Centroid motion in periodically focused beams

Abstract

The role of the centroid dynamics in the transport of periodically focused particle beams is investigated. A Kapchinskij-Vladimirskij equilibrium distribution for an off-axis beam is derived. It is shown that centroid and envelope dynamics are uncoupled and that unstable regions for the centroid dynamics overlap with previously stable regions for the envelope dynamics alone. Multiparticle simulations validate the findings. The effects of a conducting pipe encapsulating the beam are also investigated. It is shown that the charge induced at the pipe may generate chaotic orbits which can be detrimental to the adequate functioning of the transport mechanism.

Combined centroid-envelope dynamics of intense, magnetically focused charged beams surrounded by conducting walls

“…The present results extend the previous investigation on the coupling of envelope and centroid dynamics in the absence of surrounding walls. 6,7 In these previous works it has been possible to show formally the uncoupled nature of the combined dynamics. Here we make use of analytical estimates as well as Poincaré plots and full simulations to conclude likewise.…”

“…The conclusion is that the coupling of the centroid and envelope dynamics is absent in the present case of beams surrounded by conducting walls, similar to what happens when walls are not present. 6,7 It should be remarked that while the beam preserves axisymmetry with respect to its own center, it cannot exchange energy with the centroid motion, since under this symmetry condition the centroid is unaware of the beam size; Eq. ͑8͒.…”

“…One thing we know for sure though is that when the walls are absent, centroid and envelopes become uncoupled. 6,7 Another key information, given by Gauss' law, is that even in the presence of conducting walls, surface charges induced by circular beams perfectly centered at the symmetry axis do not act in the inner region r Ͻ r w . These two facts suggest that provided the centroid oscillations are moderate, an initially circular beam approximately preserves its circular shape at least during the initial stages of the dynamics.…”

“…6,7 Under these conditions there is no available channel along which the excess energy of a possible centroid motion could be thermalized or converted into emittance, which is ultimately associated with the rms size of the beam envelope. The fact is that one has not the needed nonlinearity to secure the coupling between the envelope and the centroid.…”

Off-axis stability of intense continuous relativistic beams

“…1,2 In that regard, a matter of recent interest is to investigate the physics of beams displaying some misalignment with respect to the symmetry axis of the focusing field. [3][4][5][6] Small deviations between the beam injection direction and the focusing field axis may drive off-axis beam dynamics that are potentially hazardous to the transport. Offaxis dynamics can ultimately lead to collision between the charges and the conducting walls surrounding the system, causing particle beam losses, activation of the walls, 7 and pulse shortening in high-power microwave sources.…”