Symplectic Integrators for Nonlinear Wiggler Fields

To achieve fast damping, the NLC Main Damping Ring uses a wiggler with high field strength, 2.15 T, and over 45 m in length. An ideal wiggler with infinitely wide pole pieces may be treated as a linear element, and has no impact on the dynamic aperture. However, the integrated nonlinear components from a real wiggler with integrated field over 100 Tm can be significant, and the choice of methods for studying the effects in such cases is limited at present. We present two possibilities for symplectic tracking through a wiggler taking full account of the nonlinear components of the field, compare the results with numerical integration of the equations of motion through the field in the case of the SPEAR BL11 wiggler, and consider the effects of the wiggler in the NLC Main Damping Ring. CBP Tech Note-228 LCC-0062 Symplectic Integrators for Nonlinear Wiggler Fields Andrzej Wolski Lawrence Berkeley National Laboratory April 27, 2001 Abstract To achieve fast damping, the NLC Main Damping Ring uses a wiggler with high field strength, 2.15 T, and over 45 m in length. An ideal wiggler with infinitely wide pole pieces may be treated as a linear element, and has no impact on the dynamic aperture. However, the integrated nonlinear components from a real wiggler with integrated field over 100 Tm can be significant, and the choice of methods for studying the effects in such cases is limited at present. We present two possibilities for symplectic tracking through a wiggler taking full account of the nonlinear components of the field, compare the results with numerical integration of the equations of motion through the field in the case of the SPEAR BL11 wiggler, and consider the effects of the wiggler in the NLC Main Damping Ring.