Correction of spherical aberrations of lenses by partially compensated beam parts

A self-consistent thermal compensation exhibits a radially dropping degree of space charge compensation. The amount of the central compensation as well as the radial variation is only dependent on the temperature of the compensating particles with respect to the potential variation in the uncompensated beam. This non-uniform compensation provides stronger beam spreading for the outer part of the beam and therefore may compensate the spherical aberration of lenses, when used in proper position of a beam line. culated this effect in a one-dimensional radial self-consistent analysis of space charge compensation for different ion temperatures and compared the radial behaviour of the field strength with a cubic power law, which gives best aberration correction. An ion temperature of 13% of the potential energy of the non compensated electron beam fits well for large radii with the cubic power law. We also present a schematic drawing for the construction of such a correction unit.