivities of the CEPC to the parameter space at the , , , and levels.

Impedance driven collective effects in CEPC

The Circular Electron Positron Collider is a double ring lepton collider covering beam energy from 45 GeV (Z) to 180 GeV (tt-bar). Beam coupling impedance and the collective effects that are triggered by the impedance are important subjects when targeting high machine performance of an electron positron collider. A robust impedance model is required for the instabilities evaluations as well as to investigate their possible mitigations. Meanwhile, a thorough investigation on the collective effects is essential to identify the critical issues on the beam instabilities. In this paper, a detailed impedance model has been built for the collider ring and dominant impedance contributors have been identified by evaluating the effective impedances. The potential collective instabilities driven by the impedance are also discussed.