Spectrometer for hard X‐ray free‐electron laser based on diffraction focusing

X‐ray free‐electron lasers (XFELs) generate sequences of ultra‐short spatially coherent pulses of X‐ray radiation. A diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of ΔE/E? 2 × 10^?6, is proposed. This is much better than for most modern X‐ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single‐crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from a metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. It is shown that the DFS can be used in a wide energy range from 5 keV to 20 keV.     

Polycapillary‐optics‐based micro‐XANES and micro‐EXAFS at a third‐generation bending‐magnet beamline

A focusing system based on a polycapillary half‐lens optic has been successfully tested for transmission and fluorescence µ‐X‐ray absorption spectroscopy at a third‐generation bending‐magnet beamline equipped with a non‐fixed‐exit Si(111) monochromator. The vertical positional variations of the X‐ray beam owing to the use of a non‐fixed‐exit monochromator were shown to pose only a limited problem by using the polycapillary optic. The expected height variation for an EXAFS scan around the Fe K‐edge is approximately 200 µm on the lens input side and this was reduced to ～1 µm for the focused beam. Beam sizes (FWHM) of 12–16 µm, transmission efficiencies of 25–45% and intensity gain factors, compared with the non‐focused beam, of about 2000 were obtained in the 7–14 keV energy range for an incoming beam of 0.5 × 2 mm (vertical × horizontal). As a practical application, an As K‐edge µ‐XANES study of cucumber root and hypocotyl was performed to determine the As oxidation state in the different plant parts and to identify a possible metabolic conversion by the plant.     

Ionization dynamics of dense matter generated by intense ultrashort X‐ray pulses

We investigate a pump‐probe X‐ray Thomson scattering (XRTS) experiment that might be carried out at a free electron laser facility to study warm‐to‐hot states of dense matter. Ultrashort and intense X‐ray pulses with different energies (1,560–1,830 eV) heat a 1 µm thick Al target isochorically and create homogeneous and uncompressed warm‐to‐hot states of dense matter. A second pulse with variable delay probes this heated state via XRTS. The X‐ray laser–target interaction is modelled within radiation‐hydrodynamic simulations applying the HELIOS‐CR code. The HELIOS‐CR results qualitatively agree with Monte‐Carlo simulations, where the laser pulse absorption is simulated based on a uniform random sequence of events. The electron feature in the simultaneously observed X‐ray scattering spectrum is a function of the degree of ionization and the target temperature. Therefore, the temporal evolution of the plasmon peak measures the ionization dynamics on ultra‐short time scales. The XRTS spectrum is calculated based on the Chihara formula utilizing the Born‐Mermin approximation for the free electron dynamic structure factor. The proposed experiment will reveal important details of the ionization dynamics on ultra‐short time scales as well as of the relaxation on ps time scales.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laser‐Triggered Proton Acceleration From Micro‐Structured thin Targets

By using relativistic massively parallel PIC code MANDOR, which features arbitrary target design including 3D micro‐structuring, a study of ion acceleration in short laser pulse interaction with different thin targets has been performed. Based on 3D simulation results it has been shown that micro‐structures on the front surface of thin plane targets increase a number and energy of hot electrons in comparison with that for the case of pure plain foils of optimal thickness. As a result, the energy of accelerated ions also increases up to 50%. However, the efficiency of ion acceleration from structured target reduces with laser pulse intensity increase, so that for laser pulses of ultra‐relativistic intensity a positive role of surface micro‐structuring diminishes. We have also studied to which extent a sub‐ps imperfection of the laser pulse shape, which smoothes the surface micro‐structures suppresses high‐energy ion generation. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Attosecond‐precision ultrafast photonics

We review our recent progress toward attosecond‐precision ultrafast photonics based on ultra‐low timing jitter optical pulse trains from mode‐locked lasers. In femtosecond mode‐locked lasers, the concentration of a large number of photons in an extremely short pulse duration enables the scaling of timing jitter into the attosecond regime. To characterize such jitter levels, we developed new attosecond‐resolution measurement techniques and show that standard fiber lasers can achieve sub‐fs high‐frequency jitter. By leveraging the ultra‐low jitter of free‐running mode‐locked lasers, we pursued high‐precision optical‐optical and optical‐microwave synchronization techniques. Optical signals spanning 1.5 octaves were synthesized by attosecond‐precision timing and phase synchronization of two independent mode‐locked lasers. High‐stability microwave signals were also synthesized from mode‐locked lasers with drift‐free sub‐10‐fs precision. We further demonstrated the attosecond‐precision distribution of optical pulse trains to remote locations via timing‐stabilized fiber links. Finally, the application of optical pulse trains for high‐resolution sampling and analog‐to‐digital conversion is discussed.     

Canonical transformations and exact invariants for time‐dependent Hamiltonian systems

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical transformation is performed in the framework of the extended phase‐space. We apply this approach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase‐space a finitecanonical transformation of the initially time‐dependent Hamiltonian to a time‐independent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time‐dependent auxiliary function ξ (t) that represents a solution of a linear third‐order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the generally involved phase‐space symmetry associated with the conserved quantity of a time‐dependent non‐linear Hamiltonian system. Our results are applied to three examples of time‐dependent damped and undamped oscillators. The known invariants for time‐dependent and time‐independent harmonic oscillators are shown to follow directly from our generalized formulation.     

On the Theory of Hydrogen Atom Ionization by Ultra‐Short Electromagnetic Pulses

An investigation of the probability of hydrogen atom ionization by ultra‐short electromagnetic pulses is carried out in the frame of perturbation theory We consider the case when the electric field strength amplitude E₀ in a pulse by two orders lower than characteristic atomic field strength E_a (E_a ? 5.1 · 10⁹ V/cm). A detailed investigation of the dependence of the probabilities on the pulse duration was performed for Gaussian pulse shapes. In the case where the carrier frequency of the Gaussian pulse is larger than the atomic ionization potential, the probability goes to the standard limit of perturbation per unit time. At the same pulse durations, the probabilities for carrier frequencies less than the ionization potential go to zero. The frequency dependence of the ionization probability becomes equal to the standard threshold dependence with increasing pulse duration time. A comparison between the ionization effects caused by wavelet pulses without carrier frequency and Gaussian pulses with carrier frequency shows that the same ionization probability values are achieved when the pulse carrier frequency is detuned by about 20% from the ionization threshold. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measuring picosecond excited‐state lifetimes at synchrotron sources

A new analysis method for the short excited‐state lifetime measurement of photosensitive species in crystals is described. Based on photocrystallographic techniques, this method is an alternative to spectroscopic methods and is also valid for non‐luminescent excited species. Two different approaches are described depending on the magnitude of the lifetime τ. For very short lifetimes below the width of the synchrotron pulse, an estimated τ can be obtained from the occurrence of the maximal system response as a function of the pump–probe delay time Δt. More precise estimates for both short and longer lifetimes can be achieved by a refinement of a model of the response as a function of the pump–probe delay time. The method also offers the possibility of the structure determination of excited species with lifetimes in the 40–100 ps range.     

THz Radiation Generation via the Interaction of Ultra‐short Laser Pulses with the Molecular Hydrogen Plasma

In this paper, a two dimensional Particle In Cell‐Monte Carlo Collision simulation scheme is used to examine the THz generation via the interaction of high intensity ultra‐short laser pulses with an underdense molecular hydrogen plasma slab. The influences of plasma density, laser pulse duration and its intensity on the induced plasma current density and the subsequent effects on the generated THz signal characteristics are studied. It is observed that the induced current density in the plasma medium and THz spectral intensity are increased at the higher laser pulse intensities, laser pulse durations and plasma densities. Moreover, the generated THz electric field amplitude is reduced at the higher laser pulse durations. A wider frequency range for the generated THz signal is shown at the lower laser pulse durations and higher plasma densities. Additionally, it is found that the induced current density in hydrogen plasma medium is the dominant factor influencing the generation of THz pulse radiation. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of the non‐linear screening on a modification of the Debye–Hückel plus hole approximation in complex plasma

The authors analyse two‐component electroneutral systems of classical macroions of finite size and point‐like oppositely charged microions. This article deals with the modification of the Debye–Hückel plus hole approximation when a non‐linear screening effect is taken into account in a complex plasma. Parameters of non‐linear screening of the macroions by surrounding microions are calculated within the framework of the Poisson–Boltzmann approximation. Two effects are found as a result of such calculations: (a) subdivision of all microions into two subclasses, free microions and bound microions and (b) a significant reduction of an effective charge Z^* of the macroion in comparison with its true value Z due to the non‐linear screening by a thin high‐density envelope of the bound microions. We show that the value of a non‐ideal portion of an internal energy differs considerably in the case when the non‐linear screening effect is taken into account in the vicinity of the macroion.     

Spatiotemporal Evolution of Intense Short Gaussian Laser Pulses in Weakly Relativistic Magnetized Plasma

The weakly relativistic regime of propagation of a short and intense laser pulse in the magnetized plasma is investigated. By considering relativistic nonlinearity and using non‐linear Schrödinger equation with paraxial approximation, two second‐order coupled differential equations are obtained for the longitudinal pulse width parameter (in time) and for the transverse pulse width parameter (in space). The simultaneous evolution of spot size and length of a relativistic Gaussian laser pulse in a magnetized plasma can be calculated by the numerical solution of the equations. The effect of magnetic field is investigated. It is observed that in the presence of magnetic field both the self‐compression and the self‐focusing can be enhanced. Furthermore, the interplay between the longitudinal self‐compression and the transverse self‐focusing in a magnetized plasma is investigated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non‐linear interaction of a q‐Gaussian laser beam in a plasma channel created by the ignitor‐heater technique

This paper presents a theoretical investigation of the propagation characteristics of a q‐Gaussian laser beam propagating through a plasma channel created by the ignitor‐heater technique. The ignitor beam creates the plasma by tunnel‐ionization of air. The heater beam heats the plasma electrons and establishes a parabolic channel. The third beam (q‐Gaussian beam) is guided in the plasma channel under the combined effects of density non‐uniformity and non‐uniform ohmic heating of the plasma channel. Numerical solutions of the non‐linear Schrodinger wave equation (NSWE) for the fields of laser beams are obtained with the help of the moment theory approach. Particular emphasis is placed on the dynamical variations of the spot size of the laser beams and the longitudinal phase shift of the guided beam with the distance of propagation.     

Refraction and ultra‐small‐angle scattering of X‐rays in a single‐crystal diamond compound refractive lens

In this work a double‐crystal setup is employed to study compound refractive lenses made of single‐crystal diamond. The point spread function of the lens is calculated taking into account the lens transmission, the wavefront aberrations, and the ultra‐small‐angle broadening of the X‐ray beam. It is shown that, similarly to the wavefront aberrations, the ultra‐small‐angle scattering effects can significantly reduce the intensity gain and increase the focal spot size. The suggested approach can be particularly useful for the characterization of refractive X‐ray lenses composed of many tens of unit lenses.     

时频分布技术在激光与等离子体相互作用粒子模拟诊断中的应用

在对超短超强激光与等离子体相互作用进行粒子模拟诊断的研究中,输出量普遍为时间或空间上的非平稳信号。将时频分布技术引入粒子模拟结果的诊断,指出用时频分布技术等现代信号处理技术诊断模拟结果中的非平稳信号具有重要意义。作为实例,考察了用线性啁啾激光打靶条件下,包含nc/4(nc为等离子体临界密度）的非均匀等离子体区域中的受激拉曼散射的演化,并用时频分布技术得到了清晰的物理图像。     

New hierarchy for the Liouville equation,irreversibility and Fokker‐Planck‐like structures

The issue of irreversibility is revisited for a closed system formed by N classical non‐relativistic particles inside a volume Ω, interacting through two‐body potentials, for large N and Ω. The classical phase‐space distribution function f, multiplied by suitable Hermite polynomials and integrated over all momenta, yields new moments. The Liouville equation and the initial distribution f_in imply a new non‐equilibrium linear infinite hierarchy for the moments. That hierarchy differs from the BBGKY one for distribution functions and displays some suggestive Fokker‐Planck‐like structures. A physically motivated ansatz for f_in (which introduces statistical assumptions), used by previous authors, is chosen. All moments of order n ≥ n₀ are expressed in terms of those of order n₀ — 1 and of f_in. The properties of the Fokker‐Planck‐like structures (hermiticity, non‐negative eigenvalues) allow for implementing a natural long‐time approximation in the hierarchy, so as to introduce relaxation to equilibrium and irreversibility, consistently with the hydrodynamical balance equations. Further (more restrictive) assumptions and approximations lead to new irreversible models, generalizing non‐trivially the Fokker‐Planck equation. They are described through a truncated hierarchy of linear equations for moments of order n ≤ n₀ — 1 (n₀ being finite). The connections with Brownian particle dynamics and Fluid Dynamics are analyzed, for consistency.     

The (3+1)‐dimensional dust‐acoustic waves in multi‐components magneto‐plasmas

A three‐dimensional four components magneto‐plasma system consists of super‐thermal κ‐distributed electrons and positrons, Maxwellian ions, and inertial massive negatively charged dust grains is considered to examine the modulational instability (MI) of the dust‐acoustic waves (DAWs), which propagates in such a magneto‐plasma system. The reductive perturbation method, which is valid for small but finite amplitude DAWs, is employed to derive the (3 + 1)‐dimensional non‐linear Schrödinger equation (NLSE). The NLSE leads to the MI of DAWs as well as the formation of dust‐acoustic rogue waves (DARWs) which are formed due to the effects of non‐linearity in the propagation of the DAWs. It is found that the basic features (viz. amplitude and width) of the DAWs and DARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as κ‐distributed electrons and positrons, temperatures, and number densities of plasma species, and so on. The application of the results in both space and laboratory magneto‐plasma systems is briefly discussed.     

Non‐paraxial theory of self‐focusing/defocusing of Hermite cosh Gaussian laser beam in rippled density plasmas

Present research work focuses on study of self‐focusing and self‐trapping of Hermite cosh Gaussian (HchG) laser beams in rippled density plasma by considering relativistic non‐linearity. The coupled non‐linear differential equations for the beam width parameters (for modes m = 0, 1, and 2) were derived by employing higher‐order correction in comparison to paraxial ray theory by expanding dielectric function and eikonal up to r⁴ terms. It is observed that the inclusion of higher‐order terms significantly influence the off‐axial properties for m ≥ 1 mode indices. Furthermore, the effect of parameters including beam intensity, ripple factor, depth of density modulation, and decentred parameter on self‐focusing and self‐trapping is analysed and discussed both analytically and numerically.     

High‐energy X‐ray optics with silicon saw‐tooth refractive lenses

Silicon saw‐tooth refractive lenses have been in successful use for vertical focusing and collimation of high‐energy X‐rays (50–100 keV) at the 1‐ID undulator beamline of the Advanced Photon Source. In addition to presenting an effectively parabolic thickness profile, as required for aberration‐free refractive optics, these devices allow high transmission and continuous tunability in photon energy and focal length. Furthermore, the use of a single‐crystal material (i.e. Si) minimizes small‐angle scattering background. The focusing performance of such saw‐tooth lenses, used in conjunction with the 1‐ID beamline's bent double‐Laue monochromator, is presented for both short (～1:0.02) and long (～1:0.6) focal‐length geometries, giving line‐foci in the 2 µm–25 µm width range with 81 keV X‐rays. In addition, a compound focusing scheme was tested whereby the radiation intercepted by a distant short‐focal‐length lens is increased by having it receive a collimated beam from a nearer (upstream) lens. The collimation capabilities of Si saw‐tooth lenses are also exploited to deliver enhanced throughput of a subsequently placed small‐angular‐acceptance high‐energy‐resolution post‐monochromator in the 50–80 keV range. The successful use of such lenses in all these configurations establishes an important detail, that the pre‐monochromator, despite being comprised of vertically reflecting bent Laue geometry crystals, can be brilliance‐preserving to a very high degree.