Ionization Regime Research Articles

Electronic transport in partially ionized water plasmas

We use ab initio simulations based on density functional theory to calculate the electrical and thermal conductivities of electrons in partially ionized water plasmas at densities above 0.1 g/cm3. The resulting conductivity data are then fitted to analytic expressions for convenient application. For low densities, we develop a simple and fully analytic model for electronic transport in low-density plasmas in the chemical picture using the relaxation-time approximation. In doing so, we derive a useful analytic expression for electronic transport cross sections with neutral particles, based on a model potential. In the regime of thermal ionization, electrical conductivities from the analytic model agree with the ab initio data within a factor of 2. Larger deviations are observed for the thermal conductivity, and their origin is discussed. Our results are relevant for modeling the interior and evolution of water-rich planets as well as for technical plasma applications.

The possibility for calibrating laser intensity in strong-field-ionization experiments

SynopsisWe present a simple method, based on an improved Perelomov-Popov-Terent’ev (PPT) model, for calibrating laser intensities from the measured ionization probabilities (or signals) of atoms or molecules in an intense laser fields. We emphasize that the PPT model can work very well both in the multiphoton and tunneling ionization regimes.

Effects of ultrashort laser pulses on angular distributions of photoionization spectra

We study the photoelectron spectra by intense laser pulses with arbitrary time dependence and phase within the Keldysh framework. An efficient semianalytical approach using analytical transition matrix elements for hydrogenic atoms in any initial state enables efficient and accurate computation of the photoionization probability at any observation point without saddle point approximation, providing comprehensive three dimensional photoelectron angular distribution for linear and elliptical polarizations, that reveal the intricate features and provide insights on the photoionization characteristics such as angular dispersions, shift and splitting of photoelectron peaks from the tunneling or above threshold ionization(ATI) regime to non-adiabatic(intermediate) and multiphoton ionization(MPI) regimes. This facilitates the study of the effects of various laser pulse parameters on the photoelectron spectra and their angular distributions. The photoelectron peaks occur at multiples of 2ħω for linear polarization while odd-ordered peaks are suppressed in the direction perpendicular to the electric field. Short pulses create splitting and angular dispersion where the peaks are strongly correlated to the angles. For MPI and elliptical polarization with shorter pulses the peaks split into doublets and the first peak vanishes. The carrier envelope phase(CEP) significantly affects the ATI spectra while the Stark effect shifts the spectra of intermediate regime to higher energies due to interference.

Correlation dynamics in double photoionization of excited helium atom by a single ultrashort XUV pulse

SynopsisWe study single- and two-photon double ionization of helium by short XUV pulses by numerically solving the time-dependent Schrödinger equation in full dimensionality within a finite element discrete variable representation scheme. We discuss the joint energy and angular distributions, identify sequential and non-sequential contributions in the double ionization by ultrashort pulse, and track the dynamics of the ionization process in distinct double ionization regimes.

Coulomb potential effects in strong-field photoelectron holography with a midinfrared laser pulse

A profound ringlike pattern coming from the interplay between the intra- and the intercycle interference of electron trajectories can be observed in the deep tunneling ionization regime, and an appropriate experimental condition for the observation of the photoelectron holography was provided.

An improved large-signal model by artificial neural network for the MOSFETs operating in the breakdown region

An improved large-signal breakdown model establishment applying an artificial neural network (ANN) approach is presented for metal-oxide-semiconductor field-effect transistors (MOSFETs) operating in the breakdown regime for the first time. A neural network program with the feed-forward back propagation algorithm and Levenberg Marquardt optimization is utilized to obtain the MOSFET large-signal model for breakdown operation. When compared with the conventional model without the breakdown effects considered, more accurate large-signal characteristics in the breakdown regime can be obtained by incorporating the avalanche network using the ANN approach. The breakdown network is demonstrated to be significant for large-signal characterization at high bias according to the analysis of minimum acceptable error. Besides, the divergence problem due to the neglected avalanche network can be avoided during ANN training in the avalanche regime. The accuracy of the presented model can keep about 2% error. The presented ANN approach can be applied to device large-signal modeling in the impact ionization regime.

Search for the best analytical formula in the tunneling and the barrier-suppression ionization regimes

In this work we derive an analytical formula for the ionization rate of the hydrogen atom in its ground state in the strong linearly polarized laser field. The derivation utilizes Keldysh-like probability amplitude in the length gauge in the dipole approximation including Coulomb effects in the final state of the ionized electron. We apply a properly chosen pre-exponential factor into the Gordon–Volkov wave function. We compare our theory with many previously known numerical or theoretical results for the field parameters for which (the laser frequency is less than the binding energy of the atom; usually ) and ( is the peak laser field). Thus, we consider both the tunneling and the barrier-suppression ionization regimes. It appears that in most cases ionization rates computed here are very close to those obtained long ago within the Perelomov, Popov and Terent’ev theory or its later modification by Popruzhenko et al. However, including Coulomb effects in the final state of the ionized electron in the present Keldysh-like theory leads to non-trivial changes (in relation to ordinary Keldysh theory without these Coulomb effects) in photoelectron energy spectra or angular distributions.

Pulse length of ultracold electron bunches extracted from a laser cooled gas.

We present measurements of the pulse length of ultracold electron bunches generated by near-threshold two-photon photoionization of a laser-cooled gas. The pulse length has been measured using a resonant 3 GHz deflecting cavity in TM110 mode. We have measured the pulse length in three ionization regimes. The first is direct two-photon photoionization using only a 480 nm femtosecond laser pulse, which results in short (∼15 ps) but hot (∼104 K) electron bunches. The second regime is just-above-threshold femtosecond photoionization employing the combination of a continuous-wave 780 nm excitation laser and a tunable 480 nm femtosecond ionization laser which results in both ultracold (∼10 K) and ultrafast (∼25 ps) electron bunches. These pulses typically contain ∼103 electrons and have a root-mean-square normalized transverse beam emittance of 1.5 ± 0.1 nm rad. The measured pulse lengths are limited by the energy spread associated with the longitudinal size of the ionization volume, as expected. The third regime is just-below-threshold ionization which produces Rydberg states which slowly ionize on microsecond time scales.

Superponderomotive regime of tunneling ionization

The photoelectron spectrum in the ultra-relativistic limit of tunneling ionization is strongly affected by wave-particle resonance and finite spot-size effects, in contradistinction with the usual assumptions of strong field physics. Near term laser facilities will access a regime where ionized electrons are abruptly accelerated in the laser propagation direction, such that they stay in phase with the laser fields through a substantial portion of the confocal region. The final momentum of the electron depends significantly on where in the confocal region it originated. By manipulating the target and collection geometry, it is possible to obtain low emittance, low energy spread, gigavolt photoelectrons. Radiation reaction effects play a negligible role in near term scenarios, but become interesting in the multi-exawatt regime. A significant advance in numerical particle tracking is introduced.

Quantum-Mechanical Description of Ionization-Induced Generation of Tunable Mid-Infrared Pulses

The work is devoted to the analytical study of the excitation of low-frequency current density (with frequencies much smaller than the frequency of the optical wave) which radiates in mid-infrared band in the gas ionization by two-color laser pulses. We calculate the low-frequency current density using the analytical solution of time-dependent Schrödinger equation on the basis of strong-field approximation. Closed-form analytical formulas for the low-frequency current density are obtained for laser-pulse parameters corresponding the tunneling and multiphoton ionization regimes. The features of excitation of low-frequency current density are analyzed in both regimes.

Terahertz and higher-order Brunel harmonics: from tunnel to multiphoton ionization regime in tailored fields

Brunel radiation appears as a result of a two-step process of photo-ionization and subsequent acceleration of electron, without the need of electron recollision. We show that for generation of Brunel harmonics at all frequencies, the subcycle ionization dynamics is of critical importance. Namely, such harmonics disappear at the low pump intensities when the ionization dynamics depends only on the slow envelope (so-called multiphoton ionization regime) and not on the instantaneous field. Nevertheless, if the pump pulse contains incommensurate frequencies, Brunel mechanism does generate new frequencies even in the multiphoton ionization regime.

Exit point in the strong field ionization process

We analyze the process of strong field ionization using the Bohmian approach. This allows retention of the concept of electron trajectories. We consider the tunnelling regime of ionization. We show that, in this regime, the coordinate distribution for the ionized electron has peaks near the points in space that can be interpreted as exit points. The interval of time during which ionization occurs is marked by a quick broadening of the coordinate distribution. The concept of the exit point in the tunneling regime, which has long been assumed for the description of strong field ionization, is justified by our analysis.

Quasi-classical description of the stark effect for an electron in an image-potential state

The quasi-classical approximation is used for establishing the positions of the classical turning points of an electron in an image-potential state exposed to an electric field of arbitrary strength perpendicular to the metal surface. It is demonstrated that the behavior of the system in electric fields of different directions is fundamentally different, which makes the dynamics of the low-dimensional system qualitatively different from that of its three-dimensional analog. The electric field strength leading to transition from the tunnel ionization regime to the regime of above-barrier decomposition is determined. The wavefunction of the bound electron state, which explicitly takes into account the influence of the electric field, is expressed in terms of elliptic integrals. The quantization condition is formulated, and the linear and quadratic in the field corrections to the electron energy are found. It is demonstrated that the difference between the linear Stark effect calculated by means of the perturbation theory and the quasi-classical energy shift in a weak field rapidly decreases with increasing quantum level number.

Calculation of Stark resonance parameters for valence orbitals of the water molecule

An exterior complex scaling technique is applied to compute Stark resonance parameters for two molecular orbitals ($1b_{1}$ and $1b_{2}$) represented in the field-free limit in a single-center expansion. For electric DC field configurations that guarantee azimuthal symmetry of the solution the calculation is carried out by solving a two-dimensional partial differential equation in spherical polar coordinates using a finite-element method. The resonance positions and widths as a function of electric field strengths are shown for field strengths starting in the tunnelling ionization regime, and extending well into the over-barrier ionization region.

Momentum mapping of continuum-electron wave-packet interference

We analyze the two-dimensional photoelectron momentum distribution of an Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below $2{U}_{p}$. By using a generalized quantum trajectory Monte Carlo simulation and comparing with the numerical solution of the time-dependent Schr\"odinger equation, we demonstrate that a profound ringlike pattern coming from the interplay between the intra- and the intercycle interferences of electron trajectories can be observed in the deep tunneling ionization regime. Moreover, we found that the rescattered electrons play a negligible role on the formation of a ringlike interference pattern, and the appearance of the ringlike interference pattern masks the holographic interference structure. Our results provide an appropriate experimental condition for the observation of the photoelectron holography and help to gain physical insight into the corresponding ultrafast electron dynamic process with attosecond temporal resolution.

Universality of photoelectron circular dichroism in the photoionization of chiral molecules

Photoionization of chiral molecules by circularly polarized radiation gives rise to a strong forward/backward asymmetry in the photoelectron angular distribution, referred to as photoelectron circular dichroism (PECD). Here we show that PECD is a universal effect that reveals the inherent chirality of the target in all ionization regimes: single photon, multiphoton, above-threshold and tunnel ionization. These different regimes provide complementary spectroscopic information at electronic and vibrational levels. The universality of the PECD can be understood in terms of a classical picture of the ionizing process, in which electron scattering on the chiral potential under the influence of a circularly polarized electric field results in a strong forward/backward asymmetry.

Exploration of laser-driven electron-multirescattering dynamics in high-order harmonic generation.

Multiple rescattering processes play an important role in high-order harmonic generation (HHG) in an intense laser field. However, the underlying multi-rescattering dynamics are still largely unexplored. Here we investigate the dynamical origin of multiple rescattering processes in HHG associated with the odd and even number of returning times of the electron to the parent ion. We perform fully ab initio quantum calculations and extend the empirical mode decomposition method to extract the individual multiple scattering contributions in HHG. We find that the tunneling ionization regime is responsible for the odd number times of rescattering and the corresponding short trajectories are dominant. On the other hand, the multiphoton ionization regime is responsible for the even number times of rescattering and the corresponding long trajectories are dominant. Moreover, we discover that the multiphoton- and tunneling-ionization regimes in multiple rescattering processes occur alternatively. Our results uncover the dynamical origin of multiple rescattering processes in HHG for the first time. It also provides new insight regarding the control of the multiple rescattering processes for the optimal generation of ultrabroad band supercontinuum spectra and the production of single ultrashort attosecond laser pulse.

Photoelectron angular distributions of H ionization in low energy regime: Comparison between different potentials**Project supported by the National Natural Science Foundation of China (Grant Nos. 11322437 and 11574010) and the National Basic Research Program of China (Grant No. 2013CB922402).

We theoretically investigate the low energy part of the photoelectron spectra in the tunneling ionization regime by numerically solving the time-dependent Schrdinger equation for different atomic potentials at various wavelengths. We find that the shift of the first above-threshold ionization (ATI) peak is closely related to the interferences between electron wave packets, which are controlled by the laser field and largely independent of the potential. By gradually changing the short-range potential to the long-range Coulomb potential, we show that the long-range potential’s effect is mainly to focus the electrons along the laser’s polarization and to generate the spider structure by enhancing the rescattering process with the parent ion. In addition, we find that the intermediate transitions and the Rydberg states have important influences on the number and the shape of the lobes near the threshold.

Unraveling nonadiabatic ionization and Coulomb potential effect in strong-field photoelectron holography

Strong field photoelectron holography has been proposed as a means for interrogating the spatial and temporal information of electrons and ions in a dynamic system. After ionization, part of the electron wave packet may directly go to the detector (the reference wave), while another part may be driven back and scatters off the ion(the signal wave). The interference hologram of the two waves may be used to extract target information embedded in the collision process. Unlike conventional optical holography, however, propagation of the electron wave packet is affected by the Coulomb potential as well as by the laser field. In addition, electrons are emitted over the whole laser pulse duration, thus multiple interferences may occur. In this work, we used a generalized quantum-trajectory Monte Carlo method to investigate the effect of Coulomb potential and the nonadiabatic subcycle ionization on the photoelectron hologram. We showed that photoelectron hologram can be well described only when the effect of nonadiabatic ionization is accounted for, and Coulomb potential can be neglected only in the tunnel ionization regime. Our results help paving the way for establishing photoelectron holography for probing spatial and dynamic properties of atoms and molecules.

Complete characterization of single-cycle double ionization of argon from the nonsequential to the sequential ionization regime

Selected features of nonsequential double ionization have been qualitatively reproduced by a multitude of different (quantum and classical) approaches. In general, however, the typical uncertainty of laser pulse parameters and the restricted number of observables measured in individual experiments leave room for adjusting theoretical results to match the experimental data. While this has been hampering the assessment of different theoretical approaches leading to conflicting interpretations, comprehensive experimental data that would allow such an ultimate and quantitative assessment have been missing so far. To remedy this situation we have performed a kinematically complete measurement of single-cycle multiple ionization of argon over a one order of magnitude range of intensity. The momenta of electrons and ions resulting from the ionization of the target gas are measured in coincidence, while each ionization event is tagged with the carrier-envelope phase and intensity of the 4-fs laser pulse driving the process. The acquired highly differential experimental data provide a benchmark for a rigorous test of the many competing theoretical models used to describe nonsequential double ionization.