John Adams Institute Frank Tecker Linear Colliders Frank Tecker – CERN Linear Colliders Lecture 3 Subsystems II Main Linac (cont.) Transverse Wakefields RF system Beam Delivery System Alignment

John Adams InstituteFrank Tecker Page 2 Last Lecture Particle production Damping rings with wiggler magnets Bunch compressor with magnetic chicane => small, short bunches to be accelerated w/o emittance blowup Main linac: longitudinal wakefields cause energy spread => Chromatic effects Electron Gun Deliver stable beam current Damping Ring Reduce transverse phase space (emittance) so smaller transverse IP size achievable Bunch Compressor Reduce σ z to eliminate hourglass effect at IP Positron Target Use electrons to pair- produce positrons Main Linac Accelerate beam to IP energy without spoiling DR emittance Final Focus Demagnify and collide beams

John Adams InstituteFrank Tecker Page 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

John Adams InstituteFrank Tecker Page 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!!!

John Adams InstituteFrank Tecker Page 5 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 aNaN RNRN a1a1 R1R1 Long range wake of a dipole mode spread over 2 different frequencies 6 different frequencies

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

John Adams InstituteFrank Tecker Page 7 HOM damping Each cell damped by 4 radial WGs terminated by SiC RF loads HOM enter WG Long-range wake efficiently damped Test results

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

John Adams InstituteFrank Tecker Page 9 Two particle model 2 particles: charge Q/2 each, 2σ z apart Bunch at max. displacement x: tail receives kick  from head  /2 in betatron phase downstream: tail displacement ≈β   /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 head tail

John Adams InstituteFrank Tecker Page 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

John Adams InstituteFrank Tecker Page 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 δY rms Partially compensated by: higher G, lower β, lower N ~

John Adams InstituteFrank Tecker Page 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 structures evtl. RF pulse compression Accelerating structures: transfer RF power → beam Chris Adolphsen

John Adams InstituteFrank Tecker Page 13 RF systems Klystron Modulator Energy storage in capacitors charged up to kV (between pulses) U kV I A f GHz P ave < 1.5 MW P peak < 150 MW efficiency 40-70% High voltage switching and voltage transformer rise time > 300 ns => for power efficient operation pulse length t P >> 300 ns favourable

John Adams InstituteFrank Tecker Page 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 Electron Gun Input Cavity Drift Tube Output Cavity Collector

John Adams InstituteFrank Tecker Page 15 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 T fill ≈ 1 for SC SW cavities

John Adams InstituteFrank Tecker Page 16 Beam Delivery: Final Focus Need large demagnification of the (mainly vertical) beam size  y * of the order of the bunch length σ z (hour-glass effect) Need free space around the IP for physics detector Assume f 2 = 2 m => f 1 ≈ 600 m Can make shorter design but this roughly sets the length scale f1f1 f 2 (=L * )

John Adams InstituteFrank Tecker Page 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:

John Adams InstituteFrank Tecker Page 18 Final focus: Chromaticity Small β* => β FD very large (~ 100 km) for  rms ~ 0.3% Definitely much too large We need to correct chromatic effects => introduce sextupole magnets Use dispersion D:

John Adams InstituteFrank Tecker Page 19 Chromaticity correction Combine quadrupole with sextupole and dispersion x + D  IP quadsextup. KSKS KFKF Quad: Sextupole: Second order dispersion chromaticity Could require K S = K F /D => ½ of second order dispersion left Create as much chromaticity as FD upstream => second order dispersion corrected y plane straightforward x plane more tricky

John Adams InstituteFrank Tecker Page 20 Final Focus: Chromatic Correction Relatively short (few 100 m) Local chromaticity correction High bandwidth (energy acceptance) Correction in both planes

John Adams InstituteFrank Tecker Page 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)

John Adams InstituteFrank Tecker Page 22 Stability and Alignment Tiny emittance beams => Tight component tolerances Field quality Alignment Vibration and Ground Motion issues Active stabilisation Feedback systems Some numbers: Cavity alignment (RMS)~  m Linac magnets:100 nm FF magnets: nm Final quadrupole:~ nm !!!

John Adams InstituteFrank Tecker Page 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

John Adams InstituteFrank Tecker Page 24 Ground Motion Site dependent ground motion with decreasing amplitude for higher frequencies

John Adams InstituteFrank Tecker Page 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 less disturbing Absolute motion Relative motion over dL=100 m 1nm

John Adams InstituteFrank Tecker Page 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

John Adams InstituteFrank Tecker Page 27 Dynamic effects corrections IP feedback, orbit feedbacks can fight luminosity loss by ground motion

John Adams InstituteFrank Tecker Page 28 Linear Collider Stability

John Adams InstituteFrank Tecker Page 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  =  x /  z ) 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

John Adams InstituteFrank Tecker Page 30 Post-Collision Line (CLIC)