Charged particle beam transport for a cyclotron facility - Merry, Corinne Margaret (Department of Physics, 2016)
We develop a number of new techniques and systems to be used in the design of beamlines for charged particle beam transport. A few of these refer specifically to beamlines to or from a cyclotron, while others may be used in beamlines from any accelerator. In the former category, we develop a method for determining the eigen-ellipsoid in all six dimensions of phase space, when the beam under consideration is to be (a) extracted from a cyclotron, or (b) injected into a cyclotron. We also develop an alternative method to (a) above, which uses the data derived from tracking (i) central momentum particles through the extraction elements of an accelerator in 4-dimensional (x, x´, y, y´) phase space and (ii) a single particle with higher momentum. For this purpose we expand the convenient E-matrix formalism from a 2-dimensional treatment to a 6-dimensional treatment, and relate this to the more usual σ-matrix formalism. We describe the eight possible symmetry types of beams transport systems and examine their group properties. We also examine the second-order aberrations in these systems. We use the symmetry properties to examine various configurations of two quadrupole triplets. This system may be used to achieve unit magnification, as is well known: or variable magnification in one or both of the horizontal or vertical planes, independently of the beam parameters, as we describe. We also develop a system of quadrupoles which may be used for independent horizontal and vertical beam control. We calculate the optimum spacing and field strength of these quadrupoles. Dipole systems which are used to control the dispersed rays are discussed. In particular we consider a system of two quadrupoles between two dipoles: this system has the least number of beamline elements necessary to control the position and direction of the dispersed ray while simultaneously permitting momentum-selection. We discuss the principles of transfer beamline design and illustrate these (and the techniques described above) by reference to the design of a specific transfer beamline between cyclotrons. The design of a specific external beamline is also described and used to illustrate the techniques developed.