Classical Trajectory Monte Carlo Simulations Research Articles

Efficient three-photon excitation of quasi-one-dimensional strontium Rydberg atoms withn∼300

The efficient production of very-high-$n$, $n\ensuremath{\sim}300$, quasi-one-dimensional (quasi-1D) strontium Rydberg atoms through three-photon excitation of extreme Stark states in the presence of a weak dc field is demonstrated using a crossed laser-atom beam geometry. Strongly polarized quasi-1D states with large permanent dipole moments $\ensuremath{\sim}1.2{n}^{2}$ a.u. can be created in the beam at densities ($\ensuremath{\sim}{10}^{6}$ cm${}^{\ensuremath{-}3}$) where dipole blockade effects should become important. A further advantage of three-photon excitation is that the product $F$ states are sensitive to the presence of external fields, allowing stray fields to be reduced to very small values. The experimental data are analyzed using quantum calculations based on a two-active-electron model together with classical trajectory Monte Carlo simulations. These allow determination of the atomic dipole moments and confirm that stray fields can be reduced to $\ensuremath{\le}25\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}$V cm${}^{\ensuremath{-}1}$.

Classical trajectory Monte Carlo simulations of particle confinement using dual levitated coils

The particle confinement properties of plasma confinement systems that employ dual levitated magnetic coils are investigated using classical trajectory Monte Carlo simulations. Two model systems are examined. In one, two identical current-carrying loops are coaxial and separated axially. In the second, two concentric and coplanar loops have different radii and carry equal currents. In both systems, a magnetic null circle is present between the current loops. Simulations are carried out for seven current loop separations for each system and at numerous values of magnetic field strength. Particle confinement is investigated at three locations between the loops at different distances from the magnetic null circle. Each simulated particle that did not escape the system exhibited one of four modes of confinement. Reduced results are given for both systems as the lowest magnetic field strength that exhibits complete confinement of all simulated particles for a particular loop separation.

Artificially Structured Boundary for a high purity ion trap or ion source

A plasma enclosed by an Artificially Structured Boundary (ASB) is proposed here as an alternative to existing ion source assemblies. In accelerator applications, many ion sources can have a limited lifetime or frequent service intervals due to sputtering and eventual degradation of the ion source assembly. Ions are accelerated towards the exit canal of positive ion sources, whereas, due to the biasing scheme, electrons or negative ions are accelerated towards the back of the ion source assembly. This can either adversely affect the experiment in progress due to sputtered contamination or compromise the integrity of the ion source assembly. Charged particle trajectories in the proximity of an ASB experience electromagnetic fields that are designed to hinder ion–surface interactions. Away from the ASB there is an essentially field free region. The field produced by an ASB is considered to consist of a periodic sequence of electrostatically plugged magnetic field cusps. A classical trajectory Monte Carlo simulation is extended to include electrostatic plugging of magnetic field cusps. The conditions necessary for charged particles to be reflected by the ASB are presented and quantified in terms of normalized parameters.

Characterizing high-nquasi-one-dimensional strontium Rydberg atoms

The production of high-$n$, $n\ensuremath{\sim}300$, quasi-one-dimensional (quasi-1D) strontium Rydberg atoms through two-photon excitation of selected extreme Stark states in the presence of a weak dc field is examined using a crossed laser-atom beam geometry. The dipolar polarization of the electron wave function in the product states is probed using two independent techniques. The experimental data are analyzed with a classical trajectory Monte Carlo simulation employing initial ensembles that are obtained with the aid of quantum calculations based on a two-active-electron model. Comparisons between theory and experiment highlight different characteristics of the product quasi-1D states, in particular, their large permanent dipole moments, $\ensuremath{\sim}$1.0 to 1.2${n}^{2}e{a}_{0}$, where $e$ is the electronic charge and ${a}_{0}$ is the Bohr radius. Such states can be engineered using pulsed electric fields to create a wide variety of target states.

COMPREHENSIVE RATE COEFFICIENTS FOR ELECTRON-COLLISION-INDUCED TRANSITIONS IN HYDROGEN

Energy-changing electron-hydrogen atom collisions are crucial to regulating the energy balance in astrophysical and laboratory plasmas and relevant to the formation of stellar atmospheres, recombination in H-II clouds, primordial recombination, three-body recombination and heating in ultracold and fusion plasmas. Computational modeling of electron-hydrogen collision has been attempted through quantum mechanical scattering state-to-state calculations of transitions involving low-lying energy levels in hydrogen (with principal quantum number n < 7) and at large principal quantum numbers using classical trajectory techniques. Analytical expressions are proposed which interpolates the current quantum mechanical and classical trajectory results for electron-hydrogen scattering in the entire range of energy levels, for nearly all temperature range of interest in astrophysical environments. An asymptotic expression for the Born cross-section is interpolated with a modified expression derived previously for electron-hydrogen scattering in the Rydberg regime using classical trajectory Monte Carlo simulations. The derived formula is compared to existing numerical data for transitions involving low principal quantum numbers, and the dependence of the deviations upon temperature is discussed.

Classical analysis of Coulomb effects in strong-field ionization of H2+by intense circularly polarized laser fields

We analyze the distortion of the molecular frame photoelectron angular distributions of H${}_{2}$${}^{+}$ ionized by a strong, circularly polarized infrared laser field using classical trajectory Monte Carlo simulations. We find that the nonisotropic field of the molecular ion rotates the final electron momenta. The degree of distortion from the strong-field approximation's predictions is thereby sensitive to the field strength and the internuclear distance but, counterintuitively, does not necessarily decrease for high field strengths. Furthermore, the distortion also depends crucially on the initial momentum of the classical electron after tunneling, while the exact shape of the ionization rate seems to be less important. A trajectory analysis within our simple model allows us to interpret recent experimental results.

Classical trajectory Monte Carlo investigation for Lorentz ionization of H (1s)

Lorentz ionization of H(1s) is investigated by classical trajectory Monte Carlo (CTMC) simulation. The effect of the transverse magnetic field on the considered process is analyzed in terms of the time evolution of interactions in the system, total electron energy, and electron trajectories. A classical mechanism for the ionization is found, where the variation of the kinetic energy of the nuclei is found to be important in the process. Compared with the results of tunneling ionization, the classical mechanism becomes more and more important with the increase of the velocity of the H-atom or the strength of the magnetic field.

Classical simulation of single-electron capture and ionization in ion-atom collisions

Classical trajectory Monte Carlo (CTMC) simulation method and the four-body formalism of boundary corrected continuum intermediate state (BCCIS-4B) approximations have been employed to determine total single electron capture cross section and total single ionization cross section in collisions of H+, He2+ and Li3+ with helium atom and energy in range of 30–200 keV/amu. Present theoretical study using CTMC method is based on three-body formalism, where interaction of the active electron in target ion has been approximated by a model potential containing both long and short range part. As a consequence, initialization of the problem has been made on a multiperiodic orbit in sharp contrast to singly periodic orbit occurring in hydrogenic model. In BCCIS-4B formalism, distortion in the final channel related to Coulomb continuum states of projectile ion and active electron in the field of residual target ion are included. Results so obtained from both methods are in very good agreement with available experimental findings.

Classical-trajectory simulation of accelerating neutral atoms with polarized intense laser pulses

In the present paper, we perform the classical trajectory Monte Carlo simulation of the complex dynamics of accelerating neutral atoms with linearly or circularly polarized intense laser pulses. Our simulations involve the ion motion as well as the tunneling ionization and the scattering dynamics of valence electron in the combined Coulomb and electromagnetic fields, for both helium (He) and magnesium (Mg). We show that for He atoms, only linearly polarized lasers can effectively accelerate the atoms, while for Mg atoms, we find that both linearly and circularly polarized lasers can successively accelerate the atoms. The underlying mechanism is discussed and the subcycle dynamics of accelerating trajectories is investigated. We have compared our theoretical results with a recent experiment [Eichmann Nature (London) 461, 1261 (2009)].

Classical-quantum correspondence in atomic ionization by midinfrared pulses: Multiple peak and interference structures

Atomic ionization by strong and ultrashort laser pulses with frequencies in the midinfrared spectral region have revealed novel features such as the low-energy structures. We have performed fully three-dimensional quantum dynamical as well as classical trajectory Monte Carlo simulations for pulses with wavelengths from $\ensuremath{\lambda}=2000$ to 6000 nm. Furthermore, we apply distorted-wave quantum approximations. This allows to explore the quantum-classical correspondence as well as the (non) perturbative character of the ionization dynamics driven by long-wavelength pulses. We observe surprisingly rich structures in the differential energy and angular momentum distribution which sensitively depend on $\ensuremath{\lambda}$, the pulse duration ${\ensuremath{\tau}}_{p}$, and the carrier-envelope phase ${\ensuremath{\phi}}_{\mathrm{CEP}}$.

Orientation effects in collisions with protons and positrons

We investigate ionization processes by impact of protons and positrons at intermediate incident velocities, between 0.8 and 2 a.u. Current experimental results for protons and recent results for positrons are compared with Classical Trajectory Monte Carlo simulations.

Experimental and theoretical results on electron emission from helium by the impact of bare Li3+ ions

We investigate experimentally and theoretically the ionization of helium atoms by the impact of bare Li3 + projectiles at intermediate and high incident energies. We report on measured absolute values of doubly differential cross-sections, as a function of the emitted electron energies and angles, at collision energies of 200 and 440 keV u−1. Different physical aspects of the reaction are interpreted theoretically by comparison of the data with quantum-mechanical continuum distorted wave and continuum distorted wave–eikonal initial state calculations as well as classical trajectory Monte Carlo simulations. There is an overall good agreement of the calculations with the experimental data, which improves considerably for higher collision energies.

SU-E-T-489: Quantum versus Classical Trajectory Monte Carlo Simulations of Low Energy Electron Transport.

Widely-used classical trajectory Monte Carlo simulations of low energy electron transport neglect the quantum nature of electrons; however, at sub-1 keV energies quantum effects have the potential to become significant. This work compares quantum and classical simulations within a simplified model of electron transport in water. Electron transport is modeled in water droplets using quantum mechanical (QM) and classical trajectory Monte Carlo (MC) methods. Water droplets are modeled as collections of point scatterers representing water molecules from which electrons may be isotropically scattered. The role of inelastic scattering is investigated by introducing absorption. QM calculations involve numerically solving a system of coupled equations for the electron wavefield incident on each scatterer. A minimum distance between scatterers is introduced to approximate structured water. The average QM water droplet incoherent cross section is compared with the MC cross section; a relative error (RE) on the MC results is computed. RE varies with electron energy, average and minimum distances between scatterers, and scattering amplitude. The mean free path is generally the relevant length scale for estimating RE. The introduction of a minimum distance between scatterers increases RE substantially (factors of 5 to 10), suggesting that the structure of water must be modeled for accurate simulations. Inelastic scattering does not improve agreement between QM and MC simulations: for the same magnitude of elastic scattering, the introduction of inelastic scattering increases RE. Droplet cross sections are sensitive to droplet size and shape; considerable variations in RE are observed with changing droplet size and shape. At sub-1 keV energies, quantum effects may become non-negligible for electron transport in condensed media. Electron transport is strongly affected by the structure of the medium. Inelastic scatter does not improve agreement between QM and MC simulations of low energy electron transport in condensed media.

Spatially Periodic Electromagnetic Force Field For Plasma Confinement and Control

A scientific concept referred to as a is defined as a short-range, static electromagnetic field that can reflect a charged particle of either sign of charge that approaches at any angle of incidence. A force field is envisioned as consisting of a spatially periodic sequence of magnetic cusps that are electrostatically plugged using applied electrostatic voltage variations similar to those found in nested Penning traps. The effective range of the force field would be small compared to the dimensions of a nearby source of charged particles, such as a plasma confined by the force field. A theoretical understanding is developed of the single-particle reflection properties of a force field, considering the incident charged particles to have a non-drifting, isotropic velocity distribution. Classical trajectory Monte Carlo simulations and analytical modeling are employed. The initiation of an experimental effort to study force fields is described.

ANGULAR MOMENTUM CHANGING TRANSITIONS IN PROTON-RYDBERG HYDROGEN ATOM COLLISIONS

Collisions between electrically charged particles and neutral atoms are central for understanding the dynamics of neutral gases and plasmas in a variety of physical situaziones of terrestrial and astronomical interest. Specifically, redistribution of angular momentum states within the degenerate shell of highly excited Rydberg atoms occurs efficiently in distant collisions with ions. This process is crucial in establishing the validity of the local thermal equilibrium assumption and may also play a role in determining a precise ionization fraction in primordial recombination. We provide an accurate expression for the non-perturbative rate coefficient of collsions between protons and H(n_l) ending in a final state H(n_l'), with n being the principal quantum number and l,l' the initial and final angular momentum quantum numbers, respectively. The validity of this result is confirmed by results of classical trajectory Monte Carlo simulations. Previous results, obtained by Pengelly and Seaton only for dipole-allowed transitions, l--->l+-1, overestimate the l-changing collisional rate approximately by a factor of six, and the physical origin of this overestimation is discussed.

Creating and Transporting Trojan Wave Packets

Nondispersive localized Trojan wave packets with n(i) ~ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n(f) ~ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.

Antiprotonic helium atomcules

About 3% of antiprotons (p) stopped in helium are long-lived with microsecond lifetimes, against picoseconds in all other materials. This unusual longevity has been ascribed to the trapping of p on metastable bound states in pHe+ helium atom-molecules thus named atomcules. Apart from their unique dual structure investigated by laser spec-troscopy - a near-circular quasi-classical Rydberg atom with l ∼ n - 1 ∼ 37 or a special diatomic molecule with a negatively charged p nucleus in high rotational state with J = l - the chemical physics aspects of their interaction with other atoms or molecules constitute an interesting topic for molecular physics. While atomcules may resist to million collisions in helium, molecular contaminants such as H2 are likely to destroy them in a single one, down to very low temperatures. In the Born-Oppenheimer framework, we interpret the molecular interaction obtained by ab initio quantum chemical calculations in terms of classical reactive channels, with activation barriers accounting for the experiments carried out in He and H2. From classical trajectory Monte Carlo simulations, we show that the thermalization stage strongly quenches initial populations, thus reduced to a recovered 3 % trapping fraction. This work illustrates the pertinence of chemical physics concepts to the study of exotic processes involving antimatter. New insights into the physico-chemistry of cold interstellar radicals are anticipated.

Continuum-orientation phenomena in ionization by positron impact

Ionization collisions by positron impact at low and intermediate energies are investigated by means of a classical trajectory Monte Carlo (CTMC) simulation. Calculations of fully differential cross sections unveil a remarkable dynamical orientation of the electron–positron continuum dipole. Actually, by means of the CTMC simulation we show that, for electron velocities close to the final positron velocity, the dipole is narrowly oriented along the direction of motion of its centre-of-mass, with the negative charge pointing towards the residual target, i.e. emitted at lower energies than the positron. The characteristic features of this phenomenon are studied. Also, several future experiments and calculations are proposed. The possible outcomes of this further research might help to unveil the mechanisms responsible for the appearance of this orientation effect.

Theory of below-threshold kinetic electron emission

We investigate the electron emission from clean monotonically flat crystalline aluminum surfaces due to the impact of rare gas atoms at the surface under grazing angles of incidence. Recent improvements of experimental methods allowed for the first time the measurement of electron yields as small as γ ≈ 0.01 electrons/projectile. Using these methods kinetic electron emission (KE) was found for projectile velocities well below the classical threshold vth for KE, the minimum velocity a projectile has to have in order to transfer in a binary collision enough momentum to an electron at the Fermi edge (with k = kF) to overcome the surface potential. Quantum mechanical effects smear out the Fermi edge creating electrons with momenta above kF. We present a calculation of γ in the below threshold region within the framework of a classical trajectory Monte Carlo simulation in which special emphasis is put on the description of the projectile trajectory and on an accurate determination of the momentum distribution, i.e. the Compton profile of the surface electronic structure. We employ different methods for calculating the electronic structure and study its influence on. We find that realistic momentum distributions can account for kinetic electron emission in the below threshold region.

Drifting Plasma Confinement With a Spatially Periodic Field

Some possible plasma confinement configurations are identified in which a spatially periodic electrostatic or magnetostatic field may provide or enhance ion confinement. The plasma drifts at a speed much faster than the ion thermal speed. The periodic field has a spatial period that is much smaller than the plasma size, and the field has a nonnegligible strength only at the plasma edge. The periodic field could be produced, for example, by a sequence of electrodes with alternating applied voltages or a sequence of wires with alternating current directions. Classical trajectory Monte Carlo simulation results are used to develop expressions for predicting the conditions under which ions are reflected away from an artificially structured boundary that produces a spatially periodic field, without the ions reaching the artificially structured boundary.