The Convergence in Spatial Tasks

The article reveals the problem of convergence of direct and inverse problems in Earth Sciences, describes the features and application of these problems, discloses analytical features of direct and inverse problems. The convergence criteria and conditions for convergence were presented. This work is supported by the Grant of the Government of the Russian Federation for support of scientific research, implemented under the supervision of leading scientists in Russian institutions of higher education in the field "Space Research and Technologies" in 2011–2013

Flying mirror model for interaction of a super-intense laser pulse with a thin plasma layer: Transparency and shaping of linearly polarized laser pulses

A self-consistent one-dimensional (1D) flying mirror model is developed for description of an interaction of an ultra-intense laser pulse with a thin plasma layer (foil). In this model, electrons of the foil can have large longitudinal displacements and relativistic longitudinal momenta. An approximate analytical solution for a transmitted field is derived. Transmittance of the foil shows not only a nonlinear dependence on the amplitude of the incident laser pulse, but also time dependence and shape dependence in the high-transparency regime. The results are compared with particle-in-cell (PIC) simulations and a good agreement is ascertained. Shaping of incident laser pulses using the flying mirror model is also considered. It can be used either for removing a prepulse or for reducing the length of a short laser pulse. The parameters of the system for effective shaping are specified. Predictions of the flying mirror model for shaping are compared with the 1D PIC simulations, showing good agreement.open

Generating nearly single-cycle pulses with increased intensity and strongly asymmetric pulses of petawatt level

Generation of petawatt-class pulses with a nearly single-cycle duration or with a strongly asymmetric longitudinal profile using a thin plasma layer are investigated via particle-in-cell simulations and the analytical flying mirror model. It is shown that the transmitted pulses having a duration as short as about 4 fs (1.2 laser cycles) or one-cycle front (tail) asymmetric pulses with peak intensity of about 10(21) W/cm(2) can be produced by optimizing system parameters. Here, a new effect is found for the shaping of linearly polarized laser pulses, owing to which the peak amplitude of the transmitted pulse becomes larger than that of the incoming pulse, and intense harmonics are generated. Characteristics of the transmitting window are then studied for different parameters of laser pulse and plasma layer. For a circular polarization, it is shown that the flying mirror model developed for shaping laser pulses with ultrathin foils can be successfully applied to plasma layers having a thickness of about the laser wavelength, which allows the shape of the transmitted pulse to be analytically predicted.open6

Theoretical investigation of controlled generation of a dense attosecond relativistic electron bunch from the interaction of an ultrashort laser pulse with a nanofilm

For controllable generation of an isolated attosecond relativistic electron bunch [relativistic electron mirror (REM)] with nearly solid-state density, we propose using a solid nanofilm illuminated normally by an ultraintense femtosecond laser pulse having a sharp rising edge. With two-dimensional (2D) particle-in-cell (PIC) simulations, we show that, in spite of Coulomb forces, all of the electrons in the laser spot can be accelerated synchronously, and the REM keeps its surface charge density during evolution. We also developed a self-consistent 1D theory, which takes into account Coulomb forces, radiation of the electrons, and laser amplitude depletion. This theory allows us to predict the REM parameters and shows a good agreement with the 2D PIC simulations.open524

Flying mirror model for interaction of a super-intense nonadiabatic laser pulse with a thin plasma layer: Dynamics of electrons in a linearly polarized external field

Interaction of a high-power laser pulse having a sharp front with a thin plasma layer is considered. General one-dimensional numerical-analytical model is elaborated, in which the plasma layer is represented as a large collection of electron sheets, and a radiation reaction force is derived analytically. Using this model, trajectories of the electrons of the plasma layer are calculated numerically and compared with the electron trajectories obtained in particle-in-cell simulations, and a good agreement is found. Two simplified analytical models are considered, in which only one electron sheet is used, and it moves transversely and longitudinally in the fields of an ion sheet and a laser pulse (longitudinal displacements along the laser beam axis can be considerably larger than the laser wavelength). In the model I, a radiation reaction is included self-consistently, while in the model II a radiation reaction force is omitted. For the two models, analytical solutions for the dynamical parameters of the electron sheet in a linearly polarized laser pulse are derived and compared with the numerical solutions for the central electron sheet (positioned initially in the center) of the real plasma layer, which are calculated from the general numerical-analytical model. This comparison shows that the model II gives better description for the trajectory of the central electron sheet of the real plasma layer, while the model I gives more adequate description for a transverse momentum. Both models show that if the intensity of the laser pulse is high enough, even in the field with a constant amplitude, the electrons undergo not only the transverse oscillations with the period of the laser field, but also large (in comparison with the laser wavelength) longitudinal oscillations with the period, defined by the system parameters and initial conditions of particular oscillation.open282

A laser-plasma accelerator driven by two-color relativistic femtosecond laser pulses

A typical laser-plasma accelerator (LPA) is driven by a single, ultrarelativistic laser pulse from terawatt- or petawatt-class lasers. Recently, there has been some theoretical work on the use of copropagating two-color laser pulses (CTLP) for LPA research. Here, we demonstrate the first LPA driven by CTLP where we observed substantial electron energy enhancements. Those results have been further confirmed in a practical application, where the electrons are used in a bremsstrahlung-based positron generation configuration, which led to a considerable boost in the positron energy as well. Numerical simulations suggest that the trailing second harmonic relativistic laser pulse is capable of sustaining the acceleration structure for much longer distances after the preceding fundamental pulse is depleted in the plasma. Therefore, our work confirms the merits of driving LPAs by two-color pulses and paves the way toward a downsizing of LPAs, making their potential applications in science and technology extremely attractive and affordable

A laser-plasma accelerator driven by two-color relativistic femtosecond laser pulses

A typical laser-plasma accelerator (LPA) is driven by a single, ultrarelativistic laser pulse from terawatt- or petawatt-class lasers. Recently, there has been some theoretical work on the use of copropagating two-color laser pulses (CTLP) for LPA research. Here, we demonstrate the first LPA driven by CTLP where we observed substantial electron energy enhancements. Those results have been further confirmed in a practical application, where the electrons are used in a bremsstrahlung-based positron generation configuration, which led to a considerable boost in the positron energy as well. Numerical simulations suggest that the trailing second harmonic relativistic laser pulse is capable of sustaining the acceleration structure for much longer distances after the preceding fundamental pulse is depleted in the plasma. Therefore, our work confirms the merits of driving LPAs by two-color pulses and paves the way toward a downsizing of LPAs, making their potential applications in science and technology extremely attractive and affordable