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Figure G.5: Discrepancy factor between the horizontal single-bunch tune shifts measured and simulated, in various cases.
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In this thesis, the problem of the transverse coupled-bunch instabilities created by the Large Hadron Collider (LHC) beam-coupling impedance, that can possibly limit the machine operation, is addressed thanks to several new theories and tools. A rather complete vision of the problem is proposed here, going from the calculation of the impedances and...
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The correct functioning of a collimation system is crucial to safely and successfully operate high-energy particle accelerators, such as the Large Hadron Collider (LHC). However, the requirements to handle high- intensity beams can be demanding, and accident scenarios must be well studied in order to assess if the collimator design is robust agains...
Citations
... The typical vacuum chamber of Elettra 2.0 is rhomboidal with internal dimensions 27×17 mm. In practice, the IW2D code [39,40] is used to calculate the RW impedance with a rectangular approximation of the vacuum chamber, considering the NEG coating. The chamber materials include copper (45%), aluminum (20%), and stainless steel (35%). ...
Longitudinal impedances at high frequencies, which extend far beyond the width of the beam spectrum, can pose a threat to the performance of modern low-emittance electron storage rings, as they can establish a relatively low threshold for microwave instability. In such rings, 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 Elettra 2.0, a ring of fourth-generation light sources, and the SuperKEKB low-energy ring, a ring of $e^+e^-$ circular colliders, 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 interactions with broadband impedances from discontinuities in vacuum chambers.
... Studies have been performed since the first LHC run to compare the impedance model with its effects in the machine, in terms of tune shifts, growth rates, and octupole thresholds (i.e. the minimum octupole current necessary to stabilise the beam through Landau damping), gradually improving the measurement procedure over the years [27,[68][69][70][71][72][73]. ...
... The impedance model was also refined over time, in particular that of individual collimators, which currently contains both the large resistive-wall contribution of the jaws [69], and the impedance of geometric features such as small angle taperings [74], including their resistive-wall contribution [33]. Finally, for low-impedance primaries and secondaries, the geometric impedance now provides a relatively important contribution compared to the resistive-wall part which has been considerably reduced; hence, recently significant effort was made to further refine their model, ultimately using electromagnetic simulations and measurements [75][76][77]. ...
The High Luminosity (HL-LHC) project aims to increase the integrated luminosity of CERN's Large Hadron Collider (LHC) by an order of magnitude compared to its initial design. This requires a large increase in bunch intensity and beam brightness compared to the first three LHC runs, and hence poses serious collective-effects challenges, related in particular to electron cloud, instabilities from beam-coupling impedance, and beam-beam effects. Here, we present the associated constraints and the mitigation measures proposed to achieve the baseline performance of the upgraded LHC machine. We also discuss the interplay of these mitigation measures with other aspects of the accelerator, such as optics, physical and dynamic apertures, the collimation system, and crab cavities. Additional potential sources of intensity limitations are also briefly discussed.
... In section 2 the analytical approach for evaluating the impedance and wakefield of a taper transition, as proposed in [13,14], is discussed in order to better understand the parameters that can be used to reduce the collimators' geometric contribution. Then, in section 3, we study both the geometric and resistive wall wakefields, also in comparison with the other sources, by means of the electromagnetic codes ECHO3D [15] and IW2D [16] and, in section 4, their impact, in particular on the transverse beam dynamics, is studied with the help of the tracking code PyHEADTAIL [17]. ...
... In addition to the geometric contribution, also the resistive wall term, produced by the finite conductivity of the pipe walls plays an important role. To evaluate the resistive wall contribution to the wakefield of the collimators, we used IW2D [16] and simulated parallel plates with infinite thickness. ...
The purpose of this paper is to calculate the longitudinal and transverse wakefields of the FCC collimators using the electromagnetic codes ECHO3D and IW2D. We cross-checked our results using CST particle studio for long bunches, and found them to be in good agreement. The obtained results show that the collimators give one of the highest contributions to the overall FCC-ee wake potentials. In particular, using the code PyHEADTAIL, we have found that the geometric contribution of the collimators' wakefield reduces significantly the transverse mode coupling instability threshold. Therefore, it is imperative to explore and implement solutions that effectively mitigate this wakefield source.
... In addition, the wake-function can also be evaluated numerically with dedicated electromagnetic (EM) codes. In particular, IW2D (Impedance Wake 2D) allows to calculate the RW impedance per unit length of pipes with uniform but arbitrary cross section [26]. In Fig. 3 we show the wake-function per unit length for a hollow circular beam pipe made of copper (σ = 5.8 10 7 S/m and cτ = 8.1 µm) with a 2 mm radius. ...
High brightness electron beams enable a wide spectrum of applications ranging from short wavelength radiation sources to high gradient wakefield acceleration. The rich dynamics that are intrinsic in charged particles accelerated in complex systems require a careful description in the analysis and design of a given machine, particularly regarding its stability. Numerous computer codes are in use by the accelerator community for such purposes. In particular, MILES is a simple tracking code we have developed that allows fast evaluations of collective effects in RF linacs. In this paper we extend the simple models previously developed to describe specific, diverse applications that can benefit from the fast simulation tools developed in MILES. Examples of this kind include particle driven acceleration schemes in a plasma where driver and witness beams propagate in the “comb” pulse-train configuration. Specifically, we investigate the self-induced fields excited within the X-band rf-linac stage of EuPRAXIA@SPARC_LAB. Further, we discuss additional advanced topics such as resistive wall wakefield effects in planar FEL undulators and their impact on the radiation emitted.
... It has been shown that these winglets give a negligible contribution to the impedance. In particular, as one Fig. 1, for the frequency range of interest the longitudinal RW impedance calculated by the 2D electromagnetic solver VACI [10] for the geometry with the winglets practically coincides with that of the round beam pipe obtained by using IW2D code [11]. The collimation system is another important impedance source. ...
The design of the FCC-ee collider is ongoing with the goal of optimizing beam parameters and developing various accelerator systems. As a result, the modelling of coupling impedance is continuously evolving to take into account the design of the collider vacuum chamber and hardware components. Concurrently, estimates of collective effects and instabilities are being continually updated and refined. This paper presents the current FCC-ee impedance model and reports the findings of the single-bunch instability studies. Additionally, some potential mitigation techniques for these instabilities are discussed.
... The calculation of the collimator resistive-wall impedance is performed using ImpedanceWake2D [33]. The code implements the field matching technique to compute the electromagnetic fields inside an infinitely long multilayered structure of circular or flat cross section [34]. The material resistivities used for the simulations are 5 μΩm for CFC, 1 μΩm for MoGr, and 0.053 μΩm for Mo [26]. ...
The High Luminosity (HL) upgrade of the Large Hadron Collider (LHC) will increase the peak luminosity at the experiments by more than a factor of 5 with respect to the LHC design value. To achieve this goal, among the upgrade of several beam and machine parameters, the beam intensity will nearly double with respect to the operational LHC value, and the transverse beam emittance will decrease by 50% compared to the LHC design value. Past operational experience showed that coherent beam instabilities may occur for low, positive values of chromaticity, and a higher tune spread than predicted from simulations is required from the dedicated octupole magnets to provide enough Landau damping. With the HL-LHC brighter beams, stability margins will become tighter, and coherent instabilities become stronger if no dedicated mitigation measures are taken. An impedance reduction plan is therefore taking place targeting the collimation system, and the main contributor to the transverse beam coupling impedance at the flattop energy. New collimators with lower resistivity materials will replace the current LHC ones. In this work, we assess the benefits of this impedance reduction with respect to the transverse mode coupling instability threshold. This study quantifies the discrepancy between measured and predicted beam stability thresholds at low chromaticity. It also probes the expected gain of the impedance reduction plan of HL-LHC.
... To calculate the wakefields of an elliptical beam pipe using the same equations, the equivalent radius eq needs to be computed such that the wake of the circular pipe of radius eq is equal to that of the elliptical pipe. Supposing the elliptical pipe has the vertical half-aperture size of , the equivalent radius can be given by eq = /( ) 1/3 , where is the Yokoya's factor [12][13][14] for the dipolar vertical impedance. For the aperture size of the SOLEIL II booster beam pipe, it is found that = 0.8651 and eq = 11.54 mm. ...
The ultra-low emittance specification of the SOLEIL II storage ring requires a challenging lattice design of the booster that will inject the beam into it. The dimension of the vacuum chamber in the new booster must be reduced compared to that in the present machine. The resistive-wall (RW) instability is then expected to become more important than in the current booster. However, the Amplitude-Dependent Tune Shift (ADTS) is also expected to be stronger due to the strong sextupole magnets necessary for chromatic error correction in the new lattice. It could then be an important effect to fight against this instability. Therefore, evaluating this instability is important to ensure the machine's feasibility. This work studies the beam dynamics along the ramp in the RW instability regime using the code mbtrack2. The turn-by-turn tracking allows us to see the evolution of the beam thoroughly and understand how RW, synchrotron radiation, and ADTS impact the beam stability.
... Simulations were made in CST Particle Studio to determine the RW contribution of each vacuum chamber taking into account its full geometry. This was compared with ImpedanceWake2D (IW2D) [21], which uses an elliptical profile that best matches the chamber geometry. IW2D showed a reduced RW impedance contribution by approximately 20%. ...
... In the vertical plane, the wakes have the same sign, increasing the measured tune shift. This is the general case for flat chambers [21]. Both measured tune shifts are larger than predicted. ...
The European Synchrotron Radiation Facility (ESRF) storage ring (SR) has been dismantled and replaced by the Extremely Brilliant Source (EBS) which has now been commissioned. This new fourth generation light source has much smaller vacuum chambers than its predecessor, which necessitates a careful optimization of the vacuum systems and an accurate impedance model to be able to deliver all beam modes at the design current and predict future machine performance in the presence of strong collective effects. This paper will report on the first beam based measurements with a single bunch in order to characterize the short range wakefield model of the EBS SR and to make a first comparison with predictions. The results from transverse instability thresholds and tune shift measurements will be presented, as well as bunch length and phase variation with the current. Microwave instability threshold measurements have shown some discrepancy with predictions, which could arise from welding defects in the machining of the chambers. These discrepancies and other possible causes will be discussed.
... In section 2 the analytical approach for evaluating the impedance and wakefield of a taper transition, as proposed in [13,14], is discussed in order to better understand the parameters that can be used to reduce the collimators' geometric contribution. Then, in section 3, we study both the geometric and resistive wall wakefields, also in comparison with the other sources, by means of the electromagnetic codes ECHO3D [15] and IW2D [16] and, in section 4, their impact, in particular on the transverse beam dynamics, is studied with the help of the tracking code PyHEADTAIL [17]. ...
... In addition to the geometric contribution, also the resistive wall term, produced by the finite conductivity of the pipe walls plays an important role. To evaluate the resistive wall contribution to the wakefield of the collimators, we used IW2D [16] and simulated parallel plates with infinite thickness. Separating the resistive wall (RW) and geometric contributions is essential to understand the origin and relative importance of each contribution to the overall impedance of the collimators because we can identify which one is the dominant source of impedance and develop mitigation methods accordingly. ...
The purpose of this paper is to calculate the longitudinal and transverse wakefields of the FCC collimators by using the electromagnetic codes ECHO3D and IW2D. We cross-checked our results using CST particle studio for long bunches, and found them to be in good agreement. The obtained results show that the collimators give one of the highest contributions to the overall FCC-ee wake potentials. Using the code PyHEADTAIL, we have found that the presence of the geometric wakefield of the collimators leads to the occurrence of transverse mode coupling instability (TMCI) at a significantly lower bunch population as compared to that of all other contributions and solutions to reduce this geometric term must be found.
... In hadron synchrotrons operating below transition energy, the zero head-tail mode is usually suppressed by natural chromaticity. Transverse feedback systems can be an effective mitigation against head-tail and other instabilities [24,25], but can have restrictions, for example, higher-order head-tail modes in short bunches or an instability due to a resistive damper [26]. In such cases, Landau damping devices are indispensable for the beam stability. ...
... A similar method was described and employed in a proof-of-principle experiment in [27] using a transverse feedback system (as an antidamper) in the LHC study and it agreed with the known stability boundaries for LO. In addition, this model can be applied to coupled bunch instabilities with symmetric fill [25]. ...
A pulsed electron lens produces a betatron tune shift along a hadron bunch as a function of the longitudinal coordinates, which is a longitudinal detuning. An example of transverse detuning is the tune shifts due to octupole magnets. This paper considers a pulsed electron lens as a measure to mitigate the head-tail instabilities. Using a detailed analytical description within a Vlasov formalism, the coherent properties of the longitudinal and transverse detuning are presented. The analytical predictions are compared with the results of the particle tracking simulations. A pulsed electron lens is demonstrated to be a source of tune spread with two components: a static one, leading to Landau damping and a dynamic one, leading to an effective impedance modification, which we demonstrate analytically and in our particle tracking simulations. The effective impedance modification can be important for beam stability due to devices causing longitudinal detuning, especially for nonzero head-tail modes. The Vlasov formalism is extended to include the combination of longitudinal and transverse detuning. As a possible application at the SIS100 heavy-ion synchrotron [Facility for Antiproton and Ion Research (FAIR) at GSI Darmstadt, Germany], a combination of a pulsed electron lens with octupole magnets is considered.
