On matching a beam with a spatially-homogeneous quadrupole channel

The beam acceptance at the inlet of a channel with spatially homogeneous quadrupole focusing does not remain constant but rotates at a frequency of RF field. That is why the matching of the beam of an electrostatic injector with a linear accelerator remains a serious problem. Laws of hardness variation over the length of the initial matching section are suggested which ensure practically ideal matching for a micro-canonical distribution in a wide range of beam current phase density variation. The efficiency of the suggested matching instrument is shown to be weakly dependent on both the current and type of distribution up to the phase current density in the core of a beam equal to 1 A/cmxmrad