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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

  • tail

    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

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