1. Wakefields in Collimators Roger Barlow Adriana Bungau Adina Toader

2. What we’re doing • Collimator wakefields • Wakefields in Merlin • Geometric and resisitive wakes • BDS studies • Wakefields in Placet

3. ILC collimators

4. Why these are different • Collimators are not dominated by resonance structure • High order modes may matter

5. Invalid approximations • Can’t just consider dipole mode • Can’t assume ’ • Axial wakes matter as well as radial ones • Bunches are not Gaussian • Luminosity is lost by emittance growth and jitter

6. Basic Formalism Single particle wake wx=mmWm(s)r’m rm-1 {cos[(m-1)]cos[m’]+sin[(m-1)]sin[m’]} wy=mmWm(s)r’m rm-1 {-sin[(m-1)]cos[m’]+cos[(m-1)]sin[m’]} Slice wake wx=mWm(s)rm-1 {Cmcos[(m-1)]+Smsin[(m-1)]} wy=mWm(s)rm-1 {Smcos[(m-1)]-Cmsin[(m-1)]} where Cm=r’m cos(m’) Sm= r’m sin(m’)

7. What’s all that for Wake due to slice is sum of terms like Cm Wm(s) rm-1 cos[(m-1)] M=number of modes considered Particle Slice Aperture Avoid N(N-1)/2 calculations Find Cm, Sm for all slices Sum 2M terms for each of N particles

8. Implementation • Particle by particle wake calculations are possible (avoid Gaussian assumption) • All done in a couple of for loops

9. Merlin • Framework adaptable • Consider Wx and Wy, not just WT • Done by defining new classes inheriting from (almost) standard Merlin • SpoilerWakeFieldProcess:WakefieldProcess • SpoilerWakePotentials:Wakepotentials • SpoilerWakeFieldProcess does the sums • SpoilerWakePotentials is pure virtual: functions Wtrans(s,m), Wlong(s,m)

10. Geometric wakes TaperedCollimator:SpoilerWakePotentials Raimondi formula Wm(s)=2(1/a2m-1/b2m)e-ms/a

11. Results Simple setup Increasing offset More modes Note distortion

12. Resistive wakes Different Wtrans, Wlong Work in progress (AB)

13. Application to BDS Studies done (AB) showing small emittance growth for reasonable offsets Large emittance growth for unreasonable offsets

14. Other apertures Can use numerical simulations (Echo2D, GdfidL…)to compute bunch wakes Split into modes (automatic for Echo2D, needs work for GdfidL) Extract delta wakes using Fourier deconvolution

15. Bunch to Delta wakes

16. Contrast Raimondi formula

17. Where next • Still some problems with FT artefacts that need to be sorted • Can then use these values in interpolation table for Merlin etc

18. Wakes in PLACET • Includes wakefields although • Only up to 2nd order • Not generally extendable • Uses some very-short-wake approximation. Wakefields only within slice • But they do handle square apertures which our formalism doesn’t (yet)

19. PLACET studies (AT) • Comparisons with Merlin predictions • Investigate effects of wakefields on Frank Jackson’s improved ILC BDS collimator arrangements

20. Summary and Outlook • Lots being done • Lots still to do • Interesting problems and potentially useful results