Pierre Nicoletopoulos

Recent advances in the application of Boltzmann equation and fluid equation methods to charged particle transport in non-equilibrium plasmas

The kinetic theory of charged particles in gases has come a long way in the last 60 years or so, but many of the advances have yet to find their way into contemporary studies of low-temperature plasmas. This review explores the way in which this gap might be bridged, and focuses in particular on the analytic framework and numerical techniques for the solution of Boltzmanns equation for both electrons and ions, as well as on the development of fluid models and semi-empirical formulae. Both hydrodynamic and non-hydrodynamic regimes are considered and transport properties are calculated in various configurations of dc and ac electric and magnetic fields. We discuss in particular the duality in transport coefficients arising from non-conservative collisions (attachment, ionization).

The optical limit of relativistic scattering

SummaryThe high-energy, small-angle eikonal approximation of Glauber for the elastic two-particle scattering amplitude, generalized relativistically, is obtained by summing Feynman graphs. The set of graphs considered consists of all ladder diagrams where the «rungs» criss-cross in all possible ways. The result is valid for particles carrying spin and under very general conditions for arbitrary «rungs» of the criss-cross ladder. When extended to include inelastic collisions, this method makes clear what are the necessary conditions for the absorptive-correction model to single-Regge exchange to be correct.RiassuntoL’approssimazione eiconale di Glauber a piccoli angoli ed alte energie per l’ampiezza di scattering elastico di due particelle, generalizzata relativisticamente si ottiene sommando dei grafici di Feynman. L’insieme dei grafici considerati consiste di tutti i diagrammi a scala in cui i «piuoli» si intersecano in tutti i modi possibili. Il risultato è valido per particelle dotate di spin e in condizioni molto generali per «piuoli» arbitrari della scala incrociata. Qualora lo si estenda alle collisioni anelastiche, questo metodo chiarisce quali sono le condizioni necessarie perchè sia adeguato il modello di correzione assorbitiva per il singolo scambio di Regge.РезюмеСуммируя диаграммы Феинмана, получается малоугловое глауберовское приближение эйконала при высоких энергиях для амплитуды упругого двух-частичного рассеяния, обобщенной релятивистским образом. Рассмотренная система диаграмм представляет все лестничные диаграммы, в которых «ступеньки» пересекаются всевозможными способами. Этот результат справедлив для частиц, имеющих спин, и при очень общих условиях для произвольных «ступенек» пере-секающейся лестницы. Когда производится расширение приближения, чтобы включить неупругие соударения, этот метод позволяет понять, какие необходимые условия для модели абсорбционных поправок к простому обмену Редже являются корректными.

Low energy eigenvalue conditions from dynamically broken gauge symmetry

Abstract Dynamical symmetry breakdown of a gauge invariant Lagrangian may fix physical coupling constants via a condition unrelated to the Gell-Mann-Low equation. This condition arises when the Lagrangian couples each separate gauge field to massless fermions of definite chirality.

Fundamental issues in fluid modeling: Direct substitution and aliasing methods

It is shown how the accuracy of fluid models of charged particles in gases can be improved significantly by direct substitution of swarm transport coefficient data, rather than cross sections, into the average collision terms. This direct substitution method emerges in a natural way for fluid formulations in which the role of the mean energy is transparent, whatever the mass of the charged particles in equation (ions or electrons), and requires no further approximations. The procedure is illustrated by numerical examples for electrons, including the operational window of E/N for an idealized Franck-Hertz experiment. Using the same fluid formulation, we develop an aliasing method to estimate otherwise unknown mobility data for one type of particle, from known mobility data for another type of particle. The method is illustrated for muons in hydrogen, using tabulated data for protons in the same gas.

Dynamical symmetry breakdown in pure Yang-Mills field theory

Abstract It is shown, in a simple approximation consistent with gauge invariance, that Yang-Mills fields associated with a compact simple Lie group, may acquire mass through their self-interactions; this phenomenon leads to a breakdown of the original group symmetry and to an eigenvalue condition for the coupling constant of the self-interaction. It is conjectured, from an analysis of Feynman graphs, that these facts are still true in the full theory. The relevance of these conclusions to the problem of fermions interacting with Yang-Mills mesons is pointed out.

Regge cuts and the eikonal approximation in field theory. - II

SummaryIt is shown that the Mandelstam-Polkinghorne cancellation of the Regge cut in the AFS diagram is neutralized upon combining the latter with a suitable set of additional graphs. This procedure restores the AFS cut and leads to an eikonal approximation with a generalized kernel.RiassuntoSi dimostra che la cancellazione di Mandelstam-Polkinghorne del taglio di Regge nel diagramma AFS è neutralizzata combinando quest’ultimo diagramma con un opportuno gruppo di diagrammi addizionali. Questo procedimento ripristina il taglio AFS e porta ad una approssimazione iconale con nocciolo generalizzato.РеэюмеПокаэывается, что уничтожение Манделстама-Полкин гхорна раэреэа Редже в АFS диаграмме нейтралиэуется путем общединения АFS диаграммы с соответствуюшей системой дополнительных графиков. Эта процедура восстанавливает реэреэ АFS и приводит к приближению зйконала с обобшенным ядром.

Critical potentials of mercury with a Franck-Hertz tube

A classic experiment, where a four-electrode Franck-Hertz tube is used to show various energy states (critical potentials) to which a neutral mercury atom can be raised by electron impact, is upgraded and elucidated thanks to a novel arrangement of applied inter-electrode potentials. By that means, a suitably located plasma region, the working field-free scattering chamber, can be created dynamically and maintained thereafter under appropriate conditions of cathode emission current and mercury vapour pressure. Concurrently, a more efficient mechanism for displaying excitation peaks becomes operant in the adjoining electron collection cell, by means of the window for slow-electron transmission that is available in mercury below the resonance peak in the cross section at about 0.4 eV. The resultant enhanced resolution in current-voltage curves permits the identification and measurement within 0.05 eV of the leading features in the known electron impact excitation spectrum of mercury.

The '0.4 eV' shape resonance of electron scattering from mercury in a Franck-Hertz tube

The alternative version of the Franck–Hertz experiment with mercury, in which a two-grid tube is used as a combination of electron gun, equipotential collision space and detection cell, was analysed recently in considerable detail. In particular, it was inferred that, at optimal pressure, the formation of peaks in the anode current at inelastic thresholds is mediated inside the detection cell by the large variation, a maximum at 0.4 eV, in the cross section for elastic scattering. This variation is due to a shape resonance in the electron-mercury system and is observable persuasively at the onset of anode current as a sharp peak followed by a clear minimum. In this paper, the passage of electrons through the second grid to the anode region is analysed in terms of kinetic theory. The discussion is based on a simplified expression for the electron current derivable from an approximate form of the Boltzmann transport equation that maintains the spatial density gradient but omits elastic energy losses. The estimated range of pressure underlying this kind of idealization is in good agreement with experiment. An explicit solution is obtained by constructing an analytic expression for the momentum transfer cross section of mercury using a recent theory of generalized Fano profiles for overlapping resonances. This solution is used in order to model successfully the formation of peaks at the threshold of anode current and at excitation potentials, and to explain the dependence of the observed profiles on the pressure and on the sign and magnitude of the potential across the detection cell.