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An algorithm and numerical code for the up-sampling of a system of particles, from a smaller to a larger number, is described. The method introduces a Poissonian `shot-noise' to the up-sampled distribution, typical of the noise statistics arising in a bunch of particles generated by a particle accelerator. The algorithm is applied to a 6-Dimensional phase-space distribution of relatively few simulation particles, representing an electron beam generated by particle accelerator modelling software, for subsequent injection into an Free Electron Laser (FEL) amplifier which is used here to describe the model. A much larger number of particles is usually required to model the FEL lasing process than is required to model the electron beam accelerators that drive it. FEL modelling software usually requires a much greater number of simulation particles than is required for modelling the acceleration stages and an increase in simulation particles is required while introducing the correct Poisson statistical properties of a real electron distribution. A numerical code developed from the algorithm was then used to generate electron bunches for injection into to an unaveraged 3D FEL simulation code, Puffin. Results show good qualitative and quantitative agreement with analytical theory. The program and user manual is available for download.

Electron beam quality is paramount for X-ray pulse production in free-electron-lasers (FELs). State-of-the-art linear accelerators (linacs) can deliver multi-GeV electron beams with sufficient quality for hard X-ray-FELs, albeit requiring km-scale setups, whereas plasma-based accelerators can produce multi-GeV electron beams on metre-scale distances, and begin to reach beam qualities sufficient for EUV FELs. We show, that electron beams from plasma photocathodes many orders of magnitude brighter than state-of-the-art can be generated in plasma wakefield accelerators (PWFA), and then extracted, captured, transported and injected into undulators without quality loss. These ultrabright, sub-femtosecond electron beams can drive hard X-FELs near the cold beam limit to generate coherent X-ray pulses of attosecond-Angstrom class, reaching saturation after only 10 metres of undulator. This plasma-X-FEL opens pathways for novel photon science capabilities, such as unperturbed observation of electronic motion inside atoms at their natural time and length scale, and towards higher photon energies., Comment: 17 pages, 4 figures

A method to temporally tailor the properties of X-ray radiation carrying Orbital Angular Momentum (OAM) is presented. In simulations, an electron beam is prepared with a temporally modulated micro-bunching structure which, when radiating at the second harmonic in a helical undulator, generates OAM light with a corresponding temporally modulated intensity. This method is shown to generate attosecond pulse trains of OAM light without the need for any additional external optics, making the wavelength range tunable. In addition to the OAM pulse train, the method can be adapted to generate radiation where the handedness of the OAM mode may also be temporally modulated (flipped).

A new method to generate short wavelength Free Electron Laser output with modulated polarisation at attosecond timescales is presented. Simulations demonstrate polarisation switching timescales that are four orders of magnitude faster than the current state of the art and, at X-Ray wavelengths, approaching the atomic unit of time of approximately $24$~attoseconds. Such polarisation control has significant potential in the study of ultra-fast atomic and molecular processes. The output alternates between either orthogonal linear or circularly polarised light without the need for any polarising optical elements. This facilitates operation at the high brightness X-ray wavelengths associated with FELs. As the method uses an afterburner configuration it would be relatively easy to install at exciting FEL facilities, greatly expanding their research capability., Comment: 4 pages, 4 figures

Free-electron lasers (FELs) operate at wavelengths down to hard x-rays, and are either seeded or start from noise. There is increasing interest in x-ray FELs that rely on Self-Amplified Spontaneous Emission (SASE), and this involves increasing simulation activity in the design, optimization, and characterization of these x-ray FELs. Most of the simulation codes in use rely on the Slowly-Varying Envelope Approximation (SVEA) in which Maxwell's equations are averaged over the fast time scale resulting in relatively small computational requirements. While the SVEA codes are generally successful, the predictions of these codes sometimes differ in various aspects of the FEL interaction. In contrast, Particle-in-Cell (PiC) simulation codes do not average Maxwell's equations and are considered to be a more complete model of the underlying physics.Unfortunately, they require much longer run times than SVEA codes and have not been validated by comparison with experiment as often as the SVEA codes. In order to remedy this, and to resolve issues that arise due to different predictions between the SVEA codes, we present a comparison between one SVEA code (MINERVA) and a PiC simulation code (PUFFIN) with the experimental measurements obtained at the SPARC SASE FEL experiment at ENEA Frascati. The results show good agreement between the two codes and between the codes and the experiment. Since the formulations of the two codes share no common elements, this validates both formulations and demonstrates the capability to model the FEL interaction from the start of teh undulator through the undulator and into deep saturation., Comment: 1 table, 3 figures. arXiv admin note: text overlap with arXiv:1611.01649

Previous models of the quantum regime of operation of the Free Electron Laser (QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell - Schrodinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primary electron-radiation interaction., Comment: Submitted to Optics Express

It is shown via theory and simulation that the resonant frequency of a Free Electron Laser may be modulated to obtain an FEL interaction with a frequency bandwidth which is at least an order of magnitude greater than normal FEL operation. The system is described in the linear regime by a summation over exponential gain modes, allowing the amplification of multiple light frequencies simultaneously. Simulation in 3D demonstrates the process for parameters of the UK's CLARA FEL test facility currently under construction. This new mode of FEL operation has close analogies to Frequency Modulation in a conventional cavity laser. This new, wide bandwidth mode of FEL operation scales well for X-ray generation and offers users a new form of high-power FEL output., Comment: Submitted to PRL

A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undulators. Secondly, and thought to be unrelated to the undulator polarisation, a signficantly different evolution between the averaged and unaveraged simulations of the harmonic radiation evolution approaching FEL saturation., Comment: 14 pages, 5 figures

Several methods have been proposed in the literature to improve Free Electron Laser output by transforming the electron phase-space before entering the FEL interaction region. By utilising `beam by design' with novel undulators and other beam changing elements, the operating capability of FELs may be further usefully extended. This paper introduces two new such methods to improve output from electron pulses with large energy spreads and the results of simulations of these methods in the 1D limit are presented. Both methods predict orders of magnitude improvements to output radiation powers.

Studies of a broad bandwidth, two-colour FEL amplifier using one monoenergetic electron beam are presented. The two-colour FEL interaction is achieved using a series of undulator modules alternately tuned to two well-separated resonant frequencies. Using the broad bandwidth FEL simulation code Puffin, the electron beam is shown to bunch strongly and simultaneously at the two resonant frequencies. Electron bunching components are also generated at the sum and difference of the resonant frequencies., Comment: Accepted for publication

Synchronized, independently tunable and focused $\mu$J-class laser pulses are used to release multiple electron populations via photo-ionization inside an electron-beam driven plasma wave. By varying the laser foci in the laboratory frame and the position of the underdense photocathodes in the co-moving frame, the delays between the produced bunches and their energies are adjusted. The resulting multibunches have ultra-high quality and brightness, allowing for hitherto impossible bunch configurations such as spatially overlapping bunch populations with strictly separated energies, which opens up a new regime for light sources such as free-electron-lasers.

The short wavelength and high peak power of the present generation of free-electron lasers (FELs) opens the possibility of ultra-short pulses even surpassing the present (tens to hundreds of attoseconds) capabilities of other light sources - but only if x-ray FELs can be made to generate pulses consisting of just a few optical cycles. For hard x-ray operation (~0.1nm), this corresponds to durations of approximately a single attosecond, and below into the zeptosecond scale. This talk will describe a novel method to generate trains of few-cycle pulses, at GW peak powers, from existing x-ray FEL facilities by using a relatively short 'afterburner'. Such pulses would enhance research opportunity in atomic dynamics and push capability towards the investigation of electronic-nuclear and nuclear dynamics. The corresponding multi-colour spectral output, with a bandwidth envelope increased by up to two orders of magnitudes over SASE, also has potential applications., Comment: Submitted to 35th International Free Electron Laser Conference, New York, 2013

Initial studies of a 2-colour FEL amplifier using one monoenergetic electron beam are presented. The interaction is modelled using the unaveraged, broadband FEL code Puffin. A series of undulator modules are tuned to generate two resonant frequencies along the FEL interaction and a self-consistent 2-colour FEL interaction at widely spaced non-harmonic wavelengths at 1nm and 2.4nm is demonstrated., Comment: Submitted to The 35th International Free-Electron Laser Conference, Manhattan, New York (2013)

A method to achieve High-Brightness Self-Amplified Spontaneous Emission (HB-SASE) in the Free Electron Laser (FEL) is described. The method uses repeated non-equal electron beam delays to de-localise the collective FEL interaction and break the radiation coherence length dependence on the FEL cooperation length. The method requires no external seeding or photon optics and so is applicable at any wavelength or repetition rate. It is demonstrated using linear theory and numerical simulations that the radiation coherence length can be increased by approximately two orders of magnitude over SASE with a corresponding increase in spectral brightness. Examples are shown of HB-SASE generating transform-limited FEL pulses in the soft X-ray and near transform-limited pulses in the hard X-ray. Such pulses may greatly benefit existing applications and may also open up new areas of scientific research.

A method is proposed to generate trains of few-cycle x-ray pulses from a Free-Electron Laser (FEL) amplifier via a compact 'afterburner' extension consisting of several few-period undulator sections separated by electron chicane delays. Simulations show that in the hard x-ray (wavelength ~0.1 nm; photon energy ~10 keV) and with peak powers approaching normal FEL saturation (GW) levels, root mean square pulse durations of 700 zeptoseconds may be obtained. This is approximately two orders of magnitude shorter than that possible for normal FEL amplifier operation. The spectrum is discretely multichromatic with a bandwidth envelope increased by approximately two orders of magnitude over un-seeded FEL amplifier operation. Such a source would significantly enhance research opportunity in atomic dynamics, and push capability towards nuclear dynamics.

A new three dimensional model of the FEL is presented. A system of scaled, coupled Maxwell Lorentz equations are derived in the paraxial limit. A minimal number of limiting assumptions are made and the equations are not averaged in the longitudinal direction of common radiation/ electron beam propagation, allowing the effects of coherent spontaneous emission and non-localised electron propagation to be modelled. The equations are solved numerically using a parallel Fourier split-step method., Comment: Proceedings of 30th International Free Electron Laser Conference, Korea, 2008

A model is presented which demonstrates that the attosecond pulse structure of a High Harmonic Generation (HHG) seed may be retained through to saturation in an FEL amplifier. At wavelengths of ~12nm a train of attosecond pulses of widths ~300 attoseconds with peak powers in excess of 1 GW are predicted from full 3D simulation. Methods for improving these results are discussed., Comment: Submitted to 30th International Free Electron Laser Conference, Korea, 2008

In this paper we discuss extending the operating wavelength range of tunable Regenerative Amplifier FELs to shorter wavelengths than current design proposals, notably into the XUV regions of the spectrum and beyond where the reflectivity of broadband optics is very low. Simulation studies are presented which demonstrate the development of good temporal coherence in generic systems with a broadband radiation feedback of less than one part in ten thousand., Comment: Accepted for publication in NIM-A

A technique is proposed to generate attosecond pulse trains of radiation from a Free-Electron Laser amplifier. The optics-free technique synthesises a comb of longitudinal modes by applying a series of spatio-temporal shifts between the co-propagating radiation and electron bunch in the FEL. The modes may be phase-locked by modulating the electron beam energy at the mode spacing frequency. Three-dimensional simulations demonstrate the generation of a train of 400as pulses at giga-watt power levels evenly spaced by 2.5fs at a wavelength of 124 Angstrom. In the X-ray at wavelength 1.5 Angstrom, trains of 23as pulses evenly spaced by 150as and of peak power up to 6GW are predicted., Comment: Accepted for publication in Physical Review Letters

We describe a method for non-degenerate four-wave mixing in a cold sample of 4-level atoms. An integral part of the four-wave mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase-matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur, rather the density modulation acts to "self phase-match" the fields during the course of the wave-mixing process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment which would involve pumping a sample of cold Cs atoms with three infra-red pump fields to produce blue light., Comment: to appear in Physical Review Letters

A semi-classical theory of coherent light scattering from an elongated sample of cold atoms exposed to an off-resonant laser beam is presented. The model, which is a direct extension of that of the collective atomic recoil laser (CARL), describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample. It provides a simple physical picture of the recent observation of collective light scattering from a Bose-Einstein condensate [S. Inouye et al., Science N.285, p. 571 (1999)]. In addition, the model provides an analytical description of the temporal evolution of the scattered light intensity which shows good quantitative agreement with the experimental results of Inouye et al., Comment: submitted to Optics Communications, LaTex version, 2 postscript figures