Lattice Compensation of the Wiggler Effect in HLSII with Particle Swarm Optimization

The upgrade project of Hefei Light Source (HLSII) has successfully reduced the natural emittance of the electron beam to lower than 40 nm·rad at 800 MeV with five insertion devices installed. To provide enough straight sections for these insertion devices, the lattice structure has been changed to four double bend achromatic (DBA) with two super-periods from the former four triple bend achromatic (TBA). These different types of the insertion devices can greatly improve the performance of the light source, but simultaneously they can also influence the dynamics of the electron beam in the storage ring. Especially they can bring the distortion of the linear beam optics seriously. In order to make sure the stability and the quality of the beam meeting the design goal, the effect of these insertion devices must be compensated. In this paper, a direct compensation method is applied for the wiggler in the HLSII storage ring with the particle swarm optimization. INTRODUCTION The Hefei Light Source (HLS) was a second generation synchrotron radiation light source, which had been operated for over two decades in the VUV to soft X-ray range with natural emittance of 166 nm·rad at electron beam energy of 800 MeV. To better satisfy the increasing requirements of synchrotron radiation experiments, an upgrade project of HLS to enhance its performance, named HLSII, was proposed and then launched in July, 2010. The philosophy for the design of the HLSII storage ring is to reduce the natural emittance of electron beam and increase the number of straight sections for insertion devices while maintaining the former foundation. Following this philosophy, the new storage ring lattice was designed [1] and studied [2, 3]. The circumference of the new storage ring remains 66.1308 m. Strong focusing quadrupoles are employed to obtain lower natural emittance of less than 40 nm·rad at the nominal energy of 800 MeV in the achromatic mode. Table 1 shows the main design parameters of the HLSII ring. Its lattice structure is changed to 4×DBA from the former 4×TBA with two super-periods to provide more straight sections for insertion devices. The designed transverse beta functions are shown in Fig. 1. In the new lattice, there are eight straight sections in total applied for beam injection, RF cavity and insertion devices. Five insertion devices have been equipped in the HLS-II storage ring. The periodic magnetic field in these insertion devices leads to tune shift and beta function distortion, which is similar to the focusing effect of the fringe field in dipoles. Therefore the effect of these insertion devices must be compensated carefully to make them transparent to the storage ring. Table 1: Main Parameters of the HLS-II Storage Ring Beam energy [MeV] 800 Beam current [mA] 300 Natural emittance [nm·rad] < 40 Beam lifetime [hours] > 5 RF Frequency [MHz] 204 Harmonic number 45 Natural energy spread (rms) 0.00047 Slow orbit drifts < 0.1 σ Transverse tune 4.4447/2.3597 Figure 1: Transverse beta functions of the HLSII storage ring. In this paper, a direct compensation method using the particle swarm optimization (PSO) with an acurate theoretical model is applied for the compensation of the wiggler effect in the HLSII storage ring. THEORETICAL MODEL OF WIGGLER The compensation of the wiggler is the priority due to their serious effect on the beam in the storage ring. In order to analysis the exact effect of the wiggler, a theoretical model of the planar horizontal wiggler is chosen. The canonical integration routines which are programmed by Y. K. Wu [4] have been applied for the compensation. x [m ]