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The Advanced Light Source Upgrade (ALS-U) is a 4th generation diffraction-limited soft x-ray radiation source, consisting of a new accumulator ring (AR) and a new storage ring (SR). In both rings coupling-impedance driven instabilities need careful evaluation to ensure meeting the machine's high-performance goals. This paper presents the workflow followed in building the impedance models and the beam-stability analysis based on those models. We follow the commonly accepted approach of separating the resistive-wall and the geometric parts of the impedance; the former is obtained by analytical formulas, the latter by numerical electro-magnetic codes (primarily CST Studio software) with perfectly-conducting boundary conditions. Impedance budgets are established and pseudo-Green functions calculated to be used in beam dynamics studies. We also present various ways to cross-check simulation results for reliable impedance modeling. Finally, the crucial single-bunch instability current thresholds for various operation modes are determined and discussed.

The worm-gear transverse momentum dependent (TMD) function g1T is one of the eight leading-twist TMDs and has the probabilistic interpretation of finding a longitudinally polarized quark inside a transversely polarized hadron. In this work, we present the first simultaneous extraction of g1T from all the available experimental measurements. The study involves the analysis of COMPASS, HERMES, and Jefferson Lab data on semi-inclusive deep-inelastic scattering using Monte Carlo techniques. We also compare g1T obtained from this experimental data with different theoretical approaches, such as the large-Nc approximation, the Wandzura-Wilczek-type approximation, and lattice QCD.

Author(s): Hemsing, E; Marcus, G; Fawley, WM; Schoenlein, RW; Coffee, R; Dakovski, G; Hastings, J; Huang, Z; Ratner, D; Raubenheimer, T; Penn, G | Abstract: We present the results from studies of soft X-ray seeding options for the LCLS-II X-ray free electron laser (FEL) at SLAC. The LCLS-II will use superconducting accelerator technology to produce X-ray pulses at up to 1 MHz repetition rate using 4 GeV electron beams. If properly seeded, these pulses will be nearly fully coherent, and highly stable in photon energy, bandwidth, and intensity, thus enabling unique experiments with intense high-resolution soft X-rays. Given the expected electron beam parameters from start to end simulations and predicted FEL performance, our studies reveal echo enabled harmonic generation (EEHG) and soft X-ray self-seeding (SXRSS) as promising and complementary seeding methods. We find that SXRSS has the advantage of simplicity and will deliver 5-35 times higher spectral brightness than EEHG in the 1-2 nm range, but lacks some of the potential for phase-stable multipulse and multicolor FEL operations enabled by external laser seeding with EEHG.

Many research and applications areas require photon sources capable of producing gamma-ray beams in the multi-MeV energy range with reasonably high fluxes and compact footprints. Besides industrial, nuclear physics and security applications, a considerable interest comes from the possibility to assess the state of conservation of cultural assets like statues, columns etc., via visualization and analysis techniques using high energy photon beams. Computed Tomography scans, widely adopted in medicine at lower photon energies, presently provide high quality three-dimensional imaging in industry and museums. We explore the feasibility of a compact source of quasi-monochromatic, multi-MeV gamma-rays based on Inverse Compton Scattering (ICS) from a high intensity ultra-violet (UV) beam generated in a free-electron laser by the electron beam itself. This scheme introduces a stronger relationship between the energy of the scattered photons and that of the electron beam, resulting in a device much more compact than a classic ICS for a given scattered energy. The same electron beam is used to produce gamma-rays in the 10–20 MeV range and UV radiation in the 10–15 eV range, in a ~4×22 m2 footprint system.

X-ray free-electron lasers (FELs), which amplify light emitted by a relativistic electron beam, are extending nonlinear optical techniques to shorter wavelengths, adding element specificity by exciting and probing electronic transitions from core levels. These techniques would benefit tremendously from having a stable FEL source, generating spectrally pure and wavelength-tunable pulses. We show that such requirements can be met by operating the FEL in the so-called echo-enabled harmonic generation (EEHG) configuration. Here, two external conventional lasers are used to precisely tailor the longitudinal phase space of the electron beam before emission of X-rays. We demonstrate high-gain EEHG lasing producing stable, intense, nearly fully coherent pulses at wavelengths as short as 5.9 nm (~211 eV) at the FERMI FEL user facility. Low sensitivity to electron-beam imperfections and observation of stable, narrow-band, coherent emission down to 2.6 nm (~474 eV) make the technique a prime candidate for generating laser-like pulses in the X-ray spectral region, opening the door to multidimensional coherent spectroscopies at short wavelengths. Echo-enabled harmonic generation in a free-electron laser enables 45th harmonic pulses from a 264 nm wavelength seed, yielding 5.9 nm wavelength coherent output.

In Chap. 3 we showed that choosing the action-angle canonical variables in a one-dimensional Hamiltonian system dramatically simplifies the dynamics: the action remains constant and the angle increases linearly with time. With minor modifications, the same transformation can be applied to the Hamiltonian ( 6.14) that describes betatron oscillations in an accelerator. This yields an invariant of the motion and is also a useful starting point for analyzing more complicated dynamics.

A focused laser beam can easily produce an extremely high electric field at the focal point. For example, a laser beam with an energy of 1 J and pulse duration of 100 fs focused to a spot size of 10 \(\upmu \)m, has a maximum electric field of about 40 GV/cm which is many orders of magnitude larger than what is used in traditional accelerators. In this chapter we will discuss several topics related to the possibility of using laser fields for accelerating charged particles.

The radiation process is not instantaneous — it requires some time and free space around the orbit for the radiation to be formed. In this chapter we estimate the longitudinal extent and transverse size of the free space volume needed for the synchrotron radiation. We then analyze the radiation of a bunch of many particles.

Plane electromagnetic waves are solutions of the Maxwell equations that are unbounded in the plane perpendicular to the direction of propagation. They approximately describe local properties of the real field far from the source of radiation. They can also be used as building blocks from which a general solution of Maxwell’s equations in free space can be constructed. An important practical example of electromagnetic radiation that finds many applications in accelerator physics and elsewhere is a focused laser beam. The distribution of the electromagnetic field in such light is characterized by Gaussian modes which can be considered as a superposition of plane waves propagating at small angles to the direction of the beam. Gaussian beams correctly describe the field structure near the focus and the diffraction of the beam as it propagates away from the focal region. In this chapter, we will briefly summarize the main properties of plane electromagnetic waves, and then derive the field in a Gaussian beam.

In this chapter we will show how the radiation damping in electron and positron rings can be added to the Hamiltonian and Vlasov formalism, and calculate how radiation damping affects the energy, transverse actions and distribution function.

In the preceding chapters we focused our attention on the motion of a single particle. In this chapter, we will introduce the concept of the distribution function and describe the formalism of the kinetic equation for treating large ensembles of particles in a beam. While this chapter focuses on deterministic Hamiltonian motion, kinetic equations in general can also include stochastic motion and damping.

In this chapter, based on simple intuitive arguments we derive the Lienard–Wiechert potentials that solve the problem of the electromagnetic field of a point charge moving in free space.

The Lagrangian and Hamiltonian formalisms are among the most powerful ways to analyze dynamic systems. In this chapter we will introduce Lagrange’s equations of motion and discuss the transition from Lagrange’s to Hamilton’s equations. We write down the Lagrangian and Hamiltonian for a charged particle in an electromagnetic field, and introduce the Poisson bracket.

In this chapter, we derive the Hamiltonian for a particle moving in a circular accelerator. Our derivation uses several simplifying assumptions. First, we assume that there is no electrostatic field, \(\phi = 0\), and the magnetic field does not vary with time. Second, the magnetic field is arranged in such a way that there is a closed reference (or nominal) orbit for a particle with a nominal momentum \(p_0\)—this is achieved by a proper design of the magnetic lattice of the ring. We will also assume that this reference orbit is a plane curve lying in the horizontal plane. Our goal is to describe the motion in the vicinity of this reference orbit of particles having energies (or, equivalently, momenta) that can slightly deviate from the nominal one.

A typical accelerator uses a sequence of various types of magnets separated by sections of free space (so-called drifts) to control the motion of the particle beam. To specify the Hamiltonian ( 5.23) we need to know the vector potential, \(A_s\), for these magnets. We evaluate the fields and Hamiltonian for the major magnet types assuming that the field profiles are uniform over their length. Often in analysis and simulations, one has to take into account that at the end points of the magnets different field geometries appear, called fringe fields. The impact of these fields are usually treated as highly localized corrections which are calculated separately from the bulk of the magnet, and involve higher order terms that we will simply neglect in this chapter. When fringe fields are weak they can be treated as field errors, which are covered in Chap. 8.

The linear oscillator is a simple model that lies at the foundation of many physical phenomena and plays a crucial role in accelerator dynamics. Many systems can be viewed as an approximation to a set of independent linear oscillators. In this chapter, we will review the main properties of the linear oscillator including its response to resonant excitations, slowly varying forces, random kicks, and parametric variation of the frequency. We will discuss the impact of damping terms as well as how small, nonlinear terms in the oscillator equation modify the oscillator frequency and lead to nonlinear resonance.

In this chapter we consider scattering of an electromagnetic wave on a free charged particle — a process often referred to as Thomson scattering. This interaction induces a damping force on the charged particle called the radiation reaction force, which maintains the energy balance. Additionally, the radiation exerts another force in the direction of propagation called the light pressure, which is responsible for conserving the combined momentum of the particles and fields. We also briefly discuss inverse Compton scattering off a point charge moving with a relativistic velocity.

In the previous chapter we studied propagation of electromagnetic waves in free space. Free space is an idealization which can be used when the waves propagate far from material boundaries. If this is not the case, one has to take into account the interaction of the electromagnetic field with the medium. In this chapter we will study one example that is especially important for accelerator applications, when the medium can be modeled as a perfectly conducting metal whose boundaries reflect the electromagnetic field without losses. The impact of resistive losses can often be treated perturbatively, as we have seen in Chap. 12. We will consider cylindrical waveguides and resonant cavities. We will also discuss how cavity eigenmodes can be excited by relativistic beams of charged particles.

The electromagnetic field generated by a high-current, relativistic beam of charged particles plays an important role in beam dynamics. On the one hand, the force exerted on the beam by this field can lead to beam instabilities and a deterioration of its properties in the process of beam generation, acceleration and transport. On the other hand, this field induces currents and charges in the beam environment that can be used for diagnostic purposes. Hence calculation of this field and the forces associated with it constitutes an essential part of beam physics for accelerators.

Higher-order components in the magnetic field in a ring introduce nonlinear terms into the Hamiltonian and generate nonlinear resonances. This can lead to complicated motion for particles with large amplitudes of betatron oscillations. We derive the resonant structure in the phase space due to a sextupole magnet when the fractional part of the tune is close to \(\pm \frac{1}{3}\). For a Hamiltonian system with many resonances, they can interact with each other and lead to stochastic orbits in phase space. To understand this effect, we study a model called the standard map, that illustrates qualitative features of what can occur in a Hamiltonian system with many resonances. The impact on dynamics is similar whether originating from effects as diverse as nonlinear magnetic fields, RF cavities, space-charge forces among the charged particles in a bunch, or interactions between bunches.

We show that a standard Linac configuration (consisting of accelerating sections, linearizing section, and magnetic chicane compressor) currently used in drivers for single-pass EUV/x-ray FELs is compatible with energy recovery, provided that certain timing constraints are met. By circulating the spent, rather than the fresh beam as in a conventional high-power ERL FEL design, the beam brightness can be more easily preserved thus facilitating lasing at short wavelength. As in a conventional ERL, the proposed design allows for energy-spread compression, enabling low-energy beam dumping and high energy-recovery efficiency. Results from numerical simulations presented in this paper show that this configuration could, in principle, support the generation of multi-kW average radiation power required for high-volume production EUV lithography.

© 2017 by the author. Studying ultrafast processes on the nanoscale with element specificity requires a powerful femtosecond source of tunable extreme-ultraviolet (XUV) or x-ray radiation, such as a free-electron laser (FEL). Current efforts in FEL development are aimed at improving the wavelength tunability and multicolor operation, which will potentially lead to the development of new characterization techniques offering a higher chemical sensitivity and improved spatial resolution. One of the most promising approaches is the echo-enabled harmonic generation (EEHG), where two external seed lasers are used to precisely control the spectro-temporal properties of the FEL pulse. Here, we study the expected performance of EEHG at the FERMI FEL, using numerical simulations. We show that, by employing the existing FERMI layout with minor modifications, the EEHG scheme will be able to produce gigawatt peak-power pulses at wavelengths as short as 5 nm. We discuss some possible detrimental effects that may affect the performance of EEHG and compare the results to the existing double-stage FEL cascade, currently in operation at FERMI. Finally, our simulations show that, after substantial machine upgrades, EEHG has the potential to deliver coherent multicolor pulses reaching wavelengths as short as 3 nm, enabling x-ray pump-x-ray probe experiments in the water window.

The development of undulator technologies capable of generating sub-cm undulator periods is assuming an increasing importance in X-ray free electron laser (FEL) applications. Indeed, such devices jointly with the high brightness electron beams already demonstrated at operating facilities would allow for lower energy, more compact electron linacs with a beneficial impact on the size and cost of X-ray FEL facilities. A novel design super-conducting undulator is being developed at the Lawrence Berkeley National Laboratory (LBNL) with the potential of sub-cm periods with reasonably large undulator parameter and gap. The potential and capability of such undulator technology need to be experimentally demonstrated. In this paper, the possibility of constructing an infrared FEL by combining the new undulator with the high brightness beam from the APEX injector facility at LBNL is investigated. Calculations show that the resulting FEL, when operated in self-amplified-spontaneous-emission mode, is expected to deliver a saturated power of almost a MW within a ∼ 4 m undulator length, in a single-spike of coherent radiation at ∼ 2 μ m wavelength. It will be also shown that the small-period of the undulator associated with the relatively low energy of the APEX beam, forces the FEL to operate in a regime with unusual and interesting characteristics. The alternative option of laser seeding the FEL is also briefly examined, showing the potential to reduce the saturation length even further.

Attosecond X-ray pulses are an indispensable tool for the study of electronic and structural changes in molecules undergoing chemical reactions. They have a wide bandwidth comparable to the energy bands of valence electronic states and, therefore, are well suited for making and probing multiple valence electronic excitations using core electron transitions. Here we propose a method of creating a sequence of two attosecond soft X-ray pulses in a free electron laser by optical manipulation of electrons located in two different sections of the electron bunch. The energy of each X-ray pulse can be of the order of 100 nJ and the pulse width of the order of 250 as. The carrier frequency of each X-ray pulse can be independently tuned to a resonant core electron transition of a specific atom of the molecule. The time interval between the two attosecond pulses is tunable from a few femtoseconds to a hundred femtoseconds with better than 100 as precision.

Several recent reports have identified the scientific requirements for a future soft X-ray light source [1, 2, 3, 4, 5], and a high-repetition-rate free-electron laser (FEL) facility responsive to them is being studied at Lawrence Berkeley National Laboratory (LBNL) [6]. The facility is based on a continuous-wave (CW) superconducting linear accelerator with beam supplied by a high-brightness, high-repetition-rate photocathode electron gun operating in CW mode, and on an array of FELs to which the accelerated beam is distributed, each operating at high repetition rate and with even pulse spacing. Dependent on the experimental requirements, the individual FELs may be configured for either self-amplified spontaneous emission (SASE), seeded high-gain harmonic generation (HGHG), echo-enabled harmonic generation (EEHG), or oscillator mode of operation, and will produce high peak and average brightness X-rays with a flexible pulse format ranging from sub-femtoseconds to hundreds of femtoseconds. This new light s...

FERMI@elettra is a fourth-generation light source user facility under construction at the Elettra Laboratory in Trieste, Italy. The high-quality 1.2 GeV electron beam drives two-seeded Free Electron Lasers (FELs) in the wavelength range 100−10 nm. Wavelength tunability, variable polarization and higher electron beam energies to reach even shorter output wavelengths are also in the machine delivery plan. This paper describes the physics processes that have been modelled to simulate FERMI@elettra and the computer codes used to optimize the machine design. The paper focuses on several design challenges and how these translate into modelling and simulation challenges.

Hydrodynamic simulations have been carried out using the multi-physics radiation hydrodynamics code HYDRA and the simplified one-dimensional hydrodynamics code DISH. We simulate possible targets for a near-term experiment at LBNL (the Neutralized Drift Compression Experiment, NDCX) and possible later experiments on a proposed facility (NDCX-II) for studies of warm dense matter and inertial fusion energy-related beam-target coupling. Simulations of various target materials (including solids and foams) are presented. Experimental configurations include single-pulse planar metallic solid and foam foils. Concepts for double-pulsed and ramped-energy pulses on cryogenic targets and foams have been simulated for exploring direct drive beam-target coupling, and concepts and simulations for collapsing cylindrical and spherical bubbles to enhance temperature and pressure for warm dense matter studies.

We present a new plasma-based method of guiding an electromagnetic pulse. The scheme consists of an inhomogeneous magnetic field and a uniform density plasma, in contrast to existing schemes that rely on transverse plasma density gradients but need not be magnetized. The refractive index of a magnetized plasma depends on the strength and direction of the magnetic field as well as the plasma density. A guiding channel is formed by using field inhomogeneity to generate the desired transverse profile of the index of refraction. The concept is analyzed with an envelope equation and, for the specific example of a wiggler magnetic field, with a two-dimension particle-in-cell simulation. A simplified model of this scheme as producing a magnetic wall in analogy to metallic waveguides is presented, for which corresponding approximate relations for the guided mode axial wavelength and radius are derived as functions of the plasma and magnetic field parameter. These are seen to be in good agreement with particle-in-cell simulation results. Since the desired inhomogeneity of the refractive index can be made easily when the electromagnetic wave frequency is close to the cyclotron frequency, this guiding scheme is most readily applied in the microwave regime.

We present simulations and analysis of the heating of warm dense matter foils by ion beams with ion energy less than one MeV per nucleon to target temperatures of order one eV. Simulations were carried out using the multi-physics radiation hydrodynamics code HYDRA and comparisons are made with analysis and the code DPC. We simulate possible targets for a proposed experiment at LBNL (the so-called Neutralized Drift Compression Experiment, NDCXII) for studies of warm dense matter. We compare the dynamics of ideally heated targets, under several assumed equation of states, exploring dynamics in the two-phase (fluid-vapor) regime.

The performance of a free electron laser (FEL) using a low-power extreme ultraviolet (EUV) pulse as an input seed is investigated. The parameters are appropriate for 30 nm seeds produced from high-power Ti:Sapphire pulses using high harmonic generation schemes. It is found that, for reasonable beam parameters, robust FEL performance can be obtained. Both time-independent and time-dependent simulations are performed for varying system parameters using the GENESIS simulation code. A comparison is made with a two-stage harmonic FEL that is seeded by a high-power Ti:Sapphire pulse.

Preliminary studies of harmonic lasing have shown significant promise as a method to produce radiation at higher photon energies for a given electron energy and for a given undulator. The basic idea is to suppress radiation at the fundamental resonant wavelength, and allow radiation at a specific harmonic to grow exponentially without being driven by nonlinear processes at the fundamental. This has several potential benefits: higher photon energies for the same undulator field, plus significantly more power and smaller bandwidth compared to extracting nonlinear radiation at the harmonic after the fundamental has reached saturation. In this paper, we use beam parameters from the current design of LCLS-II to take a critical look at the challenge of suppressing radiation at the fundamental wavelength and to evaluate how much of an improvement in terms of photon energy reach and brightness can be achieved through harmonic lasing. For undulators with adjustable magnetic fields, a scheme is presented which can delay the onset of saturation at the fundamental wavelength by a factor of 2. Performance characteristics and especially spectral brightness are compared to self-seeded beam lines as an alternative method to reduce bandwidth, as well as with more conventional SASE beam lines.

Key scientific results from recent experiments, modeling tools, and heavy ion accelerator research are summarized that explore ways to investigate the properties of high energy density matter in heavy-ion-driven targets, in particular, strongly-coupled plasmas at 0.01 to 0.1 times solid density for studies of warm dense matter, which is a frontier area in high energy density physics. Pursuit of these near-term objectives has resulted in many innovations that will ultimately benefit heavy ion inertial fusion energy. These include: neutralized ion beam compression and focusing, which hold the promise of greatly improving the stage between the accelerator and the target chamber in a fusion power plant; and the Pulse Line Ion Accelerator (PLIA), which may lead to compact, low-cost modular linac drivers.

Beam lines using echo-enabled harmonic generation can be designed to have extremely low sensitivity to energy chirps in the electron beam, as shown through theory and detailed simulations. These designs would allow stable and coherent radiation to be produced even when using electron beams with a large amount of shot-to-shot jitter in the longitudinal profile.

Sincrotrone Trieste has received funding and has begun the final refinement of technical parameters as well as the construction of a new Free Electron Laser (FEL) called Fermi. The new light source will be located adjacent to the existing Elettra storage ring and will use the linac that presently injects electrons into this light source. The linac will shortly become fully available to the Fermi project as a new dedicated full energy injection system is also being built for Elettra. Why are VUV and X-ray FELs so important and how do they work? Most readers will know that in a bending magnet, synchrotron radiation is created by the incoherent emission of each electron as it moves in a magnetic field.

A numerical code based on an eikonal formalism has been developed to simulate laser-plasma interactions, specifically Raman backscatter (RBS). In this code, the dominant laser modes are described by their wave envelopes, avoiding the need to resolve the laser frequency; appropriately time-averaged equations describe particle motion. The code is fully kinetic, and thus includes critical physics such as particle trapping and Landau damping which are beyond the scope of the commonly used fluid three-wave equations. The dominant forces on the particles are included: the ponderomotive force resulting from the beat wave of the forward and backscattered laser fields and the self-consistent plasma electric field. The code agrees well, in the appropriate regimes, with the results from three-wave equations and particle-in-cell simulations. The effects of plasma temperature on RBS amplification are studied. It is found that increasing the plasma temperature results in modification to particle trapping and the satura...

We present the design of a single-pass free-electron laser amplifier suitable for enabling four-wave mixing x-ray spectroscopic investigations. The production of longitudinally coherent, single-spike pulses of light from a single electron beam in this scenario relies on a process of selective amplification where a strong undulator taper compensates for a large energy chirp only for a short region of the electron beam. This proposed scheme offers improved flexibility of operation and allows for independent control of the color, timing, and angle of incidence of the individual pulses of light at an end user station. Detailed numerical simulations are used to illustrate the more impressive characteristics of this scheme.

In this paper we report on start-to-end simulation of a next generation light source based on a high repetition rate free electron laser (FEL) driven by a CW superconducting linac. The simulation integrated the entire system in a seamless start-to-end model, including birth of photoelectrons, transport of electron beam through 600 m of the accelerator beam delivery system, and generation of coherent x-ray radiation in a two-stage self-seeding undulator beam line. The entire simulation used the real number of electrons ($\ensuremath{\sim}2$ billion electrons/bunch) to capture the details of the physical shot noise without resorting to artificial filtering to suppress numerical noise. The simulation results shed light on several issues including the importance of space-charge effects near the laser heater and the reliability of x-ray radiation power predictions when using a smaller number of simulation particles. The results show that the microbunching instability in the linac can be controlled with 15 keV uncorrelated energy spread induced by a laser heater and demonstrate that high brightness and flux 1 nm x-ray radiation ($\ensuremath{\sim}{10}^{12}\text{ }\text{ }\mathrm{photons}/\mathrm{pulse}$) with fully spatial and temporal coherence is achievable.

Muon cooling is a critical component of the proposed muon collider and neutrino factory. Previous studies of cooling channels have tracked single muons through the channel, which requires many particles for good statistics and does not lend itself to an understanding of channel dynamics. In this paper, a system of moment equations are derived which captures the major aspects of cooling: interactions with material and acceleration by radio frequency (rf) cavities. A general analysis of solenoid lattice types compares well with prior simulations and indicates new directions for study. (c) 2000 The American Physical Society.

This note will calculate the idealized performance of echo-enabled harmonic generation performance (EEHG), explore the parameter settings, and look at constraints determined by incoherent synchrotron radiation (ISR) and intrabeam scattering (IBS). Another important effect, time-of-flight variations related to transverse emittance, is included here but without detailed explanation because it has been described previously. The importance of ISR and IBS is that they lead to random energy shifts that lead to temporal shifts after the various beam manipulations required by the EEHG scheme. These effects give competing constraints on the beamline. For chicane magnets which are too compact for a given R56, the magnetic fields will be sufficiently strong that ISR will blur out the complex phase space structure of the echo scheme to the point where the bunching is strongly suppressed. The effect of IBS is more omnipresent, and requires an overall compact beamline. It is particularly challenging for the second pulse in a two-color attosecond beamline, due to the long delay between the first energy modulation and the modulator for the second pulse.

A longitudinally and transversely coherent, high repetition rate x-ray source with widely tunable wavelength is desired for a variety of experimental applications. A free electron laser (FEL) powered by an electron beam from a superconducting linac can reach the desired peak and average x-ray power levels with transverse coherence. However, generating longitudinally coherent x-ray pulses is a significant challenge, especially at high repetition rate. This paper presents a one-dimensional theoretical and numerical investigation of a method to achieve longitudinal coherence and high repetition rate simultaneously. We propose a ``radiator-first'' configuration, wherein an FEL oscillator follows a high gain harmonic generation (HGHG) FEL. The oscillator generates seed power that is directed upstream to initiate the HGHG process in a following electron bunch. This configuration allows for the generation of radiation at short wavelength, which is highly sensitive to energy spread, to occur before the longer wavelength oscillator, whose performance is not seriously degraded by the beam heating in the upstream radiator. The dynamics and stability of this radiator-first scheme is explored analytically and numerically. A single-pass, 1D map is derived using a semianalytic model for FEL gain and saturation. Iteration of the map is shown to be in good agreement with simulations. A numerical example is presented for a soft x-ray FEL.

CERN currently delivers antiprotons for trapping experiments with the antiproton decelerator (AD), which slows the antiprotons down to about 5 MeV. This energy is currently too high for direct trapping, and thick foils are used to slow down the beam to energies which can be trapped. To allow further deceleration to $\ensuremath{\sim}100\text{ }\text{ }\mathrm{keV}$, CERN is initiating the construction of ELENA, consisting of a ring which will combine rf deceleration and electron cooling capabilities. We describe a simple frictional cooling scheme that can serve to provide significantly improved trapping efficiency, either directly from the AD or first using a standard deceleration mechanism (induction linac or rf quadrupole). This scheme could be implemented in a short time. The device itself is short in length, uses accessible voltages, and at reasonable cost could serve in the interim before ELENA becomes operational, or possibly in lieu of ELENA for some experiments. Simple theory and simulations provide a preliminary assessment of the concept and its strengths and limitations, and highlight important areas for experimental studies, in particular to pin down the level of multiple scattering for low-energy antiprotons. We show that the frictional cooling scheme can provide a similar energy spectrum to that of ELENA, but with higher transverse emittances.