Space lattice focusing: on the way to extremely low accelerated beam divergence

It is widely known the multiple channel acceleration is the most adequate way to save initial beam parameters due to the possibility of decreasing Coulomb forces in intensive input beams. To keep beam initial emittance and divergence for high enough specific value of the injection ion beam during acceleration the input beam should be split on multiple beams and every the micro beam must be screened from each other as much as possible. On the other hand, it is very much desirable to keep the total macro beam rather compact transversally and try to accelerate all the micro beams within the same accelerator structure at the same RF field. Attempts to use conventional quadruple focusing channels both RF and electrostatic for multiple beam acceleration usually lead to extremely complicate and bulky construction of the structure. We suppose multiple beam linac channels with alternating phase focusing (APF) as more adequate for the purpose while they are limited by less values of beam capture into acceleration process. The original version of the quadruple RF focusing multiple beam system called space lattice focusing (SLF) is supposed for getting intensive ion beam with extremely low divergence. The basic principles of the theoretical approach as well as some possible advances and restrictions for the practical use in RF linac are supposed to be discussed