Transverse Coupling Impedance Research Articles

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.

Coupling impedance of a PEC angular strip in a vacuum pipe

This study deals with the evaluation of the longitudinal and transverse coupling impedance of a charge travelling in a drift tube with a perfectly electric conductive angular strip. The problem is formulated in the particle frame as dual series equations, and efficiently solved through the representation of the unknown in terms of Neumann series. Then, the electric parameters are obtained in the pipe frame through the Lorentz transforms. The presented solution can be adopted as the general methodology in case of angular discontinuities in particle accelerators.

Method for computing driving and detuning beam coupling impedances of an asymmetric cavity using eigenmode simulations

We propose a method for numerical calculation of driving and detuning transverse beam coupling impedances of an asymmetric cavity. The method relies on eigenmode simulations and can be viewed as an alternative to time domain wakefield simulations. A similar procedure is well-established for symmetric cavities, and this paper extends it to the case of an asymmetric cavity. The method is benchmarked with time-domain wakefield simulations and its practical implementation is discussed.

Model for the Evaluation of an Angular Slot’s Coupling Impedance

In high energy particle accelerators, a careful modeling of the electromagnetic interaction between the particle beam and the structure is essential to ensure the performance of the experiments. Particular interest arises in the presence of angular discontinuities of the structure, due to the asymmetrical behavior. In this case, semi-analytical models allow one to reduce the computational effort and to better understand the physics of the phenomena, with respect to purely numerical models. In the paper, a model for analyzing the electromagnetic interaction between a traveling charge particle and a perfectly conducting angular slot of a negligible thickness is discussed. The particle travels at a constant velocity along a straight line parallel to the axis of symmetry of the strip. The longitudinal and transverse coupling impedances are therefore evaluated for a wide range of parameters.

Local transverse coupling impedance measurements in a synchrotron light source from turn-by-turn acquisitions

Transverse beam coupling impedance is a source of beam instabilities that limits the machine performance in circular accelerators. Several beam based techniques have been used to measure the transverse impedance of an accelerator, usually based on the optics distortion produced by the impedance source itself. Beam position monitor turn-by-turn analysis for impedance characterization has been usually employed in large circumference machines, while synchrotron light sources have mainly used slow orbit based techniques. Instead, the work presented in this paper uses for the first time turn-by-turn data at ALBA to advance the measurement technique into the range of the typically small impedance values of modern light sources. We have measured local impedance contributions through the observation of phase advance versus bunch charge using the betatron oscillations excited with a fast dipole kicker. The ALBA beam position monitor system and the precision of the turn-by-turn analysis allowed to characterize the main sources of transverse impedance, in good agreement with the model values, including the impedance of an in-vacuum undulator.

Transverse beam coupling impedance of the CERN Proton Synchrotron

Beam coupling impedance is a fundamental parameter to characterize the electromagnetic interaction of a particle beam with the surrounding environment. Synchrotron machine performances are critically affected by instabilities and collective effects triggered by beam coupling impedance. In particular, transverse beam coupling impedance is expected to impact beam dynamics of the CERN Proton Synchrotron (PS), since a significant increase in beam intensity is foreseen within the framework of the LHC Injectors Upgrade (LIU) project. In this paper we describe the study of the transverse beam coupling impedance of the PS, taking into account the main sources of geometrical impedance and the contribution of indirect space charge at different energies. The total machine impedance budget, determined from beam-based dedicated machine measurement sessions, is also discussed and compared with the theoretical model.

Mode error analysis of impedance measurement using twin wires**Supported by Natural Science Foundation of China (11175193, 11275221)

Both longitudinal and transverse coupling impedance for some critical components need to be measured for accelerator design. The twin wires method is widely used to measure longitudinal and transverse impedance on the bench. A mode error is induced when the twin wires method is used with a two-port network analyzer. Here, the mode error is analyzed theoretically and an example analysis is given. Moreover, the mode error in the measurement is a few percent when a hybrid with no less than 25 dB isolation and a splitter with no less than 20 dB magnitude error are used.

Beam breakup instability suppression in multicell superconducting rf guns

Helmholtz-Zentrum, Berlin, Germany(Received 28 November 2009; revised manuscript received 28 November 2010; published 19 May 2011)In this paper, we provide an analytical description for transverse coupling impedances with dipole highorder modes (HOMs) and beam breakup (BBU) instability suppression of relativistic, high-current beamsundergoing strong acceleration, such as those typically produced by rf photoinjectors. The model adoptedis based on the accepted theory of coupling impedances extended to the case of beams characterized by afast transition due to strong acceleration, from the nonrelativistic to the relativistic regime in whicha bunch trajectory may not be rigidly directed parallel to the axis of the electric field. The trajectoryoscillations in a dipole HOM field in the transverse plane are effective in perturbing the bunch energy,which causes an increase of the coupling impedance up to the BBU instability. This BBU instabilityanalysis is based on equations obtained by Volkov [Phys. Rev. ST Accel. Beams 12, 011301 (2009)]inwhich external focusing due to both the applied transverse electric (TE) HOM and the acceleratingfundamental mode as well as dipole HOM damping by external loads are investigated. This analysis isvalid in the limit in which the weak nonlinearity of applied fields near the axis may be neglected. Thesolution suggests a means of enhancing the BBU threshold current. The possibility of obtaining BBUinstability suppression in a long, integrated photoinjector and linac structure, such as the superconductingrf source at Forschungs Zentrum Dresden (FZD), are numerically examined. New designs of photo-injectors that provide BBU instability suppression of all dipole HOMs to enhance the threshold currentsare suggested.

Design, test, and operation of new tapered stripline injection kickers for thee+e−colliderDAΦNE

For the injection upgrade of the $\ensuremath{\Phi}$ factory $\mathrm{DA}\ensuremath{\Phi}\mathrm{NE}$, new fast stripline kickers have been designed. They can operate with very short pulse generators to perturb only the injected bunch and the two stored adjacent ones. The design is based on tapering the striplines to simultaneously obtain low beam coupling and transfer impedances, excellent uniformity of the deflecting field, and better matching between the strip and the pulse generators. It has been done using 2D and 3D electromagnetic codes (Superfish and HFSS). The kickers have been constructed, tested, and installed in the collider. Measurements of the reflection coefficient at input ports and of the longitudinal and transverse beam coupling impedance have been also performed to characterize the structure and have been compared to the simulation results. A circuital model of general tapered striplines for a first order estimation of the transfer and longitudinal beam coupling impedances is also presented. Finally operational performances are described, pointing out the problems which occurred and the flexibility of the stripline structures that worked with both the short and with the previously installed long pulse generators and have been used as an additional damping kicker to improve the efficiency of the horizontal multibunch feedback system. This system is also a demonstration of the operation of fast kickers with similar characteristics as those for the International Linear Collider (ILC) damping rings (DRs).

Matrix solution for the wall impedance of infinitely long multilayer circular beam tubes

The coupling impedance of beam tubes is a long-standing important topic for particle accelerators that many authors have addressed. The present study was initiated in view of a specific problem, but its novel approach is broadly applicable to the longitudinal and transverse coupling impedances of coated beam tubes or multilayer tubes. The matrix method presented here derives the wall impedance by treating the radial wave propagation of the beam-excited electromagnetic fields in full analogy to longitudinal transmission lines. Starting from the Maxwell equations, the radially transverse magnetic field components are described for monopole and dipole modes by a $2\ifmmode\times\else\texttimes\fi{}2$ matrix. Assuming isotropic material properties within one layer, the transverse field components at the inner boundary of a layer uniquely are determined by matrix transfer of the field components at its outer boundary. By imposing power-flow constraints on the matrix, wave impedance mapping and field matching between layers is enforced and replaced by matrix multiplication. The longitudinal and transverse coupling impedances are derived from the wall impedance at the innermost boundary, and the different procedures for its determination are discussed. The matrix method is demonstrated via selected yet representative examples of the well-documented cases of a stainless-steel tube, and of a graphite collimator.

Numerical calculation of transverse coupling impedances: Comparison to Spallation Neutron Source extraction kicker measurements

The study of beam dynamics and the localization of potential sources of instabilities are important tasks in the design of modern, high-intensity particle accelerators. In the case of synchrotrons and storage rings, coupling impedance data are needed to characterize the parasitic interaction of critical components with the beam. In this article we demonstrate the application of numerical field simulations to the computation of transverse kicker coupling impedances. Based on the 3D simulation results, a parametrized model is developed to incorporate the impedance of an arbitrary pulse-forming network attached to the kicker. Detailed comparisons of numerical results with twin-wire and direct measurements are discussed at the example of the Spallation Neutron Source extraction kicker.

Transverse coupling impedance of the storage ring at the European Synchrotron Radiation Facility

The vertical and horizontal impedance budgets of the European Synchrotron Radiation Facility (ESRF) storage ring are calculated by element-by-element wake potential calculation. Resistive wall wakes are calculated analytically; the short range geometrical wakes are calculated by a 3D electromagnetic field solver. The effect of the quadrupolar wakes due to the flatness of most ESRF vacuum chambers is included in the model. It can well explain the sensitivity of the horizontal single bunch threshold on vacuum chamber changes, in particular, in low-gap sections of the ESRF storage ring. The values of the current thresholds on the transverse planes could be predicted correctly by the model within a factor of 2.

Coupling impedances of small discontinuities: Dependence on beam velocity

The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated [e.g., S.S. Kurennoy, R.L. Gluckstern, and G.V. Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using the Bethe diffraction theory. Here we extend the results to an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along the beam path, cross section. The longitudinal and transverse coupling impedances are derived in terms of series over cross-section eigenfunctions, while the discontinuity shape enters via its polarizabilities. Simple explicit formulas for two important particular cases - circular and rectangular chamber cross sections - are presented. The impedance dependence on the beam velocity exhibits some unusual features: for example, the reactive impedance, which dominates in the ultrarelativistic limit, can vanish at a certain beam velocity, or its magnitude can exceed the ultrarelativistic value many times. In addition, we demonstrate that the same technique, the field expansion into a series of cross-section eigenfunctions, is convenient for calculating the space-charge impedance of uniform beam pipes with arbitrary cross section.

Coupling impedance of a charge traveling in a drift tube

This paper deals with the evaluation of the longitudinal and transverse coupling impedance of a charge traveling in a drift tube. An effective procedure has been set up leading to accurate results upon application of the Galerkin method.

Impedance measurements of the Spallation Neutron Source extraction kicker system

Transverse coupling impedance measurements of the Spallation Neutron Source (SNS) beam extraction system were performed and the results are here reported. The SNS beam extraction system is composed from 14 subsystems, each of which consists of a vertical kicker magnet plus a pulse forming network (PFN). Impedance bench measurements were performed on one large and one small aperture magnet, stand-alone as well as assembled with the first-article production PFN. The impedance measuring methods to cover the interesting frequency range from below 1 to 100 MHz are described in considerable detail. The upper frequency range is properly covered by the conventional twin-wire method but it had to be supplemented at the low-frequency end by a direct input impedance measurement at the magnet busbar. Required modifications of the PFN to maintain the impedance budget are discussed. The total impedance estimate was finally obtained by quadratic scaling with vertical aperture from the two tested kicker subsystems.

Measurement of local impedance by an orbit bump method

A new method of local transverse coupling impedance measurement has been developed to estimate the impedance distribution along a storage ring. The method is based on measurement of the closed orbit deviation caused by the wake field generated at the impedance location by the off-axis beam. This method provides better accuracy than the known method based on betatron phase advance measurement, because the beam position monitors operate in narrow-band (orbit) mode, but not in wide-band (turn-by-turn) mode used for phase advance measurement. The physical principles and limitations of the method are described using both analytical formulae and computer simulation.

Coupling impedance measurements of a model fast extraction kicker magnet for the SNS accumulator ring

Both longitudinal and transverse coupling impedance of a fast extraction kicker magnet has been measured for the design and development of beam extraction in the Spallation Neutron Source accumulator ring. The conventional wire method with improved techniques is employed in the bench test. The experimental result is explained by and compared with a newly developed resonant circuit model. The impact of the measurement on the fast extraction kicker magnet design is discussed.

Improved analytical model of the transverse coupling impedance of ferrite kicker magnets

A transformer model of ferrite kicker magnets is presented in this paper. Based on this model, an equivalent circuit is derived for which the elements can be obtained by bench measurements or by estimates from the magnet geometry. Improved formulas for the transverse coupling impedance of lumped and traveling wave kicker magnets are derived from the model and the equivalent circuit. The formulas differ from the corresponding handbook results in their dependence on the external termination or aperture aspect, respectively. The effect of ferrite properties on the transverse coupling impedance is analyzed. The model was confirmed by bench measurements with the twin-wire technique made on the full-size and half-size prototypes of the extraction kicker of the SNS accumulator ring. The application of this model to the design of the kickers allowed a significant reduction of the SNS transverse coupling impedance budget.

Beam coupling impedances for perforated beam pipes with general shape from impedance boundary conditions.

An equivalent wall impedance to describe the electromagnetic boundary conditions at perforated pipe walls is introduced. The new impedance boundary condition, together with general formulas for computing longitudinal and transverse beam coupling impedances in complex heterogeneous pipes, provides a good trade-off between computational accuracy and ease.