Study on Emittance Reduction with a Robinson Wiggler in HEPS Institute of High Energy Physics Study on Emittance Reduction with a Robinson Wiggler in HEPS Peng Yuemei IHEP Low Emittance Ring workshop 2014，Italy 18- 09- 2014

outline Theoretical background of Robinson wiggler Overview the TBA optics Preliminary study on Robinson wiggler Optics development Issues and challenges summary

Theoretical background Horizontal (natural) Emittance: is horizontal damping partition number， related to the damping partition D by where introducing a magnetic element with gradient in a straight section where the dispersion is non- zero,it will contribute to the modification of D. For an isomagnetic storage ring with separate function magnets The natural energy spread of a beam is given by

An magnetic element, the field and gradient have opposite signs, its contribution to D is negative, consequently , horizontal emittance is decreased and the natural energy spread is increased . Combined magnet is one of this type magnetic element, the other is Robinson wiggler which consists of even number dipoles with field and gradient of opposite signs.

This straight section length is 9.4m ,here dispersion is zero. overview TBA optics Key parameters Lattice TBA Energy 5GeV Circumference 1283.6m Emittance 0.475 nm.rad This straight section length is 9.4m ,here dispersion is zero. Damping partition factor 0.9995 Tune 65.27/33.2 Natural energy spread 7.616E-4

Preliminary study on Robinson Wiggler G=15T/m Lw=8m

parameters choice and Optics rematch Parameters values RW’s field (T) 0.7 RW’s length (m) 8 RW’s period length(m) 0.2 RW’s gradient (T/m) 15 The betax in RW position(m) 80 The dispersion in RW position(m) 0.29 Without wiggler With wiggler

Comparison parameter Initial lattice Lattice without RW but with dispersion in long drift Lattice with a RW Beam energy(GeV) 5 Emittance (nm.rad) 0.475 0.468 0.296 Damping partition factor 0.9995 1.9072 Tune 65.27/33.2 Natural energy spread （E-4） 7.616 9.920

issues and challenges 1.Robinson wiggler is a nonlinear element ,and insert it will break the symmetry of the ring. The nonlinear effect will increase , dynamic aperture will be a problem. Injection efficiency and beam lifetime may be affected. 2.The field interference between adjacent poles needs to be solved. Some advanced magnet manufacturing and field measuring technologies are required, and might be challenging. 3.Due to the longitudinal damping partition factors reduced, longitudinal beam motion becomes a challenging issue.

Summary We presented the basic theory of Robinson wiggler and studied the concrete application of Robinson wiggler in HEPS TBA structure. A 8-m length Robinson wiggler will reduce 40% horizontal emittance. 2. The emittance reduce efficiency not proportional to Robinson Wiggler’s field strength. 3. Dynamic aperture and longitudinal beam stability are the challenging issues. This work is the first step, there are many problems need to be researched.

Thank you !