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The present work represents a theoretical study for the correction ofspherical aberration of an immersion lens of axial symmetry operating under theeffect of space charge, represented by a second order function and preassignedmagnification conditions in a focusing of high current ion beams. The spacecharge depends strongly on the value of the ionic beam current which is foundto be very effective and represents an important factor effecting the value ofspherical aberration .The distribution of the space charge was measured fromknowing it's density .It is effect on the trajectory of the ion beam wasstudied. To obtain the trajectories of the charged particles which satisfy thepreassined potential the axial electrostatic potential was represented by afourth order polynomial function . To measure the optical properties of thelens and to obtain the electrode shape of the electrostatic lens we have solvedPoissonequation.

Correction of Spherical Aberration of an Immersion Lens Operating Under Space Charge Effect Described by a 2nd Order Equation