BEAM EMITTANCE GROWTH CAUSED BY A NONUNIFORM ION DENSITY

An expression for the root-mean-square emittance of an ion beam is derived in terms of the distribution of particle density at the plasma boundary. Three distributions are considered: a uniform plasma, a linear variation due to B X v effects, and a quadratic variation. It is shown that for the nonuniform distributions additional terms enter the expression for beam emittance causing emittance growth. Experimental data, in agreement with the model, are presented for both positive and negative ion beam systems. Applying the model to the data provides values of ion temperature within the ion source and the degree of nonuniformity across the plasma boundary for several different ion source systems.