1. 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

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

3. 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

4. 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.

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

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

7. parameters choice and Optics rematch
Parameters values
RW’s field (T)
RW’s length (m)
RW’s period length(m)
RW’s gradient (T/m)
The betax in RW position(m)
The dispersion in RW position(m)
Without wiggler
With wiggler

8. 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

9. 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.

10. 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.

11. Thank you !