ThirdOrder Charged Particle Beam Optics
Abstract
The motion of a charged particle through a magnetic field configuration can be described in terms of deviation from a certain ideal trajectory. One uses power series expansion of the phasespace coordinates to obtain the transfer matrices for a particular optical system. In this thesis we present a complete thirdorder theory of computing transfer matrices and apply it to magnetic elements in an accelerator beamline. A particular attention is devoted to studying particles' orbits in an extended fringing field of a dipole magnet. Analytical solutions are obtained up to the third order in the formalism of the matrix theory. They contain form factors describing the falloff pattern of the field. These form factors are dimensionless line integrals of the field strength and its derivative. There is one such integral in the firstorder solution, two in the second, and nine in the third. An alternate way of describing charged particle optics is also presented. It is based on a Hamiltonian treatment and uses certain symplectic operators, which are defined in terms of Poisson brackets, to parametrize the transfer map of a system. We apply this approach to the fringing field problem and obtain a thirdorder solution. We furthermore show how to convert this solution into conventional transfer matrices by examining the connection between the noncanonical matrix theory and the Hamiltonian description.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.......139S
 Keywords:

 BEAM OPTICS;
 Physics: Optics