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Wakefield Studies in ILC-BDS Collimators: Geometric and Resistive Effects

This study presents the implementation and effects of geometric and resistive wakefields in ILC-BDS collimators. The results show the impact on bunch size, luminosity, and beam jitter, providing useful insights for future collider designs.

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Wakefield Studies in ILC-BDS Collimators: Geometric and Resistive Effects

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  1. ILC-BDS Collimator Study Adriana Bungau and Roger Barlow The University of Manchester CERN - October 15

  2. Since last time… • Only higher order mode geometric wakefields were implemented in the Merlin code at the last COLSIM meeting • Resistive wakefields were included in the simulations (benchmark with an experiment at SLC) • At PAC - 07: the increase in the bunch size and the decrease in the luminosity due to geometric and resistive wakefields were presented for large offsets • However, large offsets of couple of hundreds of microns are not realistic in a real machine but useful in theory when tried to find the range when the split into modes occurs • Small offsets of several sigmas are more likely to happen • Beam jitter in all ILC_BDS collimators • Wakefield tests at SLAC in March and July (see Jonny’s talk)

  3. ILC-BDS colimators

  4. Bunch size - geometric wakefields • beam parameters at the end of linac: • x = 30.4 10-6 m, y = 0.9 10-6 m • beam size at the IP in absence of wakefields: • x = 6.51*10-7 m, y = 5.69*10-9 m • last talk->modes separation at 250 um (on • logarithmic scale!); • for small offsets, modes separation occurs at • ~10 sigmas;

  5. Luminosity - geometric wakefields - at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 20% - for a luminosity of L~1038 the offset should be 2-3 sigmas

  6. Resistive wall • pipe wall has infinite thickness; it is smooth; • it is not perfectly conducting • the beam is rigid and it moves with c; • test charge at a relative fixed distance; c The fields are excited as the beam interacts with the resistive wall surroundings; b c For higher moments, it generates different wakefield patterns; they are fixed and move down the pipe with the phase velocity c;

  7. General form of the resistive wake • Write down Maxwell’s eq in cylindrical coordinates • Combined linearly into eq for the Lorentz force components and the magnetic field • Assumption: the boundary is axially symmetric ( are ~ cos mθ and are ~ sin mθ ) • Integrate the force through a distance of interest L • Apply the Panofsky-Wenzel theorem

  8. WakeFieldProcess WakePotentials SpoilerWakeFieldProcess CalculateCm(); CalculateSm(); CalculateWakeT(); CalculateWakeL(); ApplyWakefield (); SpoilerWakePotentials nmodes; virtual Wtrans(s,m); virtual Wlong(s,m); The MERLIN code Previously in Merlin: • Two base classes: WakeFieldProcess and WakePotentials - transverse wakefields - longitudinal wakefields Geometrical wakes: • Some functions made virtual in the base classes • Two derived classes: - SpoilerWakeFieldProcess - does the summations - SpoilerWakePotentials - provides prototypes for W(m,s) functions (virtual) • The actual form of W(m,s) for a collimator type is provided in a class derived from SpoilerWakePotentials

  9. Implementation of the Resistive wakes WakeFieldProcess WakePotentials SpoilerWakeFieldProcess CalculateCm(); CalculateSm(); CalculateWakeT(); CalculateWakeL(); ApplyWakefield (); SpoilerWakePotentials nmodes; virtual Wtrans(s,m); virtual Wlong(s,m); ResistiveWakePotentials Modes; Conductivity; pipeRadius; Wtrans(z,m,AccComp); Wlong(z,m, AccComp);

  10. Resistive wakes • Benchmark against an SLC result

  11. Bunch size - resistive wakefields • For small offsets the mode separation starts at ~10 sigmas • At larger offsets (30-35 sigmas) there are particles lost in the last collimators The increase in the bunch size due to resistive wakefields is far greater than in the geometric case

  12. Luminosity - resistive wakes - at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 10% • for a luminosity of L~1038 the offset should be less than 1 sigma • the resistive effects are dominant!

  13. Bunch Shape Distortion • The bunch shape changes as it passes through the collimator; the gaussian bunch is distorted in the last collimators • But the bunch shape at the end of the linac is not a gaussian so we expect the luminosity to be even lower than predicted

  14. Beam offset in each BDS collimator • No wakefields <y>=4.74e-12; • Jitter of 1 nm of maximum tolerable bunch-to-bunch jitter in the train with 300 nm between bunches; for 1nm: <y>=8.61e-11 • Jitter about 100 nm which intratrain ffedback can follow with time constant of ~100 bunches; for 100nm: <y>=5.4e-10 • Maximum beam offset is 1 um in collimator AB7 for 1nm beam jitter and 9um for 100 nm jitter

  15. Beam jitter • Beam jitter of 500 nm of train-to-train offset which intratrain feedback can comfortably capture • The maximum beam offset in a collimator is 40 um (collimator AB7) for a 500nm beam jitter • For 500nm: <y>=2.37e-9

  16. Next plans • Study the wakefields of one collimator for the material damage tests in Japan (Ti coated with Be - emittance dilution and performance with Ti and Be resistivity) • Merlin code development for implementation of ECHO/GDFIDL results • …other suggestions?

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