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

Abstract

In this paper we analyze the combined envelope-centroid dynamics of magnetically focused high-intensity charged beams surrounded by conducting walls. Similar to the case where conducting walls are absent, it is shown that the envelope and centroid dynamics decouple from each other. Mismatched envelopes still decay into equilibrium with simultaneous emittance growth, but the centroid keeps oscillating with no appreciable energy loss. Some estimates are performed to analytically obtain characteristics of halo formation seen in the full simulations.

Off-axis stability of intense continuous relativistic beams

“…A more detailed analysis of the centroid nonlinear dynamics reveals that the onset of the instability is due to a bifurcation of the equilibrium solution r 0 = 0 caused by a collision with an unstable fixed point already present in the nonrelativistic case. 3,6,12 In Ref. 9 an analogous stability condition was derived for the trajectory of a single particle located at the centroid position.…”

“…8 For the particular case of intense, continuous, and round beams propagating with nonrelativistic velocities throughout a conducting cylindrical pipe, it has been shown that despite the occurrence of an unstable orbit in the centroid dynamics of off-axis beams, 3 this orbit alone cannot be responsible for pushing rms matched beams toward the wall. 6 It was also found that there is virtually no coupling between the centroid oscillation and the beam particles dynamics, which prevents conversion of the centroid motion energy into beam particles thermalization and the overall degradation of the beam quality. 6 These results indicate that off-axis dynamics do not impose severe limitations in the transport of such beams.…”

“…6 It was also found that there is virtually no coupling between the centroid oscillation and the beam particles dynamics, which prevents conversion of the centroid motion energy into beam particles thermalization and the overall degradation of the beam quality. 6 These results indicate that off-axis dynamics do not impose severe limitations in the transport of such beams.…”

“…This state is most desirable in practical beam transport devices because it prevents emittance growth, halo formation, and, ultimately, beam losses. 6,10,[13][14][15][16][17] Setting r b Љ= 0 in Eq. ͑10͒ and solving for the perveance, we obtain…”

“…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.…”