Li Wang et al 1995 J. Phys. D: Appl. Phys. 28 1791 doi:10.1088/0022-3727/28/9/006
Li Wang, J Orloff, D Book and Tiantong Tang
Show affiliationsIt is well known that the spherical aberration is positive for an axisymmetric electrostatic lens that is empty and free from space charge. However, a space charge profile can be tailored to introduce negative spherical aberration in such a lens. This could be useful for modern high-resolution focused ion beam systems. A new technique is described for calculating potentials and their derivatives and is used to calculate the trajectories of charge particles propagating in regions in which space charge is present. The charge density and potential are expanded in powers of r and z and the Poisson equation is solved term by term. The method has been implemented numerically for axisymmetric configurations. An illustrative example is presented.
41.85.Gy Chromatic and geometrical aberrations
41.85.Ne Electrostatic lenses, septa
41.85.Lc Particle beam focusing and bending magnets, wiggler magnets, and quadrupoles
02.60.Lj Ordinary and partial differential equations; boundary value problems
Issue 9 (14 September 1995)
Li Wang et al 1995 J. Phys. D: Appl. Phys. 28 1791
L Wiesenfeld et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1319
J. Strempfer et al 1997 Europhys. Lett. 40 569
Arnd Bäcker and Roman Schubert 2002 J. Phys. A: Math. Gen. 35 527
R J Radwanski 1987 J. Phys. F: Met. Phys. 17 267
Nikodem J Popławski 2006 Class. Quantum Grav. 23 2011
Pia Astone et al 1994 Class. Quantum Grav. 11 2093
A Hizal 1978 J. Phys. D: Appl. Phys. 11 261
Xiaobing Fan et al 2006 Phys. Med. Biol. 51 211
L O Becerra et al 2006 Metrologia 43 426