Analytical Considerations for Reducing the Effective Emittance with Variable Dipole Field Strengths

Abstract

The basic optics design scope in lepton rings is to match the sections in either side of the bending magnets in order to minimise the equilibrium emittance. A further important emittance reduction can be achieved by incorporating dipoles for which the deflecting field varies along the electron beam path in the magnet. The figure of merit for such lattices when used in a synchrotron light source is the minimisation of the so-called effective emittance. The effective emittance is computed in the middle of the undulator straight section as the product of the rms size and divergence and therefore includes contributions from the betatron emittance and from the electron energy spread. In this paper, analytical formulas are obtained for the minimum betatron and effective emittance in arbitrary dipole fields and the associated optics functions at the dipole entrance. Examples are given for specific dipole field functions and their properties with respect to the effective emittance minimisation. Finally, the effective emittance is parameterised with respect to standard cell optics properties.

Compact low emittance light sources based on longitudinal gradient bending magnets

“…An analytical solution was derived for the minimum emittance, whereas the integrals forming the minimum emittance were solved numerically. The same field model was then further analyzed in [8]. In [9], a step-function bend was considered for a possible upgrade of the ESRF lattice.…”

Emittance reduction with variable bending magnet strengths: Analytical optics considerations and application to the Compact Linear Collider damping ring design

“…This evolution guides the bending radius choice for achieving an emittance reduction by using a variable bend. In fact, the variable bend should be designed such that the minimum bending radius is at the dipole's center and then it should decrease towards the edge of the dipole [6][7][8][9]. For the present work, two different bending radii functions are used to describe the field evolution.…”

“…Based on studies of preceding works for the longitudinally variable bends [4][5][6][7][8][9], two dipole profiles are presented where the bending radius forms a step and a trapezium shape. The step profile shown in Fig.…”

Beam dynamics of a new low emittance third generation synchrotron light source facility

“…The longitudinal gradient provided with the super-bend magnet helps beam emittance reduction [26][27][28][29][30]. To simplify magnet design, avoiding a curve orbit dipole and easy fabrication procedure of this combination with home industry, the central dipole is split in three straight low field bending sections.…”