The dynamical behavior of a bounded plasma system (BPS) is, by definition, characterized by the simultaneous and self-consistent interaction of the plasma itself, its material boundaries. and whatever external circuit...
The dynamical behavior of a bounded plasma system (BPS) is, by definition, characterized by the simultaneous and self-consistent interaction of the plasma itself, its material boundaries. and whatever external circuit(s) there may be. A full theoretical description of these systems. which are of relevance in a variety of fields (e.g., plasma technology), must involve (microscopic or macroscopic) evolution equations for the plasma, Maxwell's equations for the fields, boundary conditions for the plasma and the fields, and the external-circuit equation(s). By ''BPS simulation'' we mean obtaining theoretical (including numerical) results from models accounting, at least conceptually. for all the basic features mentioned above. This paper is exclusively concerned with microscopic (i.e., kinetic and particle) BPS simulation. A very general system of basic equations for kinetic BPS simulation is proposed. With the PD (''plasma device'') codes from U.C. Berkeley [BIRDSALL, C. K., IEEE Trans. Plasma Sci. 19 (1991) 651, particle simulations of (1d, 3v) BPS's can now be routinely performed by everybody. Particular emphasis is laid on an alternative method called ''trajectory simulation'', which has shown great potential for kinetic BPS simulation with high accuracy and resolution. From the point of view of nonlinear dynamics, BPS's are rather complex dissipative systems exhibiting, in particular, regular and chaotic attractor states. For their proper interpretation, an advisable (if not indispensable) first step is to carefully study relatively simple, but still representative ''archetypal'' BPS's, such as the Pierce diode [GODFREY, B. B., Phys. Fluids 30 (1987) 15531 and the single-emitter plasma diode or ''KDSI'' [CRYSTAL, T. L., et al., Phys. Fluids B 3 (1991) 244]. These systems and representative results obtained therewith are surveyed, and both recent developments and future perspectives of BPS physics are addressed.
An analytic solution to the BCS equation for the superconducting transition temperature has been obtained. Instead of the electron-phonon interaction being assumed to be a constant in a certain range as was done in BC...
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An analytic solution to the BCS equation for the superconducting transition temperature has been obtained. Instead of the electron-phonon interaction being assumed to be a constant in a certain range as was done in BCS theory, it has been considered varying with energy, a case more physical in nature. The resulting equation for the superconducting transition temperature T(c) reduces to the standard BCS form when T(c) is small but this equation does not put any higher limit on T(c). The gap parameter at the absolute zero has also been analytically obtained. These equations have been successfully applied to the high temperature superconductors.
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