Linear Colliders Lecture 3 Subsystems II

1. Linear CollidersLecture 3Subsystems II • Main Linac (cont.) • Transverse Wakefields • RF system • Beam Delivery System • Alignment

2. Last Lecture • Particle production • Damping rings withwiggler magnets • Bunch compressorwith magnetic chicane => small, short bunchesto be accelerated w/o emittance blowup • Main linac: longitudinal wakefields cause energy spread => Chromatic effects Final FocusDemagnify and collide beams Main LinacAccelerate beam toIP energy without spoiling DR emittance Bunch CompressorReduce σz to eliminate hourglass effect at IP Damping RingReduce transverse phase space (emittance) so smaller transverse IP size achievable Positron TargetUse electrons to pair-produce positrons Electron GunDeliver stable beam current

3. Linac: emittance dilution • Linac must preserve the small beam sizes, in particular in y • Possible sources for emittance dilutions are: • Dispersive errors: (ΔE → y) • Transverse wakefields: (z → y) • Betatron coupling: (x, px → y) • Jitter: (t → y) • All can increase projection of the beam size at the IP • Projection determines luminosity

4. Linac: transverse wakefields • Bunches induce field in the cavities • Later bunches are perturbed by these fields • Bunches passing off-centre excite transverse higher order modes (HOM) • Fields can build up resonantly • Later bunches are kicked transversely • => multi- and single-bunch beam break-up (MBBU, SBBU) • Emittance growth!!!

5. aN a1 RN R1 Transverse wakefields • Effect depends on a/λ(a iris aperture) and structure design details • transverse wakefields roughly scale as W┴∝f 3 • less important for lower frequency:Super-Conducting (SW) cavities suffer less from wakefields • Long-range minimised by structure design • Dipole mode detuning Long range wake of a dipole mode spread over 2 different frequencies 6 different frequencies

6. Damping and detuning • Slight random detuning between cells makes HOMs decohere quickly • Will recohere later: need to be damped (HOM dampers) C. Adolphsen / SLAC

7. Test results HOM damping • Each cell damped by 4 radial WGs • terminated by SiC RF loads • HOM enter WG • Long-range wakeefficiently damped

8. tail head Single bunch wakefields • Head particle wakefields deflect tail particles • Particle perform coherent betatron oscillations • => head resonantly drives the tail Tail particle Equation of motion: Driven Oscillator !! More explicit:

9. Two particle model head • 2 particles: charge Q/2 each, 2σz apart • Bunch at max. displacement x: • tail receives kick θ from head • π/2 in betatron phase downstream: • tail displacement ≈βθ • π/2 in phase further (π in total): • -x displacement, tail kicked by –θ • but initial kick has changed sign • => kicks add coherently • => tail amplitude grows along the linac tail

10. BNS damping • Counteract effective defocusing of tail by wakefield by increased focusing (Balakin, Novokhatski, and Smirnov) • Done by decreasing tail energy with respect to head • By longitudinally correlated energy spread (off-crest) • Wakefields balanced by lattice chromaticity • 2 particle model: • W┴ non linear • Good compensation achievable at the price of • lower energy gain by off-crest running • Larger energy spread

11. ~ Random misalignments • BNS damping does not cure random cavity misalignment • Emittance growth: • For given Δε, it scales as • Higher frequency requires better structure alignment δYrms • Partially compensated by: higher G, lower β, lower N

12. RF systems • Need efficient acceleration in main linac • 4 primary components: • Modulators: convert line AC → pulsed DC for klystrons • Klystrons: convert DC → RF at given frequency • RF distribution: transport RF power → accelerating structuresevtl. RF pulse compression • Accelerating structures: transfer RF power → beam Chris Adolphsen

13. RF systems Klystron U 150 -500 kV I 100 -500 A f 0.2 -20 GHz Pave < 1.5 MW Ppeak < 150 MW efficiency 40-70% Modulator Energy storage in capacitors charged up to 20-50 kV (between pulses) High voltage switching and voltage transformer rise time > 300 ns =>for power efficient operation pulse length tP >> 300 ns favourable

14. Klystrons • narrow-band vacuum-tube amplifier at microwave frequencies (an electron-beam device). • low-power signal at the design frequency excites input cavity • Velocity modulation becomes time modulation in the drift tube • Bunched beam excites output cavity Collector Electron Gun Drift Tube Output Cavity Input Cavity

15. ≈ 1 for SC SW cavities RF efficiency: cavities • Fields established after cavity filling time • Steady state: power to beam, cavity losses, and (for TW) output coupler • Efficiency: • NC TW cavities have smaller fill time Tfill

16. f1 f2 (=L*) Beam Delivery: Final Focus • Need large demagnification of the (mainly vertical) beam size • βy* of the order of the bunch length σz(hour-glass effect) • Need free space around the IP for physics detector • Assume f2 = 2 m => f1 ≈ 600 m • Can make shorter design but this roughly sets the length scale

17. Final Focus: chromaticity • Need strong quadrupole magnets for the final doublet • Typically hundreds of Tesla/m • Get strong chromatic aberations for a thin-lens of length l: change in deflection:change in IP position:RMS spot size:

18. Final focus: Chromaticity • Small β* => βFD very large (~ 100 km) • for δrms ~ 0.3% • Definitely much too large • We need to correct chromatic effects • => introduce sextupole magnets • Use dispersion D:

19. Create as much chromaticity as FD upstream => second order dispersion corrected Chromaticity correction • Combine quadrupole with sextupole and dispersion sextup. quad x + Dδ y plane straightforward x plane more tricky IP Second order dispersion KS KF Quad: Could require KS = KF/D => ½ of second order dispersion left chromaticity Sextupole:

20. Final Focus: Chromatic Correction Correction in both planes • Relatively short (few 100 m) • Local chromaticity correction • High bandwidth(energy acceptance)

21. Final focus: fundamental limits • From the hour-glass effect: • For high energies, additional fundamental limit:synchrotron radiation in the final focusing quadrupoles=> beamsize growth at the IP • so-called Oide Effect: • minimum beam size: • for F is a function of the focusing optics: typically F ~ 7(minimum value ~0.1)

22. Stability and Alignment • Tiny emittance beams • => Tight component tolerances • Field quality • Alignment • Vibration and GroundMotion issues • Active stabilisation • Feedback systems • Some numbers: • Cavity alignment (RMS) ~ µm • Linac magnets: 100 nm • FF magnets: 10-100 nm • Final quadrupole: ~ nm !!!

23. Quadrupole misalignment • Any quadrupole misalignment and jitter will cause orbit oscillations and displacement at the IP • Precise mechanical alignment not sufficient • Beam-based alignment • Dynamic effects of ground motion very important • Demonstrate Luminosity performance in presence of motion

24. Ground Motion • Site dependent ground motion with decreasing amplitude for higher frequencies

25. Ground motion: ATL law • Need to consider short and long term stability of the collider • Ground motion model: ATL law • This allows you to simulate ground motion effects • Relative motion smaller • Long range motion lessdisturbing Absolute motion Relative motionover dL=100 m 1nm

26. Beam-Beam feedback • Use the strong beam-beam deflection kick for keeping beams in collision • Sub-nm offsets at IP cause well detectable offsets (micron scale) a few meters downstream

27. Dynamic effects corrections • IP feedback, orbit feedbacks can fight luminosity lossby ground motion

28. Linear Collider Stability

29. Other IP issues • Collimation: • Beam halo will create background in detector • Collimation section to eliminate off-energy and off-orbit particle • Material and wakefield issues • Crossing angle: • NC small bunch spacing requires crossing angle at IP to avoid parasitic beam-beam deflections • Luminosity loss (≈10% when θ= σx/σz ) • Crab cavities • Introduce additional time dependant transverse kick to improve collision • Spent beam • Large energy spread after collision • Design for spent beam line not easy

30. Post-Collision Line (CLIC)