Analytical solution to the Langmuir spherical problem
Dimitar G. Stoyanov
TL;DR
This paper provides an analytical solution to the Langmuir spherical problem, deriving a parametric form expressed via Airy functions, and applies it to the electric potential in a spherical vacuum diode with limited electron flow.
Contribution
It introduces a novel analytical solution to the Langmuir spherical problem using Airy functions, applicable to spherical vacuum diodes.
Findings
Derived a general parametric solution in terms of Airy functions.
Solved for electric potential in a spherical vacuum diode with limited electron flow.
Provides a new analytical framework for spherical plasma problems.
Abstract
The current paper discusses and analytically solves the Langmuir spherical problem. A general solution has been obtained in a parametric representation and expressed in terms of the Airy function. A solution to the electric potential in a spherical vacuum diode with limited electron flow has also been reached.
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Taxonomy
TopicsGyrotron and Vacuum Electronics Research · Vacuum and Plasma Arcs · Plasma Diagnostics and Applications