Electron Trajectories Research Articles

Variable-density imaging of high concentration of NV centers with three-dimensional optical scanning techniques at sub-micrometer scale in millimeter area

In order to enhance the spin-dependent fluorescence signal coupled with outer fields, accurate positioning of the center of nitrogen-vacancy (NV) in bulk diamond is important in enhancing the sensitivity of the solid-state quantum magnetometry. In this paper, we have developed a new approach of three-dimensional optical scanning techniques for the imaging of variable-density of high concentration of NV centers in the interior of the diamond at the micrometer scale. The research defined the definite trajectories of electrons with different energies to generate NV– centers in diamond based on Monte-Carlo simulation results. Moreover, it also confirmed experimentally that the accurate location for the center of NV– in the diamond is at the depth of 100 μm, using three-dimensional optical vertical scanning techniques. This research paves the way to produce various depth-confined NV centers, with high coherence, important in wide-field magnetometry applications.

Coulomb-induced ionization time lag after electrons tunnel out of a barrier.

After electrons tunnel out of a laser-Coulomb-formed barrier, the movement of the tunneling electron can be affected by the Coulomb potential. We show that this Coulomb effect induces a large time difference (longer than a hundred attoseconds) between the tunneling-out time at which the electron exits the barrier and the ionization time at which the electron is free. This large time difference has important influences on strong-field processes such as above-threshold ionization and high-harmonic generation, with remarkably changing time-frequency properties of electron trajectories. Some semi-quantitative evaluations on these influences are addressed, which provide new insight into strong-field processes and give suggestions on attosecond measurements.

A Lorentz-covariant interacting electron–photon system in one space dimension

A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of multi-time wave functions, i.e., wave functions $\Psi(\mathbf{x}_{{ph}},\mathbf{x}_{{el}})$ where $\mathbf{x}_{{el}},\mathbf{x}_{{ph}}$ are the generic spacetime events of the electron and photon, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifold $\{\mathbf{x}_{{el}}=\mathbf{x}_{{ph}}\}$, compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed. Electron and photon trajectories are shown to exist globally in a Hypersurface Bohm--Dirac theory, for typical particle initial conditions. Also presented are the results of some numerical experiments which illustrate Compton scattering as well as a new phenomenon: photon capture and release by the electron.

Spatial coherence of trajectory-resolved higher-order harmonics generated from an argon-filled gas cell using single- and two-color laser pulses

An experimental study on spatial coherence of electron trajectory-resolved higher-order harmonic generation (HHG) in an argon-filled gas cell (length \ensuremath{\sim}15 mm) using single-color (\ensuremath{\lambda} \ensuremath{\sim} 800 nm) and two-color laser pulses (\ensuremath{\lambda} \ensuremath{\sim} 800 nm + 400 nm) is performed. The contribution of both a long and short electron trajectory is observed in HHG using single-color laser pulse, whereas a dominant contribution of short trajectory is observed in HHG using two-color laser pulses. The spatial coherence of trajectory-resolved higher-order harmonics is investigated using a double slit experiment. The fringe visibility is higher (\ensuremath{\sim}0.7) at low gas cell pressure, for both short and long trajectory harmonics. At higher gas pressure ($\ensuremath{\ge}50$ mbar), the fringe visibility of short trajectory harmonics (\ensuremath{\sim}0.7) is significantly higher than the long trajectory harmonics (\ensuremath{\sim}0.3--0.4). In the case of two-color laser pulses, the fringe visibility (\ensuremath{\sim}0.75) is found to be further higher than the single-color short trajectory harmonics and is nearly independent of gas pressure (\ensuremath{\sim}10--100 mbar). A theoretical model is used to explain the observed result and the intensity dependent dipole coefficient for short and long trajectory is estimated, which is in good agreement with the other reported results. The study provides an easy tool to study and control the role of different electron trajectories responsible for higher-order harmonic generation and also the spatial coherence property of higher-order harmonics generated from gas cell.

Investigation of Transient and Steady-State Behavior of Current Components in Spatial Harmonic Magnetron by Drift Orbital Resonance Theory

The drift orbital resonance theory has the potential to analyze and estimate the electron dynamics in a magnetron. Hence it has been utilized to examine the behavior of the rotating electron cloud in a spatial harmonic magnetron (SHM). Alteration of the theory variables, namely the orbital velocities, coefficients of radial expansion, gyrating circle radius, accelerating factor, etc., affects the electron trajectory forming numerous epicycloid, hypocycloid, and circular patterns. These variables are dependent on some of the physical and electrical input parameters, namely the structural geometry, the applied voltage, the applied magnetic field, etc. They thus can be used to alter and predict the rotating electron's trajectories, which in turn control the device performance as well as help to understand and visualize the response of the rotating electron cloud in the designed SHM. The manuscript also presents the analysis of the nature of the steady-state and transient response of the current components of the designed SHM (operating at 136 GHz) obtained from CST simulations and provide reasonable explanation using drift orbital resonance theory.

Tunable magnetic focusing using Andreev scattering in superconductor-graphene hybrid devices

We perform the wavepacket dynamics simulation of a graphene-based device where propagating electron trajectories are tamed by an applied magnetic field toward a normal/superconductor interface. The magnetic field controls the incidence angle of the incoming electronic wavepacket at the interface, which results in the tunable electron–hole ratio in the reflected wave function due to the angular dependence of the Andreev reflection. Here, mapped control of the quasiparticle trajectories by the external magnetic field not only defines an experimental probe for fundamental studies of the Andreev reflection in graphene but also lays the foundation for further development of magnetic focusing devices based on nanoengineered superconducting two-dimensional materials.

Effect of circularly polarized laser pulse beam waist radius on the dynamic and radiation characteristics of collided electrons

In this paper, the trajectory as well as the temporal and spatial characteristics of the electromagnetic radiation of high-energy electrons collided by fields of relativistically circularly polarized laser pulses are studied theoretically and calculated numerically, based on Lorentz equation, energy equation of electrons, and the basic equations of electron radiation. Results shows that the head-on collision of a single counter-streaming electron and an intense circularly polarized laser pulse can produce an ultra-intense pulse with zeptosecond duration in the direction where the azimuth angle and the polar angle . The amplitude of the electron trajectory and the peak power of its radiation are positively related to the beam waist radius. However, as the radius of the laser beam increases, its influence on the dynamic and radiation characteristics of the electron weaken gradually and become negligible when the beam waist radius is greater than 4 times the laser wavelength.

Effect of the Divergence of a Relativistic Electron Beam on the Diffracted Transition Radiation Excited by Them in a Single-Crystal Target

The dependence of the angular density and the photon yield of collimated diffracted transition radiation (DTR) generated in a thin single-crystal plate by a beam of relativistic electrons on the beam divergence are studied. An expression describing the DTR angular density averaged over all the rectangular trajectories of electrons in the beam is derived. For the averaging, the two-dimensional Gaussian distribution is used. A significant dependence of the angular density of collimated DTR photons on the electron-beam divergence is shown. An expression describing the number of collimated DTR photons is obtained. The significant dependence of the photon number of the collimated DTR is shown.

Graphene gets bent

Graphene gets bent

Plasma Wave Acceleration of Electron in Bubble Regime in Presence of a Planar Wiggler

The plasma wave acceleration of electron in the bubble regime is investigated in a new configuration containing a planar wiggler. The space-charge field of the laser-created ion channel can focuse and stabilize the electron trajectory to guide it toward the acceleration region. The high-gradient plasma wave field can resonantly accelerate the trapped electron to higher energies in the presence of a planar wiggler compensating the electron dephasing. The results show that in the lower plasma wave amplitudes the planar wiggler plays a more significant role on the electron energy enhancement. The increment of the electron energy in this configuration isvalidated using a three-dimension single-particle code. The energy gain of electrondependency on the planar wiggler, ion channel field, plasma wave angle and amplitude as well as the initial energy of electron has been investigated. The results of paper will be of importance in the optimization of electron energy and improving the quality of the accelerated electrons in the plasma wakefield accelerators.

Glory oscillations in photoionization microscopy: Connection with electron dynamics and Stark spectral structures in the continuum

In classical scattering theory, the term “glory scattering” implies the divergence of the classical differential cross section that occurs as soon as the deflection function goes through zero for a nonzero value of the impact parameter. This critical effect also occurs in slow photoelectron imaging where near-threshold atomic photoionization is performed in the presence of an external static electric field. In this case, glory scattering manifests itself by the appearance of an intense peak at the center of the photoelectron momentum distribution. In the present work we examine the magnitude variation of this central peak as a function of electron energy. We experimentally study near-threshold two-photon ionization of ground state magnesium atoms, below as well as above the field-free ionization limit. It is found that, apart from its behavior of classical origin, the glory signal additionally exhibits strong oscillations and beating effects over the full spectral range of the recordings. Of particular interest are its oscillations above the zero-field limit, many aspects of which are expected to be independent of the atomic target. Our results are analyzed with the help of classical, semiclassical, and quantum mechanical calculations devoted to the hydrogenic Stark effect. It is theoretically found that these continuum glory oscillations are related to the resonantlike Stark structures appearing under certain conditions in the total photoionization cross section and implying energy quantization in the continuum. The striking outcome of the present study, however, is that both theory and experiment clearly support the connection between the energy- and static field-dependent periodicity of glory oscillations with the classical dynamics of electron motion. In particular, it is shown that the Fourier transform of the glory signal provides information on the differences between the origin-to-detector times of flight corresponding to specific pairs of classical electron trajectories.

Simulation of Magnetic Electron Cut-off in a Vacuum Switch with an Anode in the Form of an Inductor

The simulation of the process of magnetic cut-off of electrons in a vacuum switch (VC) with an anode in the form of an inductor was performed. Calculations were performed according to the physico-topological model of physical processes in the vacuum switch, which took into account current distribution along electrodes, the trajectory of electrons emitted by the cathode and the conditions of current interruption in VC. Determination of current distribution along the anode, as well as configurations of electric and magnetic fields were performed according to a mathematical model based on Maxwell's equations for vacuum and conductive medium of the anode and boundary conditions adapted to the shape of the elements of the VC. Material equations were also used for certainty. The initial kinetic energy of electrons emitted from the cathode was set equal to zero. Their direction of departure from the cathode surface was determined by the direction of the lines of force of the electric field near the surface. Electron emission was given by the uniform distribution of emission points on the surface of the cathode tip. The calculation of the structure of the magnetic field was performed taking into account the secondary magnetic fields and the current distribution over the cross section of the anode inductor, which is caused by the skin effect.It is established that a decrease in the step of the inductor turns and an increase in the amplitude of the current pulse in it lead to an increase in the magnetic field strength in the cathode region, which improves the focusing of electrons. At anode-cathode voltage of 10 kV, the step of the inductor of 6 mm and the amplitude of the anode inductor current pulse of 900 A, all the electrons emitted from the cathode are focused outside the anode.The influence of design parameters on the electron cut-off efficiency is determined. For the investigated design, the optimal cathode-anode distance was 12 mm with a step between the turns of the inductor of 6 mm. The results of calculations showed that reducing the distance between the turns of the inductor increases the efficiency of electron cut-off, which confirms the physical adequacy of the mathematical model and the correctness of the calculations. Calculations also showed that at a cathode-anode distance below 12 mm, the focusing of electrons deteriorates.In the proposed design of the VC with the anode inductor in the form of three turns, the complete cut-off of electrons, i.e. the time of flight of electrons through the electrode system, at anode-cathode voltage of 10 kV, occurred by less than 1 ns at an inductor current pulse of 900 A. The inductor current pulse duration was 5 μs had the form of the half-sinusoid arc. The used method of modeling allows to establish in what part of the inductor pulse the full cut-off of electrons is provided.The obtained results can be used in the development of the VC with interruption of the current of vacuum-arc discharge.

Excited state dynamics of cis,cis-1,3-cyclooctadiene: UV pump VUV probe time-resolved photoelectron spectroscopy.

We present UV pump, vacuum ultraviolet probe time-resolved photoelectron spectroscopy measurements of the excited state dynamics of cis,cis-1,3-cyclooctadiene. A 4.75 eV deep UV pump pulse launches a vibrational wave packet on the first electronically excited state, and the ensuing dynamics are probed via ionization using a 7.92 eV probe pulse. The experimental results indicate that the wave packet undergoes rapid internal conversion to the ground state in under 100 fs. Comparing the measurements with electronic structure and trajectory surface hopping calculations, we are able to interpret the features in the measured photoelectron spectra in terms of ionization to several states of the molecular cation.

Nonlinear Compton scattering of polarized photons in plane-wave backgrounds

We investigate the phenomenology of nonlinear Compton scattering of polarized photons by unpolarized electrons in plane-wave backgrounds. The energy and angular spectra of polarized photons are calculated for linearly and circularly polarized pulses, monochromatic fields and constant crossed field backgrounds. When the field intensity is in the weakly nonlinear regime, photons in different polarization states are predicted to possess very different energies and angular distributions. We explain this difference by calculating the spectrum for nonlinear Thomson scattering in a linearly polarized monochromatic background and projecting the electron's trajectory onto the different polarization directions. Finally, we calculate a scenario for multi-GeV electrons and, by considering the energy and angular-resolved photon polarization purity, find one can achieve a GeV-photon beam with polarization purities of over $90%$.

Dynamics of Rydberg states and terahertz waves generated in strong few-cycle laser pulses

Physical processes near threshold in strong-field ionization are complex owing to the important role of many intermediate states. Two typical near-threshold processes in few-cycle laser pulses, the generations of Rydberg electrons and terahertz waves, are investigated using classical trajectory Monte Carlo simulations. Mapping final energies of electrons to the tunneling coordinates, the two processes are distinguished based on the contributions from different kinds of electron trajectories, which highlights the complex interplay between the Coulomb potential and the laser field on the electron dynamics. We clarify the dependence of momentum and energy spectra on the carrier-envelope phase. We find that the optimal phases for terahertz wave generation and creation of the Rydberg state in few-cycle laser pulses are opposite. This finding can be applied to further experiments on attosecond electron dynamics.

Single and double ionization of helium in intense bicircular laser fields

The single and double ionization of helium in intense 2ω:ω bicircular laser fields is analyzed with a classical ensemble method. A high-performance computational cluster is utilized to generate high-resolution data and to probe low-rate events. It is found that both counter- and co-rotating fields support rescattering and non-sequential double ionization (NSDI). The effects of scattering off of the ionic core are evident in the single-ionization energy spectra, and the role of the Coulomb potential is clearly visible in the electron momentum distributions. The dynamics of the double ionization processes are investigated by analyzing ionization phase, electron energy and momenta, and rescattering timing. For corotating fields, rescattering is only possible for ionization near the field minimum, placing limits on the efficiency of NSDI. For counterrotating fields, the electron trajectories that contribute to rescattering are found to fall into only three categories (looping, triangular, or a combination of the two), and the contributions from these trajectories is distinguishable in the resulting double-ion electron momentum distributions. This study explores the full range of field amplitude ratios that contribute to the dynamics of rescattering, and therefore provides an overall view of the limitations of using bicircular fields for applications in strong-field physics.

Electron beam guiding by a laser Bessel beam

We formulate the set of equations that describe the trajectories of electrons counter-propagating along a radially polarized optical Bessel beam (OBB). It is shown that a significant fraction of the electrons can be transversally trapped by the OBB even in the case of “un-matched” injection. Moreover, these transversally trapped particles (TTP) can be transported without loss over more than half a meter long interaction region.

Monte Carlo track-structure for the radionuclide Copper-64: characterization of S-values, nanodosimetry and quantification of direct damage to DNA

TOPAS-nBio was used to simulate, collision-to-collision, the complete trajectories of electrons in water generated during the explicit simulation of 64Cu decay. S-values and direct damage to the DNA were calculated representing the cell (C) and the cell nucleus (N) with concentric spheres of 5 μm and 4 μm in radius, respectively. The considered ‘target’←‘source’ configurations, including the cell surface (Cs) and cytoplasm (Cy), were: C←C, C←Cs, N←N, N←Cy and N←Cs. Ionization cluster size distributions were also calculated in a cylinder immersed in water corresponding to a DNA segment of 10 base-pairs in length (diameter 2.3 nm, length 3.4 nm), modeling a radioactive point source moving from the central axis to the edge of the cylinder. For that, the first moment (M1) and cumulative probability of having a cluster size of 2 or more ionizations in the cylindrical volume (F2) were obtained. Finally, the direct damage to the DNA was estimated by quantifying double-strand breaks (DSBs) using the clustering algorithm DBSCAN.The S-values obtained with TOPAS-nBio for 64Cu were 7.879 × 10−4 ± 5 × 10−7, 4.351 × 10−4 ± 6 × 10−7, 1.442 × 10−3 ± 1 × 10−6, 2.596 × 10−4 ± 8 × 10−7, 1.127 × 10−4 ± 4 × 10−7 Gy Bq-s−1 for the configurations C←C, C←Cs, N←N, N←Cy and N←Cs, respectively. The difference of these values, compared with previously reported S-values for 64Cu with the code MNCP and software MIRDCell, ranged from −4% to −25% for the configurations N←N and N←Cs, respectively. On the other hand, F2 was maximum with the source at the center of the cylinder 0.373 ± 0.001, and monotonically decreased until reaching a value of 0.058 ± 0.001 at 2.3 nm. The same behavior was observed for M1 with values ranging from 2.188 ± 0.004 to 0.242 ± 0.002. Finally, the DBSCAN algorithm showed that the mean number of DNA DSBs per decay were 0.187 ± 0.001, 0.0317 ± 0.0005, and 0.0125 ± 0.0002 DSB-(Bq-s)−1 for the configurations N←N, N←Cs, and N←Cy, respectively.In conclusion, the results of the S-values show that the absorbed dose strongly depends on the distribution of the radionuclide in the cell, the dose being higher when 64Cu is internalized in the cell nucleus, which is reinforced by the nanodosimetric study by the presence of DNA DSBs attributable to the Auger electrons emitted during the decay of 64Cu.

Holographic detection of parity in atomic and molecular orbitals

We introduce a novel and concise methodology to detect the parity of atomic and molecular orbitals based on photoelectron holography, which is more general than the existing schemes. It fully accounts for the Coulomb distortions of electron trajectories, does not require sculpted fields to retrieve phase information and, in principle, is applicable to a broad range of electron momenta. By comparatively measuring the differential photoelectron spectra from strong-field ionization of N$_{2}$ molecules and their companion atoms of Ar, some photoelectron holography patterns are found to be dephased for both targets. This is well reproduced by the full-dimensional time-dependent Schr\"{o}dinger equation and the Coulomb quantum-orbit strong-field approximation (CQSFA) simulation. Using the CQSFA, we trace back our observations to different parities of the 3$p$ orbital of Ar and the highest-occupied molecular orbital of N$_{2}$ via interfering Coulomb-distorted quantum orbits carrying different initial phases. This method could in principle be used to extract bound-state phases from any holographic structure, with a wide range of potential applications in recollision physics and spectroscopy.

Quantum Transport in Topological Surface States of Selectively Grown Bi2Te3 Nanoribbons

AbstractQuasi‐1D nanowires of topological insulators are candidate structures in superconductor hybrid architectures for Majorana fermion based quantum computation schemes. Here, selectively grown Bi2Te3 topological insulator nanoribbons at cryogenic temperatures are investigated. The nanoribbons are defined in deep‐etched Si3N4/SiO2 nano‐trenches on a silicon (111) substrate followed by a selective area growth process via molecular beam epitaxy. The selective area growth is beneficial to the device quality, as no subsequent fabrication needs to be performed to shape the nanoribbons. In the diffusive transport regime of these unintentionally n‐doped Bi2Te3 topological insulator nanoribbons, electron trajectories are identified by analyzing angle dependent universal conductance fluctuation spectra. When the sample is tilted from a perpendicular to a parallel magnetic field orientation, these high frequent conductance modulations merge with low frequent Aharonov–Bohm type oscillations originating from the topologically protected surface states along the nanoribbon perimeter. For 500 nm wide Hall bars low frequent Shubnikov–de Haas oscillations are identified in a perpendicular magnetic field orientation. These reveal a topological, high‐mobility, 2D transport channel, partially decoupled from the bulk of the material.