Radial Matching Section of RFQ revisited

Radial Matching Section (RMS) which is the crucial part of Radio Frequency Quadru/-pole (RFQ) Linac matches a stationary input beam to the time-varying focusing of RFQ. In this paper, the theory of RMS has been examined comprehensively from the point of view of the continuity of the potential function and the electric field. A methodology has been developed to include higher order term in the RMS potential function and an improved form of the focusing profile is derived which is also verified by a multi-particle tracking code. The continuity of various focusing and vane profiles for ideal RMS is also determined.