Long-range Wakefields Research Articles

PLACET3: 6D tracking through PETS and accelerating structures wakefields

We present the latest updates to the PLACET3 tracking package, which focus on the impact of both transverse and longitudinal wakefields on a beam travelling through accelerating and decelerating structures. The main focus of this update was the first implementation of 6D tracking through Power Extraction and Transfer Structures (PETS) for the Compact Linear Collider (CLIC), which is described through short and long-range longitudinal wakefields. Additionally, we present the impact of different numerical schemes on the computation of wakefields in accelerating structures.

Modeling and mitigation of long-range wakefields for advanced linear colliders

The luminosity requirements of TeV-class linear colliders demand use of intense charged beams at high repetition rates. Such features imply multi-bunch operation with long current trains accelerated over the km length scale. Consequently, particle beams are exposed to the mutual parasitic interaction due to the long-range wakefields excited by the leading bunches in the accelerating structures. Such perturbations to the motion induce transverse oscillations of the bunches, potentially leading to instabilities such as transverse beam break-up. Here we present a dedicated tracking code that studies the effects of long-range transverse wakefield interaction among different bunches in linear accelerators. Being described by means of an efficient matrix formalism, such effects can be included while preserving short computational times. As a reference case, we use our code to investigate the performance of a state-of-the-art linear collider currently under design and, in addition, we discuss possible mitigation techniques based on frequency detuning and damping.

Submacropulse electron-beam dynamics correlated with higher-order modes in a Tesla-type cryomodule

Experiments were performed at the Fermilab Accelerator Science and Technology (FAST) facility to elucidate the effects of long-range wakefields (LRWs) in TESLA-type superconducting rf cavities. In particular, we investigated the higher-order modes (HOMs) generated in the eight cavities of a cryomodule (CM) due to off-axis steering with correctors located ~4 m upstream of the CM. We have observed correlated submacropulse centroid slews of a few-hundred microns and centroid oscillations at ~240 kHz in the rf BPM data after the CM. The entrance energy into the CM was 25 MeV, and the exit energy was 100 MeV with 125 pC/b and 400 pC/b in 50-bunch pulse trains. These experimental results were evaluated for machine learning training aspects which will be used to inform the commissioning plan for the Linac Coherent Light Source-II injector CM.

X -band linac design

In order to explore physics in the EUV to soft x-ray region, we have designed a machine which is capable of accelerating a $\ensuremath{\sim}250\text{ }\text{ }\mathrm{pC}$ electron bunch to an energy of $\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$. The front end of the CLARA (Compact Linear Accelerator for Research and Applications) system at Daresbury Labs will be used as an S-band injector of $\ensuremath{\sim}180\text{ }\text{ }\mathrm{MeV}/\mathrm{c}$, sub-ps FWHM, $\ensuremath{\sim}250\text{ }\text{ }\mathrm{pC}$ electron bunches into the XARA (X-Band Accelerator for Research and Application) system. A rf feasibility study has been carried out for a structure operating in the $2\ensuremath{\pi}/3$ mode at a frequency of 11.9942 GHz which is fed by a SLED klyston setup. The average cell of this structure has an iris radius of $⟨a⟩=3.2\text{ }\text{ }\mathrm{mm}$ and a shunt impedance of $⟨{R}_{s}⟩=106.55\text{ }\text{ }\mathrm{M}\mathrm{\ensuremath{\Omega}}/\mathrm{m}$. A high target gradient of $80\text{ }\text{ }\mathrm{MV}/\mathrm{m}$ for a single-bunch operation of the linac is necessary due to spatial constraints at Daresbury Labs. We have also implemented Gaussian detuning of the linac in order to future-proof the project for potential multibunch operation of the machine. After combining the rf study with an analysis of the uncoupled long-range wakefield and the short-range transverse wakefields, the optimal structure parameters are outlined as a compromise between the shunt impedance, electrical breakdown rate and wakefields in the structure. As novel designs will be tested using this free-electron laser (FEL) an increased beam charge may be useful. Therefore a beam dynamics study via the particle tracking code elegant has been performed to assess how the beam quality evolves while traveling through the XARA rf structures for different bunch charges and beam offsets. These simulations reveal how the bunch is disturbed for varying bunch charges and offsets and give an initial indication of how sensitive the beam parameters (beam centroid position, emittance, RMS beam size, etc.) are to the wakefields generated in XARA. An analytical formulation of the beam motion as it travels through the XARA linac has been utilized to calculate the emittance growth. This allows for comparison between analytical and numerical simulation of the beam dynamics to give confidence in the results. The beam dynamics study shows that for a bunch charge of ${Q}_{b}=250\text{ }\text{ }\mathrm{pC}$ and a beam offset of ${C}_{x}={\ensuremath{\sigma}}_{z}/2=0.253\text{ }\text{ }\mathrm{mm}$, the normalized emittance growth at the end of the XARA linac is $\mathrm{\ensuremath{\Delta}}{\ensuremath{\epsilon}}_{Nx}/{\ensuremath{\epsilon}}_{Nx}\ensuremath{\sim}270%$. This may be mitigated by the design of a magnetic lattice which would include kickers to recenter the beam on the electrical axis of the structure, reducing the effect of the wakefields on the bunch. Currently it is probable that a maximum bunch charge of $\ensuremath{\sim}250\text{ }\text{ }\mathrm{pC}$ will be utilized for this machine; however a future design of a magnetic focusing lattice may allow higher charges to be viable and will reduce the emittance growth.

Stabilizing effects of chromaticity and synchrotron emission on coupled-bunch transverse dynamics in storage rings

We present a theory that can compute the transverse coupled-bunch instability growth rates at any chromaticity and for any longitudinal potential provided only that the long-range wakefield varies slowly over the bunch. The theory is expressed in terms of the usual coupled-bunch eigenvalues at zero chromaticity, and when the longitudinal motion is simple harmonic our solution only requires numerical root-finding that is easy to implement and fast to solve; the more general case requires some additional calculations, but is still relatively fast. The theory predicts that the coupled-bunch growth rates can be significantly reduced when the chromatic betatron tune spread is larger than the coupled-bunch growth rate at zero chromaticity. Our theoretical results are compared favorably with tracking simulations for the long-range resistive wall instability, and we also indicate how damping and diffusion from sychrotron emission can further reduce or even stabilize the dynamics.

Observation of Wakefield Suppression in a Photonic-Band-Gap Accelerator Structure.

We report experimental observation of higher order mode (HOM) wakefield suppression in a room-temperature traveling-wave photonic-band-gap (PBG) accelerating structure at 11.700GHz. It has been long recognized that PBG structures have the potential for reducing long-range wakefields in accelerators. The first ever demonstration of acceleration in a room-temperature PBG structure was conducted in 2005. Since then, the importance of PBG accelerator research has been recognized by many institutions. However, the full experimental characterization of the wakefield spectrum and demonstration of wakefield suppression when the accelerating structure is excited by an electron beam has not been performed to date. We conducted an experiment at the Argonne Wakefield Accelerator test facility and observed wakefields excited by a single high charge electron bunch when it passes through a PBG accelerator structure. Excellent HOM suppression properties of the PBG accelerator were demonstrated in the beam test.

Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity

The NSLS-II storage ring is designed to operate with superconducting RF-cavities with the aim to store an average current of 500mA distributed in 1080 bunches, with a gap in the uniform filling for ion clearing. At the early stage of the commissioning (phase 1), characterized by a bare lattice without damping wigglers and without Landau cavities, a normal conducting 7-cell PETRA-III RF-cavity structure has been installed with the goal to store an average current of 25mA. In this paper we discuss our analysis of coupled-bunch instabilities driven by the Higher Order Modes (HOMs) of the 7-cell PETRA-III RF-cavity. As a cure of the instabilities, we apply a well-known scheme based on a proper detuning of the HOMs frequencies based upon cavity temperature change, and the use of the beneficial effect of the slow head–tail damping at positive chromaticity to increase the transverse coupled-bunch instability thresholds. In addition, we discuss measurements of coupled-bunch instabilities observed during the phase 1 commissioning of the NSLS-II storage ring. In our analysis we rely, in the longitudinal case, on the theory of coupled-bunch instability for uniform fillings, while in the transverse case we complement our studies with numerical simulations with OASIS, a novel parallel particle tracking code for self-consistent simulations of collective effects driven by short and long-range wakefields.

Simultaneous computation of intrabunch and interbunch collective beam motions in storage rings

We present the multibunch tracking code mbtrack developed to simulate, in 6-dimensional phase space, single- and multibunch collective instabilities driven by short- and long-range wakefields in storage rings. Multiple bunches, each composed of a large number of macroparticles, are tracked, allowing simulation of both intra- and interbunch motions. Besides analytical impedance models, the code allows employment of numerical wake potentials computed with electromagnetic (EM) field solvers. The corresponding impedances are fitted to a number of known analytical functions and the coefficients obtained in the fit are used as an input to the code. mbtrack performs a dynamic treatment of long-range resistive-wall and harmonic cavity fields, which are likely to be the two major factors impacting multibunch collective motions in many present and future ring-based light sources. Furthermore, it is capable of simulating beam-ion interactions as well as transverse bunch-by-bunch feedback. We describe the physical effects considered in the code and their implementation, which makes use of parallel processing to significantly shorten the computation time. mbtrack is benchmarked against other codes and applied to the MAX IV 3GeV ring as an example, where the importance of the interplay of various physical effects as well as coupling among different degrees of freedom is demonstrated.

Characterization of coherent Cherenkov radiation source

Engineering formulae for calculation of peak, and spectral brightness of resonant long-range wakefield extractor are given. It is shown that the brightness is dominated by beam density in the slow wave structure and antenna gain of the outcoupling. Far field radiation patterns and brightness of circular and high aspect ratio planar radiators are compared. A possibility to approach diffraction limited brightness is demonstrated. The role of group velocity in designing of the Cherenkov source is analyzed. The approach can be applied for design and characterization of various structure-dominated sources (e.g., wakefield extractors with gratings or dielectrics, or FEL-Cherenkov combined sources) radiating into a free space using an antenna (in microwave to sub-mm wave regions). The high group velocity structures can be also effective as energy dechirpers and for diagnostics of microbunched relativistic electron beams.

Raising gradient limitations in 2.1 GHz superconducting photonic band gap accelerator cavities

We report results from recent 2.1 GHz superconducting radio frequency (SRF) photonic band gap (PBG) resonator experiments at Los Alamos. Two 2.1 GHz PBG cells with elliptical rods were fabricated and tested at high power in a liquid helium bath at the temperatures of 4 K and below 2 K. The described SRF PBG cells were designed with a particular emphasis on changing the shape of the PBG rods to reduce peak surface magnetic fields and at the same time to preserve its effectiveness at damping higher-order-modes. The superconducting PBG cavities have great potential for damping long-range wakefields in SRF accelerator structures without affecting the fundamental accelerating mode. The cells performed in accordance with simulation's predictions and the maximum achieved accelerating gradient was 18.3 MV/m. This represents a 30% increase over gradients previously demonstrated in superconducting PBG cavities with round rods.

Optimizing the configuration of a superconducting photonic band gap accelerator cavity to increase the maximum achievable gradients

We present a design of a superconducting rf photonic band gap (SRF PBG) accelerator cell with specially shaped rods in order to reduce peak surface magnetic fields and improve the effectiveness of the PBG structure for suppression of higher order modes (HOMs). The ability of PBG structures to suppress long-range wakefields is especially beneficial for superconducting electron accelerators for high power free-electron lasers (FELs), which are designed to provide high current continuous duty electron beams. Using PBG structures to reduce the prominent beam-breakup phenomena due to HOMs will allow significantly increased beam-breakup thresholds. As a result, there will be possibilities for increasing the operation frequency of SRF accelerators and for the development of novel compact high-current accelerator modules for the FELs.

Implications of long-range wakefields on multi-bunch beam dynamics in the ILC with a new low surface field superconducting cavity

This article focusses on a beam dynamics study for the linacs of the ILC. In particular, the impact of long-range transverse wakefields on the beam quality is studied for the case in which the ILC would be built using the new low surface field (NLSF) superconducting cavities. This presents an alternative design to the baseline TESLA-style cavities. The progress of the beam down ~10km of each linac is simulated using the tracking computer code PLACET. In addition, the results of an analytical matrix method, in which the beam is subjected to identical wakefields from each cavity, are also presented. Both systematic and random errors, arising as a natural process during fabrication, are implemented in the beam tracking study. The latter source of error is found to be beneficial, as emittance dilution is reduced due to the beam receiving non-coherent kicks.

First High Power Test Results for 2.1 GHz Superconducting Photonic Band Gap Accelerator Cavities

We report the results of the recent high power testing of superconducting radio frequency photonic band gap (PBG) accelerator cells. Tests of the two single-cell 2.1 GHz cavities were performed at both 4 and 2 K. An accelerating gradient of 15 MV/m and an unloaded quality factor Q(0) of 4×10(9) were achieved. It has been long realized that PBG structures have great potential in reducing long-range wakefields in accelerators. A PBG structure confines the fundamental TM(01)-like accelerating mode, but does not support higher order modes. Employing PBG cavities to filter out higher order modes in superconducting particle accelerators will allow suppression of dangerous beam instabilities caused by wakefields and thus operation at higher frequencies and significantly higher beam luminosities. This may lead towards a completely new generation of colliders for high energy physics and energy recovery linacs for the free-electron lasers.

Wakefields in photonic crystal cavities

Simulations of charged particle beams in accelerator cavities show that a two-dimensional photonic crystal can be used to create a three-dimensional hybrid cavity with a single operating mode and no significant higher order modes, greatly reducing long-range wakefields. Optimizing the photonic crystal cavity to reduce radiation leakage in the desired mode (of a finite-sized structure) yields even lower wakefields. Wakefields in photonic crystal cavities are compared to those in metal pillbox cavities.

Fast transverse multibunch coherent instabilities in a beam with a quasi-uniform filling

We study effects of the long-range wakefield memory on multibunch transverse coherent instabilities of a beam in a storage ring. We assume that the oscillation rise times substantially exceed the frequency of small synchrotron oscillations of particles. Despite the eigensolution spectrum due to the wake memory and because of essential singularity in the oscillation frequency of the function defining the dispersion equation, the amplitudes of coherent oscillations of the beam bunches non-exponentially depend on time. Such beam break-up like instabilities are always suppressed by Landau damping, or by a single bunch feedback damping system. The instability threshold is determined by an acceptable level of coherent oscillations of the beam.

Theory for wakefields in a multizone dielectric lined waveguide

A formal eigenmode method to solve for electromagnetic fields in a longitudinally translationally invariant multizone dielectric-lined waveguide is presented. The method is specialized to the development of wakefield theory for rectangular dielectric-lined structures which have an arbitrary number of dielectric layers. It is shown that the fields excited by a drive particle moving through the vacuum beam channel in such a structure can simultaneously include both propagating and decaying modes. The decaying modes characterize the short-range self-fields that move together with the particle, while the propagating modes characterize the long-range radiation fields or wakefields that carry energy away from the particle. It is also shown that the formal solution obtained in rectangular structures is applicable to all translationally invariant dielectric-lined waveguides, for example, cylindrical structures. Two important identities which the method relies upon are computationally confirmed for rectangular two-zone dielectric-lined structures. This theory may be employed for calculations of space charge effects, particularly for low or moderate-energy beams where self-field effects cannot be neglected.

High-performance computing in accelerating structure design and analysis

Future high-energy accelerators such as the Next Linear Collider (NLC) will accelerate multi-bunch beams of high current and low emittance to obtain high luminosity, which put stringent requirements on the accelerating structures for efficiency and beam stability. While numerical modeling has been quite standard in accelerator R&D, designing the NLC accelerating structure required a new simulation capability because of the geometric complexity and level of accuracy involved. Under the US DOE Advanced Computing initiatives (first the Grand Challenge and now SciDAC), SLAC has developed a suite of electromagnetic codes based on unstructured grids and utilizing high-performance computing to provide an advanced tool for modeling structures at accuracies and scales previously not possible. This paper will discuss the code development and computational science research (e.g. domain decomposition, scalable eigensolvers, adaptive mesh refinement) that have enabled the large-scale simulations needed for meeting the computational challenges posed by the NLC as well as projects such as the PEP-II and RIA. Numerical results will be presented to show how high-performance computing has made a qualitative improvement in accelerator structure modeling for these accelerators, either at the component level (single cell optimization), or on the scale of an entire structure (beam heating and long-range wakefields).

Fabrication and cold test of photonic band gap resonators and accelerator structures

We present the detailed description of the successful design and cold test of photonic band gap (PBG) resonators and traveling-wave accelerator structures. Those tests provided the essential basis for later hot test demonstration of the first PBG accelerator structure at 17.140 GHz [E. I. Smirnova, A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).]. The advantage of PBG resonators is that they were built to support only the main, ${\mathrm{TM}}_{01}$-like, accelerator mode while not confining the higher-order modes (HOM) or wakefields. The design of the PBG resonators was based on a triangular lattice of rods, with a missing rod at the center. Following theoretical analysis, the rod radius divided by the rod spacing was held to a value of about 0.15 to avoid supporting HOM. For a single-cell test the PBG structure was fabricated in X-band (11 GHz) and brazed. The mode spectrum and $Q$ factor ($Q=5\text{ }000$) agreed well with theory. Excellent HOM suppression was evident from the cold test. A six-cell copper PBG accelerator traveling-wave structure with reduced long-range wakefields was designed and was built by electroforming at Ku-band (17.140 GHz). The structure was tuned by etching the rods. Cold test of the structure yielded excellent agreement with the theoretical design. Successful results of the hot test of the structure demonstrating the acceleration of the electron beam were published in E. I. Smirnova, A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, Phys. Rev. Lett., 95, 074801 (2005).

Group velocity effect on resonant, long-range wake-fields in slow wave structures

Synchronous wake-fields in a dispersive waveguide are derived in a general explicit form on the basis of a rigorous electro-dynamical approach using Fourier transformations. The fundamental role of group velocity in wake-field propagation, calculation of attenuation, amplitudes, form-factors and loss-factors is analyzed for single bunch radiation. Adiabatic tapering of the waveguide and bunch density variation is taken into account analytically for the time-domain fields. Effects of field “compression/expansion” and group delays are demonstrated. The role of these effects is discussed for single bunch wake-fields, transient beam loading, BBU and HOMs. A novel waveguide structure with central rf coupling and both positive and negative velocities is proposed. It can be used effectively in both high-energy accelerators and single-section linacs.

Analytical formulae for the wakefields produced by the nonrelativistic charged particles in periodic disk-loaded structures

In this paper we consider the wakefields induced in periodic disk-loaded cavities by charged particles of velocities less than that of light. In frequency domain the particle velocity-dependent wakefields can be calculated by generalizing the analytical formulae given in J. Gao (Nucl. Instr. and Meth. A 381 (1996) 174; or LAL/RT 95-01, April 1995). The physical picture of this effect can be drawn so that the frequencies of the excited modes in cavities felt by the particles are increased by a factor of 1/ β ( β is the normalized particle's velocity). Some examples are given to demonstrate the utility of these formulae in obtaining the quantities, such as loss factors, short-range and long-range wakefields as functions of cavity dimension, bunch length and particle velocity.