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KEK has been designing the 10 mA class ERL-EUV light source accelerator. The main linac uses 9-cell superconducting cavities with beamline HOM damper. The target accelerating gradient is 12.5 MV/m. The 9-cell cavity is designed from experience of the KEK compact ERL (cERL) main linac. The cERL main linac was designed to suppress the HOM-BBU with beam current of 100mA by enlarging the iris diameter to 80mm. This resulted into the high ratio of the peak surface electric field and the accelerating field (Ep/Eacc) of 3. The accelerating gradient is limited from 8.5 to 10 MV/m during the CW beam operation due to field emission. The EUV can accept lower BBU limit than cERL because the target beam current of the EUV is 10 mA. The iris diameter is set to 70mm to lower Ep/Eacc around 2. The target accelerating gradient can be achieved if the surface peak electric field is equal to cERL. EUV end cells were designed to minimize HOM Q factor in the above condition. The optimal shape was designed by matching HOM frequencies of the two end cells and center cells calculated individually. The absorption heat of HOM damper is estimated to about 10 W. The AlN is planning to be used as HOM damper material because it has high RF absorption at 80 K. HOM damper shape has been designed by the data measured at 80K. The cryomodule has been designed to be suitable for CW operation by modifying those of STF type. In this workshop, RF design of the EUV cavity and cryomodule will be reported.
Suppression of the higher order modes (HOMs) is one of the most critical issues in an accelerator dealing with the intense bunches and the high beam repletion rate. In a superconducting (SC) machine like the LCLS-II, intense short bunches passing through SC cavities (1.3 GHz and 3.9 GHz 9-cell ), interconnecting cavity bellows and beam pipe transition at intermediate warm sections excites the broad-spectrum of the HOMs that extends up to terahertz. These high frequency modes (above cut-off) cannot be extracted by HOMs coupler effectively and therefore, they deposit a significant portion of their power at 2K after several reflections. This additional power deposited by HOMs not only increases operating cost of the SC machine but also enhances potential risk of cooper pair breaking due to excessive power dissipation at surface of the SC cavity that might eventually lead to a quench. In this paper we review HOMs effects in electron machine in framework of the LCLS-II SC linac. A study is performed to analyze power losses due to transient modes, probability of resonance excitation of HOMs and emittance dilution due to HOMs cumulative effects. Damping requirements of HOMs are outlined and an assessment for need of the beamline absorber is also discussed.
Higher Order Modes (HOM) excited by bunched electron beams in accelerating cavities carry information about the beam position and phase. This principle is used at the FLASH facility, at DESY, for beam position monitoring in 1.3 and 3.9 GHz cavities. Dipole modes, which depend on the beam offset, from the lowest order bands are used. Similar monitors are now under design for the European XFEL. In addition to beam position, the beam phase wrt accelerating RF will be also monitored using monopole modes from the first higher order monopole band. The HOM signals are available from two HOM couplers installed on each cavity. Their monitoring will allow the on-line tracking of the phase stability over time, and we anticipate that it will improve the stability of the facility. As part of the monitor designing, the HOM spectra in the 8 cavities of the 1.3 GHz cryo-module installed in the European XFEL injector have been measured. This paper will present their dependence on the beam position and charge. The variation in the modal distribution from cavity to cavity will be discussed. Based on the results, initial phase measurements based on a fast Tektronix oscilloscope are planned.
Superconducting cavities are used in particle accelerator machines to efficiently accelerate charged particles up to the desired energy. To characterize the resonator with respect to the interaction to moving particles the well-known concept of narrow-band impedances is used. A suitable method to determine the desired impedance is given by a proper eigenmode calculation of the given structure and a successive postprocessing of the available fields. While in the past the eigenmodes have been calculated for closed structures only, the consideration of coupling effects to the sources or to the dumps were completely neglected. In the last years sophisticated algorithms have been developed where the interaction of the resonator to the external devices can be incorporated into the system description. Analogous to frequency-domain solvers we apply the port boundary conditions straightaway into the original eigenvalue formulation without further postprocessing steps to enable the coupling. Unfortunately, this concept leads to large complex-valued systems with high numerical costs because a real-valued arithmetic is no longer useful. Since the port bondary conditions are frequency dependent, the underlying eigenvalue system is naturally nonlinear and proper eigenvalue solvers have to be applied. For large-scale applications, we implemented a complex-valued Jacobi-Davidson algorithm to extract one eigenvalue after the other starting from a given frequency target. In the presentation, the modeling of the open structures will be illustrated and real-life applications for TESLA-type resonators will be shown.
Superconducting radio frequency (SRF) cavities used for accelerating charged particle beams are commonly used in accelerator facilities around the world. The design and optimization of modern SRF cavities requires intensive numerical simulations. Vast number of operational parameters must be calculated to ensure appropriate functioning of the accelerating structures.
The increased demand for complicated simulations of SRF structures brought into focus a concatenation procedure that allows to speed up computations. The State-Space Concatenation (SSC) scheme makes use of model order reduction to speed up numerical simulations. It allows to break the long SRF structure into separate segments, proceed with relevant simulations for these segments and to perform the concatenation into a full structure at the end. Afterwards, vital parameters, like resonance frequencies, external quality factors, and geometrical longitudinal and transverse impedances, can be extracted for the modes of the full structure in the frequency range of interest.
In this study, we primarily focus on estimation and behavior of higher order modes (HOMs). In the elliptical cavities discussed in this work, used to accelerate electron beams, the HOMs have frequencies higher than the fundamental accelerating mode. Charged particle beams traversing such cavities lose part of their energy. The lost energy is manifested in form of electromagnetic resonant HOMs characteristic of a given cavity. Due to low intrinsic losses in SRF cavities the HOMs decay very slowly and interact destructively with the beam. Thus it is crucial to dampen HOMs to ensure beam stability.
The analysis of HOMs in large SRF structures is discussed on an example of a module of three 1.3 GHz cavities, being designed for the bERLinPro energy recovery linac. The second example used in this work is the planned upgrade to BESSY-VSR, where four new cavities will be installed. The new BESSY-VSR SRF cavities will be operating at two different accelerating frequencies of 1.5 GHz and 1.75 GHz. This gives a rare opportunity to investigate a chain of mixed cavities and their interaction.
The BESSY VSR project is a future upgrade of the 3th generation BESSY II light source. The key feature of the project is the simultaneous storage of long (ca. 15 ps) and short (ca. 1.7 ps) electron bunches under “standard” user optics. This challenging goal requires the installation
of SRF higher harmonic cavities of the fundamental 500MHz at two different frequencies.
Therefore four new SRF cavities (2x1.5 GHz and 2x1.75 GHz) are considered and currently are in the design stage. These cavities will operate in CW mode at high field level (E_acc =20 MV/m).
The combination of these factors with a high beam current (Ib =300 mA) make the cavity design a challenging goal, since stable operation must be ensured. Thus special attention must be paid to the damping of HOMs excited by the beam that may otherwise lead to coupled bunch
instabilities.
The technique for calculation of RF power propagation of HOMs excited by the circulating beam in SRF cavities will be presented. The method makes use of long range wakefield
simulations using the CST wakefield solver and an external post-processing of the port signals.
The calculations were performed for different bunch filling patterns of the BESSY VSR project.
The RF power of propagating HOMs is obtained by spectral weighting of port signals (single bunch) with bunch train spectrum. In this manner the cavity resonances excited by the periodic bunch pattern will be detected. The evaluation procedure is used for the calculation of the expected HOM powers (broadband) to be absorbed in the RF loads and of the efficiency of HOM dampers in terms of power flow balance between FPC, HOM waveguides and beampipes
supplied to the SRF cavities. Effects of geometry optimizations of the damping waveguides and the fundamental-power-coupler will be presented as well.
In this report we estimate the long- and the short-range wake functions at the third harmonic module of the European XFEL. The estimations are based on direct time-domain calculations with code ECHO. We use rotationally symmetric approximation of the geometry (without RF couplers). The complete cryomodule with 8 cavities including steps and bellows is considered.
The electromagnetic field distribution as well as the resonating frequency of various modes in cavities are very sensitive to small geometry deformations. We propose the application of Isogeometric Analysis (IGA) for the spatial discretization of the problem since IGA allows for the exact description of the domains and for a straightforward and convenient way of handling geometrical variations, [1].
The variations are given by measurements. A small number N of relevant and independent deformations can be extracted by using a truncated Karhunen–Loève expansion [2]. The random deformations are used in an uncertainty quantification workflow to determine the sensitivity of the higher order modes. For the propagation of uncertainty a stochastic collocation method based on sparse grids defined from numerically-generated orthogonal polynomials is employed. It requires the repeated solution of Maxwell's eigenvalue problem for the perturbed cavity with different realizations in the parameter space, e.g. $2^k N^k/k!$ evaluations in the Clenshaw-Curtis case, where $k$ is the polynomial degree and $N\gg1$ cf. [2].
This contribution focuses on the efficient solution of the repeated eigenvalue problems. We propose to create a homotopy between points in the parameter space and use a Newton-like approach [3] to solve the eigenvalue problem along the homotopy. This is can be efficiently parallelized while tracking the eigenpairs is still guaranteed.
[1] Jacopo Corno, Carlo de Falco, Herbert De Gersem und Sebastian Schöps. Isogeometric Simulation of Lorentz Detuning in Superconducting Accelerator Cavities. In: Computer Physics Communications 201 (Feb. 2016), S. 1–7. issn: 0096-3003. doi: 10.1016/j.cpc.2015.11.015.
[2] Dongbin Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, 2010.
[3] Dan Yang und Venkataramana Ajjarapu. Critical Eigenvalues Tracing for Power System Analysis via Continuation of Invariant Subspaces and Projected Arnoldi Method. In: IEEE Transactions on Power Systems 22.1 (Feb. 2007), S. 324–332. issn: 0885-8950. doi: 10.1109/TPWRS.2006.887966.
In the design study of future circular collider (FCC) a lepton collider (FCC-ee) is foreseen as a potential intermediate step toward building a 100 TeV pp-collider (FCC-hh). The lepton collider shall operate at four different energies in order to study the properties of Z, W, H and top quark with unprecedented precision. Based on the preliminary studies, a single cavity design that can serve all four setups is not feasible. The H and $\mathrm{t\overline{t}}$ are two demanding cases that require an RF system that can provide high accelerating voltage of up to 10 GV. In this talk we will present a cavity design considering the requirements of the different options.
Dielectrically lined waveguides are planned to be used as a passive wakefield dechirper for the electron beam at the ELBE facility of the Helmholtz-Zentrum Dresden Rossendorf. In this work we introduce the design of such a passive wakefield dechirper based on the analysis of dielectrically lined rectangular waveguides with a semi-analytical model developed at the University of Rostock. The model uses an eigenmode expansion of the electric field, which is possible since a closed analytic formulation for the eigenmodes of the dielectrically lined rectangular waveguide is available. The generality of the developed model allows for a quick calculation of the wakefields of numerous different beam types via the Green’s function method.
We also present the dechirped phase-spaces of a variety of beam distributions, as well as the theoretically possible dechirping for the ELBE beam. The author would like to thank the BMBF under contract number 05K13HR2 for funding.
For the design and the operation of particle accelerators, detailed knowledge about the electromagnetic behaviour of
the accelerating structures plays a crucial role. The electromagnetic fields are generally computed numerically by solving the
Helmholtz equation in a certain frequency interval of interest. A goal for the design is the damping of so-called Higher-Order
Modes (HOMs) which might lead to a deflection of the beam or a reduction of the beam quality. The damping of these HOMs
is enabled by certain coupler structures that couple the energy out of the resonator. These losses are denoted as external losses.
The computation of external losses generally leads to a nonlinear, complex-valued eigenvalue problem (NLEVP), in which
the boundary conditions at the waveguide ports depend on the eigenvalues. While this problem is solved straight forward for
small structures, the solution of this NLEVP for real-life applications with several millions of unknowns is generally solved
introducing some simplifications (e.g. linearisation). The effective solution of the full problem is currently an open question in
accelerator physics. The above mentioned simplifications can lead to large errors in the arising field-patterns and in the external
quality factors (up to several orders of magnitude). In this paper we present a method that can solve the full NLEVP for several
millions of unknowns on standard workstation computers and by this, compute the arising field pattern and external quality
factors precisely. To accomplish that, we will first perform a model-order reduction (MOR) for the closed and lossless structure.
For this reduced-order model, in a perturbation approach, a termination condition is defined such that no energy is reflected
back into the structure. The arising NLEVP can be solved by simple techniques like Newton-Iteration since the combination
with a suiting MOR keeps the systems size relatively small. An application example for the FLASH third harmonic module
is shown, where the solution of the NLVEP is compared to a commercial software as well as linearisation approach and
pole-fitting.
TESLA-type accelerating cavities installed at FLASH and the European XFEL are equipped with two higher order mode (HOM) couplers damping these modes in order to prevent beam breakup instabilities. The dipole mode signals from the HOM couplers can be used for beam based cavity alignment measurements since their excitation is proportional to the offset and kick of the transferring beam with respect to the cavity axis. The measurement procedure as well as the results for the accelerating modules installed at FLASH will be presented.
Part of the HiLumi LHC upgrade includes the use of superconducting Niobium crab cavities. The two proposed cavity designs are the Double Quarter Wave (DQW) and Radio Frequency Dipole (RFD). The DQW crab cavity will be tested in the Super Proton Synchrotron (SPS) at CERN in 2018. Both cavities require Higher Order Mode (HOM) couplers to prevent beam excited HOMs from perturbing the crabbing regime.
HOM couplers commonly have complex geometries which are often difficult to machine/manufacture. Small geometric errors which result from manufacturing processes can incur large offsets in the filter’s operation, meaning tight tolerances are often needed. In order to quantify that these tolerances have been adhered to, and hence that the designed operation of the filter has been met, test-boxes have been developed which are capable of providing broadband analysis of the HOM couplers.
The test-boxes have been designed to allow both the spectral analysis at low power but with the further possibility of allowing high power conditioning of the Niobium couplers before installation onto the cavities. Thus far the designs of both test boxes have been completed with construction and assembly currently taking place at both Lancaster University and CERN.
The control of the RF phase and amplitude in accelerating cavities is vital for the operation of superconducting accelerators. The beam phase is normally inferred from the beam induced accelerating mode. On the contrary, the beam phase can also be obtained from beam induced higher order modes by comparing to the fundamental mode. We present results of beam phase measurements carried out at the injector of the European XFEL based on a fast scope. The two methods will be compared.
A superconducting (SC) 1.4 GHz (4th harmonic) cavity is being developed for bunch lengthening in the Advanced Photon Source Upgrade. The cavity will be excited by the average 200 mA, 15.3 nC max, and ~50 ps long electron beams with the repetition rate of 13 – 88 MHz. Proper damping of higher order modes (HOM) in this cavity is an integral part of the development. A pair of the graphite-direct-sintered silicon carbide (SiC) HOM absorbers located outside the cryomodule are being developed. The silicon carbide HOM absorber assemblies were constructed and measurements of damping efficiency of the HOMs integrated with the cavity assembly were performed at room temperature. In addition, the cavity fundamental couplers are equipped with a ‘mode converting’ antenna for extraction of HOMs through the couplers transmission lines. The RF simulations, development, fabrication features, and room temperature measurement results will be discussed in this talk.
eRHIC SRF linac generates up to 7.8 kW of HOM power per 647 MHz 5-cell BNL4 cavity, presenting a big challenge for the machine design. A ridge waveguide is a natural high pass filter and has a smaller size than the regular waveguide. A HOM damping with combination of ridge wave-guide for low frequency HOM and two room temperature HOM damper (between cryomodules) for high frequency HOM was proposed to damp the high power, full spectrum HOM in eRHIC. The eRHIC SRF linac con-figuration and the results of ridge waveguide design will be presented. The prototype waveguide HOM damper and its measurement plan are de-scribed as well.
ALBA is a third generation synchrotron light source of 3GeV, located at 20km from Barcelona, Spain. To a user of synchrotron radiation, the beam lifetime and beams stability is one of the most important aspects of synchrotron light. A particularly attractive option for improving the lifetime and reduce beam instabilities is to lengthen the electron bunches using a harmonic cavity. This approach may be adopted to increase the beam lifetime at ALBA. In this presentation the results of the electromagnetic simulations of a temperature nose cone HOM damped cavity tuned at 1500 MHz (third harmonic) are presented.
Helmholtz-Zentrum Berlin (HZB) is currently designing and building a high average current all superconducting CW driven 50 MeV ERL as a prototype to demonstrate low normalized beam emittance of 1 mm·mrad at 100mA and short pulses of about 2 ps. In this contribution an update about the progress of the ERL's contruction is given, the different types of SRF cavities forming this accelerator are presented and the foreseen HOM damping concept is being reviewed. The design and production process of the two structures forming the injector, being a 1.4 cell SRF photoinjector cavity and three 2 cell Booster cavities will be shown, as well as latest horizontal acceptance tests at HZB and insights to the assem bly of the coldmass and cryo-module. For the Linac cavity the latest cavity and module design studies are being shown.
A 5 cell cavity was chosen for CEPC Preliminary Conceptual Design Report (pre-CDR) design. The higher order mode (HOM) power for each cavity is 3.6 kW. The waveguide couplers were chosen for HOMs damping. After the completion of pre-CDR, the CEPC study group starts to the conceptual design report (CDR). A 2 cell cavity design is chosen for CEPC partial double ring (PDR) scheme. The HOM power is calculated based on the beam parameters. To keep the beam stable, the thresholds for the longitudinal and transverse impedance are also given. In order to extract the higher order modes and reach the damping requirements for beam stability, the HOM coupler designing scheme is given.