Bunching Factor Research Articles

Analytical formulas of coherent-synchrotron-radiation induced microbunching gain and emittance growth in an arbitrary achromatic four-bend chicane

The coherent synchrotron radiations (CSR) emitted by a high-brightness electron beam during transport in a bending magnet is a double-edged sword in electron accelerators. While CSR contributes to a stronger radiation field than the incoherent radiation, it simultaneously leads to degradation of the electron beam quality. Specifically, CSR effects manifest in increases of the beam energy spread and the projected emittance, and amplification of the microbunching instability. A dedicated design of the multi-bend transport lines to mitigate CSR effects has recently become a crucial consideration in modern high-brightness electron accelerators. This paper presents analytical formulas for the CSR-induced microbunching instability gain and for the induced emittance growth in an arbitrary achromatic four-bend chicane with inclusion of both the steady-state and transient CSR effects. For the microbunching instability, an iterative method is employed to solve the integral equation for the bunching factor, providing satisfactory gain formulas. Regarding the CSR-induced emittance growth, based on the linear transfer matrices and incorporating the expressions of the CSR-induced energy spread, analytical formulas are derived for the projected emittance growth in an arbitrary four-bend transport section. The analytical formulas are compared and show good agreement with semi-analytical Vlasov calculations and particle tracking simulations. As an application, the obtained analytical formulas are applied to evaluate the CSR effects in the design of a general achromatic four-bend bunch compressor chicane, providing a quick estimate on the microbunching gain and the induced emittance growth. From the widely adopted symmetric C-shape chicane to a non-symmetric S-shape chicane, a design recently proposed by the co-authors, our analytical formulas offer insight into the evolution of the microbunching gain and the emittance growth with the variations of design parameters. In comparison to the time-consuming, full numerical particle tracking simulations currently employed for CSR effect analyses, the analytical formulas presented in this paper significantly reduce the evaluation time, enabling systematic study of parametric dependencies and comprehensive optimization with inclusion of CSR effects within specified design parameter ranges.

Matched phase sweep method for the optimization of bunching factor in dual rf systems of high-intensity hadron synchrotrons

The scheme of multiturn painting beam injection in a dual harmonic rf system is widely employed in high-intensity proton or heavy ion synchrotrons to alleviate space charge effects. With a momentum offset of the injected beams, a large bunching factor can be achieved at the end of multiturn painting injection process. However, the momentum offset can increase the instantaneous beam peak current during the first 1/4 synchrotron period, causing a reduced bunching factor during the beam injection process. To address this issue, a matched phase sweep method is developed. By matching the synchrotron oscillation frequency and beam injection period, an optimal curve for phase sweeping can be directly obtained. The effectiveness of the method has been checked via simulations and machine study, which are in good agreement. The matched phase sweep method is employed for the increase of the beam power in the upcoming upgrade project of the China Spallation Neutron Source and can also be generally applied for the operation in the presence of dual harmonic rf system in high-intensity hadron synchrotrons. Published by the American Physical Society 2024

Theory and design consideration of a THz superradiant waveguide FEL

We present theoretical analysis and design considerations of a THz superradiant FEL. We derive analytical expressions for the spectral parameter of THz radiation, emitted superradiantly in a rectangular waveguide using a Longitudinal Section Magnetic mode expansion. The results compare well with numerical simulations using UCLA GPTFEL code. GPT simulations of the accelerator e-beam transport show that the chirp provided by a hybrid photocathode RF gun, can produce tight bunching at the undulator site below σ = 100fs. This enables intense superradiant emission up to 3THz, limited by the beam bunching factor. Phase-space analysis of the beam transport indicates that keeping the beam bunching parameter small enough for higher THz frequency operation is limited by the energy spread of the beam in the gun.

Calculation of space-charge tune shift in a cylindrical chamber for bunched beams employing Green’s function formalism

When computing the space-charge tune shift for a relativistic bunched beam within a cylindrical chamber, mirror currents for a coasting beam, initially introduced to replace the chamber wall, are employed. Subsequently, the obtained result is extended to encompass the bunched beam, taking into account the bunching factor which quantifies the distribution of bunches around the accelerator ring. In the process of derivation, the terms that characterize the bunch length are intuitively integrated into the formula. As a result, the validity of this approach has never been established. This study provides the derivation of the space-charge tune shift formula for both relativistic and nonrelativistic bunched beams right from the outset, employing the Green function formalism. Subsequently, it is compared with the earlier formula derived using mirror currents. Published by the American Physical Society 2024

Fully coherent soft X-ray pulse generation based on ERL

Energy recovery linacs (ERLs) possess the bright prospect of fully coherent X-ray generation. Recently, we designed a 600 MeV energy recovery linac capable of producing high power fully coherent radiation pulses at 13.5 nm with a relatively low-intensity 256.5 nm seed laser profiting from the employment of angular-dispersion-induced microbunching (ADM) technology. We also designed a matched multiplexed system that can deflect each radiator by 8 mrad with a carefully choreographed multi-bend achromat (MBA) scheme. As a result of downstream MBA’s dispersion compensation, bunching factors will be enhanced both at the fundamental wavelength and high harmonics. The bunching factor of the 19th harmonic increased from 10% to 26%, and that of the 57th harmonic became 8.4%, which is sufficient to generate fully coherent radiation in the soft X-ray range.

Strong evidence of inter-layer optical phonons and low-temperature acoustic-phonon bunching in WS2/WSe2 hetero-structure

The nature of inter-layer optical phonons observed in the hetero-structure is being reported in this work. Additionally, phonon bunching between modes of both and can be ascertained in the acoustic region. The second-order bunching factor, , is seen to improve sharply upon reduction of temperature, below a critical temperature. Moreover, the integral intensity of the peaks increases almost exponentially with the applied power of the laser source. To a good approximation, the phonon frequency corresponding to most of the Raman active modes varies linearly with altered temperature (78–300 K). However, the mixed mode located at exhibits a non-linear temperature dependence over the working range of temperature. Prevailing phonon bunching aspects of the phonon replica discussed in terms of bunching factor, frequency correlation parameter, etc., are highlighted based on acquired low-temperature Raman data and theoretical analogy.

Analytical study of higher harmonic bunching and matrix formalism in linear high-gain free-electron laser model

Short-wavelength single-pass free electron lasers (FEL) are capable of generating transverse-coherent and high-power radiations. Compared with the self-amplified spontaneous emission (SASE) FEL scheme, seeded FEL schemes can, in principle, improve the longitudinal coherence of radiation pulses. In recent years, the research community has pursued the realization of high-repetition-rate (MHz) and high-average-power (kW) seeded FELs. To alleviate the requirements of external seeding lasers, many novel seeding schemes have been proposed, which are currently limited by the state-of-the-art laser systems. An analytical study of a recently proposed seeding scheme based on direct-amplification-enabled harmonic generation (DEHG) is presented herein. In contrast to the complete numerical simulations and optimization design, this study starts from one-dimensional FEL equations of motion and derives an analytical formula for the harmonic bunching factor at the chicane exit after the electron beam traverses the modulator undulator. Additionally, to obtain a quick estimate of downstream high-gain FEL performance, we constructed a linear high-gain FEL transport matrix, including the three-dimensional effects incorporated by the Ming-Xie formula. As an application of the analytical formulas, we discuss three different cases for designing and optimizing the seeding scheme. We expect this analytical approach to shed light on seeding designs that aim to produce the desired high-brightness mirobunched electron beam.

Improving the Performance of an Ultrashort Soft X-ray Free-Electron Laser via Attosecond Afterburners

In this study, we implement attosecond afterburners in an ultrashort soft X-ray free-electron laser (FEL) to improve the performance of generating attosecond pulses. In this scheme, the FEL pulse produced in the normal radiator section is dumped while the well bunched electron beam is reserved and reused in downstream afterburners. Subsequently, radiation in the afterburners gains rapidly as the bunching factor in the current spike is large, making the radiation pulse much shorter and cleaner than that from a normal radiator. Multi-shot simulations are carried out to demonstrate the performance and stability of the proposed technique.

Characterizations of the longitudinal beam behaviors and impedances measurements at HLS-II

In this article, the longitudinal beam bunch behaviors of the Hefei Light source-II (HLS-II) are effectively investigated and analyzed based on the beam multi-parameter measurement system. Simultaneously, the temporal beam characteristic parameter extraction (T-BCPE) method is developed for measuring the longitudinal impedances of machine. In the case of 100.4 kV radio-frequency (RF) voltage, the inductance and resistance in the longitudinal coupling impedance of HLS-II are obtained as 115 ± 13 nH and 1320 ± 310 Ω by extracting bunch lengthening factor and asymmetry factor, respectively. In addition, the longitudinal beam dynamical characteristics and potential-well distortion are also in-depth analyzed above the threshold current of the microwave instability. As a result, the longitudinal broadband impedance of HLS-II is measured to be 8.94 ± 0.44 Ω while 0.339 ± 0.004 of the scaling factor in combination with the theoretical analysis.

Near-ideal energy modulator for tunable THz pulse generation using sectioned hollow channel plasma system

To break the bottleneck in generating high-power tunable coherent THz radiation with a narrow spectral bandwidth, we propose a novel scheme of using a hollow channel plasma to generate energy modulation in relativistic electron beams. Using magnetic optics, the energy modulation is then effectively converted into beam density modulation, forming microbunches with high-quality and very high bunching factors. The arrangement of segmented multistage hollow channels can further improve the bunching factor, thus significantly increasing the THz energy. We show both theoretical analyses and simulations of this scheme, showing that scheme can be realized in accelerator facilities with repetition rates on the order of kHz, providing great potential in revolutionizing science and related technologies.

Analysis of modulation parameters for high repetition rate seeded FEL

For high repetition rate seeded Free electron lasers (FELs), the seed laser with sufficient pulse energy and high repetition rate is a challenge. Several schemes to address this issue were proposed. In this paper, the modulation parameters for high repetition rate seeded FEL are analyzed for the modulator lengthening scheme, the seeded oscillator–amplifier scheme, and the scheme of the self-modulation, respectively. Taking account of the optical field gain, the energy modulation formulas modified with the equivalent length of the modulation undulator are given for the corresponding schemes. For the modulator lengthening scheme, when the length of the modulation undulator is longer than three gain lengths the effect of the optical field gain should be considered. For the self-modulation scheme, the magnitude of the energy modulation depends on the bunching factor generated in the pre-modulation section and the equivalent length of the self-modulation undulator. For the seeded oscillator–amplifier scheme, it is found that there is an optimal return fraction of the radiation power and a corresponding modulator length to maximize the energy modulation, which are 63% and about three gain lengths, respectively.

Generation of Tunable 10-mJ-Level Terahertz Pulses through Nonlinear Plasma Wakefield Modulation

High-density electron-bunch train--based tunable coherent terahertz radiation with a narrow spectral bandwidth is highly essential for many scientific applications. Here we propose a scheme to produce ultrahigh-peak-current (more than 10 kA) electron-bunch trains with tunable picosecond spacing for the generation of such terahertz sources. Passing through a plasma section and interacting with the self-excited nonlinear plasma wake, the beam gains a ``sawtooth'' energy modulation. By means of magnetic optics, it is then effectively converted into a beam density modulation forming microbunches with a high charge of up to a few nanocoulombs and a bunching factor as high as approximately $0.8$. Tunable narrowband terahertz radiation with energy on the order of 10 mJ can be generated, which we show in both theoretical analyses and simulations via this process. This scheme can be realized in accelerator facilities with repetition rates on the order of kilohertz or even submegahertz, which provides great potential in modern science and related technologies.

Longitudinal equilibrium density distribution of arbitrary filled bunches in presence of a passive harmonic cavity and the short range wakefield

We propose a novel scheme for the calculation of bunch profiles and synchronous phase shifts for arbitrary fill patterns in electron storage rings considering both the effects of the passive harmonic cavity and the short range wakefield. This scheme treats the bunch as a charge distribution rather than a point charge with a bunch form factor, and divides the voltage induced in the cavity into two groups: that induced by the previous passages and that by the present passage, where the latter is integrated with the short range wakefield from all the other vacuum components. An iteration loop for computing the bunch profiles, including a subloop using Newton iteration for calculating the synchronous phase deviations, is built and implemented into a matlab-based code. Using this code, we study the bunch lengthening and centroid transient effects for several possible fill patterns in the Hefei Advanced Light Facility storage ring under design. We find the method is very efficient, and the CPU time for the whole calculation on a regular personal computer is less than 30 seconds for each case even with more than 700 bunches. Using the case of a long gap fill as a benchmark example, both the results given by our code and the multiparticle tracking simulation with elegant are in very good agreement.

Longitudinal dynamics study and optimization in the beam commissioning of the rapid cycling synchrotron in the China Spallation Neutron Source

The China Spallation Neutron Source (CSNS) is a high intensity proton accelerator-based facility, and its accelerator complex includes two main parts: a H- linac and a rapid cycling synchrotron (RCS). The RCS accumulates the 80 MeV proton beam, and accelerates it to 1.6 GeV, with a repetition rate of 25 Hz. The beam commissioning of RCS began in May, 2017 and reached the target beam power of 100 kW in February, 2020. The longitudinal beam dynamics study plays the key role in the commissioning. The study and optimization include the synchronicity between the ramping magnet field and the RF system, the mitigation of the high intensity effects to minimize the beam loss and the measurement of the longitudinal dynamics. Through the optimization of the bunch factor, the strong space charge effects with high intensity is mitigated, thus the RCS transmission efficiency arrives mostly at 100 %. The beam distribution is not affected by the phase loop with a new algorithm and the beam loss is smaller than the original one. The beam commissioning in longitudinal plane is reviewed in the paper.

Lattice design for angular dispersion enhanced microbunching in storage rings

Generation of coherent radiation pulses is of remarkable interest in the synchrotron light source community. A novel technique has been proposed to produce temporal coherent radiation in ref. [1]. In this scheme, an oblique incidence seed laser is utilized to introduce an angular modulation which is converted to microbunching by an angular dispersion section. In this paper, a specific design of the angular dispersion section is given to realize the coupling between transverse and longitudinal directions which satisfied the microbunching requirements of this technique. Numerical simulation results demonstrate that this lattice can be used to enhance the bunching factor at very high harmonics of the seed laser. The lattice structure has good flexibility, the elements of the transport matrix related to microbunching can be easily adjusted, and the beta function in the radiator can be simply optimized by adjusting the magnets of the transport line.

Intensity optimization of x-ray free-electron laser by using phase shifters

This paper presents a method that uses a gap scan of the phase shifter to optimize the intensity of a free-electron laser (FEL) by matching its phase with that of the electron beam. Phase shifters are essential instruments, especially for a long undulator line, which is segmented by drift sections. The phase-matched (in-phase) and the 180\ifmmode^\circ\else\textdegree\fi{} offset (out-of-phase) conditions are investigated using linear theory, FEL simulations, and experiments to understand how the phase shifter affects FEL amplification. We show that the FEL intensity is dominantly reduced by phase mismatch in the saturation region, where the microbunched electron beam is sufficiently developed, and that the difference of FEL intensity between the in-phase and out-of-phase conditions is an effect of evolution of the bunching factor. At the Pohang Accelerator Laboratory x-ray Free-Electron Laser (PAL-XFEL), the gap scan of the phase shifter at 9.7 keV increased FEL intensity by 4 times compared to the calculated gap of the phase shifter. This intensity increase was obtained dominantly in the saturation region.

Higher harmonic voltage analysis of magnetic-alloy cavity for CSNS/RCS upgrade project

A rapid cycling synchrotron (RCS) in China Spallation Neutron Source (CSNS) would be upgraded, and the proton beam power will reach 200–500 kW. Three RF cavities loaded by magnetic-alloy (MA) material will be added in RCS tunnel to form a dual-harmonic RF system with eight ferrite-loaded cavities in RCS. The bandwidth of the MA cavity is wide because of its intrinsic Q value of less than 1. Higher harmonics can be excited in MA cavities, because the RF power is directly fed into the MA cavity from the final stage of the RF power amplifier. The distortion of voltage in the cavity gap caused by higher harmonics may deteriorate the beam quality. The influence of the higher harmonics to beam needs to be evaluated and the amplitude of higher harmonics should to be suppressed. We built a mathematical model with two functions based on the RF bucket acceptance and bunch factor to evaluate this influence. Groups of harmful amplitudes and phases of higher harmonics were found according to the mathematical model by using multi-objective particle swarm optimization (MOPSO). The dual-harmonic RF system with higher harmonics in CSNS/RCS and a suitable harmonic suppression for MA cavities was discussed according to the results of MOPSO and the beam dynamics simulations.

Benchmarking coherent radiation spectroscopy as a tool for high-resolution bunch shape reconstruction at free-electron lasers

We present a systematic comparison of two complementary methods for determining the longitudinal charge density profile of the compressed electron bunches in the soft x-ray free-electron laser FLASH: a frequency-domain technique---coherent transition radiation (CTR) spectroscopy---and a time-domain technique---streaking of the electron beam with a transversely deflecting microwave structure (TDS). While the direct time-profile measurement with a TDS is a well-established method invented at SLAC, our group has pioneered high-resolution bunch shape analysis based on coherent radiation spectroscopy. We have developed a broadband spectrometer covering the wavelength range from $5\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ to $433\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ with two sets of remotely interchangeable staged reflection gratings. The measured spectral intensity allows to compute the absolute magnitude of the bunch form factor but not its phase which, however, is needed to retrieve the bunch profile. Two phase retrieval methods are investigated in detail: analytic phase computation by means of the Kramers-Kronig dispersion relation, and iterative phase retrieval. Several computational techniques are compared and evaluated in view of their applicability and efficiency. For a large variety of bunch shapes, the time profiles derived from the spectroscopic data are compared with the TDS profiles, and generally excellent agreement is observed down to the 10 fs level. For part of the measurements, two independent CTR spectrometer systems have been available, yielding almost identical bunch shapes. In summary, we demonstrate that using well calibrated and broadband spectroscopy data, a fast and reliable phase reconstruction algorithm leads to bunch profiles competitive to high resolution TDS measurements.

Performance Simulation for a Prototype 1.5 GHz Superconducting Harmonic Cavity

Superconducting radio frequency cavities are used as main accelerating cavities and harmonic cavities in modern light sources. The addition of a harmonic cavity provides the possibility to increase the electron bunch length and therefore to improve the beam life time. The effects on instabilities and the bunch lengthening factor by harmonic cavities can be obtained from theoretical calculations. However, these calculations ignore phase transient effects and may overestimate the desired performance of the harmonic cavities. A multibunch multiparticle tracking method was developed to simulate the performance of harmonic cavities for non-uniform filling patterns, which take into account phase transient effects. Performance simulations using this tracking method for a prototype 1.5-GHz superconducting harmonic cavity for the Taiwan photon source are presented here.

Obliquely incident laser and electron beam interaction in an undulator

The angular drift of a laser beam is of particular concern in applications such as seeded free-electron lasers. A systematical study of the obliquely incident laser and electron beam interaction in an undulator is presented in this paper. Theoretical analysis and numerical simulations demonstrate that the interaction would imprint energy and angular modulations on the electron beam simultaneously. Compared with the normally incident pattern, the obliquely incident laser-electron interaction leads to reductions in the bunching factors of HGHG and EEHG. In the meanwhile, proactive applications of this multi-dimensional modulation technique may bring vitality to the field of laser-electron manipulation