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Since 2008, longitudinal coupled-bunch instabilities are suppressed at DELTA by a modulation of the phase of the accelerating RF field inside the cavity. To achieve a deeper understanding of the interaction of both effects, experimental studies have been made in 2016. These studies show a quadratic dependency of the coupled-bunch mode damping rates on the phase modulation amplitude. Recently, a numerical particle tracking code has been developed to confirm the experimental results. It is based on long range wake field effects produced inside an RF cavity acting on multi particle bunches of arbitrary charge, together with phase focusing by a phase modulated accelerating field. The numerical results confirm the quadratic dependency of damping rates on the phase shift obtained in experimental studies before., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

Closed-Orbit Bilinear-Exponential Analysis (COBEA) is an algorithm to decompose monitor-corrector response matrices into (scaled) beta optics values, phase advances, scaled dispersion and betatron tunes. No explicit magnetic lattice model is required for COBEA - only the sequence of monitors and correctors along the beam path (no lengths, no strengths approach). To obtain absolute beta values, the length of one drift space can be provided as optional input. In this work, the application of COBEA to the DELTA storage ring, operated by TU Dortmund University, is discussed, and its results for betatron tunes and scaled dispersion are compared with those of conventional, direct measurement methods. COBEA is also put in a historical perspective to other diagnostic algorithms. Improvements in the Python implementation of COBEA, which is available as free software, are presented. Due to COBEA being relatively modest regarding its requirements on input data respectively hardware, it should be applicable to the majority of existing storage rings., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

The slow orbit feedback at the electron storage ring at DELTA will be upgraded with new software. Finding a set of dipole-field-strength variations which minimize the deviation of the orbit from a reference orbit requires solving a convex optimization problem subject to inequality constraints. This work focuses on exploiting properties of a special type of interior point methods, which can solve this problem, for orbit correction at DELTA. After comparing runtimes of an interior point method to a Newton-like optimization algorithm, the performance of the new slow-orbit-feedback software is assessed based on measurement results., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

YACS is a 2.5D finite element method solver capable of solving for the full 3D eigenfrequency spectra of resonant axisymmetric structures while reducing the computational problem to a 2D rotation plane. The most recent revision of YACS now supports arbitrary order basis functions for the geometry and field discretization. In earlier revisions of YACS spurious modes were introduced by increasing the order of either the geometry or field basis functions. To prevent the emergence of spurious modes, YACS now matches the function spaces of the in-plane and out-plane function basis, and thus yields spurious free solutions. To demonstrate the capabilities of YACS, extensive cavity characterization studies on curved multicell microwave cavities are presented. Due to the combined utilization of the rotation symmetry, higher order basis functions and curved elements, eigenfrequency spectra above 10 GHz for L-band multicell structures can be easily obtained., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

YACS is a 2.5D finite element method solver capable of solving for the full 3D eigenfrequency spectra of resonant axisymmetric structures while reducing the computational problem to a 2D rotation plane. The most recent revision of the code introduced arbitrary order basis functions and curved meshes, for both triangular and quadrilateral unstructured meshes. This led to significant increases in convergence rates. However, due to the utilization of curved meshes and the complex coordinate transformations that are involved, spurious modes were introduced when solving the axisymmetric problem. Although workarounds do exist that circumvent these issues by lowering the likelihood and frequency of spurious modes, linear triangular meshes with higher order basis functions were chosen due to their simplicity and spurious free solutions. In order to support the usage of spline cavities as an alternative parameterization to the well known elliptical cavities, parameter space scans were carried out for non-reentrant spline cavities. In addition a new optimization strategy is presented that exploits the arbitrary polynomial order of Bézier curves by utilizing the degree elevation technique., Proceedings of the 8th Int. Particle Accelerator Conf., IPAC2017, Copenhagen, Denmark

YACS is a 2.5D finite element method solver capable of solving for the full 3D eigenfrequency spectra of resonant axisymmetric structures while reducing the computational problem to a 2D rotation plane. Prior studies and benchmarks, comparing YACS to well known commercial 3D and 2D applications, already demonstrated its capabilities of performing fast optimizations of geometries, due to its minimal computational overhead. However, because of the first order elements and basis functions used for approximation of the domain and field, this solving speed advantage vastly diminishes when targeting higher accuracies. In order to circumvent these issues, YACS was upgraded to support arbitrary order basis functions and curved meshes, leading to, but not limited to, isoparametric finite elements. This led to distinct performance and convergence improvements, especially when considering curved geometries, ideally representable by a polynomial mapping, e.g. when choosing a cavity geometry parametrization based on splines., Proceedings of the 7th Int. Particle Accelerator Conf., IPAC2016, Busan, Korea

Utilizing superconducting multicell rf cavities with fundamental frequencies of 1.5 GHz and 1.75 GHz and therefore modulating the rf gradient, the upcoming BESSY II upgrade BESSY VSR aims to provide both short and long electron bunches simultaneously. However, beam induced excitation of higher order modes (HOM) inside those superconducting cavities is a major concern for beam stability in a recirculating accelerator. Thus it is important to develop and apply proper HOM damping techniques. Current design considerations involve HOM coupler which usually introduce discontinuities in the cross section while also breaking the axisymmetry. To circumvent these issues we investigate in a layout with ring ferrites as an alternative or additional HOM damping technique. We also present an alternative superstructure setup that uses two instead of four cavities for VSR., Proceedings of the 7th Int. Particle Accelerator Conf., IPAC2016, Busan, Korea

Analyzing the interaction of RF phase modulation and coupled-bunch instabilities requires a method to determine damping rates of coupled-bunch modes at presence of RF phase modulation. This paper shows, that the common way of using exponential fits to determine damping rates is not viable for high modulation amplitudes. It presents a new method, which is capable of acquiring damping rates of coupled-bunch modes for phase shifts up to 5°, using a bunch-by-bunch feedback system. For this purpose a specific mode is excited by the feedback system and the saturation value, i.e. the maximum excitation, is measured to calculate the damping rate. With this new method, the modulation amplitude of the RF phase modulation is swept from 0° to 5° and it can be shown, that the damping rate is proportional to the square of the modulation amplitude., Proceedings of the 7th Int. Particle Accelerator Conf., IPAC2016, Busan, Korea

Most feasibility studies for modern accelerator concepts, including superconducting multicell RF-cavity-resonators in circular accelerators, depend on computing a large number of eigenmode frequencies and field patterns to obtain typical figures of merit. This task includes computational intensive numerical studies. To obtain the full eigenfrequency spectra most of these studies are performed in 3D, require a great amount of computation resources and thus are limited to a few hundred or thousand eigenmodes. To overcome this issue, some codes make use of the axisymmetric geometry of most of the RF-cavity-resonator structures and solve the problem in 2D. Solving in 2D however reduces the eigenmode spectra to eigenmodes with no azimuthal dependencies (so called monopole-modes). Due to the lack of freely available and easy to use 2.5D eigenmode solvers which are able to solve for the full 3D field in a reduced 2.5 dimensional problem, we developed yet another cavity solver (Yacs), a simple FEM based solver capable of solving for the full 3D eigenmodes of axisymmetric problems while only requiring a fraction of the computation resources required by most modern 3D codes., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

The upcoming upgrade of BESSY II, called BESSY-VSR*, involves the utilization of superconducting multicell RF-resonators with high accelerating gradients to provide short and long bunches in an electron storage ring simultaneously. Even under the assumption of strongest available damping of beam induced modes, the residual impedances of the cavities may cause collective multibunch instabilities at the frontier of stability available from current bunch-by-bunch feedback systems. At the DELTA electron storage ring, a phase modulation of the driving RF is used to suppress coupled-bunch instabilities and to increase the lifetime. The time dependent frequency variation in the order of the synchrotron frequency gives rise to additional damping of the bunch oscillators by decoherence and Landau damping. The behaviour and the additional damping of the bunch oscillators is investigated by the existing bunch-by-bunch feedback system e.g. the increase of the overall damping might support the capability of feedback systems under extreme operating conditions of BESSY-VSR., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Closed-orbit perturbations and oscillating beam solutions in storage rings are closely related. While techniques exist to fit accelerator models to closed-orbit perturbations or to oscillation data, the exploitation of their relation has been limited. In this work, two orbit theorems that allow an efficient computation of optical parameters in storage rings with older hardware are derived for coupled linear beam motion. The monitor theorem is based on an uncoupled case study described by the author in an earlier work and has been generalized as well as simplified in mathematical abstraction to provide a reliable and computationally stable framework for beam optics measurements. It is based on a closed-orbit measurement utilizing 4 dipole correctors (2 for each plane). The corrector theorem allows to obtain parameters of these dipole correctors using two turn-by-turn monitors at almost arbitrary positions in the ring (which do not need to be located in a drift space), so that it is possible to uniquely resolve closed orbits into optical parameters without sophisticated lattice models., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Higher order mode (HOM) propagation and damping is a major concern in feasibility studies regarding the upcoming upgrade of BESSY II, named BESSY-VSR*, which involves the utilization of superconducting multicell RF-resonators in a storage ring while maintaining a reasonably high beam current typical for third generation synchrotron radiation facilities. In addition to the computation of the typical figures of merit, we focus on studies of the mode propagation in axisymmetric structures. Due to the focus on axisymmetric studies we are able to use 2D codes to investigate in eigenmodes with substantial higher frequencies than usually considered with full 3D codes in parametric studies. In this work we present preliminary studies involving mode propagation in superconducting elliptical multicell cavities., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Modern accelerator concepts for high intensity electron beams often require superconducting multicell RF-cavity-resonators in circular accelerators (e.g. storage rings). Caused by strong beam-cavity interaction and due to high quality factors of superconducting RF-structures special care of lower order (LOM) and higher order (HOM) modes must be taken. Various numerical studies were performed to numerically calculate the dependence of different figures of merit (e.g. external quality factors Qext) with respect to the geometry parameters and cell number of the RF-structure, focused on the propagation and damping of low and higher order modes. To ease the numerical effort an optimization routine has been developed which automatically optimizes the geometry based on goal functions. In this context it turned out that cell geometries defined by spline functions have advantages compared to the standard elliptical parametrization regularly used. The number of free parameters is substantially reduced which facilitates the search for optimum solutions., Proceedings of the 5th Int. Particle Accelerator Conf., IPAC2014, Dresden, Germany