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While no simple image method exists that yields an exact solution for the potential around the parallel conducting cylinders of a quadrupole electrostatic lens, we have found that using two line image charges in each cylinder makes an excellent approximation. Graphs are presented of the equipotentials and contours of electric field squared for different rod spacing.

We present a condensed perspective on the contribution of studies of normal and peculiar hot stars to delineating facts/implications of chromosphere/coronae occurring throughout the HRD: (1) empirical evidence of nonradiative heating in hot stars atmospheres, with a strong continuum opacity dependence of the Te(r)-rise, like the Sun; (2) the observed existence of a multi-regional atmospheric structure, linked to nonradiative energy (Te-rise, grad ρ-fall) and mass (grad ρ-fall, Te-change) fluxes, like the Sun; (3) an observed long-term (decades) variability of all atmospheric regions and all energy and mass fluxes, in some well-observed stars, which implies that the character of atmospheric regions follows, not produces, the character of the stellar fluxes; (4) the strong suggestion by (2) and (4) of a stellar interior origin for the mass flux; (5) a representation/delineation of (1)-(2), and of the solar, hot star contrast, via the Temperature-Control-Bracket logic; (6) a clarification/modeling of the ensemble interior and atmosphere via an expanded Eddington, general, nonEquilibrium thermodynamics.

If I understand correctly, this session of the Symposium on Mass-Loss and Evolution of O Stars aims at clarifying the merits and demerits of four “theories” for the observed, nonthermal mass-loss from these stars. Hearn has summarized what he considers to be the essential characteristics of each of the four, especially relative to a set of questions which, he considers, put the observational requirements on the “theories” in focus. Representatives of each of the “radiation-pressure initiated, radiative-equilibrium controlled”, “hot corona”, and “warm corona” alternatives have elaborated on Hearn's summary, to stress what they consider essential. So, now, I would do the same for what we caricature as the “imperfect wind-tunnel” model — not theory, which I assert does not yet exist — both for nonthermal mass-flux, and for other observed nonthermal phenomena, in stellar atmospheres generally, not just in O stars particularly. I assert, that in studying nonthermal mass-flux from O stars, if you limit your attention only to nonthermal mass-flux, and only to O stars, you handicap, a priori, your chance to understand what is required for the general model of a stellar atmosphere, in order to produce this variety of nonthermal phenomena observed, alike in all varieties of stars.

I begin by stating very explicitly and unambiguously that I completely disagree with any idea that a stellar atmosphere can be in any sense a boundary of the star, or that the atmosphere sets boundary conditions on stellar structure. Such an idea is what underlies all the single-layer, LTE atmospheric models, which misdirected atmospheric studies for so many years by introducing a false separation between “normal” and “extended” atmospheric phenomena. On the contrary, I assert that a more correct physical picture for the atmosphere than as a boundary comes from the characterization of star and atmosphere as:(1) The STAR is: a concentration of matter and energy, C (M, E), in its parental environment, the interstellar medium (ISM); with boundary conditions on stellar structure being set by the way one models (a) storage modes for matter and energy in the star and ISM, and (b) energy generation in the star.

We suggest that some general questions of irreversibility and of quasi-Equilibrium vs. non-Equilibrium configurations (terminology is explained in the text), with respect to both biophysical and physical structures, can be clarified by generalizing results from investigations of stellar structure in relation to its environment. Such work has evolved from considerations of the stellar atmosphere as a transition zone between the quasi-Equilibrium stellar interior and the non-Equilibrium interstellar medium. As opposed to suggestions of irreversibility originating in the large (Gal-Or, e.g.), we suggest that the origin is local, in coupling between different storage modes for matter and energy. In contract to suggestions of non-Equilibrium biophysical structures arising in fluctuations from a quasi-Equilibrium state (Prigogineet al.), we suggest that they arise via condensations within a non-Equilibrium, steady-state, unstable environment. Generalization from stellar prototype studies of the process of such concentration indicates that the general process of forming structures in the Universe follows a hierarchy of such greater degree ofEquilibrium concentrations formed in lower degree ofEquilibrium environments.

The Organizers of this Symposium asked that I make some introductory remarks on the general problems of extended atmospheres, the degree of common behaviour among stars having such a feature, and how the Wolf-Rayet stars may contribute to the progress of our inference in this area. In a Symposium entitled Wolf-Rayet and High Temperature Stars, not ‘Stars With Extended Atmospheres’, the implication of your charge to me is clear. You are implicitly assuming that the Wolf-Rayet phenomenon is primarily one of extended atmospheres. I can indeed give you a succinct summary of my outlook on these three points under such an implicit assumption, elaborating in more detail only to the extent as is necessary in order to be specific. And, as I am sure you had planned, because my outlook is considerably contrary to this implicit assumption, at least my remarks will spark controversy from the outset of this Symposium. I would like to emphasize that it is the summary of outlook to which I attach most weight and which I think is correct. The more specific details may change as we develop the mosaic of the summary, which has two main points. First, when you ask the physical picture of the general structure of a stellar atmosphere, you will eventually reach the conclusion that part of this general structure is an extended atmosphere for all stars. A focus upon some class, or classes, of them as exhibiting ‘extended atmospheres’ simply reflects the degree to which particular observations focus upon a particular part of the atmosphere as a function of the particular characteristics of the considered star. Second, in this context, I think that the implication that the Wolf-Rayet phenomenon is primarily one of extended atmospheres is incorrect. You are confusing a single system with a more deep-seated disease. My emphasis will lie on the disease as a whole, and the Wolf-Rayet stars as a guide to its diagnostics. I want to emphasize that this outlook on the general model of an atmosphere has developed jointly with K. B. Gebbie, J-C. Pecker, and F. Praderie; so most of what I say simply reflects this joint work.

Chromospheres-coronas satisfy the last two of the proposed classification schemes: inadequacy of the classical atmosphere (CA) model to represent observations and a priori rejection of the CA model So we survey the question of what is required for more knowledge from the standpoint of asking what conceptual modifications will increase knowledge and what new observations are required. We stress that continued progress requires a continual interchange of ideas between the solar situation and the range of stellar situations.

WE PRESENT here a summary of a current investigation of the radiative transfer problem in the solar corona, in its effect upon the excitation state of coronal ions. [Complete details of the investigation will be published elsewhere; C. PECKER and THOMAS”).] The investigation is one phase of a systematic treatment of the influence of ionic configuration and physical environment upon the excitation state of an ion. We have called this treatment the New Spectroscopy, to contrast it with the Local Thermodynamic Equilibrium treatment of a gas, where the excitation state of an ion depends only upon the local electron temperature, and is independent of ionic configuration or the physical environment. The situation usually assumed for the solar corona falls, conceptually, intermediate to the LTE situation and that of the chromososphere and photosphere. The coronal optical thickness is taken to be so small that any radiation field produced by the corona itself has negligible effect upon excitation of the ions. Consequently, the excitation state depends upon ionic configuration, but only locally upon physical environment. That is, the excitation state at a point depends only upon the values of electron density, electron temperature, and photospheric radiation field at the point. It does not depend upon the atmosphere as a whole-upon values of electron density and temperature at other points in the atmosphere-as it would were the optical thickness of the atmosphere large enough to produce significant self-emission. In the present work we have asked whether the assumption of negligible optical thickness for the corona is valid and, if not, what is the influence of coronal self-emission as a function of coronal optical thickness. We show that an upper limit on the effect of coronal self-emission in any transition comes from isolating the transition to solve the radiative transfer problem in it. That is, the actual atomic configuration is replaced by that of the 2-level-atom. Thus this upper limit does not depend upon ionic configuration, but only upon physical environment. An estimate of the largest optical depths likely to be encountered in resonance transitions of the most abundant ions falls below 104. At coronal densities, the ratio of collisional to radiative de-excitation, c, does not exceed 10-r. In this situation, the excitation effect due to coronal self-emission in some transition can be expressed as a function only of the coronal optical thickness in this transition, for an isothermal, constant-ns corona. Numerical results are given in the complete investigation cited. Here, we note only that a detection of the presence of a significant, optical depth in some line, by observing a self-reversed emission profile, appears to demand an optical thickness exceeding a value which lies between 10 and 100.

An attempt is made to investigate features of the hydrogen spectrum which may be unambiguously interpreted to specify certain gross features of the structure of the chromosphere. A theoretical analysis of the data to be obtained at the 1952 eclipse is given. Resolution of the dilemma between radio and optical observations of the outer solar atmosphere is desired. On the basis of thermodynamic equilibrium and an atmosphere transparent to its own radiation, the computed Balmer decrement is in every case to high. Departures from thermodynamic equilibrium are included by introducing the standard b sub n which is defined so as to help give agreement between the theoretical and observed Balmer decrement. Self-absorption effects are also included, and no attempt is made to specify the electron temperature Tau sub epsilon. From a comparison of 2 methods of estimating the hydrogen density gradient, a demonstration of the direction of deviation of the chromosphere from thermodynamic equilibrium is obtained in which b sub n > b sub n+k > 1, where the subscripts refer to the quantum numbers. The application of the proposed methods to the reduction of the 1952 eclipse data should provide values of Nu , Tau sub epsilon, Delta Tau sub epsilon and Delta Nu sub epsilon at a number of heights in the atmosphere.

La récente proposition de Schatzman d'adopter un modèle acoustique de la granulation solaire trouve un appui dans une discussion du modèle turbulent de la granulation. On suggère cependant que la limite supérieure de la taille des granules reflète l'opacité acoustique de l'atmosphère. On suggère également que le maximum secondaire de 15.000 km. dans l'étude de granulation et de turbulence de Frenkiel-Richardson-Schwarzschild, semble établir l'existence d'un réseau de convection cellulaire ayant ce diamètre caractéristique., Thomas Richard N. Commentaire sur la granulation solaire. In: Bulletin de la Classe des sciences, tome 40, 1954. pp. 621-624.

A form of representation of the drag curve at supersonic velocity is suggested. Only two unknown constants are required for each shell, hence firings at two velocities fix the function. For the case of a conical head and square base, the problem can be reduced to one constant. Good experimental confirmation is found.

Stellar atmosphere radiation field quantity vs quality, deriving electron temperature as function of tau

Temperature control bracket energy equation as measure of temperature distribution in pure hydrogen stellar atmosphere, considering electron energy and radiation field