1 / 23

Electron-Cloud Effects in Fermilab Booster

Electron-Cloud Effects in Fermilab Booster. K.Y. Ng Fermilab Electron-Cloud Feedback Workshop IUCF, Indiana March 14-15, 2007. Motivation I. E-Cloud observed at CERN SPS. Want to know what happens to Fermilab Booster. Motivation II. Fermilab Booster is injected at 400 MeV.

malaya
Download Presentation

Electron-Cloud Effects in Fermilab Booster

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Electron-Cloud Effects in Fermilab Booster K.Y. Ng Fermilab Electron-Cloud Feedback Workshop IUCF, Indiana March 14-15, 2007 ECloud Feedback, IUCF

  2. Motivation I • E-Cloud observed at CERN SPS.Want to know what happens to Fermilab Booster. ECloud Feedback, IUCF

  3. Motivation II • Fermilab Booster is injected at 400 MeV. • Space-charge tune shift is ~0.4. • Sextupole tune spread << 0.4 will be shifted awayfrom coherent frequency. • Or no Landau damping • How come sextupole tune spread work in damping coherent instabilities? • Is it possible that e-cloud cancels part of thespace-charge effect of the beam? • However, e-cloud effects should not be too large to introduce new instabilities. ECloud Feedback, IUCF

  4. Simulations with POSINST • Booster circumference: 474.203 m. • 80 consecutive bunches + 4 empty buckets. • Bunch intensity Nb = 6 x 1010. • Near injection, total energy E = 1.4 GeV.γ = 1.492, β = 0.7422. • Betatron tunes ≈ 6.8. • RMS bunch length: σz = 70 cm (3.15 ns). • Transverse beam sizes: σx = σy = 4.477 mm,(rms normalized emittances ~2 mm mr.) • Gaussian distribution assumed. • Vacuum pressure: 2 x 10-7 Torr. ECloud Feedback, IUCF

  5. Booster Magnets • F Quad approximatedas 6”x1.64” rectangular opening. • D Quad approximatedas 6”x2.25” rectangular opening. • There are also 1.125”long-straight sectionsand 2.125”short-straight sections. ECloud Feedback, IUCF

  6. Booster does not have a beam pipe inside the magnets. • Beam sees magnet laminations, for which we do not know the SEY. Av. proton linear density ECloud Feedback, IUCF

  7. Magnets cover only ~60% of Booster Rings. • The rest are cylindrical S.S. beam pipes joining the magnets. Av. proton linear density ECloud Feedback, IUCF

  8. Landau Damping in Presence of Sp-Ch • E. Métral and F. Ruggiero studied Landau dampingwith octupole tune spread in presence of sp-ch.[CERN-AB-2004-025 (ABP), 2004; Möhl earlier] • They solved a simplified dispersion relation analytically. • Non-linear incoherent sp-ch tune shift as well asoctupole incoherent tune shift are included. • They plot ReΔncoh vs. ImΔncoh, showing the stableand unstable regions. • LHC parameters are used. ECloud Feedback, IUCF

  9. Stability Contours in Presence of Octopole Tune Spread and Decreasing Space Charge Tune Spread rms ΔQoct=0.000056 Outside unstable coh Nb/2 Nb=1.15x1011 coh Inside stable coh coh Nb/4 coh Nb/10 coh coh coh ECloud Feedback, IUCF

  10. Outside unstable Inside stable ECloud Feedback, IUCF

  11. Stability Contours in Presence of Space Charge with Octupole Tune Spread (ΔQoct) Decreasing rms rms rms ΔQoct=0.000056 coh ΔQoct/2 coh ΔQoct=0.000056 Outside Unstable coh coh Inside Stable rms rms ΔQoct/4 coh ΔQoct/10 coh coh coh ECloud Feedback, IUCF

  12. Conclusion • Without octupole tune spread, • incoherent sp ch tune spread alone does not provideLandau damping. • With octupole tune spread, • damping region is increased in the presence of sp ch to roughly sp ch tune spread, • there is a big shift of the damping region. • To be Landau damped, there must be large inductiveimpedance. • This result has been verified by simulations.(V. Kornilov, O. Boine-Frankenheim and I. Hofmann, HB2006) ECloud Feedback, IUCF

  13. ECloud Feedback, IUCF

  14. ECloud Feedback, IUCF

  15. Transverse Impedance of Booster • Left: Computed Z1V of magnet laminations. • Right: Im Z1V of Booster inferred from tune- depression measurement (X. Huang). ECloud Feedback, IUCF

  16. Contribution of Inductive Walls • From inductive magnet laminations and beam pipe,= 0.026 at injection • Inductive tune shift is too small to counteract space charge. ECloud Feedback, IUCF

  17. Electron Cloud Density (D Quad) ρσ • Electron density is ρσ ~ 2.5 x 1013 m-3, ρc ~ 1 x 1013 m-3. • Proton density is ρσ ~ 6.4 x 1014 m-3, ρc ~ 1.7 x 1014 m-3. • Space charge canceled by small amount at bunch center,but more at head and tail. ρc ρav ECloud Feedback, IUCF

  18. Short-Range Wake from E-Cloud p = σy/σx • Heifets derived short range wake from e-clouddepends on cloud/beam trans sizes, (Σy/σy) • Can be approx. by a resonance: Σy/σy=2, Q = 6.0, μ =0.9,Wmax = 1.014 ECloud Feedback, IUCF

  19. Impedance from E-Cloud • Fitted impedance • Near injection,with ρe = 1013 m-3,ImZ1V ~ 9.4 MΩ/mat low frequencies. • ωe/2π~100 MHz is small, because of long σz and large σx, σy. • ρe = 1012 m-3 is often used for analysis of beam stability?? ECloud Feedback, IUCF

  20. Bunch Length and Electron Bounce Frequency ECloud Feedback, IUCF

  21. Trans. Microwave (Strong Head-Tail) • ωeσt≤ ½π but ωetL~ 6 to 11 >> π • Linear part of e-cloud wake contributes. • Use Métral’s long-bunch formula to compute Upsilon. • Upsilon > 2 implies instability. ωetL ωeσt ECloud Feedback, IUCF

  22. Booster cannot operate with ξx = ξy= 0, beam unstable. • With ξx and ξy setting, Upsilon is reduced, but still > 2when close to transition. • Maybe space charge will help. (Blaskiewicz, PR STAB 044201) • Maybe peak of ReZ1V is not so sharp (or Q is lower). • Maybe e-cloud density is much less than 1013 m-3. ECloud Feedback, IUCF

  23. Summary • Simulations show that e-cloud accumulation is large.Saturation has been reached. • ρe~ 1013 m-3 amounts to only 1/10 of proton density.It is unsure whether enough sp-ch will be canceledto ensure Landau damping. • E-cloud leads to a wake that may cause strong head-tail instability. • Upsilon >2 close to transition, not good. • Maybe sp ch will delay 2 azimuthal modes to collide. • Maybe ReZ1V peak is not so sharp (lower Q). • Maybe actual e density is smaller, thus lowering Upsilon. ECloud Feedback, IUCF

More Related