FIG. 1. X-rayRaman scattering geometry in a reference sys- tem moving with the electron bunch.
A conceptually different new scheme considers a rel-
ativistic electron bunch injected into the overlap region between two transversally incident, counter-propagating intense lasers beams [ 9 ]. The setup is depicted in Fig. 1, directly in the reference frame of the electron bunch. The interference between the laser beams forms an optical lattice, and induces a spatially corrugated ponderomo- tive potential for the incident electrons that is trapping them transversely. The electron dynamics then consists of high frequency oscillations induced by the two lasers along the laser polarization direction, and of low fre- quency oscillations along the interference direction, simi- lar to betatron oscillations, with a characteristic angular frequency Ω. Light is hence scattered at the betatron fre- quency, and on the Stokes and anti-Stokes lines around the laser frequency. In the laboratory frame, this scat- tering is Doppler up-shifted by 2γ 2 , where γ is the elec- tron Lorentz factor. Scattering is spontaneous as long as the electron motions are uncorrelated; however, elec- trons may also exhibit a collective low-frequency oscilla- tory behaviour, so that we can expect a stimulated Ra- man instability and coherent emission of X-ray radiation in the forward direction. This Raman-type scattering should be distinguished from the known Raman instabili- ties in conventional long wavelength FreeElectron Lasers, where the system oscillations are the Langmuir plasma waves [ 10 ]. This new Raman instability dominates if the bounce frequency Ω is greater than the electron beam plasma frequency ω p .
4.2 Effect of electron velocity mismatch
The energy dispersion of the incident electron bunch is a major concern for X-rayfreeelectron lasers. In partic- ular, all the simulations on the FEL effect with optical undulators, in the Compton regime, demonstrate that a remarkable value of mono-energeticity is required, typi- cally of the order of 10 −4  to few 10 −4 for electron energies of few tens of MeV . Indeed, in the Compton regime, amplification occurs throughout the laser undu- lator length only if δγ/γ < 1/2N , N being the number of undulator periods over the whole amplification length . The Doppler frequency shift is therefore limited to the emission linewidth due to the finite emission time. This very stringent condition on the electron energy dis- persion is obviously one of the major reasons why this op- tical undulator scheme has not been demonstrated up to now. How the proposed Raman scheme for aX-ray FEL copes with the electron energy dispersion is therefore a major issue; however, a detailed study of Raman ampli- fication with a spread of electron energies is beyond the scope of the present study, leading us to restrict ourselves to discuss the spectral broadening induced the electron energy spread, and the amplification regime between a monochromatic X-ray field, and an out-of-resonance elec- tron population.
M.L.G., M.St., M.K., R.L.S. and R.B.D. performed injection, E.H. and I.S. prepared crystals, M.H. and L.Fou. performed online data analysis, A.G., J.-P.C., and T.R.M.B. performed ofﬂine analysis. J.B., M.Me., K.D., R.B., T.S.,Y. K., A.P.M. and R.L. performed data collection. M.Me., J.S.-D., S.H., N.R., A.Mü., A.K. and M.R. developed, controlled and operated the detector. M.Sch. and L.Fr. prepared and tested the speciﬁc repetition rates of the accelerator. H.F., T.M., A.S., S.B., J.Z., T. K., S. E. and W.E. developed control and online analysis software. K.W., D.B., L.M., G.P., J.S., N.Al Q. and M. Ma. performed data management. T.S., J.B., R.L., M. L. G. and C.A.S. set up femtosecond jet imaging, I.S. and C.A.S. conceived the experiment. I.S., C.A.S, J.B., B.W. and A.P.M. designed the experiment. M.L.G., A.G., M.St., R.B., J.B., M.C., K.D., E.H., M.H., Y.K., M.K., R.L., J.S.- D., A.P.M., M.Me., G.M., G.N.K., C.M.R., T.S., M.Sl., M.W., B.W., G. M., M.R., R.B.D., R. L.S., L.Fou., J.-P.C., T.R.M.B., C.A.S. and I.S. prepared the experiment. F.P., S.V., G.P., M. E. and M.L. designed and set up the femtosecond laser. M.L.G., T.R.M.B., C.A.S. and I.S. wrote the paper with input from all authors.
process is inner-shell photoionization. Within a few femtoseconds, shell holes decay mainly by autoionization, giving Auger electrons in addition to the primary photoelectrons. From these electrons, a collisional-radiative cascade takes place where secondary electrons resulting from collisional ionization are produced. At this step, one faces the problem of evaluating the incident X-ray electric field inside the material, along with the non-local thermodynamical equilibrium (NLTE) atomic physics problem where populations of inner-shell ionized atoms must be followed as a function of time. From these populations, one can built the opacity in the material. At each time, a complex refractive index can then be calculated which in turn allows one to compute the X-ray electric field. From the local NLTE opacity and from the local value of the electric field, it is possible to compute a local source of free electrons. As mentioned in the introduction, it seems suitable to consider two main classes of x-ray induced free electrons: those which deposit quasi-locally their energy (i.e. those thermalizing locally) and those (i.e. the most energetic) which can escape the interaction zone and deposit their energy elsewhere. After typically an hundred of femtoseconds, thermalized free electrons start to transfer their energy to the ions. Well after the end of the pulse, i.e. after about one picosecond, the heated matter experiences a macroscopic motion. In the continuum approximation, this behavior can be described by a set of hydrodynamics equations which must describe first the coupling electron-ion and then, the macroscopic ionic motion. As a consequence, there are two main classes of physical problems to present and to discuss here: (i) the internal X-ray electric field and energy deposition, with a special attention on the complex refractive index and on the transport of the energetic free electrons, (ii) the hydrodynamics and potential elasto-plastic behavior.
Recently, M. Colin and T. Colin , starting from , derived a complete set of quasi-linear Zakharov equations describing the interactions between the laser fields, the stimulated Raman processes, the electronic plasma waves and the low-frequency variations of density of the ions. The system involves four Schr¨ odinger equations coupled by quasi- linear terms and a wave equation and describes a three-waves interaction. Physically, the lasers interacts with the plasma, part of it backscattered through aRaman-type process to create an electron plasma wave. These three waves interact in order to create a low- frequency variation of density which has itself an influence on the three preceding waves. However, this model that is obtained starting from the fluid equations does not take into account the kinetic effects such the Landau damping effect which is a wave-particle process which occurs in under-dense plasma. The Landau damping process is especially important in the context of fusion by inertial confinement by lasers because electrons are accelerated to high energy and this induces a preheat of the fusion fuel and reduces the target gain. This wave-particle process corresponds to a resonant effect between the electrons of the plasma and the plasma electronic waves. This effect implies an exchange of energy between electrons and the plasma waves. As a result, the plasma waves are damped.
Different models have been developed in order to de- scribe this new regime of the laser-matter interaction (cluster radius R laser wavelength λ). Inspired by the physics at the atomic and molecular level, the first one has been proposed by the group of C.K. Rhodes : the so-called ”Coherent Electron Motion Model” (CEMM) . In this model, the free electrons (Z ) from the ionized cluster oscillate coherently in the external laser field. They are considered as a quasi-particle possess- ing effective charge Ze and mass Zm, increasing signifi- cantly the ionization efficiency in the collisions with intra- cluster ions and atoms. Limited to the treatment of small clusters (. 1000 atoms), the CEMM reproduces the ex- tremely high ionization levels observed in the x-ray mea- surements and predicts x-ray emission bursts as short as the laser duration.
3.2 Off-axis colliding pulse injection
Decoupling injection from acceleration is a key challenge to achieving compact, reli- able, tunable laser-plasma accelerators (LPAs) [9, 12]. Although capillary-guided LPAs have demonstrated high-quality electron beams at 1 GeV  with 2.5% r.m.s. energy spread, most of present LPAs [39, 41, 40] still rely on transverse wavebreaking effects  of highly nonlinear waves  to inject electrons into the accelerating phase of the electron density wave. In this scheme, injection and acceleration are coupled, limiting control of the acceleration structure which is essential for LPAs’ applications such as free-electron lasers , THz [77, 70] and X-ray radiation sources [84, 85, 128]. Elec- trons injected at different longitudinal positions behind the laser pulse, i.e., different phases of the periodic structure of the accelerating wakefield, experience different elec- tric fields, due for example to beam loading effects (Sec. 2.6), which can lead to a large energy spread. Several methods to control trapping of the electrons have been pro- posed and demonstrated: external injection of an electron beam froma conventional accelerator [16, 17, 18], triggering injection in plasma density gradients with density decreasing in the laser propagation direction [63, 2], and using additional laser pulses [20, 66, 129, 22, 67].
Undulator radiation has already been measured using such a source [ 9 – 12 ] but not with the quality achieved on synchrotron radiation facilities. LPA based FEL [ 13 ] demonstration is still challenged by the electron beam quality. In this paper, the main setbacks posed by an LPA based electron beam, in the view of an FEL amplification, are reported, alongside solutions that can qualify such beams for an FEL application. Undulator radiation achieved so far with LPA beams is discussed, including the COXINEL experiment equipped with an advanced manipulation line. The paper presents combined analytic approaches for electron beam manipulation in the LPA transfer line starting from the source parameters to the ones at the undulator center, undulator radiation and FEL calculations. Emphasis is put on the electron beam brightness evolution and undulator brilliance. Finally, the FEL performance is examined for different initial electron beam parameters for the COXINEL baseline reference case. 2. Issues of LPA Based FEL
Accelerator based light sources presently know a very wide development , with the FEL  advent in the X- ray domain  coming along with an increase of the peak brightness by several orders of magnitude, enabling fifty years after the laser invention  to decipher the matter structure in unexplored areas and dynamics on ultra-fast time scales unraveling the processes involved various do- mains ... Following the laser invention, alternately of developing FELs relying on non bounded relativistic elec- trons in an undulator periodic permanent magnetic field as a gain medium , laser have been considered to gen- erate and accelerate electrons in plasmas . An intense laser focused onto a gas target ionizes the gas and creates a plasma. As the laser pulse propagates, the ponderomotive force expels electrons from the optical axis, forming a cavi- ty free of electrons in the laser wake with large amplitude electric fields where electrons can be trapped and acceler- ated. With the growth of ultra high power laser making advantage of Chirped Pulse Amplification techniques ,
In this paper, we characterize the performance of a seeded FEL where frequency chirping on the seed laser is instead exploited to generate two independent pulses spectrally and temporally separated in an externally controllable fashion. The generation of multiple pulses of different colours in FEL’s is opening new opportunities for pump and probe experiments in spectral regions ranging from vacuum-ultraviolet to hard X-rays with unprecedented brightness. Re- cently, the LCLS group has reported the generation of pairs of temporally and spectrally sep- arated soft X-ray FEL pulses via a double undulator scheme [ 9 ]. Similar studies are ongoing at SPARC [ 10 ], where two distinct electron bunches at different energies generate independent pulses of radiation. At FERMI@Elettra, multiple pulses have also been obtained recently with a different technique, based on the simultaneous injection of two different seed pulses on the same electron bunch [ 11 ]. In this case the two pulses minimum separation is limited by the seed pulse length. The method we propose here allows to reduce this distance by using a single seed pulse and exploiting saturation to generate the pulse splitting [ 12 , 13 ].
All x rays coming from the same zone pair of the off-axis zone plate reach the sample at the same time and therefore probe the same delay. On the CCD camera, which records a magnified image of the off-axis zone plate, these intensities lay on the curved trace of the corresponding zone pair and can thus be averaged by an angular integration (e.g., along the dashed blue line for zero delay). This procedure yields the projection of the signal onto the pump-probe time delay axis, as shown in Fig. 2(c) for the accumulation of 500 shots (red) and the single-shot measurement (green). These intensities are normalized by the unpumped signal and are therefore equal to 1 before time 0. The error bars are de- termined from the standard deviation of the binning of the temporal axis. The good signal to noise ratio of the single-shot measurement underlines the potential of this technique. In this particular configuration of circular polarization and magnetic field orientation, the laser-induced demagnetization leads to a signal increase reflecting the expected rapid quenching of the magnetization.
bance of the sample at the pump wavelength was B1.0 optical density. Given the size, energy of the photolysis beam, the concentration and molar extinction coef- ﬁcient of the haem, B1.6 photons are expected to be absorbed by each haem molecule at each photolysis pulse. A monochromatic X-ray beam at 9 keV was produced by a Si(111) double-crystal monochromator and focused to 100 mm by beryllium refractive lenses. Time-resolved X-ray scattering images were acquired with a two-dimensional charge-coupled device detector (Rayonix SX165, 2,048 2,048 pixels) at 16.8 cm from the sample. Each image is the result of the accumulation of 360 X-ray shots. Investigated time delays ranged between 3 and 100 ps (with negative time delays corresponding to a probe pulse arriving before the photolysis one). In particular, we measured every 0.5 ps between 3 and 10 ps; every 5 ps between 10 and 50 ps; every 50 ps at longer time delays. Reference images at a time delay of 100 ps were also recorded every 7 other images. The scattering pattern at each time delay is the result of an average over 50 repetitions. The repetition rate of the experiment was 120 Hz and the estimated time resolution was B500 fs.
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photon index and hydrogen column density) by performing detailed X-ray spectral analyses. This is because the latter has already been well realized by many specialized X-ray codes such as XSPEC ( Arnaud 1996 ) and Sherpa ( Freeman et al. 2001 ), and there is no need for X-CIGALE to perform similar analyses. Also, it is tech- nically difficult to fit the X-ray spectra within the framework of X-CIGALE. X-CIGALE assumes that a sample of sources are ob- served with a single “filter transmission”, as is the case in UV-to-IR data. However, at X-ray wavelengths, the transmission curve varies from source-to-source, as it might depend on many factors such as position on the detectors and observation date. For example, the soft-band transmission of Chandra has been continuously declin- ing since its launch (e.g. O’Dell et al. 2017 ). In fact, each source is associated with a unique transmission curve and the curve is taken into account when fitting the X-ray spectra with, e.g. XSPEC and Sherpa.
synthesis 43 .
After evidencing the Raman spectral signature of the antibiotic effect and the spectral cells heterogeneity, we demonstrated that the AST could be performed despite the intrinsic variability of the acquired spectra and the existence of distinct spectral populations. For that purpose, we were able to train a classifier that allowed us to detect the presence or absence of (spectral) antibiotic effect on a single bacterial cell at a given antibiotic concen- tration and assign it to one of the classes “ATB effect” and “No effect”. Repeating the test on a small number of exposed bacterial cells (5 to 11 depending on the antibiotic) associated with the same number of non-exposed bacterial cells (to calculate the difference spectra) and making a vote, we could infer the phenotypic antibiotic effect at the scale of the whole bacteria population. Instead of using spectra averaged over a few cells as commonly proposed in the literature, which would result in the destruction of the signal of interest in concentrations close to the MIC, we hence propose to truly analyze bacteria at the single cell level. We leveraged on their heterogeneity for analysis and the proposed vote scheme for the final attribution of the measured phenotype accounts for the observed heterogeneity in bacterial cells state. Using this classification scheme for different antibiotic concentra- tions, we observed a sharp transition from the “No effect” labelling to the “ATB effect” one at antibiotic concen- trations very close to the considered strain reference MIC. We show that the phenotypic reference MIC is also around the concentration, within a standard 2-fold dilution range, at which we could observe a transition of the No effect ATB effect
increase of the density peaks and the good localization of the oxygen atoms lone pairs O1 and O2. The presented maps are given in the benzene ring section and the contour map is 0.05 eÅ -3 .
A residual density map in the molecular plane obtained in the final cycle of refinement (see Figure 5) shows the adequacy of the multipolar model to describe the electron experimental density of the molecule. The absence of the quasi-totality of the density peak again confirms the high quality of the recorded data and the precision of the used equipment. On the other hand, the multipole expansion model appears to be very efficient for describing the electron density distribution in structure [21-22].
norm i are the normalization factors of the spectral fits,
i.e. 10 − 14 R n e nHdV/4πd 2 , listed in Tables 4 and 5.
This parameter is sometimes used as diagnostic for the properties of the X-ray emission of massive stars (Gagn´e et al. 2011; Ignace et al. 2013). However, we found it to be not as reliable as the hardness ratio (Fig. 7). Indeed, even for bright sources, there is a trade-off between absorption and temperature, which means that a unique spectral shape can be fitted by sev- eral solutions with very different average temperatures. This effect was reported several times in the past (e.g. Naz´e et al. 2007), even when high-resolution spectra were used (Naz´e et al. 2012a). In this work, we were regularly confronted with this problem, e.g. fits with similar hardness ratios but average temperatures of 0.2 and 1.0 keV fit equally well the spectra of σ Ori E. The main problem is that it is difficult to securely constrain independently the level of additional absorption: av- erage temperatures should thus not be taken at face value. Fortunately, the same conclusions are reached for both parameters, so that we present only hardness ratios in the following.
reliable and widely used method of Quantum Crystallography that allows the determination of wavefunctions compatible with X-ray diffraction data. So far, all the existing XCW techniques have been developed in the framework of the Molecular Orbital theory and, consequently, provide only pictures of the “experimental” electronic structures that are far from the traditional chemical perception. Here we propose a new strategy that, by combining the XCW philosophy with the Spin-Coupled method of the Valence Bond theory, enables to directly extract traditional chemical information (e.g., weights of resonance structures) fromX-ray diffraction measurements. Preliminary results have shown that the new technique is really able to efficiently capture the effects of the crystal environment on the electronic structure and can be considered as a new useful tool to perform chemically sound analyses of the X-ray diffraction data.