Alternative approach to the numerical synthesis of the dense-ion-beam focusing systems - art. no. 046501

An alternative approach has been developed to the numerical synthesis of io n-beam focusing systems that prepare the dense laminar ion beams with the r equired profile of the ion trajectories. Conventionally an ill-posed synthe sis problem arises in such cases, and only low-density beams with no magnet ic field are treated. Instead, we compute both the electric and magnetic fi elds by considering two well-posed problems, the first for the equivalent p otential Q and the second for the electric potential U. An analytical solut ion for Q for the specific case of an axial system has been found and a sel f-consistent method of satisfying the axial boundary conditions for Poisson 's equation in U is described. It is shown that the beam can be focused whi le preserving its laminar structure and the required profile when applying various superpositions of both the electric and magnetic fields.