1. Progress in CLIC DFS studies Juergen Pfingstner University of Oslo CLIC Workshop 2015 26. January

2. Outline 1.On-line dispersion free steering. 2.Dispersion due to dipole kicks in the CLIC main linac. 3.Issues due to wake fields. 4.Issues due to structure tilts. 5.Conclusions.

3. 1. On-line dispersion free steering

4. Problem of long-term ground motion Start from perfectly aligned machine ATL motion and 1-2-1 correction applied ε x = 600nm ε y = 10nm 10 samples Emittance growth can be corrected with the DFS algorithm. 14h 7h 0h A = 10 -5 um 2 /m/s A = 0.5 -6 um 2 /m/s Normalised emittance along the main linac

5. Dispersion free steering (DFS) Principle: 1.The dispersion η at the BPMs is measured by varying the beam energy. 2.Corrector actuations Δy1 are calculated to minimise dispersion η and the beam orbit b. Considering many BPMs and quadrupoles leads to linear system of equations: DFS is usually applied to overlapping sections of the accelerator (36 for ML of CLIC). Δy1

6. On-line DFS Problem: only very small beam energy variation acceptable (< 1 per mil). Measurement are strongly influenced by BPM noise and usual energy jitter. Therefore, many measurement have to be averaged. Use of a Least Squares estimate (pseudo-inverse), which can be significantly simplified by the choice of the excitation:

7. Prior results On-line DFS showed excellent correction results with respect to ground motion misalignments (ATL motion): Correction to below 10% emittance growth. Necessary time about 10 min. Also the following imperfections were tested and caused not problems: BPM noise. Coherent and incoherent energy jitter of the acceleration gradients. Different errors in the correction matrices: BPM noise. Energy errors. Linearity errors of BPMs. Quadrupole movers breakdown. The algorithm was however too sensitive with respect to two imperfections: Accuracy of wakefield monitors. Tilt of accelerating structures.

8. 2. Dispersion due to dipole kicks in the CLIC main linac

9. Imperfections and dipole kicks Wakefield kicks: Head of bunch with offset Δx creates asymmetric mirror currents in the cavity wall. Resulting fields kick tail of bunch. Dispersion is created in tail. Kicks due to structure tilt: Field of a tilted cavity has also a transverse field component E kick. Resulting kick acts on whole bunch. Dispersion is created, which is dependent on acceleration gradient. The imperfections that cause problems have in common that they apply dipole kicks to the beam. As a result they create dispersion.

10. Derived dispersion due to a dipole kick Dispersion (measurement): To understand things, we only look at the dispersion of one single dipole kick. Trajectory of particle with E 0 : Trajectory of particle with E 0 (1+δ): Then the dispersion is for small approximately: The phase advance change for the CLIC main linac is: Per FODO cell: Along linac: Finally the dispersion is: Trajectory sinus oscillation becomes a cosine function and is multiplied with a linear functions (number of passed quadrupoles).

11. Dispersion can reach Filamentation reduces the beam oscillations and therefore also the dispersion after some distance. Simulated dispersion due to a dipole kick Dipole kick at quadrupole 1000 of CLIC main linac. Full beam simulated. δ of 0.001. Initially linear rise as predicted by linear estimate. For correction bin length, linear estimate is valid. After linear rise, nonlinear dispersion. The overall dispersion is the superposition of the individual dispersion due all kicks (δ can be different)

12. Dispersion dependence on energy change for measurement Dispersion due a dipole kick at location of quadrupole 1000. Full beam simulated. Dispersion nearly the same along correction bin (linear regime). The smaller the induced energy change δ, the longer the dispersion stays in the linear regime and rises. Dispersion is the nearly the same if created in the correction bin. But dispersion for smaller δ has a much larger effect further downstream!

13. 3. Issues due to wake fields

14. Wake field monitor specification Only large energy changes for the dispersion measurement are acceptable. For the target energy change of 0.05% the correction performance is unacceptable.

15. Dispersion from wakefields and DFS Effect of DFS on WF dispersion: Wakefield kicks create dispersion in tail of bunch. Measured dispersion is an average dispersion along the bunch. DFS will also act on the dispersion from wakefields. Quadrupoles are moved such that the dispersion from the quadrupoles, the head and the tail of the bunch is canceled. Effect of interaction on Δε: This does not change the wakefield effect Δε WF. But if RF alignment is applied (or QP move again): cancelation breaks down and strong Δε increased. Better to decouple dispersion from quadrupole misalignment and wakefield effects.

16. Energy dependence of WF dispersion: Quadrupole dispersion in the bin to be corrected is the same for different δ (linear regime). For smaller δ, the WF dispersion grows to higher values. WF dispersion for low δ does not decay so strongly along the linac. Minimisation of WF dispersion in correction bin: Overall dispersion due to wake fields: If the energy difference δ is created all along the linac, many cavities contribute to D WF. Also, the D k created far upstream will not decay before a bin further downstream. To minimize the wakefield dispersion energy difference should be created shortly before the correction bin: 1.Less cavities contribute to D WF 2.The dispersion of cavities that contribute is still small (linear regime)

17. Local energy change scheme 1. Global energy change: 2. Local energy change: All acceleration gradients are changed equally. Simple: change drive beam current slightly. Change of only the gradients in the decelerators before, at and after the bin to correct. Beam travels only over a short distance with different energies. A higher δ can be used, since it can be removed before the BDS. Current of drive beam has to be changed per decelerator. δ δ

18. Measured dispersion due to wake- fields with different energy changing schemes

19. Results with local energy change Local scheme with 0.1% shows similar behavior than global excitation with 5%. The increase of emittance due to the nominal CLIC wake field monitors resolution is about 6%.

20. 4. Issues due to structure tilts

21. Structure tilt sensitivity At nominal tilt of 140urad, the performance of local DFS is unacceptable. The global DFS version is much better, but also creates significant emittance growth.

22. Derived dispersion of structure tilts Model of dispersion measurement with tilted cavity to created δ: Measured dispersion: DFS bin Decelerator to create δ K QP K cav Expected cavity dispersion: Actually measured cavity dispersion: with

23. Simulated dispersion of structure tilts is the real dispersion due to the upstream cavity. is corrected by DFS with QPs. is an artifact of the measurement: 1.Cavity tilt kick creates (besides dispersion) a orbit change. 2.This kick is corrected by 1-to-1 steering at beam line setup. 3.But if cavity gradient is changed, also the tilt kick and therefore the orbit is changed. is measured as dispersion, but it is an orbit change only in the second measurement. Problem: δ can only be created without changing the gradients and therefore the orbit. Higher gradient changes make the problem worse: local scheme is worse than global one. This is not only true for small δ, but also for ordinary DFS!

24. Suppression of the tilt effect Effect gets weaker if gradient changes get small (global scheme). But relatively large changes are needed for local scheme. Try to remove orbit change from dispersion. Model orbit change before DFS bin x δ as offsets of the quadrupoles c δ in this section: Solving this equation by SVD inversion: Inversion is delicate (one 10 SV). With this model of the orbit change in the section of energy change, the orbit change in the DFS bin can be estimated by Finally orbit can be removed by

25. Emittance growth due to cavity tilts (140μm) with orbit subtraction Only one seed shown. Also no acceleration in the correction bin applied. Basic local scheme: Δε y = 4.85. With SVD orbit change subtraction there is a strong improvement: Δε y = 0.24 nm. Step-like introduction of δ is impossible in practice: Δε y = 0.08 nm.

26. 5. Conclusion On-line DFS is necessary to suppress ground motion effects on the time scale of hours. Scheme is based on tiny energy variations to measure dispersion. System identification methods are used to average out noise, e.g. BPM noise. Two imperfections cause problems: 1.Wakefields. 2.Tilt of acceleration cavities. Dispersion from wakefields degrades the performance of the DFS algorithm. This non-linear wakefield dispersion is higher for lower introduced energy changes δ. Wakefield dispersion effects can be strongly suppressed via a local excitation scheme. To introduce δ, the acceleration gradient is changed. In this case, cavity tilts create orbit changes, that are interpreted by the algorithm as dispersions. The orbit changes can be removed from measurement via SVD estimation. All fundamental problems seems to be resolved. Final simulations with a combination of all imperfections are still outstanding.

27. Thank you for your attention!