Longitudinal Space Charge Effects Research Articles

Experimental exploration of compressed beam dynamics in an energy recovery linac with comparison to simulations

The compact energy recovery linac (cERL) has been developed for industrial applications since 2017. Applications such as free electron laser require a compressed beam with a small energy spread and transverse emittance. The typical operation energy of cERL is an intermediate energy region close to 17.5 MeV; therefore, the electron bunch is easily affected by the longitudinal space-charge effects and the coherent synchrotron radiation wakefield effects. Bunch compression is demonstrated by optimizing a combination of a longitudinally chirped electron bunch and the arcs with nonzero ${R}_{56}$ parameters. When the bunch compression procedure is applied for a bunch charge of 60 pC, an increase in energy spread is observed at the short bunch length. We systematically explored the chirp phase to determine the best condition. The measurement results of the energy spread, bunch length, and transverse emittance were compared with the tracking simulation results to understand the compressed beam dynamics.

A Raman quantum free-electron laser model

Operation of a Quantum Free Electron Laser (QFEL) could provide a compact and fully coherent source of X- and γ-rays. Imperative to experimental realization is allowing for decoherence effects of either spontaneous emission or space-charge to take place, having opposing constraints. Here, for the first time, we present a one-dimensional QFEL Wigner model that includes longitudinal space-charge effects by quantizing the periodic potential derived from the Fourier components of the longitudinal electron beam density. The model is used to investigate steady-state QFEL gain and momentum state dynamics for a variety of space-charge regimes. We find increased saturation lengths and lower saturation intensity as a result of attenuated transitions in the two-level quantum system. In addition, we characterize a space-charge regime where specific transitions outside the QFEL bandwidth are targeted, such that the conventional description breaks down. These findings serve as a consistent theoretical extension of existing QFEL models.

Description of longitudinal space charge effects in beams and plasma through dielectric permittivity

We develop a universal framework that allows for quickly solving a wide class of problems for longitudinal space charge effects in beams and plasmas in cylindrical geometry. We introduce the longitudinal dielectric permittivity for the beam of charged particles, which describes its collective space charge response. The analysis yields an effective plasma frequency, which depends on the transverse geometry of the system. This dielectric permittivity mirrors the dielectric permittivity of plasma and matches the one dimensional expression once the transverse size of the beam is large. Several particle species can be included as additive terms describing susceptibility of each specie. The developed approach allows to study stability criteria for collective beam–beam and beam–plasma instabilities for arbitrary transverse distributions in particle densities.

Transparent-grid scheme for generating cathode-emittance-dominated beams in a gridded thermionic gun

A transparent-grid scheme is proposed for generating cathode-emittance-dominated beams in a gridded thermionic gun. In the proposed scheme, the grid emittance arising from the potential difference between the grid and grid-mesh center is suppressed by tuning the grid voltage to the gridless gun potential. We developed a 50 kV gridded thermionic gun that is followed by a 238 MHz cavity for 500 kV acceleration. The measured projected emittance as a function of grid voltage shows a clear minimum approaching the cathode emittance and agrees well with a numerical simulation and a theoretical grid emittance taking into account the longitudinal space-charge effect. The measured minimum emittance for a core part which represents 60% of a 1-nC electron bunch is 1.5 μm · rad making the transparent-gridded thermionic gun a promising electron source for high brightness beam application such as a soft X-ray free-electron laser.

Imposing strong correlated energy spread on relativistic bunches with transverse deflecting cavities

We demonstrate a novel scheme for imposing or removing large energy chirp on relativistic electron bunches. This method relies on the transverse-to-longitudinal mixing accomplished with a set of transverse deflecting cavities. The working principles of the new concept are explained using the first-order matrix formalism in the approximation of the linear single-particle dynamics. The scheme demonstrates versatility regarding the average beam energy and, hence, positioning along the accelerator beam line. The performance of the scheme is numerically investigated with the elegant particle-tracking code. It is shown that the associated nonlinear effects causing emittance deterioration for the extreme quantities of the total energy spread can be effectively compensated by optimization of the Twiss parameters while relying on the eigenemittance analysis. The impact of the longitudinal space charge effects on the beam dynamics in the proposed scheme is also investigated.

High-gain, short wavelength FEL in the Raman regime

While FEL technology has reached the EUV and X-ray regime at existing machines such as LCLS and SACLA, the scale of these projects is often impractical for university research and industrial applications. Sub-millimeter period undulators can reduce the size of a high-gain EUV FEL, but will impose stringent conditions on the electron beam. In particular, a high-gain EUV FEL based on undulators with a sub-mm period [1] requires electron beam currents upwards of 1kA at energies below 100MeV. Coupled with the small gap of such undulators and their low undulator strengths, K<0.1, such beam parameters bring longitudinal space-charge effects to the foreground of the FEL process. When the characteristic length associated with electron beam plasma behaviour becomes comparable to the gain-length, the relevant theoretical FEL model transitions from the Compton to the Raman limit [2], where collective field effects dominate. In this work, we investigate the behaviour of the FEL's gain-length and efficiency in these two limits. The starting point for the analysis is the one-dimensional FEL theory including space-charge forces. The derived results is compared to numerical results of Genesis 1.3 simulations. This theoretical model predicts that in the Raman limit, the gain-length scales as the beam current to the one-fourth power while the efficiency grows as the square root of the beam current. This advantage in efficiency may prove critical in the development of very compact short wavelength FELs, such as the Keck Foundation-funded SAMURAI FEL at UCLA.

Theoretical analysis and simulation of the influence of self-bunching effects and longitudinal space charge effects on the propagation of keV electron bunch produced by a novel S-band Micro-Pulse electron Gun

As an important electron source, Micro-Pulse electron Gun (MPG) which is qualified for producing high average current, short pulse, low emittance electron bunches steadily holds promise to use as an electron source of Coherent Smith-Purcell Radiation (CSPR), Free Electron Laser (FEL). The stable output of S-band MPG has been achieved in many labs. To establish reliable foundation for the future application of it, the propagation of picosecond electron bunch produced by MPG should be studied in detail. In this article, the MPG which was working on the rising stage of total effective Secondary Electron Yield (SEY) curve was introduced. The self-bunching mechanism was discussed in depth both in the multipacting amplifying state and the steady working state. The bunch length broadening induced by the longitudinal space-charge (SC) effects was investigated by different theoretical models in different regions. The 2D PIC codes MAGIC and beam dynamic codes TraceWin simulations were also performed in the propagation. The result shows an excellent agreement between the simulation and the theoretical analysis for bunch length evolution.

Simulation of a cascaded longitudinal space charge amplifier for coherent radiation generation

Longitudinal space charge (LSC) effects are generally considered as harmful in free-electron lasers as they can seed unfavorable energy modulations that can result in density modulations with associated emittance dilution. This “micro-bunching instabilities” is naturally broadband and could possibly support the generation of coherent radiation over a broad region of the spectrum. Therefore there has been an increasing interest in devising accelerator beam lines capable of controlling LSC induced density modulations. In the present paper we refine these previous investigations by combining a grid-less space charge algorithm with the popular particle-tracking program elegant. This high-fidelity model of the space charge is used to benchmark conventional LSC models. We finally employ the developed model to investigate the performance of a cascaded LSC amplifier using beam parameters comparable to the ones achievable at Fermilab Accelerator Science & Technology (FAST) facility currently under commissioning at Fermilab.

Matching sub-fs electron bunches for laser-driven plasma acceleration at SINBAD

We present theoretical and numerical studies of matching sub-femtosecond space-charge-dominated electron bunch into the Laser-plasma Wake Field Accelerator (LWFA) foreseen at the SINBAD facility. The longitudinal space-charge (SC) effect induced growths of the energy spread and longitudinal phase-space chirp are major issues in the matching section, which will result in bunch elongation, emittance growth and spot size dilution. In addition, the transverse SC effect would lead to a mismatch of the beam optics if it were not compensated for. Start-to-end simulations and preliminary optimizations were carried out in order to understand the achievable beam parameters at the entrance of the plasma accelerator.

Generation of stable subfemtosecond hard x-ray pulses with optimized nonlinear bunch compression

A simple method to generate attosecond x-ray pulses from the optimization of high-harmonic rf linearizer and longitudinal space charge effects is proposed.

Echo-enabled tunable terahertz radiation generation with a laser-modulated relativistic electron beam

A new scheme to generate narrow-band tunable terahertz (THz) radiation using a variant of the echo-enabled harmonic generation is analyzed. We show that by using an energy chirped beam, THz density modulation in the beam phase space can be produced with two lasers having the same wavelength. This removes the need for an optical parametric amplifier system to provide a wavelength-tunable laser to vary the central frequency of the THz radiation. The practical feasibility and applications of this scheme are demonstrated numerically with a start-to-end simulation using the beam parameters at the Shanghai Deep Ultraviolet Free-Electron Laser facility (SDUV). The central frequency of the density modulation can be continuously tuned by either varying the chirp of the beam or the momentum compactions of the chicanes. The influence of nonlinear rf chirp and longitudinal space charge effect have also been studied in our article. The methods to generate the THz radiation in SDUV with the new scheme and the estimation of the radiation power are also discussed briefly.

An improved transfer map approach to longitudinal beam dynamics

In this paper we present our transfer map approach for studying longitudinal beam dynamics. It combines synchrotron motion mapping equations with Differential Algebraic transfer map extraction. The novel approach can take into account a variety of effects, including non-relativistic effects, arbitrary changes to RF voltage and synchronous phase, as well as nonlinearities and coupling between transverse and longitudinal beam optics. All these are made possible efficiently and accurately, without the need for time consuming element-by-element 6D particle tracking. Moreover, longitudinal space charge effects can be readily treated too. The utility of this approach is demonstrated by applying it to the study of ion beam acceleration in a proposed pre-booster ring of the Medium Energy Electron Ion Collider (MEIC) facility at TJNAF.

Effect of nonuniform radial density distribution on the space charge dominated beam bunching

Beam dynamics of a space charge dominated beam during the bunch compression is studied self consistently for the case of fixed shape non-uniform bell shape and hollow shape density distributions in the transverse direction. We have used thick slices at different parts of the beam to account for variation in the beam radius in the study of the transverse dynamics. The longitudinal dynamics has been studied using the disc model. The axial variation of the radius of the slices and emittance growth arising from the phase dependence of the transverse rf forces are also included in the simulation. We have modified the beam envelope equation to take into account the longitudinal space charge effect on the transverse motion which arises due to the finite bunch size. To demonstrate the application of the theoretical formulations developed, we have studied a sinusoidal beam bunching system and presented detailed numerical results.

Gain length fitting formula for free-electron lasers with strong space-charge effects

We present a power-fit formula, obtained from a variational analysis using three-dimensional free-electron laser theory, for the gain length of a high-gain free-electron laser's fundamental mode in the presence of diffraction, uncorrelated energy spread, and longitudinal space-charge effects. The approach is inspired by the work of Xie [Nucl. Instrum. Methods Phys. Res., Sect. A 445, 59 (2000)], and provides a useful shortcut for calculating the gain length of the fundamental Gaussian mode of a free-electron laser having strong space-charge effects in the 3D regime. The results derived from analytic theory are in good agreement with detailed numerical particle simulations that also include higher-order space-charge effects, supporting the assumptions made in the theoretical treatment and the variational solutions obtained in the single-mode limit.

Single-shot method for measuring femtosecond bunch length in linac-based free-electron lasers

There is growing interest in the generation and characterization of femtosecond and subfemtosecond pulses from linac-based free-electron lasers (FELs). In this report, following the method of Ricci and Smith [Phys. Rev. ST Accel. Beams 3, 032801 (2000)], we investigate the measurement of the longitudinal bunch profile of an ultrashort electron bunch produced by these FELs. We show that this method can be applied in a straightforward manner at x-ray FEL facilities such as the Linac Coherent Light Source by slightly adjusting the second bunch compressor followed by running the bunch on an rf zero-crossing phase of the final linac. We find that the linac wakefield strongly perturbs the measurement, and through analysis show that it can be compensated in a simple way. We demonstrate the effectiveness of this method and wakefield compensation through numerical simulations, including effects of coherent synchrotron radiation and longitudinal space charge. When used in conjunction with a high-resolution electron spectrometer, this method potentially reveals the temporal profile of the electron beam down to the femtosecond and subfemotsecond scale.

Virtual dielectric waveguide mode description of a high-gain free-electron laser. I. Theory

A set of mode-coupled excitation equations for the slowly growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser (FEL), including the effects of longitudinal space charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single Gaussian mode.

Analytical analysis of longitudinal space charge effects for a bunched beam with radial dependence

The longitudinal space-charge (LSC) force can be a major cause of the microbunching instability in the linac for an x-ray free-electron laser. In this paper, the LSC-induced beam modulation is studied using an integral equation approach that takes into account the transverse (radial) variation of the LSC field for both the coasting-beam limit and a bunched beam. Variation of the beam energy and the transverse beam size is also incorporated. We discuss the validity of this approach and compare it with other analytical analyses as well as numerical simulations.

Experiments with electron beam modulation at the DUVFEL accelerator

Recently strong modulation of the electron bunch longitudinal phase space was obtained in the DUVFEL accelerator at NSLS. The chirped beam energy spectra exhibit a spiky structure with a subpicosecond spike separation. A model based on the longitudinal space-charge effect has been suggested as an explanation of the observed effect. For characterization of the structure and comparison with the model we performed several experiments. In this paper we present experimental data and discuss them in relation to the model.

Feasibility of projectile-fragment-beam separation in a storage ring

A secondary beam of nuclear projectile fragments is injected in a storage ring. The feasibility of separation of an ion species of a beam from the secondary beam in the ring is described. The procedure of the separation is stochastic cooling, electron cooling, RF capture, and acceleration. The longitudinal space–charge effects on the separation have been studied in performing particle-tracking simulations.

Longitudinal space-charge effects in a retarding field energy analyzer

Theoretical and experimental work has been carried out to study the longitudinal space-charge effects in a retarding field energy analyzer. A one-dimensional, steady state model for both a monoenergetic beam and a thermal beam has been developed for this purpose. Potential improvements of using two-dimensional and time-dependent solutions are also briefly discussed. The study shows that, if the current density inside the device is higher than a critical value, the longitudinal space-charge effect and the formation of a potential minimum similar to the virtual cathode formation in an electron gun will distort the measured energy spectrum. The measured FWHM and the rms energy spread will be affected. The measured mean energy will also be shifted toward the low-energy side. By using a two-dimensional correction, the theoretical model also qualitatively explains the appearance of a visible tail at the high-energy side of the spectrum, as observed in experiments. According to the theory, to avoid this measurement distortion due to the longitudinal space charge, care has to be taken to limit the current density inside the device.