Space Charge Forces Research Articles

Effects of space charge force on the beam-beam mode coupling instability

Recent e+e− colliders operate with very low emittance and high current. The space-charge tune shift is not negligible in tau-charm and B factories. The vertical space-charge tune shift is on the order of 0.02–0.1 and is comparable to the synchrotron tune and the beam-beam tune shift. The beam-beam mode coupling instability has been studied with and without vacuum environment impedance. The mode coupling is influenced by the space-charge force, which exhibits similar characteristics to the beam-beam force. The combined effect of beam-beam, space charge, and vacuum environment impedance is discussed within the framework of the mode coupling theory. Strong-strong beam-beam simulation, considering the space-charge force and the impedance, are conducted to validate the theory and to study general cases such as asymmetric colliders. Published by the American Physical Society 2024

Compensating slice emittance growth in high brightness photoinjectors using sacrificial charge

Achieving maximum electron beam brightness in photoinjectors requires detailed control of the 3D bunch shape and precise tuning of the beam focusing. Even in state-of-the-art designs, slice emittance growth due to nonlinear space charge forces and partial nonlaminarity often remains non-negligible. In this work, we introduce a new means to linearize the transverse slice phase space: a sacrificial portion of the bunch’s own charge distribution, formed into a wavebroken shock front by highly nonlinear space charge forces within the gun, whose downstream purpose is to dynamically linearize the desired bunch core. We show that linearization of an appropriately prepared bunch can be achieved via strongly nonlaminar focusing of the sacrificial shock front, while the inner core focuses laminarly. This leads to a natural spatial separation of the two distributions: a dense core surrounded by a diffuse halo of sacrificial charge that can be collimated. Multiobjective genetic algorithm optimizations of the ultracompact x-ray free electron laser injector employ this concept, and we interpret it with an analytic model that agrees well with the simulations. In simulation, we demonstrate a final bunch charge of 100 pC, peak current ∼30 A, and a sacrificial charge of 150 pC (250 pC total emitted from cathode) with normalized emittance growth of <20 nm rad due to space charge. This implies a maximum achievable brightness approximately an order of magnitude greater than existing free electron laser injector designs. Published by the American Physical Society 2024

Electric field driven focusing and transport of plasma ion beams by micro-glass capillaries beyond the self-focusing limit

Micro-glass capillaries emerge as an important tool for the lossless guiding and focusing of ion beams (Kojima 2018 J. Phys. B: At. Mol. Opt. Phys. 51 042001). The self-focusing mechanism of the capillaries is primarily governed by charged patches induced on their inner walls by the incident beam (Stolterfoht et al 2002 Phys. Rev. Lett. 88 133201). However, the dominance of space charge forces over self-focusing forces in intense (J ≈ 1 A m−2) ion beams establishes a self-focusing limit (Maurya et al 2019 J. Phys. D: Appl. Phys. 52 055205), posing challenges to beam focusing beyond this limit. In this work, a novel method is introduced, demonstrating electrical control over the charge patch dynamics through an externally applied bias voltage, thereby enabling the focusing of Ar ion beams beyond the self-focusing limit. Experimental results reveal that adjusting the biasing voltage allows overcoming the self-focusing limit, resulting in the generation of a high-intensity ( Jout≈3.05×105 A m−2) nano-beam (∼160 nm). Furthermore, electrical control is shown to enhance the performance of both straight and tapered capillaries (SC/TC), with the TC being more effective for nano-beam generation. A Particle-In-Cell (PIC) simulation code has been developed to explain the experimental results. The implications of high-intensity nano ion beams in advancing nanopatterning, nanoscale material analysis, and matter wave interferometry, underscore significant contributions to research and innovation within electronics, materials science, nanotechnology, and emerging quantum technologies.

Recent advances in the CERN PS impedance model and instability simulations following the LHC Injectors Upgrade project

Transverse instability growth rates in the CERN Proton Synchrotron (PS) are studied thanks to the recently updated impedance model of the machine. Using this model, macroparticle tracking simulations were performed with a new method well-suited for the slicing of short wakes, which achieves comparable performance to the originally implemented method while reducing the required number of slices by a factor of 5 to 10. Furthermore, dedicated beam-based measurement campaigns were carried out to benchmark the impedance model. Until now, beam dynamics simulations based on this model underestimated instability growth rates at injection energy. Thanks to a recent addition to the impedance model, namely the kicker magnets' connecting cables and their external circuits, the simulated instability growth rates are now comparable to the measured ones even when neglecting the impact of the space charge force. Finally, the space charge force is included in simulations and its impact on the instability growth rate and intra-bunch motion is studied.

Analysis of single particle and collective beam effects in high intensity beams in a periodic quadrupole channel

In high intensity proton accelerators, there are two main mechanisms that can cause beam degradation: incoherent and coherent effects due to nonlinear space charge forces. The incoherent effects represent the single particle dynamics while the coherent effects represent the collective response of the beam. Of particular interest is the region above a zero current phase advance (σ0) of 90° where the (coherent) second-order envelope instability and the (incoherent) fourth-order particle resonance are seen to lead to emittance growth. Large emittance growth is also seen below the envelope instability region as the full current beam phase advance (σ) decreases. In the present study, we have studied the nonlinear effects in a high intensity beam propagating through a focusing-defocusing (FD) quadrupole channel for σ0 greater than 90°, both analytically, by studying the solutions of Kapchinsky-Vladimirsky (KV) equation and the particle core model, and through detailed particle-in-cell (PIC) simulations using the code. The KV envelope equation gives the collective response of the beam while the particle core model gives the contribution of the single particle effects. With pic simulations, which resemble the behavior of the real beams more closely as compared to envelope calculations or the particle core model, it is possible to study the evolution of the beam in a self-consistent manner. Our studies show, that it is possible to identify the specific process responsible for beam degradation in high intensity beams. It is also possible to identify which process dominates under different conditions. We further show that the width of the emittance increase stop band calculated from PIC simulations is wider than that calculated by the envelope equations and that the width depends on the length of the channel being studied. Published by the American Physical Society 2024

Manipulation and Wakefield Effects on Multi-Pulse Driver Beams in PWFA Injector Stages

Particle-driven plasma wakefield acceleration (PWFA) exploits the intense wakefields excited in a plasma by a high-brightness driver beam in order to accelerate a trailing, properly delayed witness electron beam. Such a configuration offers notable advantages in achieving very large accelerating gradients that are suitable for applications in particle colliders and photon production. Moreover, the amplitude of the accelerating fields can be enhanced by resonantly exciting the plasma using a multi-pulse driver beam with a proper time structure. Before the injection into the plasma stage, the pulsed electron beam, conventionally termed the comb beam, is usually produced and pre-accelerated in a radio-frequency (RF) linear accelerator (linac). In this pape, we discuss challenging aspects of the dynamics that comb beams encounter in the RF injector stage preceding the plasma. In particular, the examples we analyze focus on the use of velocity bunching to manipulate the time structure of the beam and the impact of dipole short-range wakefields on the transverse emittances. Indeed, both processes crucially affect the phase space distribution and its quality, which are determinant features for an efficient acceleration in the plasma. In addition, the analyses we present are performed with the custom tracking code MILES, which utilizes semi-analytical models for a simplified evaluation of wakefield effects in the presence of space charge forces.

Characterization of relativistic electron bunch duration and traveling wave structure phase velocity based on momentum spectra measurements

The Accelerator Research Experiment at Sinbad (ARES) linac at DESY aims to generate and characterize ultrashort electron bunches (fs to sub-fs duration) with high momentum and arrival time stability for the purpose of applications related to accelerator research and development, e.g., development of advanced and compact diagnostics and accelerating structures, test of new accelerator components, medical applications studies, machine learning, etc. During its commissioning phase, the bunch duration characterization of the electron bunches generated at ARES has been performed with an rf-phasing technique relying on momentum spectra measurements, using only common accelerator elements (rf accelerating structures and magnetic spectrometers). The sensitivity of the method allowed highlighting different response times for Mo and Cs2Te cathodes. The measured electron bunch duration in a wide range of machine parameters shows excellent agreement overall with the simulation predictions, thus demonstrating a very good understanding of the ARES operation on the bunch duration aspect. The importance of a precise experimental determination of the phase velocity of the first traveling wave accelerating structure after the electron source, for which we propose a simple new beam-based method precise down to a variation of one part per ten thousand respective to the speed of light in vacuum, is emphasized for this purpose. A minimum bunch duration of 20 fs rms, resolution-limited by the space charge forces, is reported. This is, to the best of our knowledge, around 4 times shorter than what has been previously experimentally demonstrated based on rf-phasing techniques with a single rf structure. The present study constitutes a strong basis for future time characterization down to the sub-fs level at ARES, using dedicated X-band transverse deflecting structures. Published by the American Physical Society 2024

Space Charge Forces analytical model for emittance compensation

Space charge forces represent main induced effects in an RF-injector that degrade the beam quality. In this scenario the laser distribution sent on the photocathode acquires an important role in the emittance compensation process, as the slice analysis shows. Starting from the preliminary studies performed on [1], a novel semi-analytical model of space charge forces is proposed in detail for bunch with arbitrary charge distribution to derive expressions of self-induced forces. The performance of the fields at low energy regime (as the field has not expired RF forces) is under present analysis, we can investigate use of this model in low charge regime. Further, the model has been bench-marked with the behavior of the distributions present in the literature and studied for new ones. It has also been applied for the study of the optimization of a C-band hybrid photoinjector now being commissioned, thus explaining the factor two reduction of the emittance observed at the exit of the gun by changing the initial distribution at the cathode.

Plasma-based particle sources

High-brightness particle beams generated by advanced accelerator concepts have the potential to become an essential part of future accelerator technology. In particular, high-gradient accelerators can generate and rapidly accelerate particle beams to relativistic energies. The rapid acceleration and strong confining fields can minimize irreversible detrimental effects to the beam brightness that occur at low beam energies, such as emittance growth or pulse elongation caused by space charge forces. Due to the high accelerating gradients, these novel accelerators are also significantly more compact than conventional technology. Advanced accelerators can be extremely variable and are capable of generating particle beams with vastly different properties using the same driver and setup with only modest changes to the interaction parameters. So far, efforts have mainly been focused on the generation of electron beams, but there are concepts to extend the sources to generate spin-polarized electron beams or positron beams.The beam parameters of these particle sources are largely determined by the injection and subsequent acceleration processes. Although, over the last decade there has been significant progress, the sources are still lacking a sufficiently high 6-dimensional (D) phase-space density that includes small transverse emittance, small energy spread and high charge, and operation at high repetition rate. This is required for future particle colliders with a sufficiently high luminosity or for more near-term applications, such as enabling the operation of free-electron lasers (FELs) in the X-ray regime. Major research and development efforts are required to address these limitations in order to realize these approaches for a front-end injector for a future collider or next-generation light sources. In particular, this includes methods to control and manipulate the phase-space and spin degrees-of-freedom of ultrashort plasma-based electron bunches with high accuracy, and methods that increase efficiency and repetition rate. These efforts also include the development of high-resolution diagnostics, such as full 6D phase-space measurements, beam polarimetry and high-fidelity simulation tools.A further increase in beam luminosity can be achieve through emittance damping. Emittance cooling via the emission of synchrotron radiation using current technology requires kilometer-scale damping rings. For future colliders, the damping rings might be replaced by a substantially more compact plasma-based approach. Here, plasma wigglers with significantly stronger magnetic fields are used instead of permanent-magnet based wigglers to achieve similar damping performance but over a two orders of magnitude reduced length.

Improvements in longitudinal phase space tomography at PITZ

Methodical studies to improve the existing e-beam Longitudinal Phase Space (LPS) tomography were performed at the Photo Injector Test facility at DESY in Zeuthen. Proof-of-principle simulations were done to address some core concerns e.g. booster phase range, space charge effects and noisy artefacts in results. Phase advance analysis was done with the help of an analytical model that determined the booster phase range and step size. A slit was introduced before the booster to truncate the beam and reduce space charge forces. The reconstruction method adopted was image space reconstruction algorithm owing to its assurance of non-negative solution. An initial scientific presumption of LPS from low energy momentum measurements was established to reduce artefacts in the phase space. This paper will explain the proof-of-principle simulations highlighting the key aspects to obtain accurate results. Reconstructed LPS for different experimental cases will be presented to demonstrate the diagnostic capability.

Influence of extraction voltage on electron and ion behavior characteristics

The characteristics of the extracted ion current have a significant impact on the design and testing of ion source performance. In this paper, a 2D in space and 3D in velocity space particle in cell (2D3V PIC) method is utilized to simulate plasma motion and ion extraction characteristics under various initial plasma velocity distributions and extraction voltages in a Cartesian coordinate system. The plasma density is of the order of 1015 m−3–1016 m−3 and the extraction voltage is of the order of 100 V–1000 V. The study investigates the impact of various extraction voltages on the velocity and density distributions of electrons and positive ions, and analyzes the influence of different initial plasma velocity distributions on the extraction current. The simulation results reveal that the main reason for the variation of extraction current is the space-charge force formed by the relative aggregation of positive and negative net charges. This lays the foundation for a deeper understanding of extraction beam characteristics.

Fast models for the evaluation of self-induced field effects in linear accelerators

Advanced applications of modern linear accelerators (linacs) strongly rely on the quality of the particle beams produced by such machines. Key examples of this kind include particle-driven radiation sources, plasma wakefield acceleration and lepton colliders for high energy physics. Such systems require use of high brightness electron beams implying the simultaneous coexistence of high peak currents, small transverse emittances and narrow energy spectra. The associated high phase space density results in strong self-induced electromagnetic fields, causing mutual interaction of the charged particles through space-charge and wakefield forces. These two sources of collective effects may be both present at significant levels, along with the strong applied fields, both longitudinal and transverse, found in high gradient linacs. As a result, beam dynamics studies capable of investigating the performance of a given device, as well as its operational limits, are crucial. However, the modeling of collective effects in simulation codes tracking large particle ensembles often requires significant, time-intensive numerical resources. In this paper we thus present alternative, simplified approaches for the description of space-charge and wakefield effects that permit streamlined computations. The features of such models are discussed, including their limitations and validating comparisons with existing tracking codes that utilize standard but more time-consuming approaches are shown. The beamlines we consider in our analyses are part of state-of-the-art facilities now under design for which new, challenging beam physics properties due to high fields and high beam brightness are expected. Thus, in addition to the introduction of new modeling techniques, our results provide an useful insight into advanced applications.

3D theory of microscopic instabilities driven by space-charge forces

Microscopic, or short-wavelength, instabilities are known for drastic reduction of the beam quality and strong amplification of the noise in a beam. Space charge and coherent synchrotron radiation are known to be the leading causes for such instabilities. In this paper we present rigorous 3D theory of such instabilities driven by the space-charge forces. We define the condition when our theory is applicable for an arbitrary accelerator system with 3D coupling. Finally, we derive a linear integral equation describing such instability and identify conditions when it can be reduced to an ordinary second order differential equation.

Beam dynamics optimization in the LEBT of LLICTF

A Low Energy Beam Transport (LEBT) has been designed and optimized to inject both a 50[Formula: see text]keV/u, 50[Formula: see text]mA [Formula: see text] beam and a 20[Formula: see text]keV/u, 1[Formula: see text]mA [Formula: see text] beam into the downstream Radio Frequency Quadrupole (RFQ) at the Lanzhou Light Ion Cancer Therapy Facility (LLICTF). The overall aim is to increase the operation efficiency and simplify the complexity of the LLICTF. This dual-beam operation mode creates phase space distortions as a result of the intense space charge, and causes transverse asymmetry due to a mixture of solenoids and a dipole magnet. To mitigate the phase space distortions of the high-intensity proton beam, two beam scrapers have been placed at locations determined through careful analysis of the space charge forces and external focusing force of the beam. Additionally, the Particle Swarm Optimization (PSO) algorithm has been utilized to obtain an approximate solution for the dipole parameters, which helps maintain the symmetry of different symmetrical beams passing through it. Optics designs that implement these solutions are verified with multi-particle simulations.

3D beam-envelope approach for an asymmetric beam in a high intensity linac with a solenoid channel

Presented here is a theory model based on the beam-envelope approach to determine the global behavior of a charged beam propagating through a high intensity linac with a solenoid channel, namely, the orbital evolution of the root-mean-square beam size in the transverse and longitudinal direction. The model is applied to the Gaussian particle distribution, where the motion of an individual particle is governed by linear focusing/defocusing forces in the solenoid channel and RF fields, except for space-charge forces. In this model, highly nonlinear effects that originated from space-charge forces disappear by averaging over the harmonic motions such as the betatron motion and phase motion in the moving direction and the Gaussian distribution. All particles making up a 3D Gaussian bunch obey the same linear equations of motion where all information of nonlinearity in the space-charge forces and the particle distribution are carried in. The theory is validated using Gaussian macro-particle simulation and one of the widely used photonic integrated circuit codes, TraceWin. As an example, the model is applied to the case of an international fusion materials irradiation facility superconducting linac with solenoid guiding and half wave RF acceleration. The results are compared with results obtained by this model and other two approaches.

High-resolution cavity bunch arrival-time monitor for charges less than 1 pC

Pump-probe experiments using x-ray pulses or MeV ultrafast electrons as probes are important for studying ultrafast dynamic processes at the atomic level. Increasing demand is being focused on ultrashort x-ray pulses and electron pulses to research processes down to a few femtoseconds. Due to the limitation of the space charge force, only low charge electron bunches with critical synchronization can achieve such short pulses. A high-precision beam arrival-time monitor for the low charge is especially important. In this paper, a low ${Q}_{l}$ cavity with high sensitivity is designed to measure the arrival time of charges below 1 pC. The pickup is particularly optimized with high $R/Q$ at 4.76 GHz to provide the maximum signal, and the cold test results are in good agreement with the simulations. An IQ demodulation scheme is developed for the readout electronics. In the beam tests, the measured resolution of the beam arrival-time monitor is 33.46 fs at 0.5 pC.

Widely tunable electron bunch trains for the generation of high-power narrowband 1–10 THz radiation

Terahertz radiation enables the coherent excitation of many fundamental modes, such as molecular rotation, lattice vibration and spin precession. To excite the transient state of matter far out of equilibrium, high-power and tunable narrowband terahertz radiation sources have been in great demand for years. However, the terahertz source available at present cannot meet these tunability and power demands, leaving a large scientific gap that has yet to be fully explored. Here we convert the energy modulation induced by the nonlinear longitudinal space charge force to a density modulation and experimentally demonstrate the generation of electron bunch trains with modulation frequencies that are adjustable between 1 and 10 THz. The electron bunch trains can be directly used to produce tunable high-power narrowband terahertz radiation that fully covers the long-standing ‘terahertz gap’, which will open up many more possibilities in terahertz science. A tunable terahertz radiation pulse is demonstrated based on a linear accelerator. The emission frequency of this terahertz radiation is tunable from 1 to 10 THz by changing the bunching frequency of a 34 MeV electron beam. The pulse energy is at the submillijoule level.

Excitation of the σl_l = 90° resonance by the cavity rf accelerating fields

In rf linacs the longitudinal focalization is done by si-nusoidal forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal fo-cusing period σ0l_l can be high. The nonlinear compo-nents of the sinusoidal rf field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σl_l = 90°) when σ0l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. As pointed out in previous papers, the longitudinal beam dynamics is therefore complex, even when the space-charge forces are ignored. The parametric resonance excitation by the rf field is analyzed before discussing the additional effect of the space-charge forces, in particular to explain why the zero-current longitudinal phase advance per trans-verse focusing period σ0l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.

Emittance self-compensation in blow-out mode

We report an unusual regime of emittance self-compensation in an electron bunch generated in the blow-out mode by a radio-frequency photocathode gun. This regime is observed for a strong space-charge field on the cathode reaching around 30%–35% of the accelerating field. Simulations clearly show an initial growth and a subsequent self-compensation of projected emittance in a divergent electron bunch originating from the effects of: (a) strong space-charge forces of mirror charges on the cathode, (b) an energy chirp in the bunch and (c) substantial re-shaping of the electron bunch. Furthermore, we show analytically and numerically how a complex interplay between these effects leads to emittance self-compensation at the gun exit—the effect that is normally observed only in the presence of focusing fields.

APFRFQ – A SIMULATION ENVIRONMENT FOR THE DEVELOPMENT OF HIGH-CURRENT LINEAR ION ACCELERATORS WITH RF FOCUSING

Presented is an interactive environment, APFRFQ, for calculating linear accelerators based on rf field focusing of different types, namely, alternating phase focusing (APF), rf quadrupole focusing (RFQ) and a combination of previous two methods (APF&RFQ). The APFRFQ environment is capable of performing the following tasks in the interactive mode: setting the parameters of the accelerating gaps, calculating the accelerating-focusing channels of linear accelerators taking into account the real geometry of the electrodes, performing numerical simulation of particle dynamics in the calculated channels with the space charge forces taking into account, matching the input parameters of the beam with the given six-dimensional phase distribution and the accelerating structure.