Classical Trajectory Monte Carlo Method Research Articles

Antiproton collisions with excited positronium

We present results of calculations of several processes resulting from positronium (Ps) collisions with antiprotons: antihydrogen formation, Ps breakup, and ${n}_{\mathrm{Ps}}$-changing collisions. Calculations utilize the quantum convergent close-coupling (CCC) method and the classical trajectory Monte Carlo (CTMC) method. We identify a region of Ps principal quantum numbers ${n}_{\mathrm{Ps}}$ and Ps energies where the classical description is valid and where the CCC calculations become computationally too expensive. This allows us to present the most complete and reliable set of cross sections in a broad range of ${n}_{\mathrm{Ps}}$ and initial orbital momentum quantum numbers ${l}_{\mathrm{Ps}}$ which are necessary for experiments with antihydrogen at CERN.

Differential Analysis of the Positron Impact Ionization of Hydrogen in Debye Plasmas

In this work, a theoretical differential analysis of the positron impact ionization of hydrogen embedded in weakly coupled plasmas at an impact energy of 80 eV is developed. While the total and singly differential cross sections are analyzed within the classical trajectory Monte Carlo method, a Born-3DW model for screened environments, recently introduced by the authors, is used to provide a fully differential view of the process. The present results suggest that the electron emission spectra are strongly affected by the level of screening of the surrounding medium, mainly due to the loss of the postcollisional interaction mechanism.

L-Shell Ionization Cross Sections for Silver by Low-Energy Electron Impacts

The L-subshell ionization cross sections and total L–X-ray production cross sections for the Ag atom by the electron impact near the ionization threshold were calculated with a classical-trajectory Monte Carlo method. The results were compared with experimental data, quantum mechanical calculations, and the cross sections by positron impact. It was demonstrated that the classical treatments are useful for electron–atom collisions at energies higher than about six times the binding energies of target electrons but overestimate L-shell ionization and L–X-ray production cross sections at low energies near the threshold. Possible reasons for this discrepancy are discussed.

Nl-Selective Classical Charge-Exchange Cross Sections in Be4+ and Ground State Hydrogen Atom Collisions

Charge-exchange cross sections in Be4+ + H(1s) collisions are calculated using the three-body classical trajectory Monte Carlo method (CTMC) and the quasi-classical trajectory Monte Carlo method of Kirschbaum and Wilets (QCTMC) for impact energies between 10 keV/amu and 300 keV/amu. We present charge-exchange cross sections in the projectile n = 2 and nl = 2s, 2p states. Our results are compared with the previous quantum-mechanical approaches. We found that the QCTMC model is a powerful classical model to describe the state-selective charge-exchange cross sections at lower impact energies and the QCTMC results are in good agreement with previous observations.

Collisions of proton or highly charged ion–atom in a strong magnetic field and dense quantum plasmas

Magneto inertial fusion driven by heavy ions beam (HIB) is a very attractive potential approach for the nuclear energy system. One of the key issues is to investigate the interaction process of the HIB-target considering the condition of plasma screening and strong magnetic field background. In this paper, the influence of the external magnetic field and the plasma screening was investigated by simplifying the process of beam bombarding into a two-body collision between the energetic ions and target atoms. The classical-trajectory Monte Carlo method was accommodated by modifying the Hamiltonian in the collision system, where the effects of plasma screening and the account for the strong magnetic field background were considered. The total cross sections of single electron ionization and charge transfer of the projectile (H+, He2+, Xe32+, Bi31+, U34+)–atom (H, He) collisions are computed. The results indicated that the magnetic field effect becomes more obvious in the low energy regime of the projectiles. With the increase in energy, the change of total cross sections and angular differential cross sections gradually disappears. In the dense quantum plasmas, plasma screening presents very different effects for protons and heavy ion projectiles. This work may pave the way for extending the study to other collision systems calculations.

Study of the effect of higher-order dispersions on photoionisation induced by ultrafast laser pulses applying a classical theoretical method

We investigated the effect of higher order dispersion on ultrafast photoionisation with Classical Trajectory Monte Carlo (CTMC) method for hydrogen and krypton atoms. In our calculations we used linearly polarised ultrashort 7 fs laser pulses, 6.5 times 10^{14} mathrm {W/cm^{2}} intensity, and a central wavelength of 800 nm. Our results show that electrons with the highest kinetic energies are obtained with transform limited (TL) pulses. The shaping of the pulses with negative second- third- or fourth- order dispersion results in higher ionisation yield and electron energies compared to pulses shaped with positive dispersion values. We have also investigated how the Carrier Envelope Phase (CEP) dependence of the ionisation is infuenced by dispersion. We calculated the left-right asymmetry as a function of energy and CEP for sodium atoms employing pulses of 4.5 fs, 800 nm central wavelength, and 4 times 10^{12}mathrm {W/cm^{2}} intensity. We found that the left-right asymmetry is more pronounced for pulses shaped with positive Group Delay Dispersion (GDD). It was also found that shaping a pulse with increasing amounts of GDD in absolute value blurs the CEP dependence, which is attributed to the increasing number of optical cycles.

Classical and semiclassical calculations of state-selective cross sections for electron capture and excitation in Be4++H(2s) collisions

A computational study of ${\mathrm{Be}}^{4+}+\mathrm{H}(2s)$ collisions has been carried out. Two computational models have been employed: the classical trajectory Monte Carlo (CTMC) method and the numerical solution of the time-dependent Schr\"odinger equation (GTDSE). The integral $n$ and $nl$ partial cross sections for H excitation and electron capture, obtained with both methods, are compared at two energies: 20 and 100 keV/u. It is shown that the CTMC, with an improved hydrogenic initial distribution, provides excitation cross sections in good agreement with the numerical calculation for excitation to $\mathrm{H}(n$) with $n>3$. The agreement between the corresponding $nl$ partial cross sections from both methods is less satisfactory at 100 keV/u, where there is a transition from the low-energy mechanism that involves an increase of the populations with $l$, and the high-energy mechanism, where the dipole-allowed transitions are dominant. The electron capture cross sections calculated with the CTMC method do not depend on the initial distribution and show a reasonable agreement with the GTDSE ones, which supports the use of the CTMC method to calculate electron capture cross sections into highly excited levels and total cross sections. The mechanism of the electron capture process is discussed and CTMC calculations of the ionization process are also presented.

Charge transfer in collisions of H<sup>+</sup>, Li<sup>3+</sup>, Be<sup>4+</sup> and O<sup>7+</sup> ions with He atom based on 4-classical trajectory Monte Carlo method

The classical trajectory Monte Carlo (CTMC) method is a common method to study the charge-transfer and impact-ionization cross sections for the collisions between ions and atoms, and the heavy particle collision in astrophysics and laboratory plasma environment. Here in this work, we use the 4-CTMC method to study a four-body collision process including two bound electrons, and the Hamiltonian equation of the four-body dynamic system is solved numerically. The single/double electron ionization and capture cross sections are calculated for collisions of high charge state ions (Li<sup>3+</sup>, Be<sup>4+</sup> and O<sup>7+</sup>) with helium atom in a wide range of projectile energy. The calculation results show that the results from the 4-CTMC method and the experimental measurements are in better agreement in a projectile energy range of 50－200 keV/amu for proton-helium collision system. In addition, for incident ions with high charge state, the results calculated by the 4-CTMC method are in better agreement with the experimental measurements or other theoretical values in a projectile energy range of 100－500 keV/amu. Though the double ionization and capture cross sections calculated by 4-CTMC or 3-CTMC method are higher than the experimental results due to ignoring the electron correlation, the results from the 4-CTMC method are in better agreement with the experimental results.

State selective classical electron capture cross sections in Be4+ \u2009+\u2009H(1s) collisions with mimicking quantum effect

We present state-selective electron capture cross sections in collision between Be4+ and ground state hydrogen atom. The n- and nl-selective electron capture cross sections are calculated by a three-body classical trajectory Monte Carlo method (CTMC) and by a classical simulation schema mimicking quantum features of the collision system. The quantum behavior is taken into account with the correction term in the Hamiltonian as was proposed by Kirschbaum and Wilets (Phys Rev A 21:834, 1980). Calculations are carried out in the projectile energy range of 1–1000 keV/amu. We found that our model for Be4+ + H(1s) system remarkably improves the obtained state-selective electron capture cross sections, especially at lower projectile energies. Our results are very close and are in good agreement with the previously obtained quantum–mechanical results. Moreover, our model with simplicity can time efficiently carry out simulations where maybe the quantum mechanical ones become complicated, therefore, our model should be an alternative way to calculate accurate cross sections and maybe can replace the quantum–mechanical methods.

Charge exchange recombination spectroscopy of W (q = 61–66) for application to ITER neutral hydrogen beam diagnostics

In this paper, we present a detailed theoretical analysis of charge exchange recombination spectroscopy based on interactions of the planned ITER neutral beams (diagnostic beam of 100 keV u−1 and heating beam of ≈1 MeV u−1) with highly-charged ions of tungsten. The results of the present spectral synthesis are based on the new set of nl-resolved charge exchange (CX) cross sections for recombination of the W ions (q = 61–66) with atomic hydrogen calculated using the classical trajectory Monte Carlo method. A large-scale collisional-radiative model describing the population kinetics of the high-n atomic states of Si-like through O-like W ions has been developed using the NOMAD code for typical conditions of the ITER core plasma, and the resulting spectra have been generated for wavelengths in the x-ray to visible range (0.1–1000 nm). A detailed analysis of the plasma emission predicts a significant effect of CX recombination on the W line intensity ratios that can be used for more advanced diagnostics of the ITER plasma.

State-selective charge exchange cross sections in Be^{4+} -hbox {H}(2textit{lm}) collision based on the classical trajectory Monte Carlo method

A three-body classical trajectory Monte Carlo method is used to calculate the nl state-selective charge exchange cross sections in hbox {Be}^{mathrm {4+}}+ H(2lm) collisions in the energy range between 10 and 200 keV/amu. We present partial cross sections for charge exchange into hbox {Be}^{mathrm {3+}}(nl) (textit{nl} = 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f) states as a function of impact energy. Our results are compared with the previous classical and quantum-mechanical results. We show that the classical treatment can able to describe reasonably well the charge exchange cross sections.Graphic abstract

Double differential distributions of e-emission in ionization of N2 by 3, 4 and 5 keV electron impact

We report the measurement of the absolute double differential cross sections (DDCS) of secondary electrons emitted due to the ionization of N2 molecule in collisions with fast electrons having energies between 3 and 5 keV. The emitted electrons with energies from 1–500 eV have been measured for different forward and backward emission angles. The measured DDCS have been compared with the state-of-the-art first Born approximation with correct boundary condition (CB1) model calculations as well as with the classical trajectory Monte Carlo (CTMC) method. From the measured DDCS, the single differential cross sections (SDCS) as a function of the emission energies have been computed and eventually the total ionization cross sections (TCS) have been derived. The TCS values are also compared with a semi-empirical calculation, namely, the CSP-ic (complex scattering potential-ionization contribution) model.

Effect of the orientation of Rydberg atoms on their collisional ionization cross section

Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, there can exist a difference of a factor of up to $\sim2.5$ in the ionization cross section between the orientation with the highest and the lowest ionization cross section. The case of exchange ionization is examined and its dependence on the magnitude of angular momentum is studied.

Ionization Cross Sections in the Collision between Two Ground State Hydrogen Atoms at Low Energies

The interaction between two ground state hydrogen atoms in a collision was studied using the four-body classical trajectory Monte Carlo method. We present the total cross sections for the dominant channels, namely for the single ionization of the target, the ionization of the projectile, resulting from pure ionization, and also from the electron transfer (capture or loss) processes. We also present cross sections for the complete break of the system, resulting in the final channel for four free particles. The calculations were carried out at low energies, relevant to the interest of fusion research. We present our cross sections in the projectile energy range between 2.0 keV and 100 keV and compare them with previously obtained theoretical and experimental results.

Charge transfer in positronium–proton collisions: comparison of classical and quantum-mechanical theories

Charge transfer in positronium–proton collisions is calculated using the quantum-mechanical convergent close-coupling method and classical trajectory Monte-Carlo method. Previous calculations revealed that at low incident energy the cross section in both theories scales as , where nPs and EPs are the principal quantum number and the center-of-mass energy of the incident positronium atom, respectively. However, the quantum cross section is systematically lower than classical one in absolute magnitude. To investigate the origin of this quantum suppression effect, we compare the charge transfer probabilities as functions of the impact parameter. We show that the quantum suppression in the cross section is mainly due to the low-impact parameter behavior of the probabilities governed by the quantum uncertainty principle.

Interaction of Be4+ and Ground State Hydrogen Atom—Classical Treatment of the Collision

The interaction between Be4+ and hydrogen atom is studied using the three-body classical trajectory Monte Carlo method (CTMC) and the quasiclassical trajectory Monte Carlo method of Kirschbaum and Wilets (QTMC-KW). We present total cross sections for target ionization, target excitation, and charge exchange to the projectile bound states. Calculations are carried out in the projectile energy range between 10 and 1000 keV/au, relevant to the interest of fusion research when the target hydrogen atom is in the ground state. Our results are compared with previous theoretical results. We found that the classical treatment describes reasonably well the cross sections for various final channels. Moreover, we show that the calculations by the QTMC-KW model significantly improve the obtained cross sections.

Ionization of rubidium by electron impact

SynopsisThe cross sections for ionization by electron impact of rubidium 5s shell have been calculated by the Classical Trajectory Monte Carlo method. The kinetic energy of the projectile is in the range between 5 and 1000 eV. We compared our results with other theoretical and experimental data..

Ionization and electron capture in Li3+ + H2O collisions

SynopsisTotal cross sections for ionization and electron capture in Li3+ + H2O collisions are calculated at energies 20 ⩽ E ⩽ 750 keV/u. Three different models are applied: the classical trajectory Monte Carlo method, an expansion in terms of asymptotic-frozen-molecular-orbitals and the numerical solution of the time dependent Schrödinger equation. One-electron transition probabilities from the three methods show general good agreement and with those from the calculation of Luna et al Phys Rev. A 93, 052705.

Kinematically complete scattering cross sections in collisions between positron and hydrogen atom

SynopsisA three-body classical trajectory Monte Carlo (CTMC) method is used to describe positron and hydrogen atom collisions. The total and multi-differential ionization and charge exchange cross sections are calculated and compared with experimental data and other theoretical results.

Charge exchange recombination spectra for 100 keV/u and 500 keV/u atomic hydrogen beam colliding with W64+

We present synthetic spectra for light emission following charge exchange (CX) recombination for Ne-like W64+ ions colliding with neutral atomic hydrogen at 100 and 500 keV/u, which is of relevance to the plasma diagnostics of the international experimental fusion device ITER now under construction. The spectra are calculated using a detailed collisional-radiative model for the W63+ ion that includes more than 6000 singly- and doubly-excited states and accounts for major physical processes in hot fusion plasmas. The CX cross sections into excited states are computed using the classical trajectory Monte Carlo method. A comprehensive analysis of the modifications to the spectra due to CX is presented.