Longitudinal Phase Space Research Articles

Conditional guided generative diffusion for particle accelerator beam diagnostics

Advanced accelerator-based light sources such as free electron lasers (FEL) accelerate highly relativistic electron beams to generate incredibly short (10s of femtoseconds) coherent flashes of light for dynamic imaging, whose brightness exceeds that of traditional synchrotron-based light sources by orders of magnitude. FEL operation requires precise control of the shape and energy of the extremely short electron bunches whose characteristics directly translate into the properties of the produced light. Control of short intense beams is difficult due to beam characteristics drifting with time and complex collective effects such as space charge and coherent synchrotron radiation. Detailed diagnostics of beam properties are therefore essential for precise beam control. Such measurements typically rely on a destructive approach based on a combination of a transverse deflecting resonant cavity followed by a dipole magnet in order to measure a beam’s 2D time vs energy longitudinal phase-space distribution. In this paper, we develop a non-invasive virtual diagnostic of an electron beam’s longitudinal phase space at megapixel resolution (1024 × 1024) based on a generative conditional diffusion model. We demonstrate the model’s generative ability on experimental data from the European X-ray FEL.

Operation of Rf Systems During Joint Booster and Nuclotron Sessions

The article discusses the results of commissioning of RF systems of the NICA injection complex and plans for their further development. The preparation of the injection complex for injection into the collider requires an increase in the beam intensity in the Nuclotron outlet by about two orders of magnitude. Obtaining the required intensity will be achieved by accumulating the beam on injection energy using electronic cooling and reducing acceleration losses. This will require optimization of all systems of the complex, including a significant reduction in losses associated with RF systems. The experience allows us to choose the optimal strategy for the further development of HF systems. The main directions are: (1) accumulation of the beam in the longitudinal phase space during injection into the Booster, (2) reduction of the growth of the longitudinal emittance during acceleration, (3) bypass of the beam clot-in-clot from the Booster to the Nuclotron without growth of the longitudinal emittance, and (4) minimizing losses during acceleration and beam bypasses. The latter requires matching the acceleration rate with the capabilities of existing HF systems.

Wakefield generation in hydrogen and lithium plasmas at FACET-II: Diagnostics and first beam-plasma interaction results

Plasma wakefield acceleration provides ultrahigh acceleration gradients of tens of GeV/m, providing a novel path toward efficient, compact, TeV-scale linear colliders, and high brightness free electron lasers. Critical to the success of these applications is demonstrating simultaneously high gradient acceleration, high energy transfer efficiency, and preservation of emittance, charge, and energy spread. Experiments at the FACET-II National User Facility at SLAC National Accelerator Laboratory aim to achieve all of these milestones in a single-stage plasma wakefield accelerator, providing a 10 GeV energy gain in a <1 m plasma with high energy transfer efficiency. Such a demonstration depends critically on diagnostics able to measure emittance with mm mrad accuracy, energy spectra to determine both percent level energy spread, and broadband energy gain and loss, incoming longitudinal phase space, and matching dynamics. This paper discusses the experimental setup at FACET-II, including the incoming beam parameters from the FACET-II linac, plasma sources, and diagnostics developed to meet this challenge. Initial progress on the generation of beam ionized wakes in meter-scale hydrogen gas is discussed as well as commissioning of the plasma sources and diagnostics. Published by the American Physical Society 2024

Reconstructing phase space of injection beam based on the measurement of accumulated beam: A novel tomography algorithm and its applications

The measurement of phase space has always been an important topic in the field of accelerator physics, playing an indispensable role in understanding the beam dynamics. The phase space distribution of the injected beam is crucial for optimizing the multiturn accumulation injection process in synchrotrons. However, directly and accurately measuring the phase space distribution is a challenging task. In this study, we propose an innovative tomographic algorithm based on the measurement data of the accumulated beam profile obtained from the wall current monitor (WCM) in a synchrotron, to reconstruct the longitudinal phase space of the injected beam. Simulations were conducted for various initial distribution scenarios, and the results showed that this algorithm can achieve a difference of about 4% in the rms momentum spread between the initial and reconstructed phase space distribution of the injected beam. This algorithm has been applied to the China Spallation Neutron Source and successfully measured the momentum spread of the injected beam. Machine studies considering the phase error of the injected beam showed a high consistency between the reconstructed beam profiles and the measurement results from the WCM on Rapid Cycling Synchrotron. The research results demonstrate that this algorithm can be an effective approach for measuring the momentum distribution of the injected beam in a synchrotron. Furthermore, this method also has the potential to be extended to reconstruct the transverse phase space of the injected beam. Published by the American Physical Society 2024

Longitudinal phase space diagnostics with a nonmovable corrugated passive wakefield streaker

Time-resolved diagnostics at free-electron laser (FEL) facilities, in particular electron beam longitudinal phase space (LPS) and FEL power profile measurements, provide information highly valuable for users, machine development studies, and beam setup. We investigate the slice energy resolution of passive streaker setups, in particular the effect of an energy chirp on the measured slice energy spread. Downstream of the hard x-ray SASE2 beamline at the European XFEL, these measurements are enabled by a single-plate nonmovable passive wakefield streaker, essentially a rectangular corrugated plate placed inside a vacuum chamber. We show measurements with a time resolution down to a few femtoseconds and an energy resolution down to a few MeVs. Published by the American Physical Society 2024

Beam-based commissioning of a novel X -band transverse deflection structure with variable polarization

Longitudinal electron-beam diagnostics play a critical role in the operation and control of x-ray free-electron lasers, which rely on parameters such as the current profile, the longitudinal phase space, or the slice emittance of the particle distribution. On the one hand, the femtosecond-scale electron bunches produced at these facilities impose stringent requirements on the resolution achievable with the diagnostics. On the other, research and development of novel accelerator technologies such as beam-driven plasma-wakefield accelerators (PWFA) demand unprecedented capabilities to resolve the centroid offsets in the full transverse plane along the longitudinal bunch coordinate. We present the beam-based commissioning of an advanced X-band transverse-deflection rf structure (TDS) system with the new feature of providing variable polarization of the deflecting force: the PolariX-TDS. By means of a comprehensive campaign of measurements conducted with the prototype, key parameters of the rf performance of the system are validated and a phase-space characterization of an electron bunch is accomplished with a time resolution of 3.3 fs. Furthermore, an analysis of second-order effects induced on the bunch from its passage through the PolariX-TDS is presented. Published by the American Physical Society 2024

Experimental characterization of the optical klystron effect to measure the intrinsic energy spread of high-brightness electron beams

The intrinsic energy spread of electron beams needs to be measured to characterize and optimize high-brightness electron beam sources such as those driving x-ray free-electron lasers (FELs). We demonstrate the use of the optical klystron effect as a precise and high-resolution method to measure the electron beam energy spread. The optical klystron setup consists of undulator modules and magnetic chicanes placed between them. The energy spread is found by measuring the radiation power produced in the undulators as a function of the chicanes’ strengths. High resolution and simplicity are the advantages of this approach, in contrast to the standard method, which measures the longitudinal phase space of the electron beam with a transverse deflector. The demonstration was performed at Athos, the soft x-ray FEL beamline of SwissFEL, for which we measured energy spreads below 1 MeV at a central beam energy of 3.4 GeV. We have verified the consistency of the method for different parameters (radiation wavelengths, undulator polarization configurations, and electron bunch durations) and we have benchmarked it against the standard measurement approach using a transverse deflector. Our results confirm the optical klystron as a valid approach to measure the electron beam energy spread. The method can be especially useful to reconstruct low energy spread values, where the conventional approach may be resolution limited, such as in ultra high-brightness radiofrequency photoinjectors or plasma sources, or when transverse deflectors are not available. Published by the American Physical Society 2024

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.

Improvement of the longitudinal phase space tomography at the J-PARC synchrotrons

The longitudinal phase space tomography, which reconstructs the phase space distribution from the one-dimensional bunch profiles, is used in various accelerators to measure longitudinal beam parameters. At the J-PARC, an implementation of the phase space tomography based on the Convolution Back Projection method (CBP) has been used to measure the momentum spread of the injected beam. The method assumes that the beam distribution rotates without significant deformation during the synchrotron oscillation. Because of the nonlinearity of synchrotron motion with sinusoidal RF voltage, the method can be used only in limited situations such as small amplitude synchrotron oscillation. Algebraic Reconstruction Techniques (ART) in conjunction with particle tracking, which is implemented in the CERN’s tomography code, allows accurate reconstructions even for nonlinear large amplitude synchrotron oscillations. We present the overview of the application of the CERN’s tomography code to the J-PARC synchrotrons. The results of benchmarking are also reported.

Tailoring of the longitudinal phase space for improved Free-Electron Laser performance

Free-electron lasers are capable of producing high-quality radiation in a wide wavelength range and at very high power and brilliance. To reach improved performance especially regarding coherence, bandwidth and wavelength stability, different seeding techniques are often required. However, a successful implementation of seeding typically demands a very high-quality electron beam, in terms of energy distribution and emittance. Techniques like Echo-Enabled Harmonic Generation (EEHG) and High-Brightness SASE (HB-SASE) require, or are significantly enhanced, by a flat distribution of particles in the longitudinal phase space. In this paper we describe how the initially chirped longitudinal phase space in the proposed Soft X-ray Laser (SXL) at the MAX IV laboratory can be tailored by first overcompressing and then de-chirping the electron pulse. We also show that it is possible to retain the properties of the electron bunch and how such an enhanced distribution can drive HB-SASE “seeding”, resulting in a significantly reduced bandwidth and a better wavelength stability.

Linearization of an Electron Beam’s Longitudinal Phase Space Using a Hollow-Channel Plasma

The removal of undesired beam nonlinear energy chirp (time-energy correlation) or linearization of the beam longitudinal phase space (LPS) is crucial for high-brightness linac-based scientific applications, such as x-ray free-electron lasers. In this paper, we propose that a low-density hollow channel plasma can be used as a near-ideal passive linearizer to significantly linearize the beam LPS and, at the same time, preserve the beam emittance. Physically, the passage of the beam through the hollow plasma channel excites a strong quasicosinoidal longitudinal wakefield that acts to mitigate the beam nonlinear energy chirp by superimposing a reverse chirp on the beam. The theoretical analyses and large-scale three-dimensional start-to-end simulations confirm that the beam longitudinal phase space can be almost completely linearized without noticeable beam emittance growth. Application of such a near-ideal linearizer may significantly improve the performance of numerous accelerator-based applications.

A beamline to control longitudinal phase space whilst transporting laser wakefield accelerated electrons to an undulator

Laser wakefield accelerators (LWFAs) can produce high-energy electron bunches in short distances. Successfully coupling these sources with undulators has the potential to form an LWFA-driven free-electron laser (FEL), providing high-intensity short-wavelength radiation. Electron bunches produced from LWFAs have a correlated distribution in longitudinal phase space: a chirp. However, both LWFAs and FELs have strict parameter requirements. The bunch chirp created using ideal LWFA parameters may not suit the FEL; for example, a chirp can reduce the high peak current required for free-electron lasing. We, therefore, design a flexible beamline that can accept either positively or negatively chirped LWFA bunches and adjust the chirp during transport to an undulator. We have used the accelerator design program MAD8 to design a beamline in stages, and to track particle bunches. The final beamline design can produce ambidirectional values of longitudinal dispersion (R_{56}): we demonstrate values of + 0.20 mm, 0.00 mm and − 0.22 mm. Positive or negative values of R_{56} apply a shear forward or backward in the longitudinal phase space of the electron bunch, which provides control of the bunch chirp. This chirp control during the bunch transport gives an additional free parameter and marks a new approach to matching future LWFA-driven FELs.

Analytical study of FEL oscillator saturation state based on longitudinal ponderomotive bucket

Free Electron Laser(FEL) oscillator is the main working mode to produce infrared and THz wavelength range radiation. At FEL saturation state, the interaction between electron beams and radiation becomes nonlinear. Saturation power can be solved by numerical simulation of macro particle motion in longitudinal phase space or by semi-analytical formulae analogous to conventional laser system from previous study. While in this paper, the motions of macro-particle are depicted with analytical formulae in the assumption that energy transfer is mainly from captured electrons of ponderomotive bucket. Then corresponding electron beam extraction efficiency can be achieved due to initial and final state of electron beams. Therefore laser power is confirmed through equilibrium situation inside resonator cavity. These simple analytical formulae can be used to optimize output laser power and offer a better understanding in FEL oscillator saturation. Taking small signal gain regime as an example, the optimum FEL efficiency is obtained at gain to loss ratio around 4.1. This agrees well with the results of three-dimension simulation.

Twin-pulse seeding enables pump-probe capabilities in the EUV to soft X-ray spectrum at synchrotron light sources

Having previously reported that separating the two stages of echo-enabled harmonic generation (EEHG) with one or more bending magnet (BM) sections allows the BMs to serve as the desired source of momentum compaction, here we demonstrate that this arrangement can greatly reduce the total energy modulation required by any 4th generation synchrotron light source, leading to higher repetition rates as well as stronger coherent radiation output power, with significant benefits. Since the EEHG beamline performance is mainly determined by the momentum compaction, beam emittances and beta functions of a storage ring lattice, allowing for different separations between the two stages is a straightforward way to increase the momentum compaction of chicane 1. This also enables pump-probe capabilities in a novel context, where twin-pulse seeding on the same electron bunch would allow two distinct radiation pulses with an adjustable delay in the range of 0.1 to 10 ps. In the twin-pulse seeding scheme, the same electron bunch could undergo modulation from two distinct laser pulses. Later stages would produce independent harmonics in subsequent straight sections. There are two variations of this twin-pulse seeding scheme, supporting different scientific applications. With a common modulation in stage 1, the first option allows simultaneously two independent radiation sources, with a full coverage of the EUV (2.5 to 50 nm) to soft X-ray (1.25 to 2.5 nm) spectrum; for the second option, the same stage 2 undulator could generate two coherent pulses both fitting within the FEL bandwidth, or at distinct harmonics. We present particle tracking simulation studies based on the APS-U lattice, including quantum excitation and radiation damping. These simulations indicate that there is no degradation of the modulated longitudinal phase space even when the two stages are separated by as many as 10 BM sections.

Reconstruction of x-ray free-electron laser pulse duration and energy chirp from spectral intensity fluctuations

Accurate measurements of the x-ray pulse duration produced by x-ray free-electron lasers (XFELs) typically rely on longitudinal electron beam phase space diagnostics, e.g., an x-band transverse deflecting cavity (XTCAV). An alternative group of methods is based on measurements of radiation statistics and spectral correlations. In this paper, we present a statistical analysis of FEL radiation which extends the previous technique by Lutman et al. [Phys. Rev. ST Accel. Beams 15, 030705 (2012)], including the electron beam energy chirp in the FEL gain model. In doing so, we show that with measurements of the average spectrum and the spectral intensity correlations, one can reconstruct the x-ray pulse length, e-beam chirp, and corresponding spectrometer resolution. We validate our approach with 1D and 3D simulations before moving to an experimental demonstration in which our method finds results similar to those obtained from XTCAV measurements.

An analytical envelope model for space charge in cyclotrons

The statistical σ-matrix approach is used to derive general envelope equations for ellipsoidal bunches with space charge in isochronous and non-isochronous fixed-field accelerators (FFAs) These accelerators couple the radial and longitudinal phase spaces due to momentum dispersion induced by the space charge effect. This generates a rotation of the bunch around the local vertical axis which is known in the field as the vortex effect. A special invariant of the vortex is found which represents its total angular momentum with respect to its center. For the isochronous cyclotron, a special solution of the envelope equations is found which describes a circular bunch with equal radial and longitudinal RMS sizes. The existence of this solution is a direct consequence of the circular symmetry of the single particle Hamiltonian in a co-moving coordinate frame. The stationary solution of the circular bunch fixes the relation between bunch sizes and accelerated current (or the total charge per bunch) for given emittances. The general envelope equations may easily be implemented in existing numerical envelope codes.

Selective phase filtering of charged beams with laser-driven antiresonant hollow-core fibers

Emerging accelerator concepts increasingly rely on the combination of high-frequency electromagnetic radiation with electron beams, enabling longitudinal phase space manipulation which supports a variety of advanced applications. The handshake between electron beams and radiation is conventionally provided by magnetic undulators which unfortunately require a balance between the electron beam energy, undulator parameters, and laser wavelength. Here we propose a scheme using laser-driven large-core antiresonant optical fibers to manipulate electron beams. We explore two general cases using ${\mathrm{TM}}_{01}$ and ${\mathrm{HE}}_{11}$ modes. In the former, we show that large energy modulations $O$(100 keV). can be achieved while maintaining the overall electron beam quality. Further, we show that by using larger field strengths $O$(100 MV/m) the resulting transverse forces can be exploited with beam-matching conditions to filter arbitrary phases from the modulated electron bunch, leading to the production of $\ensuremath{\approx}100$ attosecond FWHM microbunches. Finally, we also investigate the application of the transverse dipole ${\mathrm{HE}}_{11}$ mode and find it suitable for supporting time-resolved electron beam measurements with sub-attosecond resolution. We expect the findings to be widely appealing to high-charge pump-probe experiments, metrology, and accelerator science.

Fast and flexible control of beam longitudinal phase space for high-repetition-rate x-ray free-electron lasers.

The wide-ranging requirements for the photon properties from multiple beamlines in superconducting based free-electron lasers (FELs) demand more challenging beam manipulation techniques. Shot-by-shot control of electron beam bunch length and peak current at high repetition rate up to megahertz is highly desired. In this paper, we present a comprehensive study of a method based on a 2-m-long normal conducting radio-frequency cavity to achieve fast and flexible control of beam compression and realize the full potential of the facility, including theoretical analysis, beam dynamics simulations, and conceptual cavity design for the Linac Coherent Light Source II and its high-energy upgrade. We illustrate the physical mechanism of the chirping cavity on the control of the final beam compression and propose methods to lower the requirements for the cavity parameters. The application of this method will allow tailored photon properties of individual beamlines to optimize their performance and drastically improve the multiplexing capabilities of a high-repetition rate FEL facility.

First measurement of energy diffusion in an electron beam due to quantum fluctuations in the undulator radiation

Plasma and beam physics are usually considered as classical physics disciplines with quantum effects featuring only rarely. In particular, free electron lasers (FELs) even in the Angstrom regime (developed recently and being upgraded towards even shorter wavelengths) are well described by classical mechanics and electrodynamics. There is, however, a quantum effect that can influence the operation of these devices and limit the shortest achievable wavelength, namely energy diffusion in an electron beam due to quantum fluctuations in undulator radiation. Although this effect has been calculated theoretically, it has never been measured. In this paper we present measurements of quantum diffusion effect at the European X-Ray Free-Electron Laser. The method uses a recently installed wakefield structure, which enables measurements of the longitudinal phase space after the hard X-ray undulator. The effect of quantum diffusion in the undulator is measured for the first time, and the results are in good agreement with theoretical predictions.

Generalisation and longitudinal extension of the Genetic Lattice Construction (GLC) algorithm

The GLC algorithm [1] allows the construction of efficient transfer lines with defined imaging properties using a minimum number of quadrupole elements. This work describes a generalisation of this algorithm to make it applicable to the use of arbitrary beam optical elements. This includes an extension to longitudinal phase space.