On the flexoelectric deformations of finite size bodies

Exact equations describing flexoelectric deformation in solids, derived previously within the framework of a continuum media theory, are partial differential equations of the fourth order. They are too complex to be used in the cases interesting for applications. In this paper, using the fact of smallness of the elastic moduli of a higher order, simplified equations are proposed. Solution of the exact equations is approximately represented as a sum of two parts: the first part obeys one-dimensional differential equations and exponentially decays near surface, the second --- obeys the equations of classical theory of elasticity. The first part can be constructed in an explicit form. For the second part, boundary conditions are obtained. They have a form of the classical boundary conditions for the body under external forces on surface

Impact of surface phenomena on direct bulk flexoelectric effect in finite samples

In the framework of a continuum theory, it is shown that the direct flexoelectric response of a finite sample essentially depends on the surface polarization energy, even in the thermodynamic limit where the body size tends to infinity. It is found that a modification of the surface energy can lead to a change of the polarization response by a factor of two. The origin of the effect is an electric field produced by surface dipoles induced by the strain gradient. The unexpected sensitivity of the polarization response to the surface energy in the thermodynamic limit is conditioned by the fact that the moments of the surface dipoles may scale as the body size

Statistical properties of the radiation from SASE FEL operating in a post-saturation regime with and without undulator tapering

We describe statistical and coherence properties of the radiation from x-ray free electron lasers (XFEL) operating in the post-saturation regime. We consider practical case of the SASE3 FEL at the European XFEL. We perform comparison of the main characteristics of the X-ray FEL operating in the post-saturation regime with and without undulator tapering: efficiency, coherence time and degree of transverse coherence.Comment: 6 pages, 5 figure

Coherence properties of the radiation from FLASH

FLASH is the first free electron laser user facility operating in the vacuum ultraviolet and soft x-ray wavelength range. Many user experiments require knowledge of the spatial and temporal coherence properties of the radiation. In this paper we present an analysis of the coherence properties of the radiation for the fundamental and for the higher odd frequency harmonics. We show that temporal and spatial coherence reach maximum close to the FEL saturation but may degrade significantly in the post-saturation regime. We also find that the pointing stability of short FEL pulses is limited due to the fact that non-azimuthal FEL eigenmodes are not sufficiently suppressed. We discuss possible ways for improving the degree of transverse coherence and the pointing stability.Comment: 17 pages, 19 figure

A possible upgrade of FLASH for harmonic lasing down to 1.3 nm

We propose the 3rd harmonic lasing in a new FLASH undulator as a way to produce intense, narrow-band, and stable SASE radiation down to 1.3 nm with the present accelerator energy of 1.25 GeV. To provide optimal conditions for harmonic lasing, we suggest to suppress the fundamental with the help of a special set of phase shifters. We rely on the standard technology of gap-tunable planar hybrid undulators, and choose the period of 2.3 cm and the minimum gap of 0.9 cm; total length of the undulator system is 34.5 m. With the help of numerical simulations we demonstrate that the 3rd harmonic lasing at 1.3 nm provides peak power at a gigawatt level and the narrow intrinsic bandwidth, 0.1% (FWHM). Pulse duration can be controlled in the range of a few tens of femtoseconds, and the peak brilliance reaches the value of 10^31 photons/(s mrad^2 mm^2 0.1%BW). With the given undulator design, a standard option of lasing at the fundamental wavelength to saturation is possible through the entire water window and at longer wavelengths. In this paper we briefly consider additional options such as polarization control, bandwidth reduction, self-seeding, X-ray pulse compression, and two-color operation. We also discuss possible technical issues and backup solutions.Comment: arXiv admin note: text overlap with arXiv:1205.250

A Method for Ultrashort Electron Pulse Shape-Measurement Using Coherent Synchrotron Radiation

In this paper we discuss a method for nondestructive measurements of the longitudinal profile of sub-picosecond electron bunches for X-Ray Free Electron Lasers (XFELs). The method is based on the detection of the Coherent Synchrotron Radiation (CSR) spectrum produced by a bunch passing a dipole magnet system. This work also contains a systematic treatment of synchrotron radiation theory which lies at the basis of CSR. Standard theory of synchrotron radiation uses several approximations whose applicability limits are often forgotten: here we present a systematic discussion about these assumptions. Properties of coherent synchrotron radiation from an electron moving along an arc of a circle are then derived and discussed. We describe also an effective and practical diagnostic technique based on the utilization of an electromagnetic undulator to record the energy of the coherent radiation pulse into the central cone. This measurement must be repeated many times with different undulator resonant frequencies in order to reconstruct the modulus of the bunch form-factor. The retrieval of the bunch profile function from these data is performed by means of deconvolution techniques: for the present work we take advantage of a constrained deconvolution method. We illustrate with numerical examples the potential of the proposed method for electron beam diagnostics at the TESLA Test Facility (TTF) accelerator. Here we choose, for emphasis, experiments aimed at the measure of the strongly non-Gaussian electron bunch profile in the TTF femtosecond-mode operation. We demonstrate that a tandem combination of a picosecond streak camera and a CSR spectrometer can be used to extract shape information from electron bunches with a narrow leading peak and a long tail.Comment: 60 pages, 39 figure