No abstract

In charged particle accelerators, higher order optics studies become important from various points of view, such as dynamic aperture, emittance dilution, beam loss, etc. For some new applications, nonlinear study has become important in single pass optics also. For studying the higher order optics, each magnetic element is represented by a higher order transfer function (map, i.e., a function that relates output coordinates of a trajectory with initial coordinates and momentum deviation). Here in this paper we have provided an alternate method to obtain the analytical formulation of the transfer function for a dipole magnet. This formulation is obtained on the basis of basic geometrical analysis and is exact up to all orders under hard edge approximation. Being an analytical expression, the estimation of higher order effects of dipole magnet can be studied quickly. For checking the correctness of this formulation, we separated terms up to third order, which can be used to obtain the standard transfer matrices up to same order. An example of emittance growth and bunch length modification for a C-chicane-type electron beam bunch compressor is provided using the analytical expression.

Indus-2 is an Indian synchrotron light source, operating at 2.5 GeV and generating synchrotron radiation from its bending magnets. In order to provide more intense synchrotron radiation to the synchrotron users, there is a plan to install five insertion devices in the Indus-2 storage ring. In the first phase of installation of insertion devices, there is a proposal to install two out-vacuum pure permanent magnet linearly polarized undulators in long straight sections of the Indus-2 storage ring. The presence of the insertion devices in the ring has inevitable effects on beam parameters like betatron tune, betatron amplitude function, closed orbit, emittance, energy spread and dynamic aperture etc. In this paper, the effect of two undulators on the above mentioned parameters of the Indus-2 stored electron beam at 2.5 GeV is presented. Moreover a correction scheme for the restoration of the betatron tune and amplitude function is also presented.