john adams institute frank tecker linear colliders frank tecker – cern linear colliders lecture 3...

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

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


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


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!!!


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 C. Adolphsen / SLAC

Damping and detuningSlight random detuning between cells makes HOMs decohere quickly

Will recohere later: need to be damped (HOM dampers)


HOM damping

Each cell damped by 4 radial WGs

terminated by SiC RF loads

HOM enter WG

Long-range wakeefficiently damped

Test results


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:


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


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


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

~


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

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


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


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


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


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:


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


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


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


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)


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 !!!


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


Ground Motion

Site dependent ground motion with decreasing amplitude for higher frequencies


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


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


Dynamic effects corrections

• IP feedback, orbit feedbacks can fight luminosity lossby ground motion


Linear Collider Stability


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


Post-Collision Line (CLIC)

john adams institute frank tecker linear colliders frank tecker – cern linear colliders lecture 3...

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