Beam Amplitude Behavior upon Crossing a Linear Coupling Resonance with Damping in One Dimension

We have shown that in a one-particle model, and for a linear sum resonance it is possible to obtain a small growth of vertical beam dimensions relative to that of the horizontal dimensions by having sufficient vertical damping. Whether the one-particle model of this paper is an adequate approximation to the n-body problem of a beam, subject to a clearing electrode, has not been studied. However, the interesting results obtained here, strongly motivate further study of this point, especially as the calculation suggests the possibility of generally controlling resonant beam growth by means of damping electrodes.