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A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

We demonstrate a simple but efficient way to optimize and improve the properties of laser-wakefield-accelerated electron beams (e beams) based on a controllable shock-induced density down-ramp injection that is achieved with an inserted tunable shock wave. The e beams are tunable from 400 to 800 MeV with charge ranges from 5 to 180 pC. e beams with high reproducibility (of ~95% in consecutive 100 shots) were produced in elaborate experiments with an average root- mean-square energy spread of 0.9% and an average divergence of 0.3 mrad. Three-dimensional particle-in-cell (PIC) simulations were also performed to accordingly verify and uncover the process of the injection and the acceleration. These tunable e beams will facilitate practical applications for advanced accelerator beam sources.

The aim of this paper is to study the following Schrodinger–Poisson problem ( SP ) − △ u + V ( x ) u + e ϕ ( x ) u = λ f ( u ) , in R 3 , − △ ϕ = u 2 , lim | x | → + ∞ ϕ ( x ) = 0 , in R 3 , u > 0 , in R 3 . We prove existence and concentration of positive solutions to system ( SP ) for suitable range of e and λ .

The Faraday effect, caused by a magnetic-field-induced change in the optical properties, takes place in a vast variety of systems from a single atomic layer of graphenes to huge galaxies. Currently, it plays a pivot role in many applications such as the manipulation of light and the probing of magnetic fields and material's properties. Basically, this effect causes a polarization rotation of light during its propagation along the magnetic field in a medium. Here, we report an extreme case of the Faraday effect where a linearly polarized ultrashort laser pulse splits in time into two circularly polarized pulses of opposite handedness during its propagation in a highly magnetized plasma. This offers a new degree of freedom for manipulating ultrashort and ultrahigh power laser pulses. Together with technologies of ultra-strong magnetic fields, it may pave the way for novel optical devices, such as magnetized plasma polarizers. In addition, it may offer a powerful means to measure strong magnetic fields in laser-produced plasmas., 18 pages, 5 figures

Laser light trapping in cavities in near-critical density plasmas is studied by two-dimensional particle-in-cell simulation. The laser ponderomotive force can create in the plasma a vacuum cavity bounded by a thin overcritical-density wall. The laser light is self-consistently trapped as a half-cycle electromagnetic wave in the form of an oscillon-caviton structure until it is slowly depleted through interaction with the cavity wall. When the near-critical density plasma contains a preformed cavity, laser light can become a standing wave in the latter. The trapped light is characterized as multi-peak structure. The overdense plasma wall around the self-generated and preformed cavities induced by the laser ponderomotive force is found to be crucial for pulse trapping. Once this wall forms, the trapped pulse can hardly penetrate.

A two-dimensional theoretical model for the evolution of solid-density plasma irradiated by short, intense laser pulse is introduced. The electrons near the target surface are pushed inward by the radiation pressure, leading to a receding electron density jump where the laser is reflected. The electrostatic field of the resulting charge separation eventually balances the radiation pressure at the laser peak. After that the charge separation field becomes dominant. It accelerates and compresses the ions that are left behind until they merge with the compressed electrons, resulting in a high-density plasma peak. The laser pulse reflected from the receding electron density jump loses energy in plasma and suffers Doppler frequency red-shift, which can provide valuable information on the laser absorption rate and the speed of the receding electrons. Electron oscillations, including the u × B oscillations across the density jump at twice the laser frequency during the laser action, as well as the low-frequency oscillations appearing after laser action, are identified.

This paper is concerned with nonlocal Kirchhoffʼs equation { − ( a + b ∫ Ω | ∇ u | 2 ) Δ u = f ( x , u ) in Ω , u = 0 on ∂ Ω , via variational methods and invariant sets of descent flow. We obtain existence of signed and sign-changing solutions with asymptotically 3-linear bounded nonlinearity.

Long distance propagation of an energetic laser pulse with intensity slightly below that for multi-photon ionization in air is considered analytically, by noting that in the process, it is mainly the peak region of the pulse that interacts with the air molecules. Similar to that of much shorter femtosecond laser pulses of similar intensity, the affected air becomes slightly ionized and self-consistently forms a co-propagating thin and low-density plasma filament along the axis. It is found that a hundred-Joule-level laser pulse with a relatively large spot radius and pulse duration can propagate (also in the form of a self-consistent filament) tens of kilometers through the atmosphere. Such laser propagation properties should have applications in many areas.

Based on a developed local linking theorem, by replacing the Palais–Smale condition with a Cerami one, we consider the following unbounded Hamiltonian system: (0.1) { ∂ t u − Δ x u + V ( x ) u = H v ( t , x , u , v ) , − ∂ t v − Δ x v + V ( x ) v = H u ( t , x , u , v ) for ( t , x ) ∈ R × Ω , where Ω ⊂ R N , N ⩾ 1 , is a bounded domain with smooth boundary ∂Ω. The nonlinearities are assumed to be super-quadratic at the infinite, which are different from those investigated previously.

In this paper, by the use of a fixed point theorem, many new necessary and sufficient conditions for the existence of positive solutions in C[0,1]∩C1[0,1]∩C2(0,1) or C[0,1]∩C2(0,1) are presented for singular superlinear and sublinear second-order boundary value problems. Singularities at t=0, t=1 will be discussed.

The two stage electron acceleration model [Wu et al., Nucl. Fusion 57, 016007 (2017)] is extended to investigate the sources of super-hot electrons at intense circularly polarized (CP) laser solid interactions. It is found that in the presence of large scale pre-formed plasmas, super-high energetic electrons can be generated. For laser of intensity 1020 W/cm2 and pre-plasma of scale-length 10 μm, the cut-off energy of electrons by CP laser can be as high as 120 MeV compared with 100 MeV by linearly polarized laser. This unexpected acceleration can be also explained by the two-stage acceleration model. The envelop modulation of reflected CP laser is figured out, and a modified scaling law of the maximal-possible energy gain when including the modulation effect is obtained.

We study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities

In this paper, we find new conditions to ensure the existence of infinitely many homoclinic type solutions for the Schrodinger equation - Δ u + V ( x ) u = g ( x , u ) for x ∈ R N . Assuming V ( x ) and g ( x , u ) depend periodically on x, we deal with the situations where g ( x , u ) is, as | u | → ∞ , asymptotically linear, or superlinear with certain hypothesis different from ones used in previous related study. Our approach is variational and we use the Cerami condition instead of the Palais–Smale one for deformation arguments.