1. Mainring progress 6 fold emit：2.3nm
Analytical results are agree with numeric results.
8 sextupole families and two tune shift variables, and we got the result showed in the plot.
This is the best solution in that condition(8 sextupole families and two tune shift variables).
2rd chrom: th chrom: Pro.Cai say it is not bad, but expect more knobs to have better result.
If we want better result, more sextupole families and more tune shift variables are expected.(but he formulae are so long that Mathematica in my labtop will breakdown, maybe the code need optimization)

5. X=72.8sigma

6. X=48.6sigma
X=24.3sigma

8. DA from my own code

9. Less than 6 min with 8 core@i7_6700Q

10. 256 turns in 109 seconds

11. 512 turns in 219 seconds

12. Phase space plot

16. Difficulties
At begining, we want to use my own element simulator and link to Zlib to obtain the one-turn-map.
Zlib is the most suitable to this situation, with high efficiency and convenient.
The picture below shows the idea how to obtain one-turn-map using Zlib.(From Yan Yitong’s reprot)

17. Difficulties
When we check the results from Zlib carefully, we find that Zlib always lose the first order in some Tps operation(such as ‘*’ and ‘/’).
I read Yan’s papers and try to understand this result. Maybe it is because his tracking scheme.
We know the core idea of Zlib, and I can also write a library like Zlib. But it is little far from accelerator physics.
Now I am try to change his code. A little difficult, without handbook and comment.
Solutions:
change the simulator
Use some symbol libraries.
All of these will lose efficiency.

22. Requirement for Linac Parameter Symbol Unit Value E- beam energy Ee-
GeV 6
E+ beam energy
Ee+
Repetition rate
frep Hz 50
E- bunch population
Ne-
2×1010
E+ bunch population
Ne+
Energy spread (E+/E-) σE
<1×10-3
Emitance (E-)
0.3 mm mrad
Emitance (E+)

23. Design Goal Consideration of injection Injected Beam p/2
Inject in X direction.
Closed orbit kickers
Injected Beam
Circulating Beam
p/2

24. Design Goal Consideration of injection
Emit in mainring is 2E-9 m*rad, asuming beta_x=590 meter in the injection point.
Asuming DA_x=20 in the mainring.
Asuming beta_x=590 meter in the injection point.
The total space for injection:
8 sigma is retained for revolution beam to get enough quantum life time:
6 sigma is retained for injection beam to loss less particles:
3.2mm is lefted for septum and emit of is 3.5E-9 m*rad.

29. Survival plot by P.Piminov (no quad SR):
Dynamic 175 GeV
Survival plot by P.Piminov (no quad SR):

30. Survival plot by P.Piminov (no quad SR):
Dynamic 45 GeV
Survival plot by P.Piminov (no quad SR):