Anisotropies in a charged particle beam

This paper examines the anisotropies of a charged particle beam moving into a linear focusing channel. Considering a high-intensity ion beam in space-charge-dominated regime and large mismatched root mean square (RMS) initial beam size, a fast increase in spatial beam anisotropy is observed. Calculations presented here are strong evidence that this anisotropy is responsible for the beam's equipartition. It is shown that particle-particle resonances and wave-particle resonances lead to anisotropization of the beam, i.e. both the envelope and emittance ratios different from unity. It indicates that this anisotropy is responsible for the beam's equipartitioning and suggest that the beam remains equipartitioned even when exhibiting a macroscopic anisotropy, which is characterized by the following properties: the development of an elliptical shape with increasing size along one axis, the presence of a coupling between transversal emittances and halo formation along a preferential direction.