Image Effects on the Transport of Intense Nonaxisymmetric Charged Beams

TL;DR

This paper analyzes how conducting pipes influence the equilibrium and shape of intense nonaxisymmetric charged beams, providing exact solutions and proving the homogeneity of beam density inside arbitrary-shaped conductors.

Contribution

It offers an exact analytical expression for electrostatic potential and proves beam density homogeneity inside conducting channels of any shape.

Findings

Exact electrostatic potential for cylindrical pipe and elliptical beam

Homogeneous beam density inside arbitrary-shaped conductors

Cross-sectional area remains unchanged by conducting pipes

Abstract

The effect of conducting pipes on the equilibrium of intense nonaxisymmetric continuous beams of charged particles is investigated. For a cylindrical pipe and an elliptical beam, we obtain an exact closed form analytical expression for the electrostatic potential. Using a variational principle, we then explore the distortions that equilibrium beams suffer due to the conducting channel. Finally, we present an exact proof that despite the nonlinear forces acting on beams of arbitrary cross section inside conducting pipes of arbitrary shape, the density of these beams remains homogeneous and their cross sectional area remains the sa me as the one in free-space.