Intense Ion Beam Transport and Space Charge Redistribution

Abstract

The main laws that govern the charge redistribution in space charge dominated (SCD) beam during its transport through a periodical channel with solenoidal focusing are considered. Physical mechanisms of halo production and establishment of uniform distribution inside core for matched and mismatched beams are described. The computer codes KERN+HALO generated for redistribution process of charge density and kinetic and potential energies visual representation are described. We have a clear knowledge of matched (or ideal) beam only in case when space charge does not change a frequency of transverse oscillations. The matched (or ideal) beam is a one which transverse behavior is repeated (or has a smooth change) from one period to the next. The question What a matched beam imply?” is arisen when the above definition is extended on the case when space charges essential for transverse oscillation frequency. We can denote that ideal beam has well-known K-V distribution and this distribution must be used for focusing field calculation and for a choice of bore radius. But real beam distributions differ from K-V one and its redistribution during beam transport leads to beam size and emittance growths. It means that such ideal beam definition results in an serious error of bore radius. The SCD-beam investigations in channel with different initial beam transverse distributions were made by authors in order to answer on the above question. A simple model must be chosen for better understanding of process of SCD-beam redistribution. It can be a continuous cylindrical beam transporting in longitudinal magnetic field. In this case a Coulomb force calculation is very much simplified. Within the context of this model there are only a few characteristics for understanding the cause and effect of halo formation. Only distributions with beam density growth(or keeping constant) from the origin to outlying area were considered as initial ones [1]. Under above considerations beam motion is described by following equations ′ ′ x = eB(z) m0cβγ ′ y + 2I I0 (βγ ) 3 Q(Z) r ⋅ x ′ ′ y = − eB(z) m0cβγ ′ x + 2I I0(βγ ) 3 Q(Z) r2 ⋅ y 