Fusion is a combining of atoms to form other atoms, which occurs when their nuclei get close enough to each other. The energy that powers the sun actually comes from nuclear fusion. The realization of fusion in laboratory conditions requires 1000 trillion watts of a charged particle beam over a period of approx. 10 billionth of a second (10 nanoseconds) to ignite a target of thermonuclear fuel. Due to natural repulsion of particles via Coulomb forces, beam space charge effects remain the key problem for designers of high intensity accelerators for heavy ion fusion. The subject of the RIKEN Symposium was to review the present understanding of space charge phenomena and to discuss possible solutions for unresolved problems.