Collisional Relaxation Research Articles

Demonstration of a diode-pumped metastable Ar laser

Pulsed lasing from optically pumped rare gas metastable atoms (Ne, Ar, Kr, and Xe) has been demonstrated previously. The laser relies on a three-level scheme, which involves the (n+1)p[5/2](3) and (n+1)p[1/2](1) states from the np(5)(n+1)p electronic configuration and the metastable (n+1)s[3/2](2) level of the np(5)(n+1)s configuration (Racah notation). Population inversions were achieved using relaxation from ((n+1)p[5/2](3) to (n+1)p[1/2](1) induced by collisions with helium or argon at pressures near 1 atm. Pulsed lasing was easily achieved using the high instantaneous pump intensities provided by a pulsed optical parametric oscillator excitation laser. In the present study we examine the potential for the development of a continuous wave (CW) optically pumped Ar laser. We report lasing of the 4p[1/2](1)→4s[3/2](2) (912.547 nm) transition following CW diode laser excitation of the 4p[5/2](3)←4s[3/2](2) line (811.754 nm). A pulsed discharge was used to generate Ar 4s[3/2](2), and the time-resolved lasing kinetics provide insights concerning the radiative and collisional relaxation processes.

Theory of relaxation parameters of the spectrum shape in the impact approximation–I:General consideration

The theory of relaxation parameters of the spectrum shape in the impact approximation is constructed as a limit case of the Fano general relaxation theory of pressure broadening. The Fano binary collision relaxation matrix is presented in the integral form and after the impact approximation is introduced it is expressed through the scattering matrix in the Liouville space of the absorbing molecule and the bath particle. By means of introducing the scattering matrix eigenvectors and solving the evolution equation in the matrix form, the method suitable for the calculation of the whole set of impact relaxation parameters of the spectrum shape has been developed.

Elastic and inelastic collisions of2Σmolecules in a magnetic field

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2\Sigma$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2\Sigma$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic cross section ratios under conditions corresponding to trapped molecular ensembles at $T \sim 10^{-3}$ K exceed 100 for the majority of $^2\Sigma$ molecules. The range of $^2\Sigma$ molecules expected to be collisionally unstable in magnetic traps at $T < 10^{-3}$ K is limited to molecules with the spin-rotation interaction constant $\gamma_{\rm SR} > 0.5$ cm$^{-1}$ and the rotational constant $B_e < 4$ cm$^{-1}$.

On the possibilities of sub-Doppler atomic spectroscopy in multilayer gas cells

Possibilities of high-resolution spectroscopy of atoms (or molecules) for optical pumping and probing with the use of a proposed cell with a series of plane-parallel thin gas layers between spatially separated regions of this cell are theoretically studied. It is shown that efficient velocity selection of optically pumped atoms is possible in view of their characteristic transit and collisional relaxation in such a cell, which leads to the formation of narrow sub-Doppler resonances in absorption of a probe monochromatic wave. The resolution of this spectroscopic method is analyzed in the cases of stationary and definite nonstationary optical pumping of atoms by broadband radiation for different geometrical parameters of these cells and pumping intensity. The proposed multilayer gas cell is a compact analog of a large number of parallel atomic (molecular) beams and can be the basis for new high-precision and compact optical frequency standards.

Lattice Boltzmann algorithms for plasma physics

Lattice Boltzmann (LB) algorithms are a mesoscopic approach to the solution of nonlinear macroscopic physics, which can be ideally parallelized on supercomputers to the full number of cores available. This is in contrast to the standard direct solution of the nonlinear physics by computational fluid dynamics codes. In its original formulation, LB algorithm consisted of a split operator method: collision relaxation at a spatial node, followed by appropriate streaming of the post-collision distribution to neighboring lattice sites. To reduce memory constraints, a minimal number of lattice streaming vectors are permitted so that one recovers the given nonlinear physics equations in the Chapman-Enskog limit. As in kinetic theory, the macroscopic transport coefficients are determined by the collisional relaxation time in the LB equation. The algorithm is explicit and typically is second-order accurate. However, the simple LB algorithm is prone to numerical instabilities for high Reynolds number flows. In this paper we review some of the recent attempts at stabilizing the LB algorithm for fluid flows – in particular multiple-relaxation operators, introduction of quasi-equiibria states as well as entropic methods. These methods are then discussed in reference to the LB representation of resistive magnetohydrodynamics. The introduction of a vector distribution function for the magnetic field permits the exact satisfaction of the zero divergence of the magnetic field. As a final example, the LB representation of Landau damping is reviewed.

Simulated ion velocity distribution and its incoherent scattering spectrum in the high-latitude ionosphere

If the relatively larger convection electric field and small the collision frequency between ions and neutrals in the high-latitude ionosphere are considered, the integral solution of the non-Maxwellian ion velocity distribution function for the relaxation collision model is simplified, and a torus distribution function of the ion velocity is obtained. Also, the feature of the torus velocity distribution function is analyzed and simulated with different parameters in high-latitude ionosphere. Furthermore, by using the electromagnetic radiation theory of Sheffield and taking into account the ion temperature anisotropy and its variation with the electric field, we simulate the incoherent scattering spectrum of ions in different directions. The research shows that the ionospheric convection electric field, the ion-neutral collision frequency and the ion anisotropic temperature distribution all have an effect on the incoherent scattering spectrum.

Fluorescence spectroscopy of anisole at elevated temperatures and pressures

Laser-induced fluorescence of anisole as tracer of isooctane at an excitation wavelength of 266 nm was investigated for conditions relevant to rapid compression machine studies and for more general application of internal combustion engines regarding temperature, pressure, and ambient gas composition. An optically accessible high pressure and high temperature chamber was operated by using different ambient gases (Ar, N2, CO2, air, and gas mixtures). Fluorescence experiments were investigated at a large range of pressure and temperature (0.2–4 MPa and 473–823 K). Anisole fluorescence quantum yield decreases strongly with temperature for every considered ambient gas, due to efficient radiative mechanisms of intersystem crossing. Concerning the pressure effect, the fluorescence signal decreases with increasing pressure, because increasing the collisional rate leads to more important non-radiative collisional relaxation. The quenching effect is strongly efficient in oxygen, with a fluorescence evolution described by Stern–Volmer relation. The dependence of anisole fluorescence versus thermodynamic parameters suggests the use of this tracer for temperature imaging in specific conditions detailed in this paper. The calibration procedure for temperature measurements is established for the single-excitation wavelength and two-color detection technique.

Collisional relaxation of two-dimensional self-gravitating systems

Systems with long range interactions present generically the formation of quasistationary long-lived nonequilibrium states. These states relax to Boltzmann equilibrium following a dynamics which is not well understood. In this paper we study this process in two-dimensional inhomogeneous self-gravitating systems. Using the Chandrasekhar-or local-approximation we write a simple approximate kinetic equation for the relaxation process, obtaining a Fokker-Planck equation for the velocity distribution with explicit analytical diffusion coefficients. Performing molecular dynamics simulations and comparing them with the evolution predicted by the Fokker-Planck equation, we observe a good agreement with the model for all the duration of the relaxation, from the formation of the quasistationary state to thermal equilibrium. We observe however an overestimate or underestimate of the relaxation rate of the particles with the slower or larger velocities, respectively. It is due to systematic errors in estimating the velocities of the particles at the moment of the collisions, inherent to the Chandrasekhar approximation when applied to inhomogeneous systems. Theory and simulations give a scaling of the relaxation time proportional to the number of particles in the system.

Time-resolved laser spectroscopy of nonreactive processes in ionic liquids and their binary mixtures with organic solvents and CO2

Nonreactive dynamics of molecules in ionic liquids (ILs) have been investigated in various environments, such as in neat aprotic and protic ILs, as well as in binary mixtures of ILs with polar organic solvents and CO2. Transient broadband absorption and fluorescence spectroscopic techniques on timescales from femtoseconds to milliseconds have been applied to elucidate the importance of different types of solute–solvent interactions in these media. Molecular probes such a 12′-apo-β-carotenoic-12′-acid and Coumarin C153 have been used as reporter molecules for ionic liquid solvation dynamics, micropolarity, hydrogen-bonding and collisional relaxation. With Coumarin C153 in ILs, the relationship between the complete solvation response and microwave-terahertz absorption measurements of the neat liquid was explored quantitatively. A reduced value for the conductivity plays a key role in such solvation experiments. Aprotic ILs exhibit a micropolarity larger than expected from their static dielectric constants, whereas the local polarity of protic alkylammonium formate ILs appears to be similar to that of alcohols having comparable dielectric constants. In IL mixtures with organic solvents or CO2, there is no indication for differences in the bulk composition and the local composition around the molecular probe. Collisional relaxation processes in ILs take place on similar timescales as in dipolar organic solvents.

Sliced Fluorescence Imaging Techniques for the Study of Photo‐initiated Dynamic Processes in Bulbs

AbstractTo study photo‐initiated dynamic processes in bulbs, sliced fluorescence imaging techniques have been developed to obtain quantum‐state resolved information on the speed and angular distributions of reaction products, and their angular momentum polarization characteristics. For fluorescent chemical species, an unconventional experimental arrangement can generate a two‐dimensional projection of the Newton sphere from a single photolysis center. Consequently, image blurring for photo‐initiated experiments in bulbs can be dramatically diminished. A combination of optical‐optical (or infrared‐optical) double resonance excitation scheme and the fluorescence imaging detection method warrants a novel technique to acquire three‐dimensional sliced fluorescence images of scattering products. A theoretical framework, which employs a double Legendre moment analysis on the central sliced images, has been developed to determine differential cross sections and kinetic energy release of co‐products in photo‐initiated dynamic processes. Experimental images of collisional relaxations of CN photofragments from disequilibrium to equilibrium are presented to illustrate the distinctive advantage of the present method in comparison with other imaging and spectroscopic techniques.

Research on the ionospheric ion velocity distribution and the incoherent scattering spectra of the radar with the 16-moments approximation for the relaxation collision model

The distribution function which given by Grad cannot be used to describe the ionospheric ion velocity distribution due to the larger anisotropic temperature appears in the high-latitude ionosphere. In this article, based on the Boltzmann equation, the relaxation collision model (RCM) was used to substitute the Boltzmann collision integration, and a non-Maxwell ion velocity distribution function with the 16-moments approximation for the bi-Maxwell distribution was given, and the ion transport equation with the 16-moments approximation was also derived and solved. Moreover, the ion velocity distribution, the solution of transport equation and the incoherent scattering spectra with the 13-moments and 16-moments approximation for the relaxation collision model were simulated, analyzed and compared. The research shows that compared with the 13-moments approximation, the 16-moments approximation with the bi-Maxwell distribution is more suitable to describe the characteristics of the anisotropic temperature ion distribution in the high-latitude ionosphere.

Study of collisional deactivation of O2(b 1Σ g + ) molecules in a hydrogen-oxygen mixture at high temperatures using laser-induced gratings

Collisional deactivation of O2(b 1Σ g + ) molecules resonantly excited by a 10 ns pulse of laser radiation with a wavelength of 762 nm in H2/O2 mixtures is experimentally studied. The radiation intensity and hence the molecule excitation efficiency have a spatially periodic modulation that leads to the formation of laser-induced gratings (LIGs) of the refractive index. The study of LIG temporal evolution allows collisional relaxation rates of molecular excited states and gas temperature to be determined. In this work, the b 1Σ g + state of O2 molecules deactivation rates are measured in a 4.3 vol % H2 mixture at the number density of 2 amg in the temperature range 291–850 K. The physical deactivation is shown to dominate in the collisions of H2 with O2(b 1Σ g + ) and O2(a 1Δ g ) up to temperatures of 780–790 K at time delays up to 10 μs after the excitation pulse. The parameters of the obtained temperature dependence of the (b 1Σ g + state deactivation rate agree well with the data of independent measurements performed earlier at lower temperatures (200–400 K). Tunable diode laser absorption spectroscopy is used to measure the temperature dependence of the number density of the H2O molecules which appear as the mixture, as the result of the dark gross reaction with O2 molecules in the ground state, O2 + 2H2 → 2H2O. The measurements show that this reaction results in complete transformation of H2 into H2O at temperatures of 790–810 K.

Atomic oxygen in the mesosphere and lower thermosphere derived from SABER: Algorithm theoretical basis and measurement uncertainty

Atomic oxygen (O) is a fundamental component in chemical aeronomy of Earth's mesosphere and lower thermosphere region extending from approximately 50 km to over 100 km in altitude. Atomic oxygen is notoriously difficult to measure, especially with remote sensing techniques from orbiting satellite sensors. It is typically inferred from measurements of the ozone concentration in the day or from measurements of the Meinel band emission of the hydroxyl radical (OH) at night. The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on the NASA Thermosphere‐Ionosphere‐Mesosphere Energetics and Dynamics (TIMED) satellite measures OH emission and ozone for the purpose of determining the O‐atom concentration. In this paper, we present the algorithms used in the derivation of day and night atomic oxygen from these measurements. We find excellent consistency between the day and night O‐atom concentrations from daily to annual time scales. We also examine in detail the collisional relaxation of the highly vibrationally excited OH molecule at night measured by SABER. Large rate coefficients for collisional removal of vibrationally excited OH molecules by atomic oxygen are consistent with the SABER observations if the deactivation of OH(9) proceeds solely by collisional quenching. An uncertainty analysis of the derived atomic oxygen is also given. Uncertainty in the rate coefficient for recombination of O and molecular oxygen is shown to be the largest source of uncertainty in the derivation of atomic oxygen day or night.

RELAXATION IN N -BODY SIMULATIONS OF DISK GALAXIES

I use N-body simulations with two mass species of particles to demonstrate that disk galaxy simulations are subject to collisional relaxation at a higher rate than is widely assumed. Relaxation affects the vertical thickness of the disk most strongly, and drives the velocity ellipsoid to a moderately flattened shape similar to that observed for disk stars in the solar neighborhood. The velocity ellipsoid in simulations with small numbers of particles quickly approaches this shape, but shot noise also dominates the in-plane behavior. Simulations with higher, but reachable, numbers of particles relax slowly enough to be considered collisionless, allowing the in-plane dispersions to rise due to spiral activity without heating the vertical motions. Relaxation may have affected many previously published simulations of the formation and evolution of galaxy disks.

Charge-to-mass-ratio-dependent ion heating during magnetic reconnection in the MST RFP

Temperature evolution during magnetic reconnection has been spectroscopically measured for various ion species in a toroidal magnetized plasma. Measurements are made predominantly in the direction parallel to the equilibrium magnetic field. It is found that the increase in parallel ion temperature during magnetic reconnection events increases with the charge-to-mass ratio of the ion species. This trend can be understood if the heating mechanism is anisotropic, favoring heating in the perpendicular degree of freedom, with collisional relaxation of multiple ion species. The charge-to-mass ratio trend for the parallel temperature derives from collisional isotropization. This result emphasizes that collisional isotropization and energy transfer must be carefully modeled when analyzing ion heating measurements and comparing to theoretical predictions.

Theoretical investigation of 2+2 resonance enhanced multi-photon ionization probability

The analytic formula of the ionization probability in the process of 2+2 resonance enhanced multi-photon ionization (REMPI) is derived from the dynamic rate equation about the interaction of photon and material. Based on the formula, the influence of laser intensity, laser pulse duration and collision relaxation rate on the ionization probability is investigated theoretically. It is shown that the ionization probability increases with the laser intensity and laser pulse duration. The ionization probability will get to one until two steps saturation with the increase of laser intensity. After that, the ionization probability will oscillates narrowly around the saturation value if the laser intensity increases further. The results also show that the ionization probability will decrease in linear manner nearly with the increase of collision relaxation rate. But the variation is small. So the influence of the collision relaxation rate (or even sample pressure) on the ionization probability can be ignored. In the practical use of REMPI, higher sample pressure will reduce the intensity of the detection signal is due to the collision complex of the positive and negative ions. This will reduce the collection efficiency of the ions, and influence the magnitude of the ion signal further.

Comparison of DNA decatenation by Escherichia coli topoisomerase IV and topoisomerase III: implications for non-equilibrium topology simplification

Type II topoisomerases are essential enzymes that regulate DNA topology through a strand-passage mechanism. Some type II topoisomerases relax supercoils, unknot and decatenate DNA to below thermodynamic equilibrium. Several models of this non-equilibrium topology simplification phenomenon have been proposed. The kinetic proofreading (KPR) model postulates that strand passage requires a DNA-bound topoisomerase to collide twice in rapid succession with a second DNA segment, implying a quadratic relationship between DNA collision frequency and relaxation rate. To test this model, we used a single-molecule assay to measure the unlinking rate as a function of DNA collision frequency for Escherichia coli topoisomerase IV (topo IV) that displays efficient non-equilibrium topology simplification activity, and for E. coli topoisomerase III (topo III), a type IA topoisomerase that unlinks and unknots DNA to equilibrium levels. Contrary to the predictions of the KPR model, topo IV and topo III unlinking rates were linearly related to the DNA collision frequency. Furthermore, topo III exhibited decatenation activity comparable with that of topo IV, supporting proposed roles for topo III in DNA segregation. This study enables us to rule out the KPR model for non-equilibrium topology simplification. More generally, we establish an experimental approach to systematically control DNA collision frequency.

Isotropic inelastic and superelastic collisional rates in a multiterm atom

The spectral line polarization of the radiation emerging from a magnetized astrophysical plasma depends on the state of the atoms within the medium, whose determination requires considering the interactions between the atoms and the magnetic field, between the atoms and photons (radiative transitions), and between the atoms and other material particles (collisional transitions). In applications within the framework of the multiterm model atom (which accounts for quantum interference between magnetic sublevels pertaining either to the same J-level or to different J-levels within the same term) collisional processes are generally neglected when solving the master equation for the atomic density matrix. This is partly due to the lack of experimental data and/or of approximate theoretical expressions for calculating the collisional transfer and relaxation rates (in particular the rates for interference between sublevels pertaining to different J-levels, and the depolarizing rates due to elastic collisions). In this paper we formally define and investigate the transfer and relaxation rates due to isotropic inelastic and superelastic collisions that enter the statistical equilibrium equations of a multiterm atom. Under the hypothesis that the atom-collider interaction can be described by a dipolar operator, we provide expressions that relate the collisional rates for interference between different J-levels to the usual collisional rates for J-level populations. Finally, we apply the general equations to the case of a two-term atom with unpolarized lower term, illustrating the impact of inelastic and superelastic collisions on scattering polarization through radiative transfer calculations in a slab of stellar atmospheric plasma anisotropically illuminated by the photospheric radiation field.

Field-free molecular alignment for probing collisional relaxation dynamics

We report the experimental study of field-free molecular alignment in CO${}_{2}$ gas mixtures induced by intense femtosecond laser pulses in the presence of collisional processes. We demonstrate that the alignment signals exhibit specific features due to nontrivial collisional propensity rules that tend to preserve the orientation of the rotational angular momentum of the molecules. The analysis is performed with a quantum approach based on the modeling of rotational $J$- and $M$-dependent state-to-state transfer rates. The present work paves the way for strong-field spectroscopy of collisional dynamics.

High-resolution Raman spectroscopy of ν2and associated hot bands of13CH12CH: global analysis of the anharmonic resonances

The Raman spectrum of the 13CH12CH molecule in the region of its ν2 vibrational band was recorded at a resolution of 2.6 × 10−3 cm−1 and analyzed. Several Q branches were observed and identified, corresponding to the ν2 fundamental and the associated hot bands ν2 + ν4 – ν4, ν2 + ν5 – ν5, ν2 + 2ν4 – 2ν4 and 2ν2 – ν2. The usual normal modes of vibration in acetylene, with the symmetric (ν1) and antisymmetric (ν3) CH stretchings, the CC stretching (ν2), the degenerate trans (ν4) and cis (ν5) bendings were adopted. All the spectra were obtained using the experimental technique of quasi-continuous stimulated Raman spectroscopy. The fundamental ν2 band and the ν2 + ν4 – ν4 and ν2 + ν5 – ν5 hot bands were recorded at room temperature, while ν2 + 2ν4 – 2ν4 was recorded at a temperature of 355 K. Finally, the spectrum of the 2ν2 – ν2 band was recorded at 170 K using a Raman-Raman double resonance technique in which a stimulated Raman pumping process is used to populate a single rotational level of the v2 = 1 state, prior to the spectroscopy stage. A 15 ns delay between pump and spectroscopy is introduced to allow partial collisional relaxation of the rotational population of v2 = 1 among rotational levels. The assigned Raman transitions and several previously observed infrared bands have been simultaneously fitted in order to derive a set of deperturbed molecular parameters, including the quartic anharmonic coupling coefficients K1,255 and K3,245. The ro-vibrational pattern of the stretching and stretching-bending combination states and an accurate description of the anharmonic resonances in this molecule have been obtained. Copyright © 2013 John Wiley & Sons, Ltd.