Inverse Backscattering Research Articles

MEPhI’s option of lab scale Compton source

A development and construction of comparatively cheap and compact (several meters scale) X-ray sources is possible with the help of inverse Compton backscattering of laser photons on an electron bunch. Such sources can be used in the field of materials science (new materials, diagnostics of nanostructures at the atomic level), research of nano- and biosystems, medicine and pharmacology (new drugs R&D), physics and chemistry of fast-flowing processes (burning, explosion). It is suggested that compact storage synchrotron will operate with normal conducting S-band top-up linac. Linac will provides bunches with tunable energy in the range of 20– 60 MeV to generate the photon flux with tunable energy [1, 2]. The use of a storage ring provides the following advantages: comparatively high average intensity of the generated photon flux, high brightness, photon beam energy tuning in a wide range, high degree of monochromaticity and coherence of the generated photons. There are current results of the design of a compact storage ring for generating the photons in the energy range of 5-45 keV and investigations of the development of relativistic picosecond electron beam dynamics instabilities in the report.

A Laser Frequency Transverse Modulation Might Compensate for the Spectral Broadening Due to Large Electron Energy Spread in Thomson Sources

Compact laser plasma accelerators generate high-energy electron beams with increasing quality. When used in inverse Compton backscattering, however, the relatively large electron energy spread jeopardizes potential applications requiring small bandwidths. We present here a novel interaction scheme that allows us to compensate for the negative effects of the electron energy spread on the spectrum, by introducing a transverse spatial frequency modulation in the laser pulse. Such a laser chirp, together with a properly dispersed electron beam, can substantially reduce the broadening of the Compton bandwidth due to the electron energy spread. We show theoretical analysis and numerical simulations for hard X-ray Thomson sources based on laser plasma accelerators.

Inverse scattering for a random potential

In this paper, we consider an inverse problem for the [Formula: see text]-dimensional random Schrödinger equation [Formula: see text]. We study the scattering of plane waves in the presence of a potential [Formula: see text] which is assumed to be a Gaussian random function such that its covariance is described by a pseudodifferential operator. Our main result is as follows: given the backscattered far field, obtained from a single realization of the random potential [Formula: see text], we uniquely determine the principal symbol of the covariance operator of [Formula: see text]. Especially, for [Formula: see text] this result is obtained for the full nonlinear inverse backscattering problem. Finally, we present a physical scaling regime where the method is of practical importance.

The inverse backscattering for Schrödinger operators for potentials with noncompact support

We consider the inverse backscattering problem for the Schrödinger operator H = −Δ + V on , n ≥ 3, as well as the higher‐order Schrödinger operator ( − Δ)m + V, m = 2,3,…. We show that in some suitable Banach spaces, the map from the potential to the backscattering amplitude is a local diffeomorphism. This kind of problem (for m = 1) was studied by Eskin and Ralston [Comm. Math. Phys., 124(2), 169‐215 (1989)], where they assumed that . In this paper, we replace the assumption on V with certain decay assumption at infinity.

Well-posedness of the Goursat problem and stability for point source inverse backscattering

We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies Hölder stability. Importantly, we also show that the point source equation is well-posed and also that the associated characteristic initial value problem, or Goursat problem, is well-posed. These latter results are difficult to find in the literature in the form required by the stability proof.

Inverse backscattering problem for perturbations of biharmonic operator

We consider the inverse backscattering problem for a biharmonic operator with two lower order perturbations in two and three dimensions. The inverse Born approximation is used to recover jumps and singularities of an unknown combination of potentials. Numerical examples are given to illustrate the practical usefulness of the method.

Compton Scattered X-Gamma Rays with Orbital Momentum.

We study the possibility of producing x-gamma rays with orbital angular momentum by means of the inverse Compton backscattering between a high brightness electron beam and a twisted laser pulse. We use the classical electrodynamics retarded fields for evaluating the orbital angular momentum of the radiation and connecting it to that of the primary laser pulse. We then propose the dimensioning of a linearly polarized x-ray source with orbital angular momentum, starting from the parameters of operating Thomson setups.

Spectral caustics in laser assisted Breit–Wheeler process

Electron-positron pair production by the Breit-Wheeler process embedded in a strong laser pulse is analyzed. The transverse momentum spectrum displays prominent peaks which are interpreted as caustics, the positions of which are accessible by the stationary phases. Examples are given for the superposition of an XFEL beam with an optical high-intensity laser beam. Such a configuration is available, e.g., at LCLS at present and at European XFEL in near future. It requires a counter propagating probe photon beam with high energy which can be generated by synchronized inverse Compton backscattering.

Inverse obstacle backscattering problems with phaseless data

In this article, we provide a numerical algorithm to reconstruct a convex sound-soft scatterer from phaseless backscattering data, assuming sufficiently high frequency. Certain uniqueness and existence results for the case of circular scatterers are given as well, based on the asymptotic expansion for the normal derivative of the total field.

Uniqueness for the inverse backscattering problem for angularly controlled potentials

We consider the problem of recovering a smooth, compactly supported potential on from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives, then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficients and have the same backscattering data then the two potentials are identical.

Inverse backscattering Born approximation for the magnetic Schrödinger equation in three dimensions

The inverse backscattering Born approximation is studied for the three‐dimensional magnetic Schrödinger operator. Under the assumption that the Born series converges in the weighted space , we calculate precisely the linear term and the first nonlinear (quadratic) term of this Born series. The estimation of smoothness of the first nonlinear term is also presented. Copyright © 2013 John Wiley & Sons, Ltd.

Inverse backscattering Born approximation for a two-dimensional magnetic Schrödinger operator

We investigate the inverse backscattering Born approximation for a two-dimensional magnetic Schrödinger operator. Under the assumption that the Born series converges in the space , we calculate precisely the linear term and the first nonlinear (quadratic) term of this Born series. The estimation of smoothness of the first nonlinear term for a two-dimensional case is also presented.

Inverse backscattering problem for the generalized nonlinear Schrödinger operator in two dimensions

The inverse Born approximation is studied for the generalized nonlinear two-dimensional Schrödinger equation where the real-valued unknown potentials αl belong to for some 2 ⩽ p ⩽ ∞ and their Fourier transforms belong to the space for some 1 < s < 2. We prove that the leading-order singularities of the sum of the unknown potentials can be recovered from the inverse Born approximation. We also prove that the approximation is equal to the true function up to sum of two functions: one of them from the Sobolev space Ht while the other being a continuous function.

Status of the inverse Compton backscattering source at Daresbury Laboratory

Inverse Compton scattering is a promising method to implement a high-brightness, ultra-short, energy tuneable X-ray source at accelerator facilities and at laser facilities using laser wake-field acceleration. We have developed an inverse Compton X-ray source driven by the multi-10-TW laser installed at Daresbury Laboratory. Polarized X-ray pulses will be generated through the interaction of laser pulses with electron bunches delivered by the energy recovery linac commissioned at the ALICE facility with spectral peaks ranging from 0.4 to 12 Å, depending on the electron bunch energy and the scattering geometry. X-ray pulses containing up to 10 7 photons per pulse will be created from head-on collisions, with a pulse duration comparable to the incoming electron bunch length. For transverse collisions the laser pulse transit time defines the X-ray pulse duration. The peak spectral brightness is predicted to be up to 10 21 photon/(s mm 2 mrad 2 0.1% Δ λ/ λ). Called COBALD, this source will be initially used as a short-pulse diagnostic for the ALICE electron beam and will explore the extreme challenges of photon/electron beam synchronization, which is a fundamental requirement for all conventional accelerator and laser wake-field-acceleration-based sources.

Inverse Compton backscattering source driven by the multi-10 TW laser installed at Daresbury

AbstractInverse Compton scattering is a promising method to implement a high brightness, ultra-short, energy tunable X-ray source at accelerator facilities. We have developed an inverse Compton backscattering X-ray source driven by the multi-10 TW laser installed at Daresbury. Hard X-rays, with spectral peaks ranging from 15 to 30 keV, depending on the scattering geometry, will be generated through the interaction of laser pulses with electron bunches delivered by the energy recovery linac machine, initially known as energy recovery linac prototype and subsequently renamed accelerators and lasers in combined experiments. X-ray pulses containing 9 × 107 photons per pulse will be created from head-on collisions, with a pulse duration comparable to the incoming electron bunch length. For transverse collisions 8 × 106 photons per pulse will be generated, where the laser pulse transit time defines the X-ray pulse duration. The peak spectral brightness is predicted to be ~1021 photons/(s mm2 mrad2 0.1% Δλ/λ).

Linearizing non-linear inverse problems and an application to inverse backscattering

We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization A, we need a stability estimate for A as well. That condition is satisfied in particular, if A ∗ A is an elliptic pseudo-differential operator. We apply this scheme to show uniqueness and Hölder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed.

Inverse fixed angle scattering and backscattering problems in two dimensions

The inverse backscattering and fixed angle scattering problems for the two-dimensional Schrödinger operator are studied. We prove new formulae for the first nonlinear terms in both problems and sharpen the estimates of this term. We prove also that all other terms in the Born series are Cα functions for the fixed angle scattering problem and they are Ht functions for the backscattering problem. These formulae and estimates allow us to conclude that all main singularities of the unknown potential can be recovered from the Born approximation. Especially, we show for the potentials in Lp for certain values of p that the approximation agrees with the true potential up to Ht function.

Inverse backscattering for the Schrödinger equation in 2D

We study the inverse backscattering problem for the Schrödinger equation in two dimensions. We prove that, for a non-smooth potential in 2D, the main singularities up to 1/2 of the derivative of the potential are contained in the Born approximation (diffraction tomography approximation) constructed from the backscattering data. We measure singularities in the scale of Hilbertian Sobolev spaces.

Measurement of particle size distribution in suspension polymerization using in situ laser backscattering

Many methods have been developed for characterizing the particle size distribution (PSD) in a suspension polymerization reactor, but are restricted to suspensions with low volume fractions of polymer or to determining the PSD only at the end of the batch. Laser backscattering can be used to measure the chord length distribution for slurries with high particle densities. Here, a combination of inverse modeling and laser backscattering is used to determine the PSD for polymer beads typical of operations for a suspension polymerization reactor. Several methods are compared for accurately determining the PSD from the reported chord length distribution (CLD), including methods that take surface roughness into account. These results demonstrate the applicability of laser backscattering for the in situ particle size distribution analysis in suspension polymerization reactors.

Inverse backscattering in even dimensions

This paper investigates the inverse backscattering problem for a potential in even dimensions. Our results are obtained through the study of a modified backscattering map. We use the wave equation approach here and extend Melrose and Uhlmann's method [6] to even dimensions.