Search

A de Branges space $ \mathcal {B} $ B is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map $ F(z) \mapsto F(-z) $ F (z) ↦ F (− z). Let $ K_\mathcal {B}(z,w) $ K B (z , w) be the reproducing kernel in $ \mathcal {B} $ B and $ S_\mathcal {B} $ S B be the operator of multiplication by the independent variable with maximal domain in $ \mathcal {B} $ B . Loosely speaking, we say that $ \mathcal {B} $ B has the $ \ell _p $ ℓ p -oversampling property relative to a proper subspace $ \mathcal {A} $ A of it, with $ p\in (2,\infty ] $ p ∈ (2 , ∞ ] , if there exists $ J_{\mathcal {A}\mathcal {B}}:{\mathbb C}\times {\mathbb C}\to {\mathbb C} $ J A B : C × C → C such that $ J(\cdot,w)\in \mathcal {B} $ J (⋅ , w) ∈ B for all $ w\in {\mathbb C} $ w ∈ C , $$\begin{align*} &\sum_{\lambda\in\sigma(S_{\mathcal{B}}^{\gamma})} \left(\frac{\left\lvert J_{\mathcal{A}\mathcal{B}}(z,\lambda) \right\rvert}{K_\mathcal{B}(\lambda,\lambda)^{1/2}}\right)^{p/(p-1)} ∑ λ ∈ σ (S B γ) (| J A B (z , λ) | K B (λ , λ) 1 / 2 ) p / (p − 1) < ∞ and F (z) = ∑ λ ∈ σ (S B γ) J A B (z , λ) K B (λ , λ) F (λ) , for all $ F\in \mathcal {A} $ F ∈ A and almost every self-adjoint extension $ S_{\mathcal {B}}^{\gamma } $ S B γ of $ S_\mathcal {B} $ S B . This definition is motivated by the well-known oversampling property of Paley-Wiener spaces. In this paper, we provide sufficient conditions for a symmetric, regular de Branges space to have the $ \ell _p $ ℓ p -oversampling property relative to a chain of de Branges subspaces of it. [ABSTRACT FROM AUTHOR]

In this paper, a method is proposed for producing monoergetic high-quality ion beams in vacuum, via direct acceleration by the electromagnetic (EM) field of two counterpropagating variable-frequency lasers. Ions are trapped and accelerated by a beat-wave structure with variable phase velocity, allowing for fine control over the energy and the charge of the beam via tuning of the frequency variation. The physical mechanism is described with a 1-D theory, providing the general conditions for trapping and scaling laws for the relevant features of the ion beam. Two-dimensional EM particle-in-cell simulations, in which hydrogen gas is considered as an ion source, confirm the validity and the robustness of the method. Index Terms--Direct acceleration, ion acceleration, laser-based acceleration, optical acceleration, optical trapping, vacuum acceleration.

We use the quasi-static particle-in-cell (PIC) code QuickPIC to perform full-scale one-to-one laser-wakefield-acceleration (LWFA) numerical experiments, with parameters that closely follow current experimental conditions. The propagation of state-of-the-art laser pulses in both preformed and uniform plasma channels is examined. We show that the presence of the channel is important whenever the laser self-modulations do not dominate the propagation. We examine the acceleration of an externally injected electron beam in the wake generated by ~10-J laser pulses, showing that, by using 10-cm-scale plasma channels, it is possible to accelerate electrons to more than 4 GeV. A comparison between QuickPIC and 2-D OSIRIS is provided. Good qualitative agreement between the two codes is found, but the 2-D full PIC simulations fail to predict the correct laser and wakefield amplitudes. Index Terms--Electron accelerators, lasers, plasma waves, simulation.

We develop a functional model for operators arising in the study of boundary‐value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of appropriate Dirichlet‐to‐Neumann maps, which can be utilised in the analysis of the properties of parameter‐dependent problems, including the study of their spectra. [ABSTRACT FROM AUTHOR]

Electron–positron pair cascades developed in the extreme electromagnetic fields of neutron star polar caps are considered a key source of magnetospheric plasma in these objects. We use a simplified model that maps the quantum electrodynamics processes governing pair cascades to analytically and numerically model these cascades, and show that large-amplitude oscillations of the electric field are inductively driven by the resulting plasma. A plasma instability arises in these oscillations, and particles accelerated in growing electric field perturbations can drive secondary pair bursts that damp the large-amplitude oscillations. An analytical model is proposed to describe this interplay between the pair production and kinetic collective plasma processes. All analytical results are shown to be in excellent agreement with particle-in-cell simulations. [ABSTRACT FROM AUTHOR]

We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one perturbations using distinguished elements from the set of functions associated with a de Branges space. The scale of rigged Hilbert spaces associated with this construction is also studied from the viewpoint of de Branges's theory. [ABSTRACT FROM AUTHOR]

On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the scattering matrix for pairs of such extensions. We use this representation to explicitly recover the coupling constants in the inverse scattering problem for a finite non-compact quantum graph with δ-type vertex conditions. [ABSTRACT FROM AUTHOR]

Three-dimensional hybrid particle-in-cell simulations, with kinetic ions and fluid electrons, of a plasma cloud expansion in the solar wind are presented, revealing the dynamics of the expansion, with shock formation, magnetic field compression, and solar wind ion deflection around the plasma bubble. The similarities of this system with a magnetosphere are also pointed out. Index Terms--Diamagnetic cavities, magnetospheres, solar wind interaction.

Three-dimensional (3-D) particle-in-cell (PIC) simulations of intense laser pulses and intense relativistic electron beams, propagating in gas targets are presented. As these beams propagate, the background gas is tunnel ionized, and the beam drives a wake, which sustains 1-100 GV/cm electric fields and propagates at the velocity of the driver. Such wakes can accelerate electrons to gigaelectronvoit energies in cm- length scale plasmas. Index Terms--Ionization, laser wakefield, plasma wakefield, three-dimensional particle-in-cell simulations.

An all-optical mechanism of ion acceleration in vacuum with two counter-propagating plane waves has been proposed by F. Peano et al., IEEE Trans Plasma Sci. 36, 1857 (2008). A suitable frequency chirping of lasers drives a beat wave with variable phase velocity that traps particles and accelerates them longitudinally. In this paper, direct ion acceleration by two counter-propagating focused laser beams with variable frequencies is considered, and the multi-dimensional effects associated with the finite transverse dimension of lasers are investigated. It is shown that the Gaussian laser beams provide a defocusing transverse force that stops the acceleration process as ions propagate towards regions of smaller laser fields. On the other hand, the Laguerre-Gaussian laser beams with identical orbital angular momentum can confine the off-axis ions radially as they accelerate to high energies. It is shown that the orbital angular momentum of the Laguerre-Gaussian lasers can be used to control the angular momentum of the accelerated ion beam. [ABSTRACT FROM AUTHOR]

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a matrix in our class and give an algorithm for recovering this matrix from the spectral function. The reconstructive algorithm is applicable to matrices which cannot be treated by known inverse block matrix methods. Our approach to the inverse problem is based on the rational interpolation theory developed in a previous paper. [ABSTRACT FROM AUTHOR]

We study how the spectrum of a Jacobi operator changes when this operator is modified by a certain finite rank perturbation. The operator corresponds to an infinite mass-spring system and the perturbation is obtained by modifying one interior mass and one spring of this system. In particular, there are detailed results of what happens in the spectral gaps and which eigenvalues do not move under the modifications considered. These results were obtained by a new tecnique of comparative spectral analysis and they generalize and include previous results for finite and infinite Jacobi matrices. [ABSTRACT FROM AUTHOR]

We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1, 1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to M G Krein. We show that these classes of operators have several distinctive properties, some of them related to the spectra of their canonical selfadjoint extensions. In particular, we provide necessary and sufficient conditions on the spectra of two canonical self-adjoint extensions of an operator for it to belong to one of our classes. Our discussion is based on some recent results in the theory of de Branges spaces. [ABSTRACT FROM AUTHOR]

Compact and affordable ion accelerators based on laser-produced plasmas have potential applications in many fields of science and medicine. However, the requirement of producing focusable, narrow-energy-spread, energetic beams has proved to be challenging. Here we demonstrate that laser-driven collisionless shocks can accelerate proton beams to ?20?MeV with extremely narrow energy spreads of about 1% and low emittances. This is achieved using a linearly polarized train of multiterawatt CO2 laser pulses interacting with a gas-jet target. Computer simulations show that laser-heated electrons launch a collisionless shock that overtakes and reflects the protons in the slowly expanding hydrogen plasma, resulting in a narrow energy spectrum. Simulations predict the production of ?200?MeV protons needed for radiotherapy by using current laser technology. These results open a way for developing a compact and versatile, high-repetition-rate ion source for medical and other applications. [ABSTRACT FROM AUTHOR]

This paper presents a computational study of D+D fusion driven by Coulomb explosion (CE) within a single, homonuclear deuterium nanodroplet, subjected to double-pulse ultraintense laser irradiation. This irradiation scheme results in the attainment (by the first weaker pulse) of a transient inhomogeneous density profile, which serves as a target for the driving (by the second superintense pulse) of nonuniform CE that triggers overrun effects and induces intrananodroplet (INTRA) D+D fusion. Scaled electron and ion dynamics simulations were utilized to explore the INTRA D+D fusion yields for double-pulse, near-infrared laser irradiation of deuterium nanodroplets. The dependence of the INTRA yield on the nanodroplet size and on the parameters of the two laser pulses was determined, establishing the conditions for the prevalence of efficient INTRA fusion. The INTRA fusion yields are amenable to experimental observation within an assembly of nanodroplets. The INTRA D+D fusion can be distinguished from the concurrent internanodroplet D+D fusion reaction occurring in the macroscopic plasma filament and outside it in terms of the different energies of the neutrons produced in these two channels. [ABSTRACT FROM AUTHOR]

Abstract: The development of new laser systems, in the 10 PW range, will push Laser Wakefield Accelerators (LWFA) to a new qualitative regime, where different configurations, approaches, and parameters can be explored. Based on the design parameters to be expected for some of these systems (e.g. the future Vulcan 10 PW OPCPA laser system), we have explored the optimal parameters for a single LWFA stage, using the theoretical scalings for these parameters (pulse duration ≈30 fs, energy ≈300 J). The scalings predict the possibility to accelerate electron bunches to energies close to the energy frontier, with self-injected electrons in excess of 10 GeV, and above 50 GeV bunches with externally-injected electrons. We have used these parameters as a baseline for 3D full scale simulations, confirming self-guiding of 10 PW lasers over distances in excess of 10 cm, and 12 GeV self-injected beams, in agreement with theoretical predictions for the maximum energy gain and the injected charge. In externally guided configurations, our simulations confirm the accelerating gradients and the stability of the laser guided propagation for the long distances required to reach the energy frontier. To cite this article: L.O. Silva et al., C. R. Physique 10 (2009). [Copyright &y& Elsevier]

We obtain the asymptotic behavior of eigenvalues of Jacobi matrices corresponding to a modified Jaynes–Cummings model with additive and multiplicative modulations using the so-called successive diagonalization method. By comparing the cases with and without modulated entries, we show the influence of periodic modulations on the eigenvalue asymptotics. [ABSTRACT FROM AUTHOR]

The effects of the highly damped modes in the energy and reaction rates in a plasma are discussed. These modes, with wave numbers k (*this character cannot be represented in ASCII text) k[sub D], even being only weakly excited, with less than k[sub B] per mode, make a significant contribution to the energy and screening in a plasma. When the de Broglie wavelength is much less than the distance of closest approach of thermal electrons, a classical analysis of the plasma can be made. It is assumed, in the classical analysis, with h → 0, that the energy of the fluctuations hω (*this character cannot be represented in ASCII text) k[sub B] T. Using the fluctuation-dissipation theorem, the spectra of fluctuations with h ≠ ≠0 is appreciably decreased. The decrease is mainly for the highly damped modes at high frequencies (∼0.5 − 3k[sub B]T). Reaction rates are enhanced in a plasma due to the screening of the reacting ions. This is taken into account by the Salpeter factor, which assumes slow motion for the ions. The implication of including the highly damped modes (with ≠ ≠0) in the nuclear reaction rates in a plasma is discussed. Finally, the investigations presently done on these effects in particle simulations with the sheet model and the multiparticle quantum simulation code are described. [ABSTRACT FROM AUTHOR]

Turbulent magnetic fields abound in nature, pervading astrophysical, solar, terrestrial and laboratory plasmas. Understanding the ubiquity of magnetic turbulence and its role in the universe is an outstanding scientific challenge. Here, we report on the transition of magnetic turbulence from an initially electron-driven regime to one dominated by ion-magnetization in a laboratory plasma produced by an intense, table-top laser. Our observations at the magnetized ion scale of the saturated turbulent spectrum bear a striking resemblance with spacecraft measurements of the solar wind magnetic-field spectrum, including the emergence of a spectral kink. Despite originating from diverse energy injection sources (namely, electrons in the laboratory experiment and ion free-energy sources in the solar wind), the turbulent spectra exhibit remarkable parallels. This demonstrates the independence of turbulent spectral properties from the driving source of the turbulence and highlights the potential of small-scale, table-top laboratory experiments for investigating turbulence in astrophysical environments. [ABSTRACT FROM AUTHOR]

Contemporary high-power laser systems make use of solid-state laser technology to reach petawatt pulse powers. The breakdown threshold for optical components in these systems, however, demands beam diameters up to 1 m. Raman amplification of laser beams promises a breakthrough by the use of much smaller amplifying media, i.e., millimeter-diameter-wide plasmas. Through the first large-scale multidimensional particle-in-cell simulations of this process, we have identified the parameter regime where multipetawatt peak laser powers can be reached, while the influence of damaging laser–plasma instabilities is only minor. Snapshots of the probe laser pulse being amplified, generated using state-of-the-art visualization techniques, are presented. [ABSTRACT FROM AUTHOR]

Abstract: For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end, we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a wide range of Jacobi matrices. [Copyright &y& Elsevier]