  The present work represents a theoretical study for the correction of
spherical aberration of an immersion lens of axial symmetry operating under the
effect of space charge, represented by a second order function and preassigned
magnification conditions in a focusing of high current ion beams. The space
charge depends strongly on the value of the ionic beam current which is found
to be very effective and represents an important factor effecting the value of
spherical aberration .The distribution of the space charge was measured from
knowing it's density .It is effect on the trajectory of the ion beam was
studied. To obtain the trajectories of the charged particles which satisfy the
preassined potential the axial electrostatic potential was represented by a
fourth order polynomial function . To measure the optical properties of the
lens and to obtain the electrode shape of the electrostatic lens we have solved
Poissonequation.
