Search

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 the associated generalised Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems as well as in the study of their spectra., 25 pages, 1 figure

This work was supported by the STFC Central Laser Facility, the STFC Centre for Fundamental physics and by EPSRC through Grant EP/G04239X/1. We acknowledge PRACE for providing access to the resource SuperMUC based in Germany at the Leibniz Research Center. LOS acknowledges the support of the European Research Council (ERC-2015-AdG Grant No. 695088). Brillouin amplification of laser pulses in plasma has been shown to be a promising approach to produce picosecond pulses of petawatt power. A key challenge is preservation of the quality of the amplified pulse, which requires control of parasitic instabilities that accompany the amplification process. At high plasma densities ( >cr /4), ponderomotive filamentation has been identified as the biggest threat to the integrity of the amplifying pulse. It has therefore been proposed to perform Brillouin scattering at densities below ncr/4 to reduce the influence of filamentation. However, parasitic Raman scattering can become a problem at such densities, contrary to densities above ncr/4 where it is forbidden. In this paper, we investigate the influence of parasitic Raman scattering on Brillouin amplification at densities below ncr/4 . We expose the specific problems posed by both Raman backward and forward scattering, and how both types of scattering can be mitigated, leading to an increased performance of the Brillouin amplification process. Publisher PDF

We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlations at the simulation start between the statistical fluctuations of weighted densities of macroparticle centers in the plasma particle phase-space. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace-Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell's equations for the fields as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelations spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon in 1970, using a macroparticle test approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes and using arbitrary macroparticle weights. Analytical estimates of statistical fluctuations single-time correlation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles., 38 pages, 11 figures

A generalized Wigner-Moyal statistical theory of radiation is used to obtain a general dispersion relation for Stimulated Brillouin Scattering (SBS) driven by a broadband radiation field with arbitrary statistics. The monochromatic limit is recovered from our general result, reproducing the classic monochromatic dispersion relation. The behavior of the growth rate of the instability as a simultaneous function of the bandwidth of the pump wave, the intensity of the incident field and the wave number of the scattered wave is further explored by numerically solving the dispersion relation. Our results show that the growth rate of SBS can be reduced by 1/3 for a bandwidth of 0.3 nm, for typical experimental parameters., 23 pages, 4 figures

BackgroundDissemination of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in healthcare institutions affects both patients and health-care workers (HCW), as well as the institutional capacity to provide essential health services.MethodsWe conducted an investigation of a cluster of SARS-CoV-2 positive cases detected in a “non-COVID-19” hospital ward during Summer 2020. The magnitude of the nosocomial outbreak was disclosed by massive testing, challenging the retrospective reconstruction of the introduction and transmission events. An in-depth contact tracing investigation was carried out to identify the contacts network during the 15-day period before the screening. In parallel, positive SARS-CoV-2 RNA samples were subjected to virus genome sequencing.ResultsOf the 245 tested individuals, 48 (21 patients and 27 HCWs) tested positive for SARS-CoV-2. HCWs were mostly asymptomatic, but the mortality among the vulnerable patient group reached 57.1% (12/21). Phylogenetic reconstruction revealed that all cases were part of the same transmission chain, thus confirming a single origin behind this nosocomial outbreak. By combining vast epidemiological and genomic data, including analysis of emerging minor variants, we unveiled a scenario of silent SARS-CoV-2 dissemination within the hospital ward, mostly driven by the close contact within the HCWs group and between HCWs and patients. This investigation triggered enhanced prevention and control measures, leading to a more timely detection and containment of novel nosocomial outbreaks.ConclusionsThe present study shows the benefit of combining genomic and epidemiological data for the investigation of complex nosocomial outbreaks, and provides valuable data to minimize the risk of transmission of COVID-19 in healthcare facilities.Short summarySARS-CoV-2 nosocomial outbreaks are of utmost public health concern. Here, we performed an in-depth investigation of a high-fatality rate nosocomial outbreak by combining vast genomic and epidemiological data, providing valuable information to understand cryptic transmission of SARS-CoV-2 within healthcare institutions.

Compton scattering of gamma rays propagating in a pair plasma can drive the formation of a relativistic electron positron beam. This process is scrutinized theoretically and numerically via particle-in-cell simulations. In addition, we determine in which conditions the beam can prompt a beam-plasma instability and convert its kinetic energy into magnetic energy. We argue that such conditions can be met at the photosphere radius of bright gamma-ray bursts.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

The laser interaction with an electron-positron-ion mixed plasma is studied, from the perspective of the associated high-order harmonic generation. For an idealized mixed plasma which is assumed with a sharp plasma-vacuum interface and uniform density distribution, when it is irradiated by a weakly relativistic laser pulse, well-defined signals at harmonics of the plasma frequency in the harmonic spectrum are observed. These characteristic signals are attributed to the inverse two-plasmon decay of the counterpropagating monochromatic plasma waves which are excited by the energetic electrons and the positron beam accelerated by the laser. Particle-in-cell simulations show the signal at twice the plasma frequency can be observed for a pair density as low as $\sim 10^{-5}$ of the plasma density. In the self-consistent scenario of pair production by an ultraintense laser striking a solid target, particle-in-cell simulations, which account for quantum electrodynamic effects (photon emission and pair production), show that dense (greater than the relativistically-corrected critical density) and hot pair plasmas can be created. The harmonic spectrum shows weak low order harmonics, indicating a high laser absorption due to quantum electrodynamic effects. The characteristic signals at harmonics of the plasma frequency are absent, because broadband plasma waves are excited due to the high plasma inhomogeneity introduced by the interaction. However, the high frequency harmonics are enhanced due to the high-frequency modulations from the direct laser coupling with created pair plasmas., Comment: Accepted in Physical Review E (Phys. Rev. E)

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data. A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

We show that the Weibel or currente filamentation instability can lead to the emission of circularly polarized radiation. Using particle-in-cell (PIC) simulations and a radiation post-processing numerical algorithm, we demonstrate that the level of circular polarization increases with the initial plasma magnetization, saturating at ~13% when the magnetization, given by the ratio of magnetic energy density to the electron kinetic energy density, is larger than 0.05. Furthermore, we show that this effect requires an ion-electron mass ratio greater than unity. These findings, which could also be tested in currently available laboratory conditions, show that the recent observation of circular polarization in gamma ray burst afterglows could be attributed to the presence of magnetized current filaments driven by the Weibel or the current filamentation instability., 8 pages, 5 figures submitted to Astrophysical Journal Letters

We study experimentally the effect of linear plasma density gradients on the self-modulation of a 400\,GeV proton bunch. Results show that a positive/negative gradient in/decreases the number of micro-bunches and the relative charge per micro-bunch observed after 10\,m of plasma. The measured modulation frequency also in/decreases. With the largest positive gradient we observe two frequencies in the modulation power spectrum. Results are consistent with changes in wakefields' phase velocity due to plasma density gradient adding to the slow wakefields' phase velocity during self-modulation growth predicted by linear theory., Comment: 14 pages, 4 figures

This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator's essential spectrum. The case of the spectral parameter being an eigenvalue is also considered. It is also shown that if the matrix entries commute, then the estimates can be refined. Finally, various examples of block Jacobi operators are given to illustrate the results., 32 pages, no figures. Typographical errors corrected

We study experimentally the longitudinal and transverse wakefields driven by a highly relativistic proton bunch during self-modulation in plasma. We show that the wakefields' growth and amplitude increase with increasing seed amplitude as well as with the proton bunch charge in the plasma. We study transverse wakefields using the maximum radius of the proton bunch distribution measured on a screen downstream from the plasma. We study longitudinal wakefields by externally injecting electrons and measuring their final energy. Measurements agree with trends predicted by theory and numerical simulations and validate our understanding of the development of self-modulation. Experiments were performed in the context of the Advanced Wakefield Experiment (AWAKE)., 4 figures

The expansion of plasma with non-parallel temperature and density gradients, and the generation of magnetic field via the Biermann battery is modeled using particle-in-cell simulations that include collisional effects via Monte Carlo methods. A scaling of the degree of collisionality shows that an anisotropy can be produced, and drive the Weibel instability, for gradient scales shorter than the mean free path. For larger collision rates, the Biermann battery dominates as the cause of magnetic field generation. When the most energetic particles remain collisionless, the Nernst effect causes the Biermann field to be dragged with the heat flux, piled up, and enhanced., 6 pages, 4 figures

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., 26 pages no figures. Typos corrected. Some remarks and an example added

We propose an all-optical dual-stage laser wakefield acceleration (LWFA), staged with co-propagating two-color laser pulses in a plasma medium, to enhance the electron bunch energy. After the depletion of the leading fundamental laser pulse that initiates self-injection and sets up the first stage particle acceleration, the subsequent second-harmonic laser pulse takes over the acceleration process and accelerates the electron bunch in the second stage over a significantly longer distance than in the first stage. In this all optical dual-stage LWFA, the electrons can gain 3 times higher energy as compared to the energy gain from the single stage LWFA driven by a single-color laser pulse with equivalent energy. Our multi-dimensional particle-in-cell simulations demonstrate that a 10-GeV electron bunch with 20-pC charge can be obtained by the two-color dual-stage LWFA using total input laser power of 0.6 PW.

Ion-scale magnetospheres have been observed around comets, weakly magnetized asteroids, and localized regions on the Moon and provide a unique environment to study kinetic-scale plasma physics, in particular in the collision-less regime. In this work, we present the results of particle-in-cell simulations that replicate recent experiments on the large plasma device at the University of California, Los Angeles. Using high-repetition rate lasers, ion-scale magnetospheres were created to drive a plasma flow into a dipolar magnetic field embedded in a uniform background magnetic field. The simulations are employed to evolve idealized 2D configurations of the experiments, study highly resolved, volumetric datasets, and determine the magnetospheric structure, magnetopause location, and kinetic-scale structures of the plasma current distribution. We show the formation of a magnetic cavity and a magnetic compression in the magnetospheric region, and two main current structures in the dayside of the magnetic obstacle: the diamagnetic current, supported by the driver plasma flow, and the current associated with the magnetopause, supported by both the background and driver plasmas with some time-dependence. From multiple parameter scans, we show a reflection of the magnetic compression, bounded by the length of the driver plasma, and a higher separation of the main current structures for lower dipolar magnetic moments.

Photon bursts with a wavelength smaller than the plasma interparticle distance can drive plasma wakes via Compton scattering. We investigate this fundamental process analytically and numerically for different photon frequencies, photon flux, and plasma magnetization. Our results show that Langmuir and extraordinary modes are driven efficiently when the photon energy density lies above a certain threshold. The interaction of photon bursts with magnetized plasmas is of distinguished interest as the generated extraordinary modes can convert into pure electromagnetic waves at the plasma-vacuum boundary. This could possibly be a mechanism for the generation of radio waves in astrophysical scenarios in the presence of intense sources of high energy photons. info:eu-repo/semantics/publishedVersion

We study electron acceleration within a sub-critical plasma channel irradiated by an ultra-intense laser pulse (a 0 > 100 or I > 1022 W cm−2). In this regime, radiation reaction significantly alters the electron dynamics. This has an effect not only on the maximum attainable electron energy but also on the phase-matching process between betatron motion and electron oscillations in the laser field. Our study encompasses analytical description, test-particle calculations and two-dimensional particle-in-cell simulations. We show single-stage electron acceleration to multi-GeV energies within a 0.5 mm-long channel and provide guidelines how to obtain energies beyond 10 GeV using optimal initial configurations. We present the required conditions in a form of explicit analytical scaling laws that can be applied to plan the future electron acceleration experiments.

Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council (grants no. EP/N013298/1, EP/R004773/1 and EP/N028694/1). This work has also been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2019–2020 (grant agreement no. 633053) and Eurofusion Enabling Research (grant no. ENR-IFE19.CCFE-01). M.V. acknowledges the support of the Portuguese Science Foundation (FCT) (grantno. SFRH/BPD/119642/2016). Two-dimensional particle-in-cell simulations are used to explore collisionless shock acceleration in the corona plasma surrounding the compressed core of an inertial confinement fusion pellet. We show that an intense laser pulse interacting with the long scale-length plasma corona is able to launch a collisionless shock around the critical density. The nonlinear wave travels up-ramp through the plasma reflecting and accelerating the background ions. Our results suggest that protons with characteristics suitable for ion fast ignition may be achieved in this way. This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 2)’. Publisher PDF

We present a Monte Carlo collisional scheme that models single Compton scattering between leptons and photons in particle-in-cell codes. The numerical implementation of Compton scattering can deal with macro-particles of different weights and conserves momentum and energy in each collision. Our scheme is validated through two benchmarks for which exact analytical solutions exist: the inverse Compton spectra produced by an electron scattering with an isotropic photon gas and the photon–electron gas equilibrium described by the Kompaneets equation. It provides new opportunities for numerical investigation of plasma phenomena where a significant population of high-energy photons is present in the system.

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov’s spectral form of this model, we find 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. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.

BACKGROUND: Older persons are the fastest growing segment of the population living in the Western hemisphere. Longevity comes at a price, including a higher rate of morbidity, functional and mental disability and the eventual loss of independence. Physical inactivity further aggravates the decline in physiological function along the aging process. Therefore, the promotion of regular exercise may be seen as one of the main non-pharmacological approaches that should be recommended to older adults. METHODS: We performed a comprehensive review on the interaction between exercise training and improved physical fitness in the elderly. Specifically, 175 papers describing the overall benefits of exercise training on the cardiovascular, neuromuscular and brain function of older adults were included. The effectiveness of training for improving quality of life at an older age was also reviewed. RESULTS: Exercise training can partially reverse the age-related physiological decline and enhance work capacity in the elderly. Numerous studies have shown that maintaining a minimum quantity and quality of physical exercise decreases the risk of cardiovascular mortality, sarcopenia, prevents the onset of osteopenia and even exerts a prophylactic role against neurodegeneration. The systemic physiologic effects are profound and may be directly linked to a favorable feedforward cycle whereby improved physiologic function begets improved physical function and so on. CONCLUSION: We conclude that structured training programs should be designed to improve the physiological function in this population. Finally, the benefits of exercise training vary as a function of training volume and this relationship is independent of age and sex. info:eu-repo/semantics/publishedVersion

When modeling laser wakefield acceleration (LWFA) using the particle-in-cell (PIC) algorithm in a Lorentz boosted frame, the plasma is drifting relativistically at beta(b)c towards the laser, which can lead to a computational speedup of similar to gamma(2)(b)=(1-beta(2)(b))-1. Meanwhile, when LWFA is modeled in the quasi-3D geometry in which the electromagnetic fields and current are decomposed into a limited number of azimuthal harmonics, speedups are achieved by modeling three dimensional (3D) problems with the computational loads on the order of two dimensional r-z simulations. Here, we describe a method to combine the speedups from the Lorentz boosted frame and quasi-3D algorithms. The key to the combination is the use of a hybrid Yee-FFT solver in the quasi-3D geometry that significantly mitigates the Numerical Cerenkov Instability (NCI) which inevitably arises in a Lorentz boosted frame due to the unphysical coupling of Langmuir modes and EM modes of the relativistically drifting plasma in these simulations. In addition, based on the space-time distribution of the LWFA data in the lab and boosted frame, we propose to use a moving window to follow the drifting plasma, instead of following the laser driver as is done in the LWFA lab frame simulations, in order to further reduce the computational loads. We describe the details of how the NCI is mitigated for the quasi-3D geometry, the setups for simulations which combine the Lorentz boosted frame, quasi-3D geometry, and the use of a moving window, and compare the results from these simulations against their corresponding lab frame cases. Good agreement is obtained among these sample simulations, particularly when there is no self-trapping, which demonstrates it is possible to combine the Lorentz boosted frame and the quasi-3D algorithms when modeling LWFA. We also discuss the preliminary speedups achieved in these sample simulations. info:eu-repo/semantics/submittedVersion

Laser pulses of extreme intensities ($I>10^{22}~ \mathrm{W/cm^2}$) are about to become available in the laboratory. The prepulse of such a laser can induce a plasma expansion that generates a low-density channel in near-critical gas jets. We present a study of channel formation and subsequent direct laser acceleration of electrons within the pre-formed channel. Radiation reaction affects the acceleration in several ways. It first interferes with the motion of the return current on the channel walls. In addition, it reduces the radial expelling efficiency of the transverse ponderomotive force, leading to the radiative trapping of particles near the channel axis. These particles then interact with the peak laser intensity and can attain multi-GeV energies., 17 pages, 9 figures

We measure the effects of transverse wakefields driven by a relativistic proton bunch in plasma with densities of 2.1×1014 and 7.7×1014 electrons/cm3. We show that these wakefields periodically defocus the proton bunch itself, consistently with the development of the seeded self-modulation process. We show that the defocusing increases both along the bunch and along the plasma by using time resolved and time-integrated measurements of the proton bunch transverse distribution. We evaluate the transverse wakefield amplitudes and show that they exceed their seed value (

25th International Conference on the Application of Accelerators in Research and Industry, CAARI 2018, Texas, USA, 12 Aug 2018 - 17 Aug 2018; AIP conference proceedings 2160(1), 040012-1 - 040012-9 (2019). doi:https://doi.org/10.1063/1.5127692, Plasma accelerators present one of the most suitable candidates for the development of more compact particle acceleration technologies, yet they still lag behind radiofrequency (RF)-based devices when it comes to beam quality, control, stability and power efficiency. The Horizon 2020-funded project EuPRAXIA (“European Plasma Research Accelerator with eXcellence In Applications”) aims to overcome the first three of these hurdles by developing a conceptual design for a first international user facility based on plasma acceleration. In this paper we report on the main features, simulation studies and potential applications of this future research infrastructure., Published by AIP Publishing, Melville, NY

Scattering relativistic electrons with optical lasers can result in a significant frequency upshift for the photons, potentially producing $\gamma$-rays. This is what linear Compton scattering taught us. Ultra-intense lasers offer nowadays a new paradigm where multi-photon absorption effects come into play. These effects can result in higher harmonics, higher yields and also electron-positron pairs. This article intends to discriminate the different laser scenarios that have been proposed over the past years as well as to give scaling laws for future experiments. The energy conversion from laser or particles to high-frequency photons is addressed for both the well-known counter propagating electron beam-laser interaction and for Quantum-electrodynamics cascades triggered by various lasers. Constructing bright and energetic gamma-ray sources in controlled conditions is within an ace of seeing the light of day., Comment: 9 pages, 9 figures

Strong magnetic fields in the magnetospheres of neutron stars (NSs) (especially magnetars) and other astrophysical objects may release their energy in violent, intense episodes of magnetic reconnection. While reconnection has been studied extensively, the extreme field strength near NSs introduces new effects: radiation cooling and electron–positron pair production. Using massively parallel particle-in-cell simulations that self-consistently incorporate these new radiation and quantum-electrodynamic effects, we investigate relativistic magnetic reconnection in the strong-field regime. We show that reconnection in this regime can efficiently convert magnetic energy to X-ray and gamma-ray radiation and thus power bright, high-energy astrophysical flares. Rapid radiative cooling causes strong plasma and magnetic field compression in compact plasmoids. In the most extreme cases, the field can approach the quantum limit, leading to copious pair production. info:eu-repo/semantics/publishedVersion

This paper provides decay bounds for Green matrices and generalized eigenvectors of block Jacobi operators when the real part of the spectral parameter lies in a bounded gap of the operator’s essential spectrum. The case of the spectral parameter being an eigenvalue is also considered. It is also shown that if the matrix entries commute, then the estimates can be refined. Finally, various examples of block Jacobi operators are given to illustrate the results.

In this paper, we determine the growth rate of the exponential radiation amplification in the ion-channel laser, where a relativistic electron beam wiggles in a focusing ion channel that can be created in a wakefield accelerator. For the first time the radiation diffraction, which can limit the amplification, is taken into account. The electron beam quality requirements to obtain this amplification are also presented. It is shown that both the beam energy and wiggler parameter spreads should be limited. Two-dimensional and three-dimensional particle-in-cell simulations of the self-consistent ion-channel laser confirm our theoretical predictions. info:eu-repo/semantics/acceptedVersion

The classical results on oversampling and undersampling (or aliasing), of functions in Paley-Wiener spaces, are generalized to the case of functions in de Branges spaces arising from regular Schr\"odinger operators with a wide range of potentials., Comment: 24 pages, no figures. Some typographical errors corrected

Twisted Laguerre-Gaussian lasers, with orbital angular momentum and characterised by doughnut shaped intensity profiles, provide a transformative set of tools and research directions in a growing range of fields and applications, from super-resolution microcopy and ultra-fast optical communications to quantum computing and astrophysics. The impact of twisted light is widening as recent numerical calculations provided solutions to long-standing challenges in plasma-based acceleration by allowing for high gradient positron acceleration. The production of ultrahigh intensity twisted laser pulses could then also have a broad influence on relativistic laser-matter interactions. Here we show theoretically and with ab-initio three-dimensional particle-in-cell simulations, that stimulated Raman backscattering can generate and amplify twisted lasers to Petawatt intensities in plasmas. This work may open new research directions in non-linear optics and high energy density science, compact plasma based accelerators and light sources., Comment: 18 pages, 4 figures, 1 table

In laboratory experiments, strong magnetic fields at the boundary of a plasma can be generated by means of laser-wakefield acceleration, enabling the study of magnetization processes in scaled versions of astrophysical plasmas. The onset and evolution of magnetic fields in laboratory and astrophysical plasmas is determined by several mechanisms1, including instabilities2,3, dynamo effects4,5 and ultrahigh-energy particle flows through gas, plasma6,7 and interstellar media8,9. These processes are relevant over a wide range of conditions, from cosmic ray acceleration and gamma ray bursts to nuclear fusion in stars. The disparate temporal and spatial scales where each process operates can be reconciled by scaling parameters that enable one to emulate astrophysical conditions in the laboratory. Here we unveil a new mechanism by which the flow of ultra-energetic particles in a laser-wakefield accelerator strongly magnetizes the boundary between plasma and non-ionized gas. We demonstrate, from time-resolved large-scale magnetic-field measurements and full-scale particle-in-cell simulations, the generation of strong magnetic fields up to 10–100 tesla (corresponding to nT in astrophysical conditions). These results open new paths for the exploration and modelling of ultrahigh-energy particle-driven magnetic-field generation in the laboratory.

Astrophysical shocks are commonly revealed by the non-thermal emission of energetic electrons accelerated in situ1–3. Strong shocks are expected to accelerate particles to very high energies4–6; however, they require a source of particles with velocities fast enough to permit multiple shock crossings. While the resulting diffusive shock acceleration 4 process can account for observations, the kinetic physics regulating the continuous injection of non-thermal particles is not well understood. Indeed, this injection problem is particularly acute for electrons, which rely on high-frequency plasma fluctuations to raise them above the thermal pool7,8. Here we show, using laboratory laser-produced shock experiments, that, in the presence of a strong magnetic field, significant electron pre-heating is achieved. We demonstrate that the key mechanism in producing these energetic electrons is through the generation of lower-hybrid turbulence via shock-reflected ions. Our experimental results are analogous to many astrophysical systems, including the interaction of a comet with the solar wind 9 , a setting where electron acceleration via lower-hybrid waves is possible. Electrons can be accelerated by astrophysical shocks if they are sufficiently fast to start with. As laboratory laser-produced shock experiments reveal, this can be achieved by lower-hybrid waves generated by a shock-reflected ion instability.

Using a generalization of the moment problem and the extremal properties of spectral measures corresponding to the selfadjoint extensions of a regular symmetric operator, we study point mass perturbations of spectral measures. We obtain general results for a wide class of operators and apply them to the analysis of point mass perturbations of spectral measures pertaining to Bessel and generalized Schr\"odinger operators., Comment: 33 pages, no figures. The title of the paper has change. There are changes in the introduction and the examples

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.

In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations from the viewpoint of the theory of de Branges spaces. Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space., Comment: 13 pages, no fugures. Theorem and remark have been added, typographical erros corrected

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [A. Lifschitz et al., J. Comp. Phys. 228 (5) (2009) 1803-1814] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion after only the first harmonic. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r-z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r-z and a gridless description in $\phi$. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples, for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.