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John Adams InstituteFrank Tecker Linear Colliders
Frank Tecker – CERN
Linear CollidersLecture 3
Subsystems II
Linear CollidersLecture 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 withwiggler magnets
Bunch compressorwith magnetic chicane
=> small, short bunches to be accelerated w/o emittance blowup
Main linac: longitudinal wakefields cause energy spread
=> Chromatic effects
Electron GunDeliver stable beam current
Damping RingReduce transverse phase space (emittance) so smaller transverse IP size achievable
Bunch CompressorReduce σz to eliminate hourglass effect at IP
Positron TargetUse electrons to pair-produce positrons
Main LinacAccelerate beam toIP energy without spoiling DR emittance
Final FocusDemagnify 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 wakefieldsDtb
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 wakefieldsEffect 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
aN
RN
a
1R1
Long range wake of a dipole mode spread over 2 different frequencies
6 different frequencies
John Adams InstituteFrank Tecker Page 6C. Adolphsen / SLAC
Damping and detuningSlight 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 wakeefficiently 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
2
12t
t h
d yk y f W y
ds
Tail particleEquation of motion:
Driven Oscillator !!
More explicit:
John Adams InstituteFrank Tecker Page 9
Two particle model
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
headtail
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
2
2
21
8 sinz cellW QL
Eq
π
D fractional tune advance per cell
FODO cell lengthcell
q
L
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 δYrms
Partially compensated by: higher G, lower β, lower N
220 2 1
2facc i
RMS e zi
ELY NrW
G E
π
D
3
1 1RMS
G GY
NW Nf
,
structure length
initial average beta function
scaling of the focusing lattice ( 0.5)
accelerating gradient
initial and final energy
acc
i
i f
L
G
E
~
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 structuresevtl. RF pulse compression
Accelerating structures: transfer RF power → beam
Chris Adolphsen
John Adams InstituteFrank Tecker Page 13
RF systems
Klystron
Modulator
Energy storage in capacitorscharged up to 20-50 kV (between pulses)
U 150 -500 kVI 100 -500 Af 0.2 -20 GHz
Pave < 1.5 MWPpeak < 150 MW
efficiency 40-70%
High voltage switching andvoltage transformerrise time > 300 ns => for power efficient operation
pulse length tP >> 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 Tfill
ηRF→ beam=Pbeam
Pbeam+ Ploss+ Pout
TbeamTfill +Tbeam
≈ 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 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
f1 f2 f2
IP
final doublet (FD)
f1 f2 (=L*)
*1 2/ / typical value 300linac yM f f
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
*f Lfor a thin-lens of length l: 1
1k l
f
D ′yquad ≈−k1l yquad1
≈−k1l yquad
DyIP ≈ fD ′yquad yquad
DyIP2 yquad
2 2 quad yrms2
change in deflection:
change in IP position:
RMS spot size:
John Adams InstituteFrank Tecker Page 18
Final focus: Chromaticity
Small β* => βFD very large (~ 100 km)
for rms ~ 0.3%
Definitely much too large
We need to correct chromatic effects
=> introduce sextupole magnets
Use dispersion D:
2 20 40 nmIPyD
2 21
2
x
y
B s x y
B s x y
ox x D
John Adams InstituteFrank Tecker Page 19
Chromaticity correction
Combine quadrupole with sextupole and dispersion
x + D
IP
quadsextup.
KS KF
Quad:
Dx' =
K F
(1+)(x+D) ⇒ K F( −x−D
2 )
Dx'=
K S
2(x+D)2 ⇒ K SD(x +
D2
2)Sextupole:
Second order dispersion
chromaticityCould require KS = KF/D
=> ½ of second order dispersion left
Dx' =K F
(1+)(x+D)+
K -match
(1+)x⇒ 2K F( −x−
D2
2)
K -match =K F K S =2K F
D
Create as much chromaticity as FD upstream
=> second order dispersion corrected
y plane straightforwardx 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)
IP
FD
Dx
sextupoles
dipole
L*
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
y≅z
1 57 71.83 e e nr F
2 37 72.39 e e nr F
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 GroundMotion issues
Active stabilisation
Feedback systems
Some numbers:
Cavity alignment (RMS) ~ m
Linac magnets: 100 nm
FF magnets: 10-100 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
* *, , *
sin( )Quads
iQ i Q i i i
i
y k y
D D D
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 lessdisturbing
2y ATLD constantsite d
time
ep
distance
endentA
T
L
A range 10−5to10−7μm2 /m/s
Absolute motion
Relative motionover 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
IP
BPM
θbb
FDBK kicker
Dy
e
e
John Adams InstituteFrank Tecker Page 27
Dynamic effects corrections
• IP feedback, orbit feedbacks can fight luminosity lossby 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 θ= 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)