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

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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.