Towards transport theory of hadron gases

An important role of hadron resonances for determining the characteristics of hadron gases is argued. A kinetic theory model of hadron gas is developed. A classical, nonquantum, distribution function of a resonance is defined with the help of the profile function being an analogue of the mass shell delta function of stable particles. The Boltzmann equation is generalized to include the resonance decay and resonance formation processes. To determine the unknown profile function, the transition rates are assumed to satisfy the bilateral normalization or the detailed balance condition. The profile function is expressed through the resonance formation cross section and the decay width. The H-theorem is proved, and it is shown that the form of the equilibrium distribution function of a resonance coincides with that of a stable particle. Macroscopic equilibrium characteristics are studied. Significance of the resonance mass smearing effect is demonstrated.     

The temperature jump and slow evaporation in molecular gases

We set up model transport equations that describe the behavior of molecular (diatomic and polyatomic) gases with a molecule collision rate proportional to the molecular velocity. In deriving these equations we allow for the internal (rotational) degrees of freedom, while the vibrational degrees of freedom are assumed “frozen.” We also set up an exact equation for the problem of the temperature jump with allowance for slow evaporation from the liquid surface into the saturated vapor atmosphere. Finally, we derive explicit formulas for calculating the coefficients of the temperature jump and gas-density jump above a flat surface and do the necessary numerical calculations. Zh. éksp. Teor. Fiz. 114, 956–971 (September 1998)     

Momentum transfer theory of ion transport under the influence of resonant charge transfer collisions: the case of argon and neon ions in parent gases

Transport properties of ion swarms in presence of Resonant Charge Transfer (RCT) collisions are studied using Momentum Transfer Theory (MTT). It was shown that, not surprisingly, RCT collisions may be represented as a special case of elastic scattering. Using the developed MTT we tested a previously available anisotropic set of cross-sections for Ar+Ar ⁺ collisions by making the comparisons with the available data for the transverse diffusion coefficient. We also developed an anisotropic set of Ne+Ne ⁺ integral cross-sections based on the available data for mobility, longitudinal and transverse diffusion. Anisotropic sets of cross-sections are needed for Monte Carlo simulations of ion transport and plasma models. Received 16 June 2002 / Received in final form 2nd August 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: vrhovac@phy.bg.ac.yu RID="b" ID="b"e-mail: zoran@phy.bg.ac.yu     

Stopping of slow recoil atoms in gases

Nuclear Resonance Fluorescence spectra contain information on the slowing-down behaviour of recoiling atoms in the energy range pertinent to the specific reaction. On the basis of conventional transport theory, measured spectra for arsenic atoms with energies ?15 eV slowing down in helium are analysed. The assumption of continuous slowing down turns out to be well justified, and the thermal motion of the gas atoms is shown to influence the effective stopping power only slightly. Somewhat surprising in view of uncertainties concerning the charge state of the recoiling atoms, theoretical predictions based on Lenz-Jensen elastic interaction agree well with the measured spectra. At present, the experimental data do not allow direct inversion, but the calculated spectra are shown to depend sensitively on the stopping-power input.     

Stopping of slow ions

The 50th anniversary of the appearance of a series of seminal papers by O.B. Firsov is taken as an occasion to have a look at some central aspects of the stopping of slow ions in matter. A brief characterization of Firsov’s model of electronic energy loss is given in comparison with alternative views. The main part of the paper is devoted to central problems such as scaling behavior, Z ₁ and Z ₂ structure, deviations from velocity proportionality, threshold behavior, metal-insulator and gas-solid differences, and correlation between nuclear and electronic stopping.     

On approximations involved in the theory of positron transport in gases in electric and magnetic fields

A multi term theory for solving Boltzmann’s equation is briefly reviewed and used to test various concepts and approximate expressions for the determination of the positron transport properties in neutral molecular gases in crossed electric and magnetic fields. Among many important approximations which have found their way into contemporary positron studies, the following are particularly discussed: (1) is the approximation of using the cross sections for the electron scattering to describe the positron behavior satisfactory, (2) how accurate is two term approximation for solving Boltzmann’s equation in the context of positron studies, and (3) what is the domain of applicability of Langevin elementary transport theory and Tonks’ theorem for positrons in electric and magnetic fields. We highlight the limitations, range of applicability and inadequacies of such assumptions for positrons in H₂ and N₂. It is pointed out that there is no real alternative to the accurate multi term theory and/or Monte Carlo simulations if high precision is required. It is demonstrated that if the demands for accuracy associated with some of these approximations are relaxed, results may not be even qualitatively correct.     

Logarithmically slow expansion of hot bubbles in gases

We predict a logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem is first solved, when the temperature has compact support. Then the temperature profile decaying exponentially at large distances is considered. The periphery of the bubble is shown to remain essentially static ("glassy") in the process of cooling until it is taken over by a logarithmically slowly expanding "core." An analytical solution to the problem is obtained by matched asymptotic expansion. This problem gives an example of how logarithmic corrections enter dynamic scaling.     

Lorentz lattice gases: Basic theory

We present several ballistic models of the Lorentz gas in two-dimensional lattices with deterministic and stochastic deflection rules, and their corresponding Liouville equations. Boltzmann-level-equation results are obtained for the diffusion coefficient and velocity autocorrelation function for models with stochastic deflection rules. The long-time behavior of the mean square displacement is briefly discussed and the possibility of abnormal diffusion indicated. Even if the diffusion coefficient exists, its low-density limit may not be given correctly by the Boltzmann equation.     

The rotating bucket of sand: Experiment and theory

The surface shape of a bucket of sand rotating about its cylindrical axis is studied experimentally and theoretically. Focusing on fast time scales on which surface shape is determined by avalanches, we identify three regimes of behavior. At intermediate and high frequencies, the surface shape is always at its critical shape determined by the Coulomb yield condition. The low frequency behavior displays an unexpected subcritical region at the center of the bucket. To understand this central region, we adapt a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. The model indicates that the subcritical region is due to a nonlinear instability mechanism. (c) 1999 American Institute of Physics.     

Energy straggling of Cl ions in gases

Energy-loss distributions for Cl ions in Ar-CH₄ and isobutane were measured at incident energiesE ₀=9.4, 17.1, 27.1 and 39.4 MeV up to relative energy lossesΔE/E ⁰?0.7. The full widths at half maximum are larger than predicted by the Landau-Vavilov-theory by more than a factor two. A semiempirical formula is derived which reproduces well all data measured. Reasonable agreement is obtained between this formula and other energy straggling data of heavy ions reported in the literature.     

Optical pumping of ions in buffer gases

A method for polarizing thermal ions in buffer gases directly by optical pumping is presented in detail. The production and storage of Sr⁺ (and Ba⁺) ions in noble gases, their diffusion and relevant collision processes are discussed. An arc discharge hollow cathode for the generation of intense ionic resonance lines is described. The Sr⁺ (5² S _1/2) and electron spin polarizations are treated by rate equations. Fitting the solutions to experimental data obtained from transient signals yields an estimate of a few times 10³Å² for the Sr⁺ion-electron spin exchange cross section.     

Optical pumping of ions in buffer gases

Transient signals measured with a pulsed rf-optical pumping method are used to determine longitudinal relaxation rates for Sr⁺ ions (even isotopes) in noble gas buffers. Depolarization cross sections of the electronic spin in the Sr⁺5² S _1/2 ground state for binary collisions with rare gas atoms are deduced. The results for σ(Sr⁺5² S _1/2) in Ų are (at temperatures between 374 and 449 °K): 2·10^?5(He),4·10^?5(Ne), 5.7·10^?3(Ar), 1.8·10^?2(Kr), and 4.0·10^?2(Xe). These cross sections for the Sr⁺ ion are about two to three orders of magnitude larger than the corresponding ones for the isoelectronic neutral Rb atom. The large increase of the Sr⁺ relaxation rates is explained with the relaxation mechanism of spin-orbit coupling, taking into account two “indirect” effects of the ionic charge: the increase in the gas kinetic cross sections and the more intimate collisions of the Sr⁺ ion with the noble gas atoms. The depolarization is shown to be predominantly due to short-range interactions. A contribution to the relaxation of the Sr⁺ ion from Sr⁺-noble gas molecule formation, induced by three-body or resonant two-body collisions, could not be established for applied pressuresp between 1.5 and 15 Torr of Ar, Kr, and Xe.     

Cross sections and transport properties of Cl<Superscript>-</Superscript> ions in noble gases

We have used a simple semi-analytic — momentum transfer theory (MTT) to develop negative halogen ions/noble gases momentum transfer integral cross sections based on the available data for reduced mobility at 300 K as a function of E/N. The unfolded cross sections were validated or further improved by assuring a good agreement between our Monte Carlo (MC) calculated transport data and the available experimental results. The data are produced with an aim to provide plasma modellers with cross section data and transport coefficients. We have also calculated the net rates of elastic scattering and detachment.     

Generation of currents in gases by fast, highly charged ions

It is shown that an exit asymmetry of the electrons and recoil ions formed during ionization of atoms in elementary collision events with fast, highly charged ions can give rise to macroscopic electron and recoil ion currents during the bombardment of a gaseous target by a beam of fast, highly charged ions. Zh. Tekh. Fiz. 68, 20–23 (September 1998)     

The HN method for solving linear transport equation: theory and applications

The system of singular integral equations which is obtained from the integro-differential form of the linear transport equation using the Placzek lemma is solved. The exit distributions at the boundaries of the various media and the infinite medium Green's function are used. The process is applied to the half-space and finite slab problems. The neutron angular density in terms of singular eigenfunctions of the method of elementary solutions is also used to derive the same analytical expressions.     

Energy losses of slow protons in inhomogeneous electron gases

Summary The energy loss of a slow proton interacting with the electron gas surrounding an ionic core in a crystal lattice is estimated on the basis of local-density approximation for the electron gas and binary-collision approximation for proton-electron interactions. Comparison is made with the dielectric function approach to the same quantity and with experimental electronic-stopping cross-sections.

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Riassunto La perdita di energia di un protone lento interagente con il gas di elettroni che circonda un nucleo atomico in un reticolo cristallino si calcola in base all'approssimazione di densità locale per il gas elettronico inomogeneo e all'approssimazione di collisione binaria per l'interazione fra protone ed elettroni. Si confrontano i risultati con quelli ottenuti dal metodo della funzione dielettrica e con le sezioni d'urto sperimentali di frenamento electtronico.

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Резюме Оцениваются энертетичекие потери медленньых, вэаимодействующих с электронньим гаэом, окружающем ионный остов в кристаллической решетке, используя приближение локальной плотности для электронного газа и приближение бинарных соударений для прптон-электронных взаимодействий. Проводится сравнение с результатами, полученными с помощью циэлектричецкой функции, и с экспериенталными поперечными сечениями электронного торможения.

     

Relaxation and transport in FCHC lattice gases

FCHC lattice gases are the basic models for studying flow problems in three-dimensional systems. This paper presents a self-contained theoretical analysis and some computer simulations of such lattice gases, extended to include an arbitrary number of rest particles, with special emphasis on non-semi-detailed balance (NSDB) models. The special FCHC lattice symmetry guarantees isotropy of the Navier-Stokes equations, and enumerates the 12 spurious conservation laws (staggered momenta). The kinetic theory is based on the mean field approximation or the nonlinear Boltzmann equation. It is shown how calculation of the eigenvalues of the linearized Boltzmann equation offers a simple alternative to the Chapman-Enskog method or the multi-time-scale methods for calculating transport coefficients and relaxation rates. The simulated values for the speed of sound in NSDB models slightly disagree with the Boltzmann prediction.     

Metal-neon compound ions in slow field evaporation

A magnetic sector atom-probe has been employed to study slow field evaporation of most of the transition metals in vacuum, in neon and in a mixture of neon and hydrogen. Various metals were found to form metal-neon molecular ions. Slow field evaporation and the presence of hydrogen are favorable for their formation. All the experiments were done at 78 K. The metals that evaporate as nei'des abundantly are Ti, Zn, Zr, Nb, Mo, Pd and Ta, of which Ti, Nb and Pd produce neïde ions as much as 80 to 90%. There were also some neïdes with W, Re, Ir and Rh, definitely above the detection limit estimated to be 3% of the field evaporating metal ions. The role of hydrogen is thought to be two-fold: At the surface, hydrogen adsorption is assumed to cause a stronger metal-neon bond, while the electron shower from free space ionization of the auxiliary gas excites or ionizes the complex by electron impact to allow evaporation at a reduced field.     

Cloaks,editors, and bubbles: applications of spacetime transformation theory

Spacetime or ‘event’ cloaking was recently introduced as a concept, and the theoretical design for such a cloak was presented for illumination by electromagnetic waves [McCall et al., J. Opt. 2011]. Here it is described how event cloaks can be designed for simple wave systems, using either an approximate ‘speed cloak’ method, or an exact full‐wave one. Further, details of many of the implications of spacetime transformation devices are discussed, including their (usually) directional nature, spacetime distortions (as opposed to cloaks), and how leaky cloaks manifest themselves. More exotic concepts are also addressed, in particular concepts that follow naturally on from considerations of simple spacetime transformation devices, such as spacetime modeling and causality editors. A proposal for implementing an interrupt‐without‐interrupt concept is described. Finally, the design for a time‐dependent ‘bubbleverse’ is presented, based on temporally modulated Maxwell's Fisheye transformation device (T‐device) in a flat background spacetime.