Potential and field distribution in a cylindrical tube filled with a dielectric material with a centre hole

Abstract

The paper presents a method of analysis of potential and field distribution in a cylindrical tube (metallic), covered at both ends with metallic plates, and containing a dielectric cylindrical shell whose axis coincides with the axis of the cylinder. The cylindrical surface and lower end are maintained at ground potential and the top plate is insulated and maintained at high potential. The resulting Laplace's equation is solved using the method of separation of variables. The constants appear in the resulting equation are found from the boundary conditions followed by representation of the functions satisfying orthogonality condition in cylindrical co-ordinates. If the field intensity exceeds the breakdown limit,

<span style="font-size:12.0pt;line-height:115%;font-family:" times="" new="" roman","serif";="" mso-fareast-font-family:"times="" roman";mso-ansi-language:en-in;mso-fareast-language:="" en-in;mso-bidi-language:hi"="" lang="EN-IN">the resulting breakdown of the gas leads to plasma generation inside the structure, which can provide a convenient method of generation of laser beam.</span>