Wakefield Calculations Research Articles

A simple, flexible technique for RF cavity wake-field calculations

It is typical in the accelerator field to model machine components, especially RF cavities, as parallel RLC resonators. To properly model wake-fields, knowledge of the time-domain voltage resulting from beam excitation is often necessary. While analytical and quasi-analytical expressions are available to accomplish this for common bunch distributions such as the Gaussian, analogous results for less standard distributions can be difficult or computationally-taxing to obtain using direct methods, which opens the door for the development of a more generalized technique. In this paper, a formulation is created that allows for the simple computation of the time-domain voltage waveform of an RLC resonator. The formulation uses the Cauchy Residue Theorem to extract the convolution result from the Fourier Domain, and if current distribution Fourier Transform has no poles, knowledge of its value is only required at one specific evaluation point. This greatly simplifies the computation of the time domain voltage for a large amount of bunch distributions both common and uncommon. Accuracy considerations for this technique and the approximation of accelerator components as RLC resonators are also discussed, resulting the development of a figure of merit for quantifying the robustness of this type of approximation.

Traveling wave method for simulating geometric beam coupling impedance of a beam screen with pumping holes

In particle accelerators, pumping holes in a vacuum chamber can be a source of unwanted broadband coupling impedance, leading to beam instabilities. Analytical methods have been previously developed to estimate the impedance of holes in circular-like chambers e.g. the beamscreen of the Large Hadron Collider (LHC). More sophisticated chamber designs like that of the High Energy LHC (HE-LHC) and the Future Circular Collider (FCC-hh) call for a different way to calculate the impedance. We propose using decomposition of the wakefield into synchronous traveling waves and employing a numerical solver to find the impedance of each wave. This method is compared to the direct time domain wakefield calculation method and its greater sensitivity to small impedances is shown.

Short-range wakefields generated in the blowout regime of plasma-wakefield acceleration

In the past, calculation of wakefields generated by an electron bunch propagating in a plasma has been carried out in linear approximation, where the plasma perturbation can be assumed small and plasma equations of motion linearized. This approximation breaks down in the blowout regime where a high-density electron driver expels plasma electrons from its path and creates a cavity void of electrons in its wake. In this paper, we develop a technique that allows to calculate short-range longitudinal and transverse wakes generated by a witness bunch being accelerated inside the cavity. Our results can be used for studies of the beam loading and the hosing instability of the witness bunch in PWFA and LWFA.

Calculation of wakefields in 2D rectangular structures

We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross-section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code ECHO(2D). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Numerical examples obtained with the new numerical code are presented.

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.

First non-intercepting emittance measurement by means of optical diffraction radiation interference

Transverse electron beam size measurements are required in order to determine the transverse emittance. In the case of high brightness electron beams produced by high repetition rate linear accelerators, conventional invasive diagnostics cannot sustain the intense power dissipated in intercepting devices. The analysis of the angular distribution of diffraction radiation has been proven to be a competent candidate for non-intercepting measurements of electron beam parameters. In addition, optical diffraction radiation interference (ODRI) has been demonstrated to be superior to the single slit ODR due to its shielding capability against the synchrotron radiation background and the possibility of avoiding complementary diagnostics. This paper reports the first transverse emittance measurement ever performed with the ODRI technique. In addition, the intrinsic non-intercepting and non-disturbing feature of the ODRI method has been checked in our experimental conditions by wakefield calculations.

On the Electromagnetic Design of a <formula formulatype="inline"><tex Notation="TeX">$\beta_{g}=0.61$ </tex></formula> 650-MHz Superconducting Radio Frequency Cavity

We present calculations for an electromagnetic design of a β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> = 0.61 multicell superconducting radio frequency cavity for the Indian Spallation Neutron Source project. The geometry parameters of the midcells are optimized using a step-by-step 1-D optimization technique. This is followed by the optimization of end cells, which is done to achieve the required field flatness and to avoid trapping of higher order modes. Calculations of the threshold beam current for the excitation of regenerative beam break-up instability excited by the dipole modes are also presented, which is followed by wakefield calculations and estimation of related effects. Specific aspects in these calculations, which are relevant for medium β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> cavities, are highlighted. Finally, studies are performed for the static and dynamic Lorentz force detuning, based on which the stiffness design of the cavity is optimized.

Point-charge wakefield calculations from finite length bunch wake potentials

We present a new method to accurately calculate point-charge geometric wakefields and/or short-bunch wake potentials from wake potentials due to a much longer bunch, typically obtained with a time-domain electromagnetic (EM) field solver. By allowing a long bunch in the EM solver, this method can significantly reduce the need for computer resources as well as drastically shorten the computing time. After explaining the method we give examples of longitudinal wakefield calculations for several 2D accelerator structures of various complexity.

Calculation of wakefields in a 17 GHz beam-driven photonic band-gap accelerator structure

We present the theoretical analysis and computer simulation of the wakefields in a 17 GHz photonic band-gap (PBG) structure for accelerator applications. Using the commercial code CST Particle Studio, the fundamental accelerating mode and dipole modes are excited by passing an 18 MeV electron beam through a seven-cell traveling-wave PBG structure. The characteristics of the longitudinal and transverse wakefields, wake potential spectrum, dipole mode distribution, and their quality factors are calculated and analyzed theoretically. Unlike in conventional disk-loaded waveguide (DLW) structures, three dipole modes (${\mathrm{TM}}_{11}$-like, ${\mathrm{TM}}_{12}$-like, and ${\mathrm{TM}}_{13}$-like) are excited in the PBG structure with comparable initial amplitudes. These modes are separated by less than 4 GHz in frequency and are damped quickly due to low radiative $Q$ factors. Simulations verify that a PBG structure provides wakefield damping relative to a DLW structure. Simulations were done with both single-bunch excitation to determine the frequency spectrum of the wakefields and multibunch excitation to compare to wakefield measurements taken at MIT using a 17 GHz bunch train. These simulation results will guide the design of next-generation high-gradient accelerator PBG structures.

Hybrid TE-TM scheme for time domain numerical calculations of wakefields in structures with walls of finite conductivity

In particle accelerators a preferred direction, the direction of motion, is well defined. If in a numerical calculation the (numerical) dispersion in this direction is suppressed, a quite coarse mesh and moderate computational resources can be used to reach accurate results even for extremely short electron bunches. Several approaches have been proposed in the past decades to reduce the accumulated dispersion error in wakefield calculations for perfectly conducting structures. In this paper we extend the TE/TM splitting algorithm to a new hybrid scheme that allows for wakefield calculations in structures with walls of finite conductivity. The conductive boundary is modeled by one-dimensional wires connected to each boundary cell. A good agreement of the numerical simulations with analytical results and other numerical approaches is obtained.

Three-Dimensional Wake Field Computations Based on Scattered-Field Time Domain Boundary Element Method

We present time domain 3-D wake field calculations based on Scattered-field Time Domain Boundary Element Method (S-TDBEM), which is retarded Kirchhoff's boundary integral equations of scattered electromagnetic fields formulated on interior region problem and has no numerical dispersion in all spatial direction. We propose two main types of S-TDBEM schemes: full 3-D scheme for general 3-D geometries and a so-called 2.5-D scheme for transverse wake field calculation in axis-symmetric structures. Several numerical examples are demonstrated for typical accelerator structures: elliptical pillbox and the TESLA 9-cell cavities. The developed 3-D/2.5-D S-TDBEM codes are verified by comparison with the modal analysis and the finite integration technique (FIT) in the numerical examples. Finally, as one of the most meaningful applications of the S-TDBEM, we demonstrate wake field simulations of a curved trajectory bunch with the developed 3-D S-TDBEM code.

Exact 1D model for coherent synchrotron radiation with shielding and bunch compression

Coherent synchrotron radiation has been studied effectively using a one-dimensional model for the charge distribution in the realm of small angle approximations and high energies. Here we use Jefimenko's form of Maxwell's equations, without such approximations, to calculate the exact wakefields due to this effect in multiple bends and drifts. It has been shown before that the influence of a drift can propagate well into a subsequent bend. We show, for reasonable parameters, that the influence of a previous bend can also propagate well into a subsequent bend, and that this is especially important at the beginning of a bend. Shielding by conducting parallel plates is simulated using the image charge method. We extend the formalism to situations with compressing and decompressing distributions, and conclude that simpler approximations to bunch compression usually overestimate the effect. Additionally, an exact formula for the coherent power radiated by a Gaussian bunch is derived by considering the coherent synchrotron radiation spectrum, and is used to check the accuracy of wakefield calculations.

Computational science research in support of petascale electromagnetic modeling

Computational science research components were vital parts of the SciDAC-1 accelerator project and are continuing to play a critical role in the SciDAC-2 accelerator project, the Community Petascale Project for Accelerator Science and Simulation (ComPASS). Presented here are recent advances and achievements in the area of computational science research in support of petascale electromagnetic modeling for accelerator design analysis, which include shape determination of superconducting RF cavities, mesh-based multilevel preconditioner for solving highly indefinite linear systems, moving window using h- or p-refinement for time-domain short-range wakefield calculations, and improved scalable application I/O.

Impact of Ion Clearing Electrodes on beam dynamics in DAΦNE

Presently clearing electrodes are being considered as a possible cure of e-cloud driven problems in existing and future colliders. ``Invisible'' electrodes, made of a thin highly resistive layer pasted on a dielectric plate, have been proposed as one of design solutions for the e-cloud clearing. For the first time such electrodes were successfully used in the Electron-Positron Accumulator (EPA) of LEP. Similar electrodes had been used for a long time for ion clearing purposes in the DAΦNE electron ring. Theoretical considerations and experimental measurements at DAΦNE have revealed a substantial contribution of the Ion Clearing Electrodes (ICE) to the machine broad-band impedance giving rise to several harmful effects degrading the collider performance. In this paper we discuss the impact of the electrodes on DAΦNE beam dynamics, show the results of ICE wake field and impedance calculations and compare them with available experimental data. We also describe the procedure of ICE removal from the wiggler sections of the electron ring that has resulted in remarkable improvements in terms of beam dynamics and geometric luminosity.

TE/TM alternating direction scheme for wake field calculation in 3D

In the future, accelerators with very short bunches will be used. It demands developing new numerical approaches for long-time calculation of electromagnetic fields in the vicinity of relativistic bunches. The conventional FDTD scheme, used in MAFIA, ABCI and other wake and PIC codes, suffers from numerical grid dispersion and staircase approximation problem. As an effective cure of the dispersion problem, a numerical scheme without dispersion in longitudinal direction can be used as it was shown by Novokhatski et al. [Transition dynamics of the wake fields of ultrashort bunches, TESLA Report 2000-03, DESY, 2000] and Zagorodnov et al. [J. Comput. Phys. 191 (2003) 525]. In this paper, a new economical conservative scheme for short-range wake field calculation in 3D is presented. As numerical examples show, the new scheme is much more accurate on long-time scale than the conventional FDTD approach.

Analytical calculation of wake fields in conical cavity

The paper is devoted to the interaction of the charged particles with cavity of conical geometry. The excited electromagnetic fields in the cavity are obtained as the expansion over the resonant modes of empty cavity. The analytical expressions for the longitudinal and transverse wake potentials of a closed conical cavity with perfectly conducting walls are given. The loss factor for a single mode is calculated.

TE/TM scheme for computation of electromagnetic fields in accelerators

We propose a new two-level economical conservative scheme for short-range wake field calculation in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase free (second order convergent). Unlike the finite-difference time domain method (FDTD), it is based on a TE/TM like splitting of the field components in time. Additionally, it uses an enhanced alternating direction splitting of the transverse space operator that makes the scheme computationally as effective as the conventional FDTD method. Unlike the FDTD ADI and low-order Strang methods, the splitting error in our scheme is only of fourth order. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach.

Wakefields in the beamline of TTF Injector II

The results of wakefield calculations for a collection of beamline elements in the TTF Injector II are presented. These elements include crosses, bellows, and steps in the beamline, valves and the bunch compressor. Methods to reduce the wakefield effects due to these elements are also investigated.

Emittance growth due to wake fields on curved bunch trajectories

Very short bunches with high peak currents are required in linac based X-ray Free Electron Lasers (SASE-FELs) and in the next generation of linear colliders. In most designs, short bunches are produced by lingitudinal compression in magnet chicanes, where particles with different energies have different path lengths so that a bunch with an energy distribution correlated with longitudinal particle position can shrink in length. However, care has to be taken that the low emittance beams are not blown up by wake field effects. Especially the wake field calculation for very short bunches on curved trajectories with relatively small bending radii (of the order of meters) requires consideration of “overtaking effects”. “Overtaking” means, that on a curved trajectory the wake of the bunch tail may reach the head because the field travels on a shorter straight path. We present a treatment to calculate these fields considering transient regimes and shielding effects as well as calculations on the emittance growth for the case of the TTF-FEL bunch compression system.

Multiple-fluid models for plasma wake-field phenomena.

In this paper we present various treatments of plasma wake-field phenomena which employ multiple-fluid models. These models generalize the one-dimensional, nonlinear, relativistic single-fluid model which has been used extensively in previous plasma wake-field calculations. Using a two-fluid model, we discuss the interaction of a low-energy continuous electron beam with wake-field-generated plasma waves. The phenomena of continuous-beam modulation and wave period shortening are discussed. The relationship between these effects and the two-stream instability is also examined. Also, using a three-fluid model, effects due to plasma electron temperature in nonlinear plasma wake-fields are examined and compared to previous work. Finally, the consequences of ion motion induced by large-amplitude electron plasma waves are calculated by including the fluid behavior of the ions.