Obtaining 1-10Â nm optimal beam spot size in the magnetic quadrupole nanoprobe

In this study the matrix method of embedding in the space of the phase moments is used to solve the non-linear equations of motion. With this method all the advantages of the linear differential equations are used, including the independence of the matrizant of the non-linear motion on the choice of the initial point of the phase space. For the same phase volume (or beam current) the spot size is minimized (optimized) by a set of two optimal matching slits: objective and divergence slits. This optimal spot size is a function of the four-dimensional emittance and both geometric and optical parameters of the system. Geometric parameters include total system length, lens lengths, drift spaces, object and working distances, minimum attainable slit openings while optical parameters include demagnifications, spherical and chromatic aberrations. The optimal beam spot size and appropriate optimal slits have been found as functions of the emittance of the system for different geometries. It is shown that the octuplets investigated here allow the possibility to obtain 1-10 nm optimal beam spot sizes. The influence of the beam energy spread on the optimal beam spot size is studied.