1. Update on the Effect of the Septum Stray Field Stephan I. Tzenov 29 April 20151EMMA Commissioning Meeting

2. The Concept of a Perturbed Reference Trajectory A reference trajectory is defined as a periodic solution of the equations of motion in the median plane (if such exists): The ideal reference trajectory is 2π/N – periodic (N is the number of the identical cells). 2π – periodic Suppose now that there are a number of imperfections in the ring. We would like to define a reference trajectory in this case as well. Obviously, such a trajectory has to be 2π – periodic. We call it a perturbed reference trajectory. 29 April 20152EMMA Commissioning Meeting

3. Ideal Reference Trajectory 29 April 20153EMMA Commissioning Meeting

4. The Concept of Perturbed Twiss Parameters In a similar fashion, an ideal Twiss parameter is defined as a periodic solution of the corresponding envelope equations, obtained after the linearization of the equations of motion around the reference trajectory: The ideal beta function is 2π/N – periodic (N is the number of the identical cells). 2π – periodic Suppose again that there are a number of imperfections in the ring. We can again define Twiss parameters. Obviously, the new beta function has to be 2π – periodic. We call it a perturbed beta function. 29 April 20154EMMA Commissioning Meeting

5. Ideal Horizontal Beta Function per Period 29 April 20155EMMA Commissioning Meeting

6. Ideal Vertical Beta Function per Period 29 April 20156EMMA Commissioning Meeting

7. Effect of Stray Fields on the Reference Trajectory The value of the measured stray fields at 20 MeV is 4 mT (respectively, 2 mT at 10 MeV) over 10 cm of distance. They can be considered constant within a time period of 2 microseconds, which means roughly 40 turns. For example, suppose the injection septum is set to inject at 10 MeV, while the extraction one operates at 20 MeV. Then, the stray fields are 2 mT and 4 mT, respectively. 29 April 20157EMMA Commissioning Meeting

8. Trajectory Results at 10 MeV 29 April 20158EMMA Commissioning Meeting

9. Trajectory Results with Correction at 10 MeV 29 April 2015EMMA Commissioning Meeting9

10. Twiss Parameter Results at 10 MeV 29 April 201510EMMA Commissioning Meeting

11. Twiss Parameter Results with Correction at 10 MeV 29 April 2015EMMA Commissioning Meeting11

12. Trajectory Results at 15 MeV 29 April 201512EMMA Commissioning Meeting

13. Trajectory Results with Correction at 15 MeV 29 April 2015EMMA Commissioning Meeting13

14. Twiss Parameter Results at 15 MeV 29 April 201514EMMA Commissioning Meeting

15. Twiss Parameter Results with Correction at 15 MeV 29 April 2015EMMA Commissioning Meeting15

16. Trajectory Results at 20 MeV 29 April 201516EMMA Commissioning Meeting

17. Trajectory Results with Correction at 20 MeV 29 April 2015EMMA Commissioning Meeting17

18. Twiss Parameter Results at 20 MeV 29 April 201518EMMA Commissioning Meeting

19. Twiss Parameter Results with Correction at 20 MeV 29 April 2015EMMA Commissioning Meeting19

20. How to Rectify Things? There are several possible solutions: Solomon type of solution motorized longer shield - Solomon type of solution. Radically decrease the stray fields. This can be achieved by introducing a motorized longer shield. This device enables to fold in the shield and after the septum is positioned to unfold the shield. This way the “wings” do not scrape the walls of the vacuum vessel. Shove couple of magnets - Shove couple of magnets (change their offsets only), adjacent to the to septa to compensate for the perturbing dipole field. Moving couple of magnets - Moving couple of magnets before and after the septum location has a positive effect. extremely complicatedradical type of solution - Due to its nonlinear character, the problem of correction is extremely complicated. Therefore, I still insist on the radical type of solution! 29 April 201520EMMA Commissioning Meeting