Resistive Wall Wakefield Research Articles

Advanced Studies for the Dynamics of High Brightness Electron Beams with the Code MILES

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.

Estimated heat load and proposed cooling system in the FCC-ee interaction region

We discuss the beam power loss related to the heating of the beam pipe walls of the FCC-ee interaction region. We analyse the excitation of trapped modes, which can accumulate electromagnetic energy and determine the locations of these modes. We study the unavoidable resistive-wall wake field, which is responsible for the direct beam pipe walls heating. We show the distribution of the heat load along the central part of the interaction region. We also present the cooling system design and results for temperature distribution in interaction region in the operational mode.

Impedance computation of cryogenic vacuum chambers using boundary element method

A two-dimensional boundary element method for calculating the impedance of infinitely long cryogenic vacuum chambers of general cross section is presented. The formulation is based on combining Kirchhoff's boundary integral representation of an electromagnetic field with the surface impedance boundary condition for the anomalous skin effect, which can occur in metals at cryogenic temperature. As a result, the electromagnetic field in the chamber is expressed as a superposition of the direct and indirect space charge fields and resistive-wall wakefield. This feature allows us to compute the corresponding three impedance contributions separately. This method does not assume a specific transverse charge density such as uniform and Gaussian distributions as well as the ultrarelativistic approximation. A technique for computing the impedances and the form factors in the method is also described. The presented method is applied to circular, rectangular, elliptical, and racetrack-type vacuum chambers. The geometric effect of the cryogenic vacuum chamber cross section on the resistive-wall impedance is shown. The effect of beam velocity is demonstrated for the racetrack-type cryogenic vacuum chamber.

Measurement of undulator section wakefield at the SXFEL test facility

In free electron laser facilities, almost every kind of device will generate wakefield when an electron beam passes through it. Most of the wakefields are undesired and have a negative effect on the electron beam, which means a decrease of FEL performance. As for the SXFEL test facility, the sophisticated layout and the cumulative effect of such a long undulator section lead to an obvious wakefield, which is strong enough that cannot be ignored. Based on two deflecting cavities at the entrance and the exit of the undulator section with corresponding profile monitors, we measured the wakefield of the undulator section. In this paper, we give the theoretical and simulation results of resistive wall wakefields which agrees well with each other. In addition, the experimental and the simulation results of the overall undulator wakefield are given showing small difference. In order to explore the impact of this wakefield on FEL lasing, we give the simulation results of FEL with and without wakefield for comparison. There is almost no impact on 44 nm FEL in stage-1 of cascaded EEHG–HGHG mode, while the impact on 8.8 nm FEL in stage-2 becomes critical and it decreases the pulse energy and peak power by 42% and 27% and broadens the bandwidth.

Multi-Bunch Resistive Wall Wake Field Tracking via Pseudomodes in the ALS-U Accumulator Ring

Multi-Bunch Resistive Wall Wake Field Tracking via Pseudomodes in the ALS-U Accumulator Ring

Power losses caused by longitudinal HOMs in 1.3-GHz cryomodule of SHINE

Shanghai high-repetition-rate XFEL and extreme light facility (SHINE), the first hard XFEL based on a superconducting accelerated structure in China, is now under development at the Shanghai Institute of Applied Physics, Chinese Academy of Sciences. In this paper, power losses caused by trapped longitudinal high-order modes (HOM), steady-state loss, and transient loss generated by untrapped HOMs in the 1.3-GHz SHINE cryomodule are investigated and calculated. The heat load generated by resistive wall wakefields is considered as well. Results are presented for power losses of every element in the 1.3-GHz cryomodule, caused by HOM excitation in the acceleration RF system of the continuous-wave linac of SHINE.

Wakefield benchmarking at a single-pass high brightness electron linac

Collective effects such as wakefields affect the dynamics of high brightness electron beams in linear accelerators (linacs) and can degrade the performance of short wavelength free-electron lasers (FELs). If a reliable model of wakefields is made available, the accelerator can be designed and configured with parameters that minimize their disrupting effect. In this paper, the simulated effect of geometric (diffractive) wakefields and of coherent synchrotron radiation on the electron beam energy distribution at the FERMI FEL is benchmarked with measurements, so quantifying the accuracy of the model. Wakefield modeling is then extended to the undulator line, where particle tracking confirms the limited impact of the resistive wall wakefield on the lasing process. The study reveals an overall good understanding of collective effects in the facility.

RF surface resistance study of non-evaporable getter coatings

In many particle accelerators the beam parameters could be affected by the beam pipe wakefield impedance. It is vital to understand how the wakefield impedance might vary due to various coatings on the surface of the vacuum chamber, and this can be derived from surface resistance measurements. The bulk conductivity of two types of NEG films (dense and columnar) is determined. This is achieved by measuring the surface resistance of NEG-coated samples using an RF test cavity and fitting the experimental data to a standard theoretical model. The conductivity values obtained are then used to compare resistive wall wakefield effects in beam pipes coated with either of the two types of film.

Broadband SIBC Formulation for a Low-Dispersion Finite Volume Method in the Time Domain

Surface impedance boundary conditions for the computation of resistive wall wakefields in linear accelerators are developed. The method represents an extension of the staggered finite volume method in the time domain (SFVTD) for the discretization of Maxwell’s equations. It uses an auxiliary differential equation formulation for general impedance functions describing the frequency-dependent wall conductivity, surface roughness, or metal oxidation. For the time discretization of the resulting dispersive equations, a particular technique based on exponential integration is employed. This allows us to preserve the basic properties of the SFVTD method such as unidirectionally optimal numerical dispersion and maximum stability bound, which are of crucial importance for electromagnetic wakefield computations.

Resistive wall wakefields of short bunches at cryogenic temperatures

In this study, we present calculations of the longitudinal wakefields at cryogenic temperatures for extremely short bunches, characteristic for modern x-ray free electron lasers. The calculations are based on the equations for the surface impedance in the regime of the anomalous skin effect in metals. This paper extends and complements an earlier analysis of B. Podobedov, Phys. Rev. ST Accel. Beams 12, 044401 (2009). into the region of very high frequencies associated with bunch lengths in the micron range. We study in detail the case of a rectangular bunch distribution for parameters of interest of LCLS-II with a superconducting undulator.

Resistive wall instability in rapid Cycling synchrotron of China spallation neutron source

China Spallation Neutron Source (CSNS) is a high intensity proton accelerator based facility, and its accelerator complex includes two main parts: an H- linac and a rapid cycling synchrotron (RCS). The RCS accumulates the 80MeV proton beam, and accelerates it to 1.6GeV, with a repetition rate of 25Hz. The 1.6GeV beam is fast extracted for striking the neutron target with average beam power of 100kW. The collective effect caused by the coupling impedance is one of the serious issues which limit the highest beam power. The impedance estimation of RCS components showed that the resistive wall impedance and its instability are serious. Based on the estimated impedance, the resistive wall instability growth time is theoretically calculated. In order to confirm the analytical results of resistive wall instability, a simplified resistive wall wake field model is used to track the bunch oscillation, and the growth time of resistive wall instability is obtained. In this model, the continuous resistive wall wake field is expressed as an equivalent wake field of one point in the ring, and the long bunch is sliced into many slices longitudinally. By tracking the dynamics of the slices, transverse growth time is obtained. The simulation results with constant energy agree well with the analytical results. The studies of energy ramping process show that if the damping effect of the chromaticity is not considered, the growth time of resistive wall instability is faster than the period of an RCS cycle, and the damping effect of chromaticity will play a key role in suppressing the instability.

Transverse modes and instabilities of a bunched beam with space charge and resistive wall impedance

Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge tune shift, and resistive wall wakefield taken into account. A boxcar model is used for a general analysis, and truncated Gaussian distribution is invoked for details. The beam spectrum, instability growth rate, and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Influence of internal bunch oscillations on the collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, and the instability thresholds of different modes of truncated Gaussian bunch are estimated.

Parameter Optimizations and Performances for the Low-Charge Beams in PAL Free-Electron Laser

We investigated optimum choices of beam and accelerator parameters for low-charge beams of self-amplified spontaneous emission (SASE) free-electron laser (FEL) at PAL. The FEL system is designed to provide a short pulse beam to generate the high power of the wavelength of 1-Å in the undulator. The designed linac provides the pulses of 10 fs rms and 3.85 fs rms for the charges of 0.2 nC and 0.02 nC, respectively. Parameters of the two-stage bunch compressors are optimized to reduce the effects of coherent synchrotron radiation. The bunch compressors are also designed such that the effects of nonlinearities due to wakefields, rf curvature, and second-order momentum compaction become as small as possible in the linear accelerator. Through these parameter optimizations, we have minimized the bunch charges that could decrease effects of emittance dilution and growth of energy spread, which may deteriorate the SASE performance. Start-to-end tracking simulations include the longitudinal and transverse wakefields, and the effects of errors such as rf gun timing, rf phase, and rf voltage are investigated. We investigated the effectiveness of a laser heater that may give Landau damping to suppress the microbunching beam instability. It is shown that a laser heater may suppress the microbunching beam instability in the FEL system. We also investigated the effects of the ac and dc resistive wall wakefields in a long undulator. It is shown that energy variations induced within the bunch over the length of the undulator are acceptable. As a result, through these optimizations studies, we could get beam parameters and accelerator parameters that can provide the FEL power of the 60 GW with FEL pulse of 10 fs and 3 fs in the wavelength of 1-Å in around a 50-m-long undulator for the charges of 0.2 nC and 0.02 nC, respectively. It is shown by our optimizations that our designed FEL system shows required performances for the low-charge beams in the 10 GeV.

The effect of NEG coating on resistive wall wake field

The procedure for calculating the resistive wall impedance is simplified using Gaussian elimination with a sufficiently large floating point precision. This procedure generalises readily to the multilayer beam pipe wall. We apply this to investigate the effect of NEG coating on the transverse wake field coupling between electron bunches in the ILC damping ring. For a 5 GeV electron beam and 3 cm radius aluminium beam pipe, a 1 μm thick NEG coating is found to increase the impedance around 10 GHz. The wake field over a distance of 300 km around the ring is required for the study of the multi-bunch instabilities. This has to be obtained by Fourier transforming over a very wide range of frequencies. To overcome the computation problem, we developed a way of splitting up the frequencies into three overlapping ranges, and then joining the transforms together to obtain the overall wake field. The results for a few NEG coating thicknesses are presented. ► A simplified procedure for calculating the resistive wall impedance is described. ► This procedure generalises readily to the multilayer beam pipe wall. ► We use this to study the effect of NEG coating on the wake field in the ILC damping ring.

Transient jitter from injection in storage rings

Injection of fresh bunches into a storage ring can induce jitter in the stored bunches. For machines demanding beams of very low emittance and high stability, such as the damping rings of a future linear collider or the storage rings of a super flavor factory, this could be a potential performance limitation. We present an analysis, for the International Linear Collider (ILC) damping rings, of the transverse jitter induced on the extracted bunches from the jitter on the injected bunches, with the coupling between bunches mediated by the resistive-wall wakefield of the vacuum chamber. We find that it is important to include details of the local transverse focusing around the ring. We consider the impact of the finite thickness of the beam pipe wall, and of nonevaporable getter coating on the inside surface: in the parameter regime of the ILC damping rings, we find that the results are only slightly modified compared to an approximation to the resistive-wall wakefield based on a single-layer wall of infinite thickness. The results from our simulations indicate a tight specification on the jitter of the injected bunches.

Resistive wall wakefields in the extreme anomalous skin effect regime

Usual treatments of resistive wall effects in accelerators are limited to the normal skin effect regime of electrical conductivity in metals. Therefore they do not generally apply to the situations when beam-exposed metallic surfaces of the vacuum chamber are held at cryogenic temperatures, where simple metals exhibit anomalous skin effect behavior. These situations occasionally occur in accelerators with cold-bore devices, such as small-gap superconducting undulators. The amount of anomalous resistivity material can be substantial to significantly influence beam dynamics. To accurately estimate these effects, we expand the conventional treatment of resistive wall in accelerators into the extreme anomalous skin effect region. Starting with the surface impedance expressions, we derive resistive wall related quantities commonly used in accelerator physics, such as wake functions, wake potentials, loss factor, etc. in the extreme anomalous skin effect region. We follow with examples for resistive wall generated heat and transverse mode-coupling instability.

Chromaticity and wakefield effect on the transverse motion of longitudinal bunch slices in the Fermilab Tevatron

The transverse turn-by-turn evolution of a bunch slice after an impulse kick is examined considering chromatic and impedance effects. It is found that by fitting the envelope of the beam slice motion to simulated data the strength of the resistive wall wakefield can be determined.

Time evolution of coupled-bunch modes from beta function variation in storage rings

We present an analytical and numerical study of the equations of motion for bunches coupled by transverse wakefields. We base our study on a recent lattice design for the damping rings in the baseline configuration of the International Linear Collider. Using the macroparticle model, and assuming resistive wall wakefield coupling, we present numerical results on the time evolution of the multibunch modes. Decay modes display growth after initial decay, and mode amplitudes exhibit high-frequency oscillations. These phenomena are not expected if the beta function is assumed to have a constant, averaged value. We show analytically that they can come from coupling between modes caused by variation of the beta function in a real lattice. The effect is shown to be comparable to the effect of a nonuniform fill pattern and significantly larger than that of the higher-order mode wakefield localized in the rf cavities. Turning to the case of constant beta function, we develop a more complete treatment of the equations of motion. We derive general formulas for the bunch trajectories, and show that such formulas can only be valid in the limit of small wakefield coupling.

Resistive-wall wake and impedance for nonultrarelativistic beams

The usual formulas for the resistive-wall wake field are derived considering ultrarelativistic beams, traveling at the speed of light. This simplifies the calculation, and it leads to a cancellation between electric and magnetic fields. However, for proton beams below 10 GeV and for many heavy-ion beams, the velocities may significantly differ from the speed of light. In this paper, we compute the longitudinal and transverse wake fields for velocities smaller than $c$ and examine under which conditions nonrelativistic effects become important. We illustrate our results by a few examples.