Systems for forming proton beams of micron diameters

The production and application of a nuclear microprobe using a beam of protons at MeV energies are discussed. Considerable attention is paid to matrix analytical and numerical methods for designing quadrupole beam-forming systems. Quadrupole and axisymmetric focusing systems are compared. The possibility of designing a high-frequency microprobe is considered. The effect of the space-charge distribution of the beam on its evolution in the microprobe optics is studied