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The fully developed turbulence can be regarded as a nonlinear system, with wave coupling inside, which causes the nonlinear energy to transfer, and drives the turbulence to develop further or be suppressed. Spectral analysis is one of the most effective methods to study turbulence system. In order to apply it to the study of the nonlinear wave coupling process of edge plasma turbulence, an efficient algorithm based on spectral analysis technology is proposed to solve the nonlinear wave coupling equation. The algorithm is based on a mandatory temporal static condition with the nonideal spectra separated from the ideal spectra. The realization idea and programing flow are given. According to the characteristics of plasma turbulence, the simulation data are constructed and used to verify the algorithm and its implementation program. The simulation results and experimental results show the accuracy of the algorithm and the corresponding program, which can play a great role in the studying the energy transfer in edge plasma turbulences. As an application, the energy cascade analysis of typical edge plasma turbulence is carried out by using the results of a case calculation. Consequently, a physical picture of the energy transfer in a kind of fully developed turbulence is constructed, which confirms that the energy transfer in this turbulent system develops from lower-frequency region to higher-frequency region and from linear growing wave to damping wave.

The ultrafast photoionization dynamics of N2 molecules by x-ray/XUV laser pulses is investigated. The molecular frame photoelectron momentum distributions (MF-PMDs) and the molecular frame photoelectron angular distributions (MF-PADs) are obtained by numerically solving 2D time-dependent Schrödinger equations within the single-electron approximation (SEA) frame. The results show that the molecular photoionization diffraction appears in 5 nm laser fields. However, when the laser wavelength is 30 nm, the molecular photoionization diffraction disappears and the MF-PMDs show four-lobe pattern. The ultrafast photoionization model can be employed to describe the MF-PMDs and MF-PADs of N2 molecules.

We present the photoelectron momentum distributions (PMDs) and the photoelectron angular distributions (PADs) of He+ ions, aligned H 2 + molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schrödinger equations (TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays T d, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.

Molecular frame photoelectron angular distributions (MFPADs) are theoretically studied by intense two color attosecond linearly polarized laser pulses. Simulations are performed on aligned H$_2^+$ from numerical solutions of corresponding time-dependent Schr\"{o}dinger equations. Asymmetric MFPADs are produced by a time delayed soft X-ray attosecond pulse in the presence of an XUV pump pulse. We present the dependence of the asymmetry ratio $\Gamma$ of MFPADs on the laser parameters of the pump-probe pulses. The asymmetry ratio $\Gamma$ varies with the time delay, illustrating the coherent superposition of electronic states. Altering the phase, intensity and duration of the pump pulse gives rise to a modulation of the asymmetry ratio $\Gamma$ as well. Moreover, the asymmetry of MFPADs disappears in the case of long duration probe pulses, illustrating the coherent charge migration dynamics on the attesecond time scale.

In order to improve and solve the capability of small and medium enterprises to design new products, the principle of operation of the three-lobe Roots blower rotor was firstly analyzed, and the characteristics of meshing of the rotor profile were analyzed. The meshing design formula was given. Based on this, the 3L41WD involute Roots blower design was taken as an example to calculate its full line type and to analyze and determine the meshing tolerance. Finally, the field test proved the rationality of the design, and provided guidance for SMEs to rapidly design the involute Roots blower rotor.

Extreme UV and x-ray table top light sources based on high-order harmonic generation (HHG) are focused now on circular polarization for the generation of circularly polarized attosecond pulses as new tools for controlling electron dynamics, such as charge transfer and migration and the generation of attosecond quantum electron currents for ultrafast magneto-optics. A fundamental electron dynamical process in HHG is laser induced electron recollision with the parent ion, well established theoretically and experimentally for linear polarization. We discuss molecular electron recollision dynamics in circular polarization by theoretical analysis and numerical simulation. The control of the polarization of HHG with circularly polarized ionizing pulses is examined and it is shown that bichromatic circularly polarized pulses enhance recollision dynamics, rendering HHG more efficient, especially in molecules because of their nonspherical symmetry. The polarization of the harmonics is found to be dependent on the compatibility of the rotational symmetry of the net electric field created by combinations of bichromatic circularly polarized pulses with the dynamical symmetry of molecules. We show how the field and molecule symmetry influences the electron recollision trajectories by a time–frequency analysis of harmonics. The results, in principle, offer new unique controllable tools in the study of attosecond molecular electron dynamics.

The above-threshold dissociation (ATD) of the HD+ molecular ion in femtosecond laser field is investigated theoretically The energy-dependent distribution of the dissociated fragments is calculated using an asymptotic-flow expression in the momentum space. The calculations show that the ATD of HD+ is sensitive to the initial vibrational level of ground electronic state. Multiphoton ATDs can be observed in the dissociation processes. The dynamics phenomena are interpreted by using the concept of light-dressed potential.

The laser-induced vibrational state-selectivity of product HF in photoassociation reaction H+F→HF is theoretically investigated by using the time-dependent quantum wave packet method. The population transfer process from the continuum state down to the bound vibrational states can be controlled by the driving laser. The effects of laser pulse parameters and the initial momentum of the two collision atoms on the vibrational population of the product HF are discussed in detail. Photodissociation accompanied with the photoassociation process is also described.

The Autler–Townes (AT) splitting in femtosecond photoelectron spectrum of three-level Li2 molecules is theoretically investigated using time-dependent quantum wave packet method. With proper femtosecond laser pulses, three peaks of the AT splitting can be observed in the photoelectron spectrum. The AT splitting stems from rapid Rabi oscillation caused by intense ultrashort laser pluses. The effects of laser parameters on the molecular ionization dynamics are also discussed.

The effect of pulse temporal profiles on the Autler–Townes (AT) splitting in photoelectron spectra is theoretically studied by employing the time-dependent wave packet method for a rotational Na2 molecule. The AT splitting which results from the sufficient Rabi oscillations is affected by the pulse profile and molecular alignment. The AT splitting may be observed only by utilizing proper pulse profiles with a certain intensity.

The method of quantum wave packet dynamics is used to study the multiphoton ionization of NO molecules via a two-photon Raman coupling and a laser-induced continuum structure (LICS) state in two-colour strong femtosecond pulsed laser fields. Time-and energy-resolved photoelectron energy spectra are calculated for describing three photoionization channels. The population transfers through the LICS and the Raman coupling passages are discussed.

A scheme used for controlling the population transfer and the dissociation rate of Na2 molecules is described by using the quantum wavepacket dynamical method. It is theoretically shown that the population transfer and the dissociation rate of Na2 molecules can be controlled by pump and probe laser pulses with appropriate widths of pulses, sequence and intensities.

Numerical solutions of time-dependent Schrodinger equations for one and two electron cyclic molecules exposed to intense bichromatic circularly polarized laser pulses of frequencies and , such that (integer) produce circularly polarized high order harmonics with a cut-off recollision maximum energy at and greater than the linear polarization law (in atomic units) , where I p is the ionization potential and is the ponderomotive energy defined by the field E 0 (intensity ) from each pulse and mean frequency . An electron recollision model in a rotating frame at rotating frequency predicts this simple result as a result of recollision dynamics in a combination of bichromatic circularly polarized pulses. The harmonic helicities and their intensities are shown to depend on compatible symmetries of the net pulse electric fields with that of the molecules.

We investigate molecular photoionization by ultrafast bichromatic linearly polarized UV laser pulses at frequencies perpendicular to the internuclear axis R involving π orbital excitation. Results from numerical solutions of time dependent Schrodinger equations for aligned show that molecular frame photoelectron angular distributions (MFPADs) exhibit signatures of asymmetry perpendicular to the molecular symmetry axis, arising from interference of coherent electron wave packets created by respectively one and two-photon absorption. A resonant excitation process between the ground state and the excited state is triggered by the pulse. The asymmetry of MFPADs varies periodically with pulse intensity I 0 and duration T, which we attribute to coherent resonant Rabi oscillations in electronic state population. A perturbative model is adopted to qualitatively describe and analyze these effects in both resonant and nonresonant photoionization processes.

We have experimentally observed the reduction of light speed in a rubidium vapour medium coherently prepared by electromagnetically induced transparency. The light speed reduction was deduced by directly measuring the time delay of a probe light when it passed through the medium. The time delay varies with the intensity of the coupling laser, and the typical time delay we recorded was 1.8 μs, corresponding to a light speed of 56000 m/s.

Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beam to sub-micrometre dimensions. We start from a two-dimensional time-dependent Schrodinger equation and reduce it to a one-dimensional equation by a paraxial approximation. We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field. It is found that two parameters, the atomic velocity and the intensity of the laser beam, play an important role in determining the deposition quality.

We present molecular photoelectron angular distributions (MPADs) in multi-photon ionization processes by circularly polarized attosecond UV laser pulses. Simulations are performed on the single electron aligned molecular ion H by solving corresponding 3D time-dependent Schrodinger equations. Numerical results of molecular above threshold ionization (MATI) show that rotations of MPADs with respect to the molecular and polarization axes depend on pulse intensities and photoelectron kinetic energies. We attribute the rotation to Γ, the difference between parallel and perpendicular ionization probabilities. It is found that in a resonant ionization process, the rotation angle is also a function of the symmetry of intermediate electronic states. The coherent population transfer between the initial and the resonant electronic states is controlled by pulse intensities. Such dependence of rotations on the pulse intensity is absent in Rydberg resonant ionizations as well as in MATI at large energy photons ω > Ip, where ω is angular frequency of photons and Ip is the molecular ionization potential. We describe these processes by a multi-photon perturbation theory model. Effects of molecular alignment and pulse ellipticities on rotations are investigated, confirming the essence of the ionization parameter Γ in rotations of MPADs.

We present molecular photoionization simulations by intense (I ~ 1016 W/cm2) few cycle circularly polarized attosecond extreme ultraviolet laser pulses for aligned H2+ from numerical solutions of the corresponding time-dependent Schrodinger equation. With appropriate laser pulse parameters, circular attosecond coherent electron wave packets (CEWPs) are created in excited Rydberg states. Such CEWPs are spatially localized during ionization processes, thus resulting in sufficient population oscillations between the resonant excited Rydberg states and the initial ground state. Consequently Autler-Townes splitting in circular polarization energy spectra is predicted, which is shown to be critically sensitive to the pulse intensity, duration, and polarization. The resulting photoelectron angular distributions are rotated with respect to the molecular axis due to the nonspherical Coulomb potential of the molecule, resulting in different ionization rates at different laser polarization-molecular angles.

We present molecular attosecond ionization with few cycle XUV laser pulses from numerical solutions of time dependent Schrodinger equations. Simulations performed on aligned H+2 exhibit signature of red-shifts in photoelectron energy spectra. This is shown to be critically sensitive to the the pulse duration and wavelength and is attributed to the broad spectral width of the ionizing pulses and diminishing electronic Franck-Condon factors with short pulses. We analyze the laser parameter dependence of the energy spectra by a perturbative model.

We present a computational study of the transmission resonances in a symmetry-broken square coaxial aperture with an inserted particle offset (δ) from the centre. According to the distribution characteristics of oscillating charges on the exit surface, the TE11- and TE21-like mode resonances in the hole may be regarded as dipole and quadrupole plasmon resonances, respectively. It is found that symmetry breaking, due to the particle offset, makes the quadrupole plasmon resonance, which is dark in symmetric geometry, visible. Based on the charge oscillation induced light emission mechanism, we qualitatively explain the variation of the transmission peaks of dipole and quadrupole plasmon resonances with the geometrical parameter δ, and the refractive index of the dielectric filled in the hole. Using polarization-dependent surface charge plots, we illustrate two distinct mode configurations of quadrupole plasmon resonance. Our findings will be of value in tuning the electromagnetic wave in subwavelength optics and designing chemical and biomedical sensors.

We present photoionization angular distributions of oriented symmetric (H + ) and asymmetric (HHe 2+ ) molecular ions from numerical solutions of two dimensionally reduced time-dependent Schr¨ odinger equations as a function of ionized electron kinetic energies with intense circularly polarized attosecond extreme ultraviolet laser pulses. Simulations for the equilibrium H + show that for single-photon ionization, relative intensities of parallel and perpendicular (to the molecular axis) photoionizations are critically sensitive to laser and photoelectron wavelengths due to ionization rates strongly depending on molecular geometry. Photoionization angular distributions are rotated to particular angles indicating high-order angular momenta and strong molecular potential effects. High-energy Ee spectra show effects of laser-induced electron diffraction (LIED) as the ionized electron wavelengths approach the internuclear distance. For HHe 2+ , such laser parameter sensitivity is reduced due to strong localization of the electron on one atom, but strong asymmetric LIED patterns are obtained. Angular distributions for both H + and HHe 2+ are also shown to be dependent on laser-pulse ellipticity and photoelectron energies. (Some figures may appear in colour only in the online journal)