1. Effect of Vane Misalignment on RFQ Resonant Frequency

2. Reasons for Study See sensitivity of frequency on vane alignment Is frequency as sensitive as beam dynamics? Do dipole modes become a nuisance? Is one direction of misalignment preferable? Tolerable misalignment for tuners to fix

3. Implementing Misalignment Mesh density increased to resolve small step in wall. Minor vane offset toward or away from beam axis by fixed amount. Whole vane (including outer wall) moved, not just the vane tip.

4. -500 µm Misalignment

5. -250 µm Misalignment

6. -100 µm Misalignment

7. -50 µm Misalignment

8. -25 µm Misalignment

9. -10 µm Misalignment

10. Zero Misalignment

11. 10 µm Misalignment

12. 25 µm Misalignment

13. 50 µm Misalignment

14. 100 µm Misalignment

15. 250 µm Misalignment

16. 500 µm Misalignment

17. Frequency Shift vs. Misalignment

18. Microns: -100 -50 -25 -10 +10 +25 +50 +100 Mhz: 324.8 324.1 323.7 323.5 323.3 323.2 323.0 322.6 321.9 Effect on frequency and modes of moving one minor vane towards and away from beam centre. Minor vane remains parallel to beam axis. Tuning range is -0.5 to + 5MHz Tuning range

19. Vane Misalignment Conclusion Negligible effect on Q or power Dipole modes mixing shouldn’t be a problem Minor vane shifted toward beam is preferable –As lowers frequency; easier to fix with tuners Tuner range: MHz (at the expense of Q…) +250 µm misalignment ok, -250 µm not ok ±100 µm or better is fine

20. Dear Scott, thank you very much for this excellent work. As expected we can conclude that by observation of the RF modes in the alignment process we can achieve the accuracy required for the particle transport, we also see which plane is missaligned by how much. Also good to see that the tuning range is more than sufficient (we wont see any particles at the output for 250 mircon anyhow). Best wishes, Merry christmas and a Happy New Year Juergen ________________________________________ From: scott.lawrie@stfc.ac.uk [scott.lawrie@stfc.ac.uk] Sent: 22 December 2011 16:02 To: Savage, Peter J; alan.letchford@stfc.ac.uk; s.jolly@ucl.ac.uk; Pozimski, Jürgen K Cc: ibon.bustinduy@essbilbao.org; david.decos@essbilbao.org; philip.wise@stfc.ac.uk; alberto.garbayo@stfc.ac.uk Subject: RFQ misalignment effect on frequency Dear All, Along the same lines as Simon's study on beam transmission, I've done a simple test in Superfish as to how the alignment affects the frequency. To do this, I simulated the effect of a minor vane shifted relative to the major vane (albeit with symmetry, so it would actually be both minor vanes moved the same amount). The frequency does shift rather markedly with misalignments, but probably not enough to trouble our tuners. The good news is that we can easily tune away any frequency shift caused by misalignments of up to 100microns. Above this is a bit iffy (especially if the alignment is such that the minor vane is moved away from the beam axis), but since we're aiming for numbers closer to 20-50microns, this seems fine. I can try doing more advanced shifts, such as a full four-quadrant model with only one vane moved (no symmetry), or a major vane displaced sideways, but that'll take a bit more work and it seems to me that the beam dynamics is a bit more sensitive to misalignments than the frequency so it's probably not worth delving any further. See the attached ppt for more details. Cheers, Scott