Effect Of Elastic Collisions Research Articles

Two-fluid implementation in MPI-AMRVAC with applications to the solar chromosphere

Context. The chromosphere is a partially ionized layer of the solar atmosphere, which acts as the transition between the photosphere where the gas is almost neutral and the fully ionized corona. As the collisional coupling between neutral and charged particles decreases in the upper part of the chromosphere, the hydrodynamical timescales may become comparable to the collisional timescale, thus calling for the application of a two-fluid model. Aims. In this paper, we describe the implementation and validation of a two-fluid model that simultaneously evolves charges and neutrals, coupled by collisions. Methods. The two-fluid equations are implemented in the fully open-source MPI-AMRVAC code. In the photosphere and the lower part of the solar atmosphere, where collisions between charged and neutral particles are very frequent, an explicit time-marching would be too restrictive, since, to maintain stability, the time step needs to be proportional to the inverse of the collision frequency. This caveat can be overcome by evaluating the collisional terms implicitly, using an explicit–implicit (IMEX) scheme. Out of the various IMEX variants implemented, we focused on the IMEX-ARS3 scheme and we used it for all simulations presented in this paper. The modular structure of the code allows us to directly apply all other code functionality – in particular, its automated grid adaptivity – to the two-fluid model. Results. Our implementation recovers and significantly extends the available (analytic or numerical) test results for two-fluid chargeneutral evolutions. We demonstrate wave damping, propagation, and interactions in stratified settings, as well as Riemann problems for coupled plasma-neutral mixtures. We generalized a shock-dominated evolution from single to two-fluid regimes and made contact with recent findings on typical plasma-neutral instabilities. Conclusions. The cases presented here cover very different collisional regimes and our results are fully consistent with related findings from the literature. If collisional time and length scales are smaller than the hydrodynamical scales usually considered in the solar chromosphere, the density structures seen in the neutral and charged fluids will be similar, with the effect of elastic collisions between charges and neutrals shown to be similar to the effects of diffusivity. Otherwise, density structures are different and the decoupling in velocity between the two species increases, and neutrals may, for instance, show Kelvin–Helmholtz roll-up while the charges do not. The use of IMEX schemes efficiently avoids the small time step constraints of fully explicit implementations in strongly collisional regimes. Implementing an adaptive mesh refinement (AMR) greatly decreases the computational cost, as compared to uniform grid runs at the same effective resolution.

Effect of elastic collisions and electronic excitation on lattice structure of NiTi bulk intermetallic compound irradiated with energetic ions

Abstract NiTi bulk intermetallic compound with the B19′ structure was irradiated with 1 MeV He, 5 MeV Al, 16 MeV Au and 200 MeV Xe ions, and the change in lattice structure near the surface by the ion bombardment was investigated by using the grazing incidence X-ray diffraction (GIXD) and the extended X-ray absorption fine structure (EXAFS). The lattice structure transformation by the irradiation strongly depends on ion species and/or energies. For the 1 MeV He irradiation, the lattice structure changed from B19′ to the A2 structure, but did not show an amorphization even after the high fluence irradiation. For the 5 MeV Al irradiation, the samples are partially amorphized. For the 16 MeV Au irradiation, the lattice structure of the NiTi samples changed nearly completely from the B19′ structure to the amorphous state via the A2 structure. The value of dpa (displacement per atom) which is needed for the amorphization is, however, much smaller than the case of the Al ion irradiation. For the 200 MeV Xe ion irradiation, the lattice structure completely changed to the A2 structure even by a small ion fluence. The dependence of the lattice structure transformation on elastic collisions (dpa), the spectrum of the primary knock-on (PKA) atoms and the density of energy deposited through electronic excitation was discussed.

Effect of Elastic Collisions on the Ion Distribution Function in Parent Gas Discharge Plasma

An analytical solution is obtained for the Boltzmann kinetic equation for ions in the plasma of its gas with allowance for the processes of resonant charge exchange and elastic ion scattering on the atom. The cross section of differential elastic scattering was assumed to be isotropic in the system of the mass center, and the resonant charge exchange process is independent of the elastic scattering. It is shown that the ion velocity distribution function is determined by two parameters and differs significantly from the Maxwellian one. The allowance for elastic scattering with these assumptions leads to a change in the ion angular distribution and also to a decrease in the average ion energy due to the transfer of part of the ion energy to atoms upon elastic collisions. The calculated values of the drift velocity, the average energy, and the coefficient of transverse diffusion of He+ ions in He, Ar+ ions in Ar are compared with the known experimental data and the results of Monte Carlo calculations; they show good agreement.

A Jost function description of zero-energy resonance and transparency effects in elastic collisions

Under certain circumstances, an elastic cross section at very low energies could differ by orders of magnitude above or below any reasonable estimate. The first case occurs near a zero-energy resonance, while the second one is akin to the well-known Ramsauer–Townsend effect. In spite of their intrinsic similarity, both effects are usually explained in very different ways, either in terms of poles of the scattering matrix or by means of a partial-wave analysis, respectively. In this paper we show that a unified description is actually possible. We demonstrate that in a zero-energy resonance or transparency, the standard ϵ2ℓ threshold law of the ℓ-wave cross section is changed into ϵ2(ℓ − 1) (ϵ−1 for ℓ = 0) or ϵ2(ℓ + 1), respectively. Finally, we show that while the zero-energy resonance occurs whenever the scattering length associated to an individual zero of the Jost function diverges, the transparent scattering is a collective effect, where the sum of all the individual scattering lengths plays a relevant role.

10.1007/s11490-008-3019-1

The effects of elastic collisions in optical-lattice atomic clocks are analyzed. Calculations are presented using a separated oscillatory fields clock arrangement. The interactions of atoms in multiply occupied lattice sites cause a linear frequency shift, and also generate asymmetric Ramsey fringe patterns, both complicate the determination of the resonance frequency and reduce the fringe visibility due to interparticle entanglement. A method of reducing these collisional effects in an optical lattice clock containing bosonic atoms by introducing a phase difference of π between the Ramsey driving fields in adjacent sites is developed. This configuration suppresses site-to-site hopping due to the interference of two tunneling pathways, without degrading the fringe visibility. The probability of double occupancy is, thereby, reduced and collisional shifts are, thus, ameliorated.

Hanle effect in the solar Ba II D2 line: a diagnostic tool for chromospheric weak magnetic fields

Context. The physics of the solar chromosphere depends in a crucial way on its magnetic structure. However there are presently very few direct magnetic field diagnostics available for this region. Aims. Here we investigate the diagnostic potential of the Hanle effect on the Ba ii D2 line resonance polarization for the determination of weak chromospheric turbulent magnetic fields. Methods. The line formation is described with a non-LTE polarized radiative transfer model taking into account partial frequency redistribution with an equivalent two-level atom approximation, in the presence of depolarizing collisions and the Hanle effect. We investigate the line sensitivity to temperature variations in the low chromosphere and to elastic collision with hydrogen atoms. We compare center-to-limb variations of the intensity and linear polarization profiles observed at THEMIS in 2007 to our numerical results. Results. We show that the line resonance polarization is very strongly affected by partial frequency redistribution effects both in the line central peak and in the wings. Complete frequency redistribution cannot reproduce the polarization observed in the line wings. The line is weakly sensitive to temperature differences between warm and cold components of the chromosphere. The effects of elastic collisions with hydrogen atoms and of alignment transfer due to multi-level coupling with the metastable 2 D5/2 levels have been studied in a recent paper showing that they depolarize the 2 P3/2 level of the line. In the conditions where the line is formed we estimate the amount of depolarization due to this mechanism as a factor of 0.7 to 0.65. If we first neglect this effect and determine the turbulent magnetic field strength required to account for the observed line polarization, we obtain values between 20 G and 30 G. We show that this overestimates the magnetic strength by a factor between 1.7 and 2. Applying these correction factors to our previous estimates, we find that the turbulent magnetic field strength is between 10 G and 18 G. Conclusions. Because of its low sensitivity to temperature variations, the solar Ba ii D2 line appears as a very good candidate for the diagnosis of weak magnetic fields in the low chromosphere (z ≥ 900 km) by means of the Hanle effect.

Effect of elastic collisions on acoustic wave propagation in simplified nuclear glass: Molecular dynamics simulation

A novel method based on classical molecular dynamics was used to measure acoustic velocities in simplified glasses and in pure silica. The method was then applied to observe the acoustic velocity variation in a simple glass subjected to displacement cascades. The Rayleigh velocity and Young’s modulus were observed to decrease; this behavior is consistent with experimental results obtained for the same glass irradiated by heavy ions. The increasing disorder and reduction in atomic density resulting from elastic collisions are thus directly related to the drop in the Rayleigh velocities and Young’s modulus.

Collisional shifts in an optical-lattice atomic clock

The effects of elastic collisions in optical-lattice atomic clocks are analyzed. Calculations are presented using a separated oscillatory fields clock arrangement. The interactions of atoms in multiply occupied lattice sites cause a linear frequency shift, and also generate asymmetric Ramsey fringe patterns, both complicate the determination of the resonance frequency and reduce the fringe visibility due to interparticle entanglement. A method of reducing these collisional effects in an optical lattice clock containing bosonic atoms by introducing a phase difference of π between the Ramsey driving fields in adjacent sites is developed. This configuration suppresses site-to-site hopping due to the interference of two tunneling pathways, without degrading the fringe visibility. The probability of double occupancy is, thereby, reduced and collisional shifts are, thus, ameliorated.

Deceleration and acceleration of fast electrons in a dense gas in an electric field

The propagation of electrons in a gas at energies higher than the excitation energy of the K shell of the gas atoms is simulated numerically. Calculations show that, without a field, the penetration depth of the electrons into a gas heavier than nitrogen is limited primarily by their elastic collisions with atomic nuclei. For electrons moving in an electric field, the effect of elastic collisions is that there is no definite electric field strength above which an electron with a given energy will be continuously accelerated. Even in an electric field much stronger than the critical one, only a fraction of electrons are accelerated. The remaining electrons turn back due to elastic collisions and lose their energy in deceleration by the field. In this case, the propagation velocity of the centroid of the electrons tends to a constant value.

Quantum-jump approach to dipole dephasing: Application to inversionless amplification

We present a model for simulating atomic dipole dephasing within the Monte-Carlo wave function formalism which leads to the same results as the standard density-matrix formalism. In this model dipole dephasing processes are accounted by quantum-jumps into one of the atomic energy eigenstates. This fact allows us to obtain analytical expressions for the effects of elastic collisions on the various physical processes responsible for amplification without population inversion in a cascade three-level atomic configuration.

Monte Carlo simulation of the effects of elastic collisions and chemical reactions on the angular distributions of the laser ablated particles

A three-dimensional Monte Carlo simulation of the laser desorbed flow of particles was performed. In addition to the gas-phase collisions, the chemical processes, i.e., recombination and dissociation are considered. The width of the angular distributions as a function of the radius of the evaporated area is analyzed. The comparison between the results obtained in the reactionless flow and in the flow with chemical reactions shows that in the presence of chemical processes the focusing effect of collisions is partly concealed and more wide angular distributions can be observed.

Monte Carlo simulations of the transport of laser-ablated atoms in a diluted gas

The interaction between gas clouds, created by laser ablation, and a diluted gas background is studied by means of Monte Carlo simulations. More specifically, the effect of elastic collisions between ablated atoms and background gas atoms on the kinetic energy and spatial distributions of atoms arriving at the substrate is investigated. The pressure regime under study is typically the range 0.1–200 mTorr. Thermalization is observed in a pressure range that varies over two orders of magnitude, dependent on the initial energy of the atoms and the ratio of the background gas and ablated atom molecular masses. During the first stages of thermalization, forward focusing is found to occur.

Astrophysical maser linewidths considering the effect of elastic collisions

The astrophysical maser linewidth is an outstanding interesting and important physical quantity to both observation and theory. When the effect of elastic collisions is considered, the linewidth of a saturated maser is smaller than predicted by the traditional standard theory, and it is smaller for stronger elastic collisions. The evolution of linewidths against saturation is shown and detailedly discussed. This may help explain some observed linewidths.

Interaction potentials and momentum transfer in ionic collisions: Uranium

The effect of elastic collisions of U/sup +/ with U, U/sup +/, and U/sup 2 +/ in a U/sup +/ plasma has been investigated. The required potential-energy curves were calculated by means of the electron-gas (Gordon-Kim-Rae) statistical method. An effective polarization potential was added to the ion-neutral potential curve. Collisional phase shifts were evaluated by the semiclassical JWKB method using a very efficient algorithm. Modifications necessary to take into account the long-range shielded Coulomb potential in ion-ion collisions are described. Momentum-transfer and viscosity cross sections, without charge transfer, are presented and their dependences on the long- and short-range potentials are examined.

Collisional effects upon optical coherences: Experimental study in a xenon three-level system

Laser induced nonlinear absorption profiles in a three-level system have been recorded to study the effect of elastic collisions upon optical coherences. In our particular system, the signal is due to a pure double-quantum term, where we have separated the effect of phase-interrupting collisions from the effect of velocity-changing collisions. Experimental results show that the effect of velocity-changing collisions is very small, and that broadening of the signal is due to phase-interrupting collisions mainly. We are able to determine the increase of the decay rate of the coherent superposition (the “coherence”) of two levels of same parity [Dγ 13/dp=(6.5±1) MHz/Torr] and an upper limit for the mean velocity change (ũ≲5m/s).

Effect of elastic collisions on drift splitting of opposite wave frequencies in a ring laser

The linear polarizability of a ring laser medium is calculated using a collisional model described by the averaged Keilson-Storer operator. An analysis is made of the opposite-wave frequency splitting in a ring laser induced by the drift of excited atoms in the active medium. It is shown that elastic collisions decrease the frequency splitting in the case of weak drift and increase this splitting under strong drift conditions. A nonmonotonic dependence of the drift frequency splitting on the collision frequency is obtained.

A suitable system for studying the effect of velocity-changing collisions in saturated absorption: Xe He

In a two-laser experiment the authors measure the broadening of the saturated absorption profile of the 3.51 mu m line of xenon, in the presence of helium. The pressure of xenon is fixed at 3 mTorr, and the helium pressure is varied between 0 and 550 mTorr. The computation of the profile includes the effect of elastic collisions without any adjustment of parameters. This is made possible since all the necessary parameters are known and a particularly simple description of the collisions is valid (Brownian motion, hard-sphere potential). The comparison with the experimental data shows that there is satisfactory agreement at high pressures of helium but an unexplained discrepancy exists at low pressure which could be attributed to inelastic processes.

Quantum Effects in Elastic Collisions between Heavy Particles.

Quantum Effects in Elastic Collisions between Heavy Particles.

Channel-coupling effects in elastic collisions of electrons with atoms

The effect of channel coupling in electron-atom collisions involving electric dipole transitions is investigated for (a) the large-angle elastic scattering of low-energy electrons by Hg and (b) the small-angle elastic scattering of low- and high-energy electrons by H. The effect in (a) is to produce changes in the phase shifts of the order of 01°. The effect in (b) is to increase the differential cross section near 0° by several orders of magnitude.

THE TOWNSEND DISCHARGE IN A COAXIAL DIODE WITH AXIAL MAGNETIC FIELD

An approximate theory is developed of the breakdown characteristics of a coaxial diode in an axial magnetic field, taking into account the effects of elastic collisions. It is assumed that the electron moves in a constant electric field between collisions and thus the theory is valid only in the appropriate range of magnetic field and voltage. Estimates of transit time and of space-charge effects are also made. Measurements in the pressure range 10−3 to 10−9 mm. Hg are in general agreement with the theory.