Space-charge dominated beam envelope transport with rotatable axes

In normal paraxial studies of self-interacting accelerator beams, coupling between x- and y-motions that rotate the elliptical beam envelope is considered undesirable. Yet in some applications, such as electron beam lithography and electron beam transmission X-ray computed tomography, external focussing elements cause this coupling by design. To meet this need, the classical 4th order Kapchinskiy-Vladimirsky (KV) differential equations have been generalized to include beam envelope rotation. This set of 10th order generalized envelope equations based on the KV distribution were applied to a 600 mA, 130 keV beam moving through a low-pressure nitrogen gas, where the absence and presence of complete plasma neutralization along its path cause the beam to diverge and converge