Beam end erosion

Abstract

The time evolution of the line charge density and energy at the ends of an initially rectangular ion bunch due to the space charge of the bunch are measured and found to be in good agreement with a one-dimensional dynamical theory. The ends erode at the space-charge wave speed into the bunch, and the end particles move at twice that speed away from the bunch.

Longitudinal confinement and matching of an intense electron beam

“…By solving the one-dimensional fluid equations through the method of characteristics, we can obtain line density and velocity analytical wave solutions. 21 Figure 1 is an illustration of the line density and velocity wave solutions at two given instants. It details the expansion and rarefaction rates, as well as the regions within the beam where the longitudinal electric fields are approximately equal to zero.…”

“…However, gradients in the line density near the bunch ends lead to longitudinal electric self-fields that push particles in the bunch ends away from the central region, causing the bunch to expand longitudinally at a rate of 2C s . [19][20][21][22] This ablation of the bunch ends is also accompanied by a rarefaction of the ends which erode into the bunch at a rate of C s .…”

Experimental study of space–charge waves in heavy ion beams

“…Simply measuring the time delay of the leading edge of the beam pulse at two different locations is not sufficiently accurate because of the relatively slow turn-on time of the beam pulse ($50-200 ns), and because longitudinal dynamics, including erosion of the beam ends [6], alters the beam waveform as the beam travels.…”

Notes on Longitudinal Dynamics in UMER

“…Longitudinal expansion of the UMER beam is governed, to first order, by the onedimensional cold fluid model (CFM) [1]. For an initially-rectangular beam, this model predicts erosion of the beam ends at a speed dependent on the "sound velocity," …”