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Linear Colliders Lecture 3 Subsystems II. Main Linac (cont.) Transverse Wakefields RF system Beam Delivery System Alignment. Last Lecture. Particle production Damping rings with wiggler magnets Bunch compressor with magnetic chicane

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linear colliders lecture 3 subsystems ii
Linear CollidersLecture 3Subsystems II
  • Main Linac (cont.)
  • Transverse Wakefields
  • RF system
  • Beam Delivery System
  • Alignment
last lecture
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

linac emittance dilution
Linac: emittance dilution
  • Linac must preserve the small beam sizes, in particular in y
  • Possible sources for emittance dilutions are:
    • Dispersive errors: (dE → 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
linac transverse wakefields
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) excited
  • Fields can build up resonantly
  • Later bunches are kicked transversely
  •  multi- and single-bunch beam break-up (MBBU, SBBU)
  • Emittance growth!!!
transverse wakefields





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

damping and detuning
Damping and detuning
  • Slight random detuning between cells makes HOMs decohere quickly
  • Will recohere later: need to be damped (HOM dampers)

C. Adolphsen / SLAC

hom damping

Test results

HOM damping
  • Each cell damped by 4 radial WGs
  • terminated by SiC RF loads
  • HOM enter WG
  • Long-range wakeefficiently damped
single bunch wakefields



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:

two particle model
Two particle model


  • 2 particles: charge Q/2 each, 2sz apart
  • Bunch at max. displacement x:
      • tail receives kick q from head
  • p/2 in betatron phase downstream:
      • tail displacement ≈bq
  • p/2 in phase further:
      • -x displacement, tail kicked by –q
      • but initial kick has changed sign
  •  kicks add coherently
  •  tail amplitude grows along the linac


bns damping
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
random misalignments


Random misalignments
  • BNS damping does not cure random cavity misalignment
  • Emittance growth:
  • For given De, it scales as
  • Higher frequency requires better structure alignment dYrms
  • Partially compensated by: higher G, lower b, lower N
rf systems
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


RF systems


U 150 -500 kV

I 100 -500 A

f 0.2 -20 GHz

Pave < 1.5 MW

Ppeak < 150 MW

efficiency 40-70%


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

  • 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

Drift Tube

Output Cavity

Input Cavity

rf efficiency cavities

≈ 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
beam delivery final focus


f2 (=L*)

Beam Delivery: Final Focus
  • Need large demagnification of the (mainly vertical) beam size
  • by* of the order of the bunch length sz(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
final focus chromaticity
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:

final focus chromaticity1
Final focus: Chromaticity
  • Small b*  bFD very large (~ 100 km)
  • for drms ~ 0.3%
  • Definitely much too large
  • We need to correct chromatic effects
  •  introduce sextupole magnets
  • Use dispersion:
chromaticity correction

Create as much chromaticity as FD upstream

 second order dispersion corrected

Chromaticity correction
  • Combine quadrupole with sextupole and dispersion



x + D d

y plane straightforward

x plane more tricky


Second order





Could require KS = KF/D

 ½ of second order dispersion left



final focus chromatic correction
Final Focus: Chromatic Correction

Correction in both planes

  • Relatively short (few 100 m)
  • Local chromaticity correction
  • High bandwidth(energy acceptance)
final focus fundamental limits
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)

stability and alignment
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) ~ mm
    • Linac magnets: 100 nm
    • FF magnets: 10-100 nm
    • Final quadrupole: ~ nm !!!
quadrupole misalignment
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
ground motion
Ground Motion
  • Site dependent ground motion with decreasing amplitude for higher frequencies
ground motion atl law
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


beam beam feedback
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
dynamic effects corrections
Dynamic effects corrections
  • IP feedback, orbit feedbacks can fight luminosity lossby ground motion
other ip issues
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 q= sx/sz )
  • 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