Classical Trajectory Monte Carlo Method Research Articles

Characterizing strong-field tunneling ionization with a phase-dependent THz polarization spectrum

The terahertz radiation emitted by asymmetrically ionized wavepackets in two-color strong-field tunneling ionization is essential for detecting the system's associated electron dynamics and structural properties. We propose to characterize and control tunneling ionization using a phase-dependent terahertz polarization (PTP) spectrum, analyzed through a combination of the classical trajectory Monte Carlo method, an analytical model based on the virial theorem, and the rigorous solution of the time-dependent Schrödinger equation as a benchmark. Our results demonstrate that the PTP spectrum offers a high-precision measure of the Coulomb effect through the relative phase of the two-color laser. Comparisons of PTP results calculated using different methods suggest how the electron can be manipulated by controlling the relative phase and laser intensity. In particular, the PTP spectrum can be used to calibrate the relative phase and provides a convenient and robust reconstruction of the time-averaging of tunneling positions with high precision using the analytical model. These insights reveal that the PTP spectrum as a whole can be a new and useful tool for the all-optical characterization of ultrafast atomic and molecular ionization.

State-selective electron capture in Ar16++H(1s) collisions for charge-exchange recombination spectroscopy

Abstract State-selective electron capture in collisions of Ar16+ ions with ground-state hydrogen atoms has been modeled using the two-center wave-packet convergent close-coupling approach. The partially stripped He-like projectile ion is represented using a model potential. Experimental measurements are not available for this collision system and to date, only the classical trajectory Monte Carlo (CTMC) method has been applied to calculate cross sections. The calculated total electron-capture cross section (TECS) is in good agreement with the previous CTMC results at the low energies but slightly larger at higher energies. This is likely because, in this work, we account for capture into highly excited states, which contribute significantly to the TECS at the intermediate energies. The n-resolved electron-capture cross sections have also been presented for capture into states with n = 6 − 19 , where n is the final-state principal quantum number. The most important of these are the cross sections for capture into the n = 14 − 17 states, which are used in charge-exchange recombination spectroscopy techniques. For these cross sections, a significant difference is observed between the present and previously published data. The cross sections differ by an order of magnitude in the 10−60 keV u−1 energy range. The agreement between the calculations is observed at the energies above 70 keV u−1. The n ℓ -resolved electron-capture cross sections have also been presented at 15, 60, 100 and 200 keV u−1 projectile energies, where ℓ is the final-state angular momentum quantum number.

Lithium inelastic cross-sections and their impact on micro and nano dosimetry of boron neutron capture

Objective. To present a new set of lithium-ion cross-sections for (i) ionization and excitation processes down to 700 eV, and (ii) charge-exchange processes down to 1 keV u−1. To evaluate the impact of the use of these cross-sections on micro a nano dosimetric quantities in the context of boron neutron capture (BNC) applications/techniques. Approach. The Classical Trajectory Monte Carlo method was used to calculate Li ion charge-exchange cross sections in the energy range of 1 keV u−1 to 10 MeV u−1. Partial Li ion charge states ionization and excitation cross-sections were calculated using a detailed charge screening factor. The cross-sections were implemented in Geant4-DNA v10.07 and simulations and verified using TOPAS-nBio by calculating stopping power and continuous slowing down approximation (CSDA) range against data from ICRU and SRIM. Further microdosimetric and nanodosimetric calculations were performed to quantify differences against other simulation approaches for low energy Li ions. These calculations were: lineal energy spectra (yf(y) and yd(y)), frequency mean lineal energy yF― , dose mean lineal energy yD― and ionization cluster size distribution analysis. Microdosimetric calculations were compared against a previous MC study that neglected charge-exchange and excitation processes. Nanodosimetric results were compared against pure ionization scaled cross-sections calculations. Main results. Calculated stopping power differences between ICRU and Geant4-DNA decreased from 33.78% to 6.9%. The CSDA range difference decreased from 621% to 34% when compared against SRIM calculations. Geant4-DNA/TOPAS calculated dose mean lineal energy differed by 128% from the previous Monte Carlo. Ionization cluster size frequency distributions for Li ions differed by 76%–344.11% for 21 keV and 2 MeV respectively. With a decrease in the N 1 within 9% at 10 keV and agreeing after the 100 keV. With the new set of cross-sections being able to better simulate low energy behaviors of Li ions. Significance. This work shows an increase in detail gained from the use of a more complete set of low energy cross-sections which include charge exchange processes. Significant differences to previous simulation results were found at the microdosimetric and nanodosimetric scales that suggest that Li ions cause less ionizations per path length traveled but with more energy deposits. Microdosimetry results suggest that the BNC’s contribution to cellular death may be mainly due to alpha particle production when boron-based drugs are distributed in the cellular membrane and beyond and by Li when it is at the cell cytoplasm regions.

Interaction of Protons with Noble-Gas Atoms: Total and Differential Cross Sections

We present a classical treatment of the ionization and electron-capture processes in the interaction of protons with neutral noble-gas atoms, namely, Ne, Ar, Kr, and Xe. We used a three-body classical-trajectory Monte Carlo (CTMC) method to calculate the total (TCS) and differential (DCS) cross sections of single-electron processes. The Garvey-type model potential was employed in the CTMC model to describe the collision between the projectile and the target, accounting for the screening effect of the inactive electrons. The TCSs are evaluated for impact energies in the energy range between 0.2 keV and 50 MeV for a number of sub-shells of the targets. The ionization DCS are evaluated for an impact energy of 35 keV, focusing on the outer sub-shells only. We found that our ionization and electron-capture TCSs are in very good agreement with the previous theoretical and experimental data for all targets. Moreover, we presented single (SDCS)- and double (DDCS)-differential cross sections as a function of the energy and ejection angle of the ionized electron for all collision systems.

Dipolar focusing in laser-assisted positronium formation

We consider positronium formation in collisions of positrons with excited hydrogen atoms H(n) in an infrared laser field theoretically. This process is assisted by the dipolar focusing effect: a positron moving in a superposition of a laser field and the dipolar field can approach the atomic target even if its trajectory starts with a very large impact parameter, leading to a significant enhancement of the Ps formation cross section. The classical trajectory Monte Carlo method, which is justified for n⩾3 , allows efficient calculation of this enhancement. A similar effect can occur in collisions of positrons with other atoms in excited states, which can lead to improvements in the efficiency of positronium formation.

Observing quantum matter-wave diffraction in the energetic He2+-He collisions

We present an experiment combined with numerical simulations to study single and double electron capture processes induced during the collisions between the He target and the He2+ projectile in the energy range 2–20 keV/u. According to our experimental observations, measuring the angular distribution of the scattered projectile He2+ reveals a clear oscillatory structure. The latter records an imprint of the collision dynamics, specifically, a signature of the matter-wave scattering and the internal electronic structure of the collisional system He2+-He. We found that this feature is sensitive to the incident projectile's energy and the nature of the involved process. With the help of four-body semiclassical close coupling and classical trajectory Monte Carlo methods, we show that the observed structure is of a quantum nature. This is further supported by a simple mathematical model based on Fraunhofer-type diffraction of light, to which the oscillations are attributed. Our findings thus provide insights into the role of quantum phenomena in characterizing collision dynamics. Published by the American Physical Society 2024

Envelope effect of Rydberg States Generation in Strong Laser Pulses

Rydberg atoms are important building blocks for quantum technologies, exploited to new applications in quantum computing, quantum communication and quantum sensing due to their unique tunable quantum properties.Besides the widely-used few-photon resonant excitation for the specific Rydberg state, multiple Rydberg states can be populated coherently and effciently through the frustrated tunneling ionization or the Coulomb potential recapture effect in strong laser field. The Rydberg states excitation in strong field provides an opportunity to realize the ultrafast quantum control on Rydberg atom and bridge the strong field physics and quantum information technology. <br>Using the Classical Trajectory Monte Carlo method and Qprop package to solve Time-Dependent increases with the parameter of the asymmetric laser envelope. Based on the Quantitative Rescattering theory, the calculated time-dependence of recapture rate is negatively related to the laser envelope and the residual laser interaction time, which is termed as envelope effect. Combined with the carrier-wave effect, an analytic formula is proposed to calculate the Rydberg states population:$Y(t) \propto W_0(t) \frac{t-\tau+c}{f(t)} \cos (\omega t+\phi)$ This results open the door to enhance the Rydberg states generation using the laser envelope control, benefiting the future quantum technology based on the Rydberg states generated in the strong laser field.(a) Laser electric fields with the same pulse duration τ = 10T<sub>0</sub> and different asymmetric parameters α. Black solid line, red dashed line and blue dashed-dotted line are for α = -0.6, 0, 0.6 respectively. (b) The yields of Rydberg states change with the asymmetric parameter under different laser pulse duration. Black solid line, red dashed line and blue dashed-dotted line are for τ = 1010T<sub>0</sub>, 1510T<sub>0</sub>, 2010T<sub>0</sub> respectively. Schrödinger Equation, we calculate the population of Rydberg states. Our results show that the population.

Differential Studies of Argon Particle and Antiparticle Interactions: Present Status and Future Possibilities

Although the comparison of fully differential ionization data for particle and antiparticle impact provides the ultimate tests of theoretical models, only very low antiparticle beam intensities are available. Hence, few experiments of this type have been performed. Therefore, available experimentally obtained single and double differential cross-sections, which are much easier to obtain, are compared in order to demonstrate differences when only the projectile mass or charge (+1 or −1) is changed. Included in the comparison are cross-sections calculated for positron and electron impact using a three-particle classical trajectory Monte Carlo method. The calculated cross-sections provide independent information about the ejected electron and the scattered projectile contributions, plus information about the impact parameters, all as functions of the collision kinematics. From these comparisons, suggestions as to where future investigations are both feasible and useful are provided.

Determining the Orbital Angular Momentum of a Vortex Beam Using Strong Field Ionization

While interferometric methods exist for classifying vortex states of light, these techniques usually require destroying the beam of interest to determine the light’s OAM. A recent two-color pump-probe experiment employed strong field ionization and beam sculpting to classify vortex beams. Here, we propose an alternative strong-field method for distinguishing OAM states of light which does not require beam sculpting and instead utilizes a noncollinear terahertz standing wave to probe ionized electrons. We then use classical trajectory Monte Carlo (CTMC) methods to simulate strong-field ionization of helium under this configuration with the terahertz field both on and off. We find that the resulting electron momenta distributions can be used to extract the OAM of the beam, as long as the vortex beam spot size does not exceed 1/4 the terahertz pulse’s wavelength.

Collisional Classical Dynamics at the Quantum Scale

During the past five decades, classical dynamics have been systematically used to gain insight on collision processes between charged particles and photons with atomic and molecular targets. These methods have proved to be efficient for systems in which numerical intensive quantum mechanical methods are not yet tractable. During the years, reaction cross sections for charge exchange and ionization have been scrutinized at the total and differential levels, leading to a clear understanding of the benefits and limitations inherent in a classical description. In this work, we present a review of the classical trajectory Monte Carlo method, its current status and the perspectives that can be envisaged for the near future.

Total and differential ionization cross sections in collision between nitrogen atom and singly charged sodium ion

We present a theoretical study of the ionization of nitrogen atom by a singly charged sodium ion using the classical trajectory Monte Carlo method. Although we suffer from a lack of cross section data of this collision system, the knowledge of the basic cross sections is essential in fusion science, because this reaction has potential applications in the diagnostic of magnetically confined fusion plasmas. In our investigations, the Na+–N collision system is reduced to a three-body problem. The interaction between the collision partners is described by the Garvey-type model potential. The results of our study provide insight into the dynamics of singly charged sodium–nitrogen interactions. The total cross sections are presented in the impact energy range between 10 keV and 10 MeV and compared them with the available experimental data. The single and double differential cross sections are presented at 30, 40, 50 and 60 keV energies related to the energies of the plasma diagnostic used in the nuclear fusion.

Calculation of Ionization, Excitation and Electron Capture Cross Sections for Be4+ + H(2s,2p) Collisions.

A computational study of Be4+ + H(2s,2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be3+(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.

Interaction of electrons and positrons with two-dimensional artificially generated proton lattice and with carbon lattice

A many-body classical trajectory Monte Carlo (CTMC) method is applied in the study of scattering probabilities of electrons and positrons after interacting with a two-dimensional (2D) artificially generated, uniform lattice, composed of fixed protons. We used different lattice parameters between the protons for different simulations, where the projectiles have kinetic energies of 500 and 1000 eV. We found a very strong focusing of electrons and a very strong defocusing of the positrons at lower lattice parameters. Furthermore, we found, these effects get weaker with increasing lattice parameters. Interesting changes took place at lattice parameters 2 and 3 au. which are close to the lattice parameter between carbon atoms in graphene of value 2.68 au. We also performed a simulation of a defective lattice by removing some protons and noticed distinguishable changes in the spectra compared to the spectra of an ideal lattice. This comparison may open a way for the detection of lattice defects in real samples.

Impact ionization of highly charged ion-atom collisions considering strong magnetic field and plasma screening effect

The impact ionization process of target is a crucial issue in the study of Heavy Ion Beam (HIB)-driven Magnetized Inertial Fusion (MIF). The collision systems between heavy projectile ions (Xeq+, Biq+, Uq+) and light target atoms/ions (H, D, T, 3He, 3He+, 11B) are promising candidate reactions for fusion power. In this study, the impact ionization process in medium-energy (ranges 1–100 MeV/u) is studied numerically based on the extended Classical-trajectory Monte Carlo (CTMC) method, where the effects of projectile charge state, external magnetic field and plasma screening on the single ionization process are considered. The results show that the existed external magnetic field results in a decrease of the yield of ionized high-energy electrons, whereas the yield of backward emitted electrons is increased. The effect of plasma screening on the ionization process is shown to be determined by the competition between the screening charge of projectile ion and the target nucleus. Thus, a significant decrease of ionization cross section is found in the low energy region since the screening charge of projectile ion is dominant. However, the screening effect of target nucleus charge is dominant in high energy region, where a significant increase of ionization cross sections is found.

Coulomb potential determining terahertz polarization in a two-color laser field.

The orientation and ellipticity of terahertz (THz) polarization generated by a two-color strong field not only casts light on underlying mechanisms of laser-matter interaction, but also plays an important role for various applications. We develop the Coulomb-corrected classical trajectory Monte Carlo (CTMC) method to well reproduce the joint measurements, that the THz polarization generated by the linearly polarized 800 nm and circularly polarized 400 nm fields is independent on two-color phase delay. The trajectory analysis shows that the Coulomb potential twists the THz polarization by deflecting the orientation of asymptotic momentum of electron trajectories. Further, the CTMC calculations predict that, the two-color mid-infrared field can effectively accelerate the electron rapidly away from the parent core to relieve the disturbance of Coulomb potential, and simultaneously create large transverse acceleration of trajectories, leading to the circularly polarized THz radiation.

Charge transfer and ionization cross-sections in collisions of singly charged lithium ions with helium and nitrogen atoms

We present a non-perturbative classical treatment of the charge transfer and ionization processes in collisions between singly charged lithium ions with helium and nitrogen atomic targets. Single capture and single ionization total cross sections are calculated using a three-body classical trajectory Monte Carlo (CTMC) method in which the interaction between the collision partners is described by a Garvey-type model potential. The cross sections are evaluated for collision energies between 20 keV and 100 MeV. In particular, we found excellent agreement between our results and the available experimental data for the case of the single capture of He(1s) by Li+ ions. In addition, our CTMC results are in a reasonable agreement with the experimental results for collision energies higher than 200 keV for single capture of N(2p) atoms by Li+. Furthermore, we present single ionization cross sections for both collision systems.

Interaction of Electrons and Positrons with Protons Aligned in One-Dimension Line

We present theoretical studies of electron and positron interaction with protons aligned in a one-dimension periodic line. The equally spaced protons were artificially generated where the individual protons are fixed in a certain position. The incident energies were 500 eV and 1000 eV. The electron and positron trajectories passing through these periodic multiple scattering objects were calculated using a classical trajectory Monte Carlo method. We show that this proton configuration has focusing and defocusing properties depending on the certain initial conditions.

Differential Description of Multiple Ionization of Uracil by 3.5 MeV/u C6+ Impact

In this work, a theoretical analysis of the impact of the multiple ionization of uracil by 3.5 MeV/u C6+ is developed in the framework of a classical trajectory Monte Carlo method, as recently introduced for multi-electronic targets. The electron emission contribution arising from the multiple electron ionization is explicitly determined and the emission geometries and the reaction regions for double and triple ionization are explicitly identified. The present results suggest that double ionization is mainly characterized by the emission of slow electrons with a relative angle of 80∘–120∘. For triple ionization, on the other hand, the emission seems to occur with the three electrons holding similar interelectronic angles.

Charge Transfer and Electron Production in Proton Collisions with Uracil: A Classical and Semiclassical Study.

Cross sections for charge transfer and ionization in proton-uracil collisions are studied, for collision energies 0.05<E<2500 keV, using two computational models. At low energies, below 20 keV, the charge transfer total cross section is calculated employing a semiclassical close-coupling expansion in terms of the electronic functions of the supermolecule (H-uracil)+. At energies above 20 keV, a classical-trajectory Monte Carlo method is employed. The cross sections for charge transfer at low energies have not been previously reported and have high values of the order of 40 Å2, and, at the highest energies of the present calculation, they show good agreement with the previous results. The classical-trajectory Monte Carlo calculation provides a charge transfer and electron production cross section in reasonable agreement with the available experiments. The individual molecular orbital contributions to the total electron production and charge transfer cross sections are analyzed in terms of their energies; this permits the extension of the results to other molecular targets, provided the values of the corresponding orbital energies are known.

Electron-Impact Ionization of Carbon

We present ionization cross-sections of collisions between electrons and carbon atoms using the classical trajectory Monte Carlo method. Total cross-sections are benchmarked against the reported experimental data and the predictions of numerically intensive theoretical methods as well as pioneering calculations for this collision system. At impact energies greater than about 100 eV, the present results are in very good agreement with the generalized oscillator strength formulation of the Born approximation as well as with the experimental data. Limitations inherent to a purely classical description of the electron impact ionization process at low impact energies are detected and analyzed, suggesting a clear route for future studies.