An Introduction to thePhysics and Technologyof e+e- Linear Colliders

Lecture 9: a) Beam Based Alignment

Nick Walker (DESY)

DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003

Emittance tuning in the LET

• LET = Low Emittance Transport– Bunch compressor (DRMain Linac)– Main Linac– Beam Delivery System (BDS), inc. FFS

• DR produces tiny vertical emittances (y ~ 20nm)

• LET must preserve this emittance!– strong wakefields (structure misalignment)– dispersion effects (quadrupole misalignment)

• Tolerances too tight to be achieved by surveyor during installation

Need beam-based alignmentmma!

YjYi

Ki

yj

gij

1

j

j ij i i ji

y g K Y Y

Basics (linear optics)

0

34 ( , )j

iij

j y

yg

y

R i j

linear system: just superimpose oscillations caused by quad kicks.

thin-lens quad approximation: y’=KY

1

j

j ij i i ji

y g K Y Y

YQy

Idiag(K)GQ

Original Equation

Defining Response Matrix Q:

Hence beam offset becomes

Introduce matrix notation

21

31 32

41 42 43

0 0 0 0

0 0 0

0 0

0

g

g g

g g g

G

G is lower diagonal:

Dispersive Emittance Growth

Consider effects of finite energy spread in beam RMS

( ) ( )1

K

Q G diag Ichromatic response matrix:

latticechromaticity

dispersivekicks0

34 34 346

( ) (0)

( ) (0)R R T

GG G

dispersive orbit: ( )( ) (0)y

Δy

η Q Q Y

What do we measure?

BPM readings contain additional errors:

boffset static offsets of monitors wrt quad centres

bnoise one-shot measurement noise (resolution RES)

0BPM offset noise 0 0

0

y

y

y Q Y b b R y y

fixed fromshot to shot

random(can be averaged

to zero)launch condition

In principle: all BBA algorithms deal with boffset

Scenario 1: Quad offsets, but BPMs aligned

BPM

Assuming:

- a BPM adjacent to each quad

- a ‘steerer’ at each quad

simply apply one to one steering to orbit

steererquad mover

dipole corrector

Scenario 2: Quads aligned, BPMs offset

BPM

1-2-1 corrected orbit

one-to-one correction BAD!

Resulting orbit not Dispersion Free emittance growth

Need to find a steering algorithm which effectively puts BPMs on (some) reference line

real world scenario: some mix of scenarios 1 and 2

BBA

• Dispersion Free Steering (DFS)– Find a set of steerer settings which minimise the

dispersive orbit– in practise, find solution that minimises difference

orbit when ‘energy’ is changed– Energy change:

• true energy change (adjust linac phase)• scale quadrupole strengths

• Ballistic Alignment– Turn off accelerator components in a given section,

and use ‘ballistic beam’ to define reference line– measured BPM orbit immediately gives boffset wrt to

this line

DFS

( ) (0)E E

E E

E

E

Δy Q Q Y

M Y

1 Y M Δy

Problem:

Solution (trivial):

Note: taking difference orbit y removes boffset

Unfortunately, not that easy because of noise sources:

noise 0 Δy M Y b R y

DFS example

300m randomquadrupole errors

20% E/E

No BPM noise

No beam jitter

m

m

DFS example

Simple solve

1 Y M Δy

original quad errors

fitter quad errors

In the absence of errors, works exactly

Resulting orbit is flat

Dispersion Free

(perfect BBA)

Now add 1m random BPM noise to measured difference orbit

DFS example

Simple solve

1 Y M Δy

original quad errors

fitter quad errorsFit is ill-conditioned!

DFS example

m

m

Solution is still Dispersion Free

but several mm off axis!

DFS: Problems

• Fit is ill-conditioned– with BPM noise DF orbits have very large unrealistic

amplitudes.

– Need to constrain the absolute orbit

T T

2 2 2res res offset2

Δy Δy y y

minimise

• Sensitive to initial launch conditions (steering, beam jitter)– need to be fitted out or averaged away

0R y

DFS example

Minimise

original quad errors

fitter quad errors

T T

2 2 2res res offset2

Δy Δy y y

absolute orbit now

constrained

remember

res = 1m

offset = 300m

DFS example

m

m

Solutions much better behaved!

! Wakefields !

Orbit not quite Dispersion Free, but very close

DFS practicalities

• Need to align linac in sections (bins), generally overlapping.

• Changing energy by 20%– quad scaling: only measures dispersive kicks from quads.

Other sources ignored (not measured)– Changing energy upstream of section using RF better, but

beware of RF steering (see initial launch)– dealing with energy mismatched beam may cause problems

in practise (apertures)

• Initial launch conditions still a problem– coherent -oscillation looks like dispersion to algorithm.– can be random jitter, or RF steering when energy is changed.– need good resolution BPMs to fit out the initial conditions.

• Sensitive to model errors (M)

Ballistic Alignment

• Turn of all components in section to be aligned [magnets,

and RF]

• use ‘ballistic beam’ to define straight reference line (BPM

offsets)

• Linearly adjust BPM readings to arbitrarily zero last BPM

• restore components, steer beam to adjusted ballistic line

62

BPM, 0 0 offset, noise,i i i iy y s y b b

Ballistic Alignment

bi qi

Lb

quads effectively aligned to ballistic reference

angle = i

ref. line

with BPM noise

62

Ballistic Alignment: Problems

• Controlling the downstream beam during the ballistic measurement– large beta-beat– large coherent oscillation

• Need to maintain energy match – scale downstream lattice while RF in ballistic

section is off

• use feedback to keep downstream orbit under control

An Introduction to thePhysics and Technologyof e+e- Linear Colliders

Lecture 9: b) Lessons learnt from SLC

Nick Walker (DESY)

DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003

Lessons from the SLC

IP Beam Size vs Time

0

1

2

3

4

5

6

7

8

9

10

1985 1990 1991 1992 1993 1994 1996 1998

Year

Beam

Size

(micr

ons)

0

1

2

3

4

5

6

7

8

9

10

x*

y

(micr

ons

2 )

SLC Design(x * y)

X

Y

X * y

New Territory in Accelerator Design and Operation

• Sophisticated on-line modeling of non-linear physics.

• Correction techniques expanded from first-order (trajectory) to include second-order (emittance), and from hands-on by operators to fully automated control.

• Slow and fast feedback theory and practice.

D. Burke, SLAC

The SLC

1980 1998

taken from SLC – The End Game by R. Assmann et al, proc. EPAC 2000

note: SLC was a single bunch machine (nb = 1)

SLC: lessons learnt

• Control of wakefields in linac– orbit correction, closed (tuning) bumps

– the need for continuous emittance measurement(automatic wire scanner profile monitors)

• Orbit and energy feedback systems– many MANY feedback systems implemented over the life time of

the machine

– operator ‘tweaking’ replaced by feedback loop

• Final focus optics and tuning– efficient algorithms for tuning (focusing) the beam size at the IP

– removal (tuning) of optical aberrations using orthogonal knobs.

– improvements in optics design

• many many more!

The SLC was an 10 year accelerator R&D project that also did some physics

The Alternatives

TESLA JLC-C JLC-X/NLC CLIC

f GHz 1.3 5.7 11.4 30.0

L 1033 cm-2s-1 34 14 20 21

Pbeam MW 11.3 5.8 6.9 4.9

PAC MW 140 233 195 175

y 10-8m 3 4 4 1

y* nm 5 4 3 1.2

2003 Ecm=500 GeV

Examples of LINAC technology

9 cell superconducting Niobium cavity for TESLA (1.3GHz)

11.4GHz structure for NLCTA

(note older 1.8m structure)

Competing Technologies: swings and roundabouts

SLC(3GHz)

RF frequencyCLIC(30GHz)

TESLA

(1.3GHz SC)

NLC(11.4GHz)

higher gradient = short linac

higher rs = better efficiency High rep. rate = GM suppression smaller structuredimensions = high wakefields Generation of high pulse peakRF power

long pulse low peak power large structure dimensions = low WF very long pulse train = feedback within train SC gives high efficiency Gradient limited <40 MV/m = longer linac

low rep. rate bad for GM suppression (y dilution) very large unconventional DR

An Introduction to thePhysics and Technologyof e+e- Linear Colliders

Lecture 9: c) Summary

Nick Walker (DESY)

DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003

The Luminosity Issue

,

BSRF RFD

cm n y

PL H

E

zy

• high RF-beam conversion efficiency RF

• high RF power PRF

• small normalised vertical emittance n,y

• strong focusing at IP (small y and hence small z)

• could also allow higher beamstrahlung BS if willing to live with the consequences

• Valid for low beamstrahlung regime (<1)

High Beamstrahlung Regime

BSbeam

,y n

L P

low beamstrahlung regime 1:

32

BSbeam

,z y n

L P

high beamstrahlung regime 1:

*y z with

Pinch Enhancement

,

BSRF RFD

cm n y

PL H

E

( )

2 2

( )

D D y

b e z b e zzy

beam y x y y x

H H D

N r N rD

f

Trying to push hard on Dy to achieve larger HD leads to single-bunch kink instability detrimental to luminosity

The Linear Accelerator (LINAC)

• Gradient given by shunt impedance:– PRF RF power /unit length– rl shunt impedance /unit length

• The cavity Q defines the fill time:– vg = group velocity, – ls = structure length

• For TW, is the structureattenuation constant:

• RF power lost along structure (TW):

( ) ( )z RF lE z P z r

2 / SW

2 Q/ / TWfills g

Qt

l v

2, ,RF out RF inP P e

2RF z

b zl

dP Ei E

dz r

power lost to structure beam loading

RF

would like RS to be as high as possible

sR

The Linear Accelerator (LINAC)

For constant gradient structures:

unloaded

av. loaded

20 1u lV r P L e unloaded structure voltage

2

beam 2

1 21

2 1l u l

eV V r Li

e

loaded structure voltage(steady state)

3

22

0opt 2

1

1 (1 2 )l

ePi

r L e

optimum current (100% loading)

The Linear Accelerator (LINAC)

Single bunch beam loading: the Longitudinal wakefield

700 kV/mz bunchE NLC X-band structure:

The Linear Accelerator (LINAC)

Single bunch beam loading Compensation using RF phase

wakefield

RF

Total

= 15.5º

RMS E/E

Ez

min = 15.5º

Transverse Wakes: The Emittance Killer!

tb

( , ) ( , ) ( , )V t I t Z t

Bunch current also generates transverse deflecting modes when bunches are not on cavity axis

Fields build up resonantly: latter bunches are kicked transversely

multi- and single-bunch beam breakup (MBBU, SBBU)

Damped & Detuned Structures

NLC RDDS1 bunch spacing

Slight random detuning between cells causes HOMs to decohere.

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

HOM2Qt

Single bunch wakefieldsEffect of coherent betatron oscillation

- head resonantly drives the tail

head

tail

22

22

0 head

tail

hy

tt wf h

d yk y

ds

d yk y w y

ds

2cell

BNS 2

1

16 sin ( )z LW q

E

Cancel using BNS damping:

Wakefields (alignment tolerances)

bunch

0 km 5 km 10 km

head

head

headtailtail

tail

accelerator axis

cavities

y

tail performsoscillation

RMS

3

1 Z

z

EYNW

f EN

higher frequency = stronger wakefields

-higher gradients

-stronger focusing (smaller )

-smaller bunch charge

Damping Rings

2 /( ) DTf eq i eq e

final emittance equilibriumemittance

initial emittance(~0.01m for e+)

damping time

wiggler

wiggler

Lwig

4

arc

EE C

6 2 2wig wig1.27 10 (T) (GeV) (m)E B E L

train

rep

2

8D

nE

P f

train b bC n n t c

Bunch Compression

• bunch length from ring ~ few mm• required at IP 100-300 m

RF

z

E /E

z

E /E

z

E /E

z

E /E

z

E /E

long.phasespace

dispersive section

The linear bunch compressor

,0 2

,0 ,0

1RF RF z c uc RF c

RF z RF z

k V E EV F

E k k

2 22 1c u

c c u cu

F F

conservation of longitudinal emittance

RF cavity

initial (uncorrelated) momentum spread: u

initial bunch length z,0

compression ration Fc=z,0/z

beam energy ERF induced (correlated) momentum spread: c

RF voltage VRF

RF wavelength RF = 2/ kRF longitudinal dispersion: R56

see lecture 6

The linear bunch compressor

2

,0 ,056 2 2 2 2

1c z zRF RF

u u

z k VR

F E F

chicane (dispersive section)

Two stage compression used to reduce final energy spread

COMP #1 LINAC COMP #2F1

F2EE0

01 2

0

0

0

f i

T i

EF F

E E

EF

E E

56

0 wiggler

0 arcR

Final Focusing IP

FD

Dx

sextupoles

dipole

0 0 0

0 1/ 0 0

0 0 0

0 0 0 1/

m

m

m

m

R

L*

FD *

FD *

SX

2 2SX

( )

( )

yy

Lx

xL

y S x y

x S x y

*

1S

Lchromatic correction

Synchrotron Radiation effects

IP

FD

x dipole

L*

LB

5B

33 *5ee

2

L

η'Lγλr19

E

ΔE

2*2y 2

y*2y

Δσ ΔEW

σ E

FD chromaticity + dipole SR sets limits on minimum bend length

Final Focusing: Fundamental limits

Already mentioned that

At high-energies, additional limits set by so-called Oide Effect:synchrotron radiation in the final focusing quadrupoles leads to a beamsize growth at the IP

zy

1 57 71.83 e e nr F minimum beam size:

occurs when 2 37 72.39 e e nr F

independent of E!

F is a function of the focusing optics: typically F ~ 7(minimum value ~0.1)

0 500 1000 1500 2000

1

0.5

0

0.5

1

0 500 1000 1500 2000

1

0.5

0

0.5

1100nm RMS random offsets

sing1e quad 100nm offset

LINAC quadrupole stability

*,

1 1

**

sin( )

Q QN N

Q i i i Q i ii i

ii i i

y k Y g k Y g

g

* 2

*2 2 2,*

1

sin ( )QN

i Q i i iji

Yy k

for uncorrelated offsets

2 22 2

*2,

0.32

j Q QY

y y n

y N k

take NQ = 400, y ~ 61014 m, ~ 100 m, k1 ~ 0.03 m1 ~25 nm

Dividing by and taking average values:

*2 * *, /y y n

Beam-Beam orbit feedback

use strong beam-beam kick to keep beams colliding

see lecture 8

IP

BPM

bb

FDBK kicker

y

e

e

Generally, orbit control (feedback) will be used extensively in LC

Beam based feedback: bandwidth

0.0001 0.001 0.01 0.1 1

0.05

0.1

0.5

1

5

10

f / frep

g = 1.0g = 0.5g = 0.1g = 0.01

f/frep

Good rule of thumb: attenuate noise with ffrep/20

Ground motion spectra

( , )

1( , ) ( , ) 1 cos( )

P k

L P k kL dk

2D power spectrum

measurable relativepower spectrum

Both frequency spectrum and spatial correlation important for LC performance

Long Term Stability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000 10000 100000 1000000

time /s

rela

tive

lum

ino

sity

1 hour 1 day1 minute 10 days

No Feedback

beam-beam feedback

beam-beam feedback +

upstream orbit control

understanding of ground motion and vibration spectrum important

example of slow diffusive ground motion (ATL law)

see lecture 8

A Final Word

• Technology decision due 2004• Start of construction 2007+• First physics 2012++• There is still much to do!

WE NEED YOUR HELP

for

the Next Big Thing

hope you enjoyed the course

Nick, Andy, Andrei and PT