Monte-Carlo simulation on discrete space charge effects of space charge lenses

The discrete space charge effects of space charge lenses consisting of electron space charge cloud are studied by Monte-Carlo simulation, taking into account the stochastic Coulomb interaction between the focused charged particles and the electrons forming the space charge cloud. Both theoretical models and practical designs are studied. The simulation results show that in general the discrete space charge effects are noticeable and may set limits On high resolution performances of space charge lenses. The energy broadening and lateral beam spreading can be reduced if space charge clouds with small average charge density but with large lateral gradient of the charge density are used. The defocusing caused by random deflection can be reduced further by using a combined lens to shorten the total focal length and working distance, and thus high resolution call be obtained.