In the presence of longitudinal coherent electron cooling, the evolution of the line-density profile of a circulating ion bunch can be described by the 1-D Fokker-Planck equation. We show that, in the absence of diffusion, the 1-D equation can be solved analytically for certain dependence of cooling force on the synchrotron amplitude. For more general cases with arbitrary diffusion, we solved the 1-D Fokker-Planck equation numerically and the numerical solutions have been compared with results from macro-particle tracking.
In order to study the single bunch longitudinal instability in BEPCII, experiments on the positron ring (BPR) for the bunch lengthening phenomenon were made. By analyzing the experimental data based on Gao's theory, the longitudinal loss factor for the bunch are obtained. Also, the total wake potential and the beam current threshold are estimated.
A new approach to the longitudinal vane modulation profile in a Radio Frequency Quadrupole (RFQ) has been discovered that significantly improves bunching and longitudinal emittance control. This procedure has been successfully tested in different RFQ models with satisfactory reduction of the longitudinal emittance; thus, this advanced method can be implemented for any RFQ. Highlights: Advanced longitudinal vane modulation profile that improves bunching and longitudinal emittance control. Vane manipulation to avoid the nonlinear effects of the accelerating field inside the cell. Analysis in the…
Knowledge of longitudinal electron bunch profiles is vital to optimize the performance of plasma wakefield accelerators and x-ray free electron laser linacs. Because of their importance to these novel applications, noninvasive frequency domain techniques are often employed to reconstruct longitudinal bunch profiles from coherent synchrotron, transition, or undulator radiation measurements. In this paper, we detail several common reconstruction techniques involving the Kramers-Kronig phase relationship and Gerchberg-Saxton algorithm. Through statistical analysis, we draw general conclusions abo…
In this paper we describe an instability, which we called a Plasma-Cascade Amplifier, occurring in electron beams propagating along a straight trajectory.
We report on the experimental generation of a train of subpicosecond electron bunches. The bunch train generation is accomplished using a beamline capable of exchanging the coordinates between the horizontal and longitudinal degrees of freedom. An initial beam consisting of a set of horizontally-separated beamlets is converted into a train of bunches temporally separated with tunable bunch duration and separation. The experiment reported in this Letter unambiguously demonstrates the conversion process and its versatility.
To understand and control the dynamics in the longitudinal phase space, time-resolved measurements of different bunch parameters are required. For a reconstruction of this phase space, the detector systems have to be synchronized. This reconstruction can be used e.g. for studies of the micro-bunching instability. It occurs if the interaction of the bunch with its own radiation leads to the formation of sub-structures on the longitudinal bunch profile. These sub-structures can grow rapidly -- leading to a sawtooth-like behaviour of the bunch. At KARA, we use a fast-gated intensified camera for …
We examine the stability of intense flat bunches in barrier buckets used in the Recycler. We consider some common stationary distributions and show that they would be unstable against rigid dipole oscillations. We then discuss an analytical model for the line density that best describes measured bunch profiles. We include space charge in this model to predict the bunch intensity at which Landau damping would be lost. The dependence of this threshold on the bunch length is studied and related to the results of an experimental study with shorter bunch lengths. The threshold for the microwave ins…
The possibility of charged particle acceleration by a longitudinal wake field excited in plasma by an electron bunch and a train of electron bunches. The exact solution of the stationary nonlinear self-consistent interaction of a monoenergetic relativistic bunch with cold plasma is obtained. It is shown that under certain conditions a self-acceleration of the bunch tail electrons up to high energies is possible.
Conditions for existence, uniqueness and stability of bunch steady states are considered. For the existence uniqueness problem, simple algebraic equations are derived, showing the result both for the action and Hamiltonian domain distributions. For the stability problem, van Kampen theory is used. Emerging of discrete van Kampen modes show either loss of Landau damping, or instability. This method can be applied for an arbitrary impedance, RF shape and beam distribution function Available areas on intensity-emittance plane are shown for resistive wall wake and single harmonic, bunch shortening…
We propose a general method for tailoring the current distribution of relativistic electron bunches. The technique relies on a recently proposed method to exchange the longitudinal phase space emittance with one of the transverse emittances. The method consists of transversely shaping the bunch and then converting its transverse profile into a current profile via a transverse-to-longitudinal phase-space-exchange beamline. We show that it is possible to tailor the current profile to follow, in principle, any desired distributions. We demonstrate, via computer simulations, the application of the…
In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In pa…
The influence of the space charge fields on the dynamics of the particles of the bunch, which is moved in a bending magnet is calculated. It is shown, that such influence of the Coulomb force on the energy of the particles of a modulated beam causes in the decreasing of the bunch energy spread during the compression due to energy deviation along the compressed bunch, i.e. bunch cooling. The necessary conditions of the maximal cooling are found. The attainable ordering of the bunch is investigated.
In DAFNE, the Frascati $e^+e^-$ collider operating since 1998, an innovative collision scheme, the crab waist, has been successfully implemented during the years 2008-09. During operations for the Siddharta experiment an unusual synchrotron oscillation damping effect induced by beam-beam collisions has been observed. Indeed, when the longitudinal feedback is off, the positron beam becomes unstable with currents above 200-300 mA due to coupled bunch instability. The longitudinal instability is damped by colliding the positron beam with a high current electron beam (of the order of 2 A). A shift…
Bunches in the Tevatron are known to exhibit longitudinal oscillations which persist indefinitely. These oscillations are colloquially called "dancing bunches". Although the dancing bunches do not cause single bunch emittance growth or beam loss at injection, it leads to bunch lengthening at collisions. In operations, a longitudinal damper has been built which stops this dance and damps out coupled bunch modes. Recent theoretical work predicts that the dance can also be stopped by an appropriate change in the bunch distribution. This paper shows the Tevatron experiments which support this theo…
The longitudinal Schottky spectra of a radio-frequency (RF) bunched and electron cooled 22Ne10+ ion beam at 70 MeV/u have been studied by a newly installed resonant Schottky pick-up at the experimental cooler storage ring (CSRe), at IMP. For an RF-bunched ion beam, a longitudinal momentum spread of has been reached with less than 107 stored ions. The reduction of momentum spread compared with coasting ion beam was observed from Schottky noise signal of the bunched ion beam. In order to prepare the future laser cooling experiment at the CSRe, the RF-bunching power was modulated at 25th, 50th an…
The development of fast detection methods for comprehensive monitoring of electron bunches is a prerequisite to gain comprehensive control over the synchrontron emission in storage rings with their MHz repetition rate. Here, we present a proof-of-principle experiment with at detailed description of our implementation to detect the longitudinal electron bunch profiles via single-shot, near-field electro-optical sampling at the Karlsruhe Research Accelerator (KARA). Our experiment is equipped with an ultra-fast line array camera providing a high-throughput MHz data stream. We characterize statis…
The J-PARC Main Ring (MR) has achieved the delivery of the 30 GeV proton beam with the beam power of 500 kW to the neutrino experiment in May 2018. The longitudinal coupled-bunch instabilities have been observed in the MR for the beam power beyond 470 kW. Since more significant coupled-bunch oscillation was observed in higher beam power, the mitigation of the coupled-bunch instabilities is necessary for the stable beam delivery with the beam power beyond 500 kW. A new feedback system was developed to suppress the coupled-bunch instabilities. The feedback system consists of a wall current monit…
The coherent radiation emitted by an electron bunch provides a diagnostic signal that can be used to estimate its longitudinal distribution. Commonly only the amplitude of the intensity spectrum can be measured and the associated phase must be calculated to obtain the bunch profile. Very recently an iterative method was proposed to retrieve this phase. However ambiguities associated with non-uniqueness of the solution are always present in the phase retrieval procedure. Here we present a method to overcome the ambiguity problem by first performing multiple independent runs of the phase retriev…
Recent studies have shown that the prospects for significantly increasing bunch intensities in the LHC for the luminosity upgrade (HL-LHC) may be severely limited by the available cryogenic cooling capacity and the electron-cloud (EC) driven beam instability. However, it is planned that during the HL-LHC era the bunch intensities in the LHC will go up by nearly a factor of two compared to the LHC-design values. This motivates the exploration of additional EC mitigation techniques that can be adopted in addition to those already in place. Preliminary simulations indicated that long flat bunches…
Transverse breathing mode oscillations in a particle beam can couple energy into longitudinal oscillations in a bunch of finite length and cause significant losses. We develop a model that illustrates this effect and explore the dependence on mismatch size, space-charge tune depression, longitudinal focusing strength, bunch length, and RF bucket length.
Recently a mechanism of storage ring operation based on the steady-state microbunching has been proposed and investigated, which contains a laser cavity modulator providing the longitudinal focusing for the circulating microbunches. In this paper we analyze the impact of the coherent undulator radiation on the longitudinal single-bunch multi-turn collective dynamics, exploring a new possible instability mechanism. We formulate the multi-turn equations of motion for the single microbunch as two sets of difference equations in the modulator and in the remaining storage ring. The dispersion equat…
A transverse deflecting structure (TDS) is a well-known device for characterizing the longitudinal properties of an electron bunch in a linear accelerator. The standard use of such a cavity involves streaking the bunch along a transverse axis and analysing the image on a screen downstream to find the bunch length and slice properties along the other transverse axis. A novel X-band deflecting structure, which will allow the polarization of the deflecting field to be adjusted, is currently being designed as part of a collaboration between CERN, DESY and PSI. This new design will allow bunches to…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameter-less integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the RF bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny c…
Laser cooling of relativistic heavy ion beams of Li-like C$^{3+}$ and O$^{4+}$ is being in preparation at the experimental Cooler Storage Ring (CSRe). Recently, a preparatory experiment to test important prerequisites for laser cooling of relativistic $^{12}$C$^{3+}$ ion beams using a pulsed laser system has been performed at the CSRe. Unfortunately, the interaction between the ions and the pulsed laser cannot be detected. In order to study the laser cooling process and find the optimized parameters for future laser cooling experiment, a multi-particle tracking method was developed to simulate…
We present theoretical and numerical studies of longitudinal compression and transverse matching of electron bunch before injecting into the Laser-plasma Wake Field Accelerator (LWFA) foreseen at the ESCULAP project in ORSAY. Longitudinal compression is performed with a dogleg chicane, the chicane is designed based on theory of beam optics, beam dynamics in dogleg is studied with ImpactT and cross checked with CSRtrack, both 3D space charge (SC) and coherent synchrotron radiation (CSR) effects are included. Simulation results show that the energy chirp at the dogleg entrance should be smaller …
Due to their ultra-short duration and peak currents in the kA range, laser-wakefield accelerated electron bunches are promising drivers for ultrafast X-ray generation in compact free-electron-lasers (FELs), Thomson-scattering or betatron sources. Here we present the first single-shot, high-resolution measurements of the longitudinal bunch profile obtained without prior assumptions about the bunch shape. Our method allows complex features, such as multi-bunch structures, to be detected. Varying the length of the gas target, and thus the acceleration length, enables an assessment of the bunch pr…
We have considered the possibility of using coherent Smith-Purcell radiation for the single-shot determination of the longitudinal profile of 50 fs (FWHM) long electron bunches. This length is typical for the bunches currently produced by Laser Wakefield Acceleration and is at the limit of what is achievable by alternative techniques, such as Electro-Optic sampling. It is concluded that there are no obstacles, either theoretical or experimental, in the implementation of this technique. A set of three gratings, with periods of 15, 85 and 500 micrometres, will produce detectable energy in the wa…
A longitudinal coupled bunch mode diagnostic was built to identify and characterize coupled bunch modes in the Max IV 3 GeV ring. A longitudinal coupled bunch Mode 0 dipole instability was identified and a longitudinal Mode 0 dipole damper was built which cured the instability. As a separate project, a radio frequency current transformer was built as an emergency backup to the DC current transformer. All the devices where built using the open-source Blinky-Lite Internet of Things platform that enabled quick and inexpensive deployment.
The generation and properties of transition radiation (TR) are thoroughly treated. The spectral energy density, as described by the Ginzburg-Frank formula, is computed analytically, and the modifications caused by the finite size of the TR screen and by near-field diffraction effects are carefully analyzed. The principles of electron bunch shape reconstruction using coherent transition radiation are outlined. Spectroscopic measure- ments yield only the magnitude of the longitudinal form factor but not its phase. Two phase retrieval methods are investigated and illustrated with model calculatio…
The formation of a double-horn current profile is a challenging issue in the achievement of electron bunch with high peak current, especially for high-repetition-rate X-ray free-electron lasers (XFELs) where more nonlinear and intricate beam dynamics propagation is involved. Here, we propose to correct the nonlinear beam longitudinal phase space distortion in the photoinjector section with a dual-mode buncher. In combination with the evolutionary many-objective beam dynamics optimization, this method is shown to be effective in manipulating the longitudinal phase space at the injector exit. Fu…
Macro-particle tracking is a prominent method to study the collective beam instabilities in accelerators. However, the heavy computation load often limits the capability of the tracking codes. One widely used macro-particle tracking code to simulate collective instabilities in storage rings is mbtrack. The Message Passing Interface (MPI) is already implemented in the original mbtrack to accelerate the simulations. However, many CPU threads are requested in mbtrack for the analysis of the coupled-bunch instabilities. Therefore, computer clusters or desktops with many CPU cores are needed. Since…
The measurement of the longitudinal behavior of the accelerated particle beams at Fermilab is crucial to the optimization and control of the beam and the maximizing of the integrated luminosity for the particle physics experiments. Longitudinal measurements in the Tevatron and Main Injector synchrotrons are based on the analysis of signals from resistive wall current monitors. This article describes the signal processing performed by a 2 GHz-bandwidth oscilloscope together with a computer running a LabVIEW program which calculates the longitudinal beam parameters.
We propose a novel scheme for final muon ionization cooling with quadrupole doublets followed by emittance exchange in vacuum to achieve the small beam sizes needed by a muon collider. A flat muon beam with a series of quadrupole doublet half cells appears to provide the strong focusing required for final cooling. Each quadrupole doublet has a low beta region occupied by a dense, low Z absorber. After final cooling, normalized transverse, longitudinal, and angular momentum emittances of 0.100, 2.5, and 0.200 mm-rad are exchanged into 0.025, 70, and 0.0 mm-rad. A skew quadrupole triplet transfo…
Through an interaction of theory and optimization-guided design, we have developed a novel bunch compression scheme based on an asymmetric double emittance exchange (DEEX) with greatly reduced coherent synchrotron radiation (CSR) effects. First, we discuss the benefits of the phase space exchange-based bunch compressor (BC) in comparison to the chicane-based counterpart in the approximation of linear single particle dynamics and with respect to microbunching instabilities driven by longitudinal space charge forces. We present simulation results for nonlinear dynamics in a symmetric DEEX BC whi…
We outline a plan for final muon ionization cooling with quadrupole doublets focusing onto short absorbers followed by emittance exchange in vacuum to achieve the small transverse beam sizes needed by a muon collider. A flat muon beam with a series of quadrupole doublet half cells appears to provide the strong focusing required for final cooling. Each quadrupole doublet has a low beta region occupied by a dense, low Z absorber. After final cooling, normalized xyz emittances of (0.071, 0.141, 2.4) mm-rad are exchanged into (0.025, 0.025, 70) mm-rad. Thin electrostatic septa efficiently slice th…
We present measurement and analyses of longitudinal timing jitter of Beijing Electron Positron Collider (BEPCII) linear accelerator electron gun. We simulated longitudinal jitter effect of the gun using PARMELA about beam performance including beam profile, average energy, energy spread, longitudinal phase of reference particle and XY emittance. The maximum percentage difference of the beam parameters are calculated to be; 100%, 13.27%, 42.24%, 7.79% and 65.01%, 86.81%, respectively due to which the bunching efficiency is reduced to 54%. The simulation results are in agreement with test and ar…
In the upgrade project of Hefei Light Source (HLS II), a new digital longitudinal bunch-by-bunch feedback system will be developed to suppress the coupled bunch instabilities in the storage ring effectively. We design a new waveguide overloaded cavity longitudinal feedback kicker as the feedback actuator. The beam pipe of the kicker is racetrack shape so as to avoid a transition part to the octagonal vacuum chamber. The central frequency and the bandwidth of the kicker have been simulated and optimized to achieve design goals by the HFSS code. The higher shunt impedance can be obtained by usin…
Longitudinal properties of electron bunches are critical for the performance of a wide range of scientific facilities. In a free-electron laser, for example, the existing diagnostics only provide very limited longitudinal information of the electron bunch during online tuning and optimization. We leverage the power of artificial intelligence to build a neural network model using experimental data, in order to bring the destructive longitudinal phase space (LPS) diagnostics online virtually and improve the existing current profile online diagnostics which uses a coherent transition radiation (C…
Cooling of hadron beams is critically important in the next generation of hadron storage rings for delivery of unprecedented performance. One such application is the electron-ion collider presently under development in the US. The desire to develop electron coolers for operation at much higher energies than previously achieved necessitates the use of radio-frequency (RF) fields for acceleration as opposed to the conventional, electrostatic approach. While electron cooling is a mature technology at low energy utilizing a DC beam, RF acceleration requires the cooling beam to be bunched, thus ext…
Longitudinal phase space manipulation is a critical and necessary component for advanced acceleration concepts, radiation sources and improving performances of X-ray free electron lasers. Here we present a simple and versatile method to semi-arbitrarily shape the longitudinal phase space of a charged bunch by using wakefields generated in tailored dielectric-lined waveguides. We apply the concept in simulation and provide examples for radiation generation and bunch compression. We finally discuss the manufacturing capabilities of a modern 3D printer and investigate how printing limitations, as…
High resolution single-shot non-relativistic ultrafast electron microscopy(UEM) relies on adaptive optics to compress high intensity bunches using Radio Frequency (RF) cavities. We present a comprehensive discussion of the analytic approaches available to characterize bunch dynamics as an electron bunch goes through a longitudinal focal point after an RF cavity where space charge effects can be large. Methods drawn from the Coulomb explosion literature, the accelerator physics literature and the analytic Gaussian model developed for UEM are compared, utilized and extended in some cases. In par…
A longitudinal beam properties, data acquisition system has been commissioned to operate in the Fermilab booster ring. This system captures real time information including beam synchronous phase, bunch length, and coupled bunch instability amplitudes as the beam is accelerated from 400 MeV to 8 GeV in 33 ms. The system uses an off-the-shelf Tektronix oscilloscope running Labview software and a synchronous pulse generator. This paper describes the hardware configuration and the software configuration used to optimize the data processing rate.
