Based on the idea of D. Gabor [1] space charge lenses are under investigation to be a powerful focussing device for intense ion beams. A stable confined electron column is used to provide strong radially symmetric electrostatic focussing, e.g. for positively charged ion beams. The advantages of Gabor lenses are a mass independent focussing strength, space charge compensation of the ion beam and reduced magnetic or electric fields compared to conventional focussing devices. Collective phenomena of the electron cloud result in aberrations and emittance growth of the ion beam. The knowledge of the behaviour of the electron cloud prevents a decrease of the beam brilliance. Numerical models developed to describe the electron confinement and dynamics within a Gabor lens help to understand the interaction of the ion beam with the electron column and show the causes of non-neutral plasma instabilities. The diagnosis of the electron cloud properties helps to evaluate the numerical models and to investigate the influence of the ion beam on the confined non-neutral plasma.Based on the idea of D. Gabor [1] space charge lenses are under investigation to be a powerful focussing device for intense ion beams. A stable confined electron column is used to provide strong radially symmetric electrostatic focussing, e.g. for positively charged ion beams. The advantages of Gabor lenses are a mass independent focussing strength, space charge compensation of the ion beam and reduced magnetic or electric fields compared to conventional focussing devices. Collective phenomena of the electron cloud result in aberrations and emittance growth of the ion beam. The knowledge of the behaviour of the electron cloud prevents a decrease of the beam brilliance. Numerical models developed to describe the electron confinement and dynamics within a Gabor lens help to understand the interaction of the ion beam with the electron column and show the causes of non-neutral plasma instabilities. The diagnosis of the electron cloud properties helps to evaluate the numerical models and to investigate the influence of the ion beam on the confined non-neutral plasma