Electron-ion Momentum Research Articles

Manipulating nonsequential double ionization of atoms by parallel polarized three-color laser fields

Nonsequential double ionization (NSDI) of He atoms in a parallel polarized three-color field is investigated by using a three-dimensional classical ensemble model. The driving field is composed of 1600-nm and 800-nm laser pulses with equal intensity. A weak 400-nm laser pulse is used as a controlling field. The results indicate that in the correlated electron momentum distribution and ion momentum distribution, the electron pairs and ions of the first returning recollision (FRR) trajectory, the odd-returning recollision (ORR) trajectory (excluding FRR), and the even-returning recollision (ERR) trajectory are located in different regions separated well from each other. The electron pairs from FRR trajectories mainly distribute around the origin, and those electron pairs from ORR and ERR trajectories respectively cluster in the first quadrant and the third quadrant. With the increase of the phase of the controlling field, the proportion of FRR trajectories in NSDI first increases and then decreases, and the proportions of those trajectories with the returning number more than one first decrease and then increase, which leads to the fact that with the increase of the phase of the controlling field, the anticorrelated emissions first increase and then decrease and correspondingly the ion momentum distribution evolves from a double-hump to a triple-hump and then to a double-hump structure. Moreover, NSDI from multiple-returning recollision trajectories mainly occur through recollision-induced direct ionization (RDI) mechanism, while NSDI from the FRR trajectories mainly occurs through recollision-induced excitation with subsequent ionization (RESI) mechanism. Thus the dominant NSDI ionization mechanism can also be controlled by changing the phase of the controlling field.

Atomic drift-less electromigration model for submicron copper interconnects

Electromigration in chip level interconnect is commonly described by atomic drift due to electron-wind force that arises from electron-ion momentum transfer. As an alternative to this model, in early 1980’s, Sah proposed a two dimensional analytical ‘void-surface bond-breaking’ model by dropping the atomic drift term that resulted from electron-wind force (in his book ‘Fundamentals of Solid-State Electronics’) and the rate of change of area of void is computed. Due to the continuous down scaling and evolution of interconnect patterning technologies, the void growth process in modern interconnect becomes more complex and electromigration failures are found to be catastrophic in nature instead of gradual type failures observed in early days. In this work, Sah’s model is revisited from the perspective of its applicability to modern submicron copper interconnects. The electromigration-induced resistance change behavior is analytically derived considering a three-dimensional atomic drift-less model. A good correlation between the findings of our model with experimental observations is presented. Keywords: Analytical model, Copper, Drift-less, Electromigration, Resistance change, Time to failure

Trends in angle-resolved molecular photoelectron spectroscopy.

The field of angle-resolved molecular photoelectron spectroscopy is reviewed, with emphasis on foundations and most recent applications in different regimes of light-matter interaction. The basic formalism underlying one-photon electron angular distributions is presented, from the primary molecular frame (MF) photoemission i.e. emission from fully oriented molecules to laboratory frame (LF) observables produced from randomly oriented targets, extensions to multiphoton and strong field processes being briefly described, followed by a survey of current quantum mechanical computational approaches. The description of experimental developments is focused on the advancements in two major instrumentation fields for angle-resolved PES of molecules in the last two decades, namely charged-particle imaging spectrometers and adiabatically or impulsively laser-induced molecular alignment, together with their interplay with the remarkable characteristics achieved nowadays by the ionizing light sources and the challenging control of complex molecules in the gas phase. Aspects and applications of LF angular observables from unoriented targets are presented, with contemporary applications, especially as probes of the target electronic structure, including higher angular observables, in particular photoelectron circular dichroism (PECD) from chiral molecules, which is confirmed as a powerful chiral technique, and higher terms arising from multiphoton or non-dipole terms. Molecular frame photoelectron angular distributions (MFPADs), which stand out as the most complete observables of molecular photoionization stereodynamics in different excitation regimes, now broadly extended to characterize molecular structure and dynamics, are then discussed stemming from fully oriented molecules tackled by electron-ion momentum coincidence techniques, or from laser aligned samples. Finally, novel developments and challenging perspectives, notably the implementation of PAD in time-resolved schemes at ultrashort time scales, high energy, and high intensity regimes are drawn.

Angle-resolved studies of XUV–IR two-photon ionization in the RABBITT scheme

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is an established technique for studying time-delay in photoionization of atoms and molecules. It has been recently extended to angle-resolved studies, accessing diverse fingerprint observables of the attosecond photoemission dynamics within the bound-continuum and continuum–continuum transitions. In this work, we address the general form of the ISB(θ,τ) two-photon photoelectron angular distributions (PADs) associated to the RABBITT sideband signal, as a function of the emission angle θ, and the delay τ between the XUV attosecond pulse train and the infrared (IR) dressing field at play in the RABBITT scheme. Relying on the expansion in Legendre polynomials, the PAD is synthesized in terms of a reduced set of coefficients which fully describe both its static (τ-independent) and dynamic (τ-dependent) components and enables us to retrieve any observable characterizing the PAD. This unified framework streamlines the comparison between different experimental or theoretical data sets and emphasizes how some observables depend on the experimental conditions. Along with the modelled analysis, we report new results of angle-resolved RABBITT direct ionization of the np valence orbital of Ar(3p6) and Ne(2p6), employing electron-ion coincidence momentum spectroscopy at the new Attolab facility. In this case, the nine coefficients synthesizing the PAD are further linked to the magnitude and phase of the transition dipole matrix elements, providing a fundamental test of theoretical predictions. Similarities and differences are found between Ar and Ne in the explored low energy region, up to 20 eV above the ionization threshold, where the electron dynamics is most sensitive to electronic correlation. Further interpretation of these results would benefit from a comparison with advanced many-body theoretical simulations.

Angle-resolved RABBITT : from atoms to molecules

SynopsisWe report recent results of photoelectron angular distributions (PADs) for photoionization (PI) of atomic and molecular targets, resolved in the time domain at the attosecond scale, combining electron-ion coincidence momentum spectroscopy and the RABBITT scheme. We propose a unified formalism synthetizing the PAD(θ, τ) results in terms of a reduced set of coefficients.

Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime.

Quantitative identification of tunneling ionization (TI) and multiphoton ionization (MPI) with Keldysh parameter γ in intermediate regime is of great importance to better understand various ionization-triggered strong-field phenomena. We theoretically demonstrate that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters. Using non-linear iterative curve fitting algorithm (NICFA), the detected time-dependent probability current of ionized electrons can be decoupled into weighted TI and MPI portions. This enables us to confirm that the observed plateau-like structure in ionization delay time picture at the intermediate γ originates from the competition between TI and MPI processes. A hybrid quantum and classical approach (HQCA) is developed to evaluate the weights of TI and MPI electrons in good agreement with NICFA result. Moreover, the well separated TI and MPI electrons using HQCA are further propagated classically for mapping their final momentum, which well reproduces the experimental or ab-initio numerical calculated signatures of ionized electron momentum distribution in a rather broad γ regime.

Non-oscillatory quasineutral fluid model of cross-field discharge plasmas

This paper presents a non-oscillatory quasineutral plasma model, in which the electric field in the ion momentum equation employs the electron drift-diffusion formulation. Due to the quasineutral assumption, the electron pressure is directly coupled with the ion pressure in the inviscid flux of the ion momentum equation, which is solved using a finite-volume method with nonlinear limiting. The electron-pressure coupled method eliminates the grid-scale numerical oscillations that occur particularly near the stagnation point (the ion bulk velocity is close to zero) of a cross-field discharge plasma when using an uncoupled method. Additionally, such numerical oscillations are also observed when using a quasineutral hybrid model where a grid- or particle-based kinetic approach is employed for ions. The importance of coupling the electron pressure and ion momentum in a quasineutral plasma model is discussed.

On the Cutoff Distance and the Classical Energy-Averaged Electron–Ion Momentum Transport Cross Section in Ideal and Nonideal Plasmas

The wide use of a speed-independent distance as a cut-off impact parameter together with Rutherford's scattering formula, within the cut-off theory, to account for charge screening in plasma environment embodies a clear inconsistency. A new physically justified choice of the cut-off distance is introduced and used to derive a closed form expression for the effective momentum transport cross section. A simple approximation for the present Coulomb logarithm, free of special functions, is also presented and assessed. A comparison with experimentally recovered data for the reduced Coulomb conductivity showed better agreement and better physical behavior of the present expressions compared to previous cut-off expressions in the literature.

Electron-ion momentum vector coincidences in electron collisions with atoms and molecules

We review experimental studies of electron impact ionization of atoms and molecules which became feasible by applying the electron-ion momentum vector coincidence technique. Besides briefly discussing excitation of metastable helium we present studies of single ionization of helium and argon and also mention a pilot experiment for positron impact ionization. The main strength of the method is revealed if three or more particles are to be detected and if the cross section of the reaction is small. Exemplarily helium double ionization close to threshold is shown. Studies of molecular ionization reveal a molecular alignment dependent collision dynamics for the molecular hydrogen target. For larger molecules ionized electronic orbital and ionic fragment can be correlated.

Turbulent current drive mechanisms

Mechanisms through which plasma microturbulence can drive a mean electron plasma current are derived. The efficiency through which these turbulent contributions can drive deviations from neoclassical predictions of the electron current profile is computed by employing a linearized Coulomb collision operator. It is found that a non-diffusive contribution to the electron momentum flux as well as an anomalous electron-ion momentum exchange term provide the most efficient means through which turbulence can modify the mean electron current for the cases considered. Such turbulent contributions appear as an effective EMF within Ohm's law and hence provide an ideal means for driving deviations from neoclassical predictions.

Multistart spiral electron vortices in ionization by circularly polarized UV pulses

Multistart spiral vortex patterns are predicted for the electron momentum distributions in the polarization plane following ionization of the helium atom by two time-delayed circularly polarized ultrashort laser pulses. For two ultraviolet (UV) pulses having the same frequency (such that two photons are required for ionization), single-color two-photon interferometry with corotating or counter-rotating time-delayed pulses is found to lead respectively to zero-start or four-start spiral vortex patterns in the ionized electron momentum distributions in the polarization plane. In contrast, two-color one-photon plus two-photon interferometry with time-delayed corotating or counter-rotating UV pulses is found to lead respectively to one-start or three-start spiral vortex patterns. These predicted multistart electron vortex patterns are found to be sensitive to the carrier frequencies, handedness, time delay, and relative phase of the two pulses. Our numerical predictions are obtained by solving the six-dimensional two-electron time-dependent Schr\odinger equation (TDSE). They are explained analytically using perturbation theory (PT). Comparison of our TDSE and PT results for single-color two-photon processes probes the role played by the time-delay-dependent ionization cross channels in which one photon is absorbed from each pulse. Control of these cross channels by means of the parameters of the fields and the ionized electron detection geometries is discussed.

On the quantum Landau collision operator and electron collisions in dense plasmas

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

Molecular frame photoelectron angular distributions for core ionization of ethane, carbon tetrafluoride and 1,1-difluoroethylene

Molecular frame photoelectron angular distributions (MFPADs) are measured in electron–ion momentum imaging experiments and compared with complex Kohn variational calculations for carbon K-shell ionization of carbon tetrafluoride (CF4), ethane (C2H6) and 1,1-difluoroethylene (C2H2F2). While in ethane the polarization averaged MFPADs show a tendency at low energies for the photoelectron to be emitted in the directions of the bonds, the opposite effect is seen in CF4. A combination of these behaviors is seen in difluoroethylene where ionization from the two carbons can be distinguished experimentally because of their different K-shell ionization potentials. Excellent agreement is found between experiment and simple static-exchange or coupled two-channel theoretical calculations. However, simple electrostatics do not provide an adequate explanation of the suggestively simple angular distributions at low electron ejection energies.

Electron and recoil ion momentum imaging with a magneto-optically trapped target.

A reaction microscope (ReMi) has been combined with a magneto-optical trap (MOT) for the kinematically complete investigation of atomic break-up processes. With the novel MOTReMi apparatus, the momentum vectors of the fragments of laser-cooled and state-prepared lithium atoms are measured in coincidence and over the full solid angle. The first successful implementation of a MOTReMi could be realized due to an optimized design of the present setup, a nonstandard operation of the MOT, and by employing a switching cycle with alternating measuring and trapping periods. The very low target temperature in the MOT (∼2 mK) allows for an excellent momentum resolution. Optical preparation of the target atoms in the excited Li 2(2)P3/2 state was demonstrated providing an atomic polarization of close to 100%. While first experimental results were reported earlier, in this work, we focus on the technical description of the setup and its performance in commissioning experiments involving target ionization in 266 nm laser pulses and in collisions with projectile ions.

Extended breakdown of Simpleman approximation

In this letter, we solve three-dimensional time-dependent Newton equations for atoms interacting with a ten-cycle elliptically polarized laser pulse. The ionized electron momentum distributions show a tilt angle between the distribution density peak and the main polarization axis. The tilt angle’s behavior changes with an increasing laser intensity. We show that this behavior change is directly related to the release time of the electron from the atom.

Perturbation theory analysis of attosecond photoionization

Ionization of an atom by a few-cycle attosecond xuv pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. Within the PT approach, we present an ab initio parametrization of the ionized electron angular distribution (AD) using rotational invariance and symmetry arguments. This parametrization gives analytically the dependence of the AD on the carrier envelope phase (CEP), the polarization of the pulse, and on the ionized electron momentum direction, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$. For the general case of an elliptically polarized pulse, we show that interference of the first- and second-order transition amplitudes causes a CEP-dependent asymmetry (with respect to $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}\ensuremath{\rightarrow}\ensuremath{-}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$) and both elliptic and circular dichroism effects. All of these effects are maximal in the polarization plane and depend not only on the CEP but also on the phase of dynamical atomic parameters that enter our parametrization of the AD. Within the single active electron model of an atom, for an initial $s$ or $p$ state we define all dynamical parameters in terms of radial matrix elements (analytic expressions for which are given for the Coulomb and zero-range potentials). For ionization of the H atom by linearly polarized pulses, our PT results are in excellent agreement with results of numerical solutions of the time-dependent Schr\"odinger equation of Peng et al. [New J. Phys. 10, 025030 (2008)]. Also, our numerical results show that the asymmetries and dichroism effects at low electron energies have a different physical origin from those at high electron energies. Moreover, our results for Gaussian and cosine-squared pulse shapes are in good qualitative agreement. Finally, we show that our analytic formulas may prove useful for determining few-cycle extreme ultraviolet (xuv) pulse characteristics, such as the CEP and the polarization.

Faster-than-Bohm Cross-BElectron Transport in Strongly Pulsed Plasmas

We report the empirical discovery of an exceptionally high cross-B electron transport rate in magnetized plasmas, in which transverse currents are driven with abruptly applied high power. Experiments in three different magnetic geometries are analyzed, covering several orders of magnitude in plasma density, magnetic field strength, and ion mass. It is demonstrated that a suitable normalization parameter is the dimensionless product of the electron (angular) gyrofrequency and the effective electron-ion momentum transfer time, omega(ge)tau(EFF), by which all of diffusion, cross-resistivity, cross-B current conduction, and magnetic field diffusion can be expressed. The experiments show a remarkable consistency and yield close to a factor of 5 greater than the Bohm-equivalent values of diffusion coefficient D(perpendicular), magnetic-diffusion coefficient D(B), Pedersen conductivity sigma(P), and transverse resistivity eta(perpendicular).

Few-cycle attosecond pulse chirp effects on asymmetries in ionized electron momentum distributions

The momentum distributions of electrons ionized from H atoms by chirped few-cycle attosecond pulses are investigated by numerically solving the time-dependent Schroedinger equation. The central carrier frequency of the pulse is chosen to be 25 eV, which is well above the ionization threshold. The asymmetry (or difference) in the yield of electrons ionized along and opposite to the direction of linear laser polarization is found to be very sensitive to the pulse chirp (for pulses with fixed carrier-envelope phase), both for a fixed electron energy and for the energy-integrated yield. In particular, the larger the pulse chirp, the larger the number of times the asymmetry changes sign as a function of ionized electron energy. For a fixed chirp, the ionized electron asymmetry is found to be sensitive also to the carrier-envelope phase of the few-cycle pulse.

Influence of Coulomb collisions on the structure of reconnection layers

The influence of Coulomb collisions on the structure of reconnection layers is examined in neutral sheet geometry using fully kinetic simulations with a Monte Carlo treatment of the Fokker–Planck operator. The algorithm is first carefully benchmarked against key predictions from transport theory, including the parallel and perpendicular resistivities as well as the thermal force. The results demonstrate that the collisionality is accurately specified, thus allowing the initial Lundquist number to be chosen as desired. For modest Lundquist numbers S≲1000, the classic Sweet–Parker solution is recovered. Furthermore, a distinct transition to a faster kinetic regime is observed when the thickness of the resistive layer δSP falls below the ion inertial length di. For higher Lundquist numbers S≳1000, plasmoids (secondary islands) are observed within the elongated resistive layers. These plasmoids give rise to a measurable increase in the reconnection rate and for certain cases induce a transition to kinetic regimes sooner than expected from the δSP≈di condition. During this transition, the reconnection electric field exceeds the runaway limit, leading to electron scale current layers in which the nonideal electric field is supported predominantly by off-diagonal components in the electron pressure tensor, along with a residual contribution from electron-ion momentum exchange. These weakly collisional electron layers are also unstable to the formation of new plasmoids.

Angular dependence of the strong-field ionization measured in randomly oriented hydrogen molecules

We employed electron-ion coincidence momentum spectroscopy to measure the relative angle between an emitted electron and a deuteron resulting from field dissociation of the molecular ion produced by a circularly polarized pulse. We deduced the angular dependence of the molecular ionization probability without having to align the molecules first. We determined that with 50 fs pulses of 1850 nm wavelength and $2\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{W}/{\text{cm}}^{2}$ intensity neutral ${\text{D}}_{2}$ molecules are 1.15 times more likely to be ionized when the laser electric field is parallel to the molecular axis than for the perpendicular orientation, in excellent agreement with our ab initio theoretical model. Our results also agree with predictions of the molecular Ammosov-Delone-Krainov (mo-ADK) theory, as well as those of a similar experiment performed with 800 nm pulses of comparable intensity and duration on ${\text{H}}_{2}$ molecules.