arXiv subjects

Peter Nicoletopoulos

Publications and source records attributed to Peter Nicoletopoulos.

3 recordsLinked to original sources

arXiv2004

Theory of a stable strong electrostatic double layer generated in a two-grid Franck-Hertz tube

There is a classic alternative to the Franck-Hertz experiment designed to show more than a recurrence of the first excited state. Instead of being subjected to a rising potential between source and accelerating grid, electrons are now accelerated in less than one excitation mean-free-path by an extra grid, and then drift towards the second grid across a large equipotential region. In this arrangement one must face the difficulty that the space potential between the grids is strongly modified by space charges. A recent analysis of this experiment with mercury showed that there is a particular form of discharge that generates and sustains the ideal design dynamically. The inevitable variations of potential inside the intergrid volume are then confined within a narrow sheath, a free double layer, joining two field-free plasma regions. The position of the double layer can be controlled so as to optimize the experiment. In the present paper, those phenomena are studied theoretically in steady-state conditions. The essence of the method is to specify velocity distributions for electrons and ions and use them to solve the Poisson equation. Vortex-type functions are used for trapped particles and mono-energetic beams for free particles. The model explains the change of position of the double layer and provides a natural explanation of a threshold condition for its amplitude that governs the transition between two critical configurations, in accordance with experiment. Stability and minimum field-energy considerations lead to a unique solution in a four-dimensional parameter space where the Langmuir ratio is equal to one. The method is adaptable to other experiments on double layer formation under discharge conditions and correctly predicts the values of several plasma parameters.

physics.plasm-ph↗

arXiv2004

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 analyzed 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 the present paper, the passage of electrons through the second grid to anode region is analyzed 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.

physics.atom-ph↗

arXiv2003

Analytic Elastic Cross Sections for Electron-Atom Scattering from Generalized Fano Profiles of Overlapping Low-Energy Shape Resonances

The variation with energy of the total cross section for elastic electron scattering from atoms of several elements is caused primarily by shape resonances corresponding to the formation of temporary negative ions. It is shown that such cross sections are expressible analytically in terms of a constant background added to a "generalized Fano profile" [Durand Ph, et al (2001) J. Phys. B: At. Mol. Opt. Phys. 34, 1953, ibid (2002) 35, 469]. In three cases (sodium, magnesium and mercury), a detailed consideration proves that this representation is accurate in a fairly wide energy range. Moreover, the related momentum transfer cross sections are tailor-made for studying "elastic" electron transport in terms of the two-term solution of the Boltzmann equation: Not only are the resulting swarm transport coefficients adjustable to the experimental values, but above all they are calculable very easily because the unnormalized energy distribution is obtainable analytically. The ample saving in computational effort is exploited in order to test the Wannier-Robson "momentum-transfer approximation"; it is found that, in these cases of resonance-dominated cross sections, the latter method can be so accurate that it can be used to recover the momentum transfer cross section from experimental data algebraically. In the margin, a model profile is presented that gives rise to negative differential conductivity.

physics.atom-ph↗