Photoinjectors & Beam Manipulations for LCs and FELs & Collimation

[MCCPB, Chapters 5,6]

• manipulations in photoinjectors– space-charge compensation– flat beam generation

• emittance exchange• some other beam manipulations for FELs• collimation in linacs & storage rings

sources of electron beams

requirements: small emittance high charge, high repetition rate, possibly high degree of polarization

• thermionic guns• dc guns with laser photocathodes• photo-cathode rf guns

(SLC)

rf wave

laser beam

e-

cross section of an earlyBNL S-band rf gun(J. Clendenin, 1996)

most popular in modern e- accelerators (in particular, if low emittances aredesired); high-power pulsed laser illuminates photocathode placed on the end wall ofan accelerating cavity, electrons are immediately accelerated in rf field

normalized emittance determined by three effects:• thermal emittance – initial transverse momenta• rf emittancee – from time-dependent focusing force• space-charge force

techniques for shaping and preserving the beam emittance from such injector:

space-charge compensation using solenoidsgeneration of a flat-beam transverse-longitudinal emittance exchange

rf photo-injector

z

r

a

zeNE br 2

02

r

ac

zeNvB b

2202

r

eEevBeEF rr 2

1

space-charge force

longitudinal bunch profile

assume transverse uniformdistribution with radius a

transverse view

if (z) not constant, different longitudinal slices will experience differentfocusing force Fr

x

x’ different slicesrotate at differentspeedprojected emittanceis increased

space-charge compensation

radius a

after drift of length s: Gcm

sNe bxN 2

00

2

16

6.02.0 G depends on shape of distribution

2,2

1,,

),(,,'

sasr

ssr

)(2

2

fd

d

zz

zf

)(

)(2

),(

),('

ldd

dl

zzz

zz

r

r

f

azzza ddl

Nyx

2222

, )(22

1

place lens of focal length f after distance zl

after total distancezd+zl:

emittance is indeed 0 at chosen value of f

in reality not constantbut above scheme reduced the emittance by a factor 10 in Los Alamos studies

‘space-chargecompensation”(B. Carlsten, ~1993)

bunch slices arerealigned

assume constant

rf

r1

'

normalized longitudinalcoordinate

normalized transverse coordinate

a

after first drift after solenoid

after finaldrift

all particlesare on one line!

center

edge

beware of bifurcation!

r

r’ r’

r

strong space charge

weak space chargebunch center

bunch edgephase-spacebifurcation

important design criterion for photo-injectors: minimize fraction of beam crossing over!

“crossover”

similar techniques to correct correlated growth in projected emittance due to nonlinear forcecan be applied elsewhere

flat-beam transformation

• proposed by Y. Derbenev to convert round

beam into flat or vice versa (1998)

• in particular can produce a flat beam from a

photoinjector if source is placed in solenoid field

and afterwards passed through a (skew) FODO

channel with /2 different phase advance in x & y

zy

zx

By

BdsB

Bx

Bx

BdsB

By

2

11'

2

11'

0

0

0

0

0

0

0'

'

kx

y

ky

x

y

y

x

x

kick at exit of solenoid

phase-space vector at exit of solenoid

quadrupole channel withphase advance difference /2 in x and y choose=1/k

this is a flat beamtilted by 45 degree!

if we use skew-quad.channel, could geta flat beam in x

0

0

0

0

0

0

0

0

10100

000

0010

0001

'

'

kx

y

ky

x

kx

y

ky

x

y

y

x

x

however initial beam has also some rms slope (temperature)

20

202

1,

1,

20

1,

'41

'

2

1

x

x

y

x

yy

k

k

0'0'00 , yxyx assuming

product of x and y emittances approximately conserved

experimental tests at Fermilab A0 line demonstrated the feasibilityof this scheme

simulated evolution of transverse emittances along the FNPL beamline for standard nominal settings

FNAL Flat Beam Experiment

schematic layout

Y.-E. Sun

Simulated and measured beam transverse density evolution. The consecutive plots corresponds to location X3, X4, X5, X6, X7 and X8. Dimensions are in mm.

Overview of the RFTB section. The letters N, S and X represents normal and skew quadrupoles, and diagnostic stations. Dimension are in mm.

simulatedmeasured

FNAL Flat Beam Experiment – cont’d

Y.-E. Sun

general emittance exchange between two planes

with2 magnitude of the coupling and is the sum of the squares of the four elements of the normalized coupling block of the transfer matrix, i.e. U :

where

and

M. Cornacchia and P. Emma

which can be rewrittenas

equal initial uncoupled emittances will always remain equal through a symplectic map; similarly, equal uncoupled emittances cannot be generated from unequal uncoupled initial emittances - setting |A| = 1/2 produces equal emittances, but they are then highly coupled with 𝜆2≠0

transverse to longitudinal emittance exchange- EEX

• proposed by M. Cornacchia and P. Emma to reduced the transverse emittance (and also shrink the bunch length) for FELs (2002)

• realized by placing a transverse deflecting mode radio-frequency cavity (“crab cavity”) in a magnetic chicane

Initial (top) and final (bottom) phase space tracking plots. The horizontal and longitudinal emittances are completely exchanged, as predicted.

M. Cornacchia and P. Emma

transverse to longitudinal emittance exchange – experimental EEX demonstration at FNAL A0 line

T. Koeth, 2009Layout of the A0 Photoinjector with straight ahead and EEX beamline sections.

EEX - key ingredients1. half chicane (dipole magnets) creates correlations between x and

2. deflecting cavity changes energy of particles with transverse offset x and and deflects particles horizontally depending on the longitudinal position

3. another half chicane thin lens deflecting cavity

P. Emma and M. Cornacchia

The 4x4 (horizontal-longitudinal) emittance exchange matrix as a function of TM110 cavity strength. The cavity is off at k=0% and is energized to the ideal emittance exchange strength at k=100%. The circles are measured points, the green (lighter) lines are fits to the data, and the red (darker) lines are calculated values. T. Koeth, 2009

calculated matrix elements

the 4x4 (horizontal-longitudinal) measured matrix

T. Koeth, 2009

nonzero due to finite cavity length

Relative output 1/σp·σz product map against input quadrupole currents. The white cross hairs indicate a choice for EEX operation.

Calculated ratio of εx,in/(σp·σz)out over input quad scan. The white and green cross hairs indicate the operating points for Feb 6 and Feb 11 data sets respectively.

T. Koeth

Transverse input parameters were tuned (by adjusting input quadrupoles) for a minimum output bunch-length energy-spread product.

February 11, 2009, Direct EEX Data Set, Reflecting Input and Output rms Normalized Emittances

T. Koeth, 2009

Undulator RadiationP. Schmüser

Undulators & Free Electron Lasers

Z. Huang,P. Schmuser

undulator

undulator parameter

fundamental wavelength of undulator radiationin forward direction

condition for sustained energy transfer from electron to light wave

exponential growth and saturation of the FEL power in SLAC LCLSat =0.15 nm; initiated by Self Amplified Spontaneous Emission (SASE) process

P. Emma,PAC09

linac based X-ray FEL - LCLS

1-D power gain length

e- density

Pierce parameters

saturation power

typical requirements

Z. Huang,P. Schmuser

combination flat-beam gun & EEX

standard rf photocathode gun:x,y

gun~ 1 m, zgun ~ 0.1 m

flat beam scheme:x,, y z) → (10, 0.1, 0.1) m

followed by transverse-to-longitudinal exchange:x,, y z) → (0.1, 0.1, 10) m

with much improved FEL performance(3x shorter undulator)

P. Emma et al, 2006

=0.4 Å

FEL power as a function of z/Lg0 (1D power gain length) in a seeded FEL and a SASE FEL (soft X-ray FEL FLASH)

P. Schmuseret al.

SASE and seeded FEL - FLASH

FEL seedingSASE exhibits shot-to-shot fluctuations in wavelength and limitedcoherence length (many uncorrelated spikes along the bunch length)

various seeding methods proposed to improve coherencelength of SASE radiation:•High harmonic generation (HHG) in gas; VUV•Self seeding: SASE signal produced by short undulator passed

through monochromator and serves as seed radiationfor main undulator

•High-gain harmonic generation (HGHG) electron is energy-modulated by interaction in an undulator by interaction with powerful laser;magnetic chicane converts energy modulation into density modulation; then second undulator for coherent emission fromdensity modulated beam at higher harmonic frequency

•Echo enabled harmonic generation (EEHG): second modulator followedby second chicane; electron beam interacts twice with two laserpulses in two modulators; density modulation at a very highharmonic number

HGHG FEL scheme

R56

laser

modulator radiator

phase space distribution

D. XiangG. Stupakov

e- shiftby /4

EEHG FEL scheme

R56(1)

laser 1

modulator 1 radiator

laser 2

Modulator 2

R56(2)

phase space distribution

e- shiftby >10

currentdistribution

D. XiangG. Stupakov

A.A. Zholends,M.S. Zolotorev,PRL 76, 6 (1996)

what happens in a modulator?laser

laser radiation spontaneous undulator radiation

total electric field

total field energy

: relative phase of the laser light wave and electron wiggling trajectory in undulator

spontaneous radiation of electrons in an undulator

→ amplitude of e- energy modulation after the modulator

applications of modulators:-laser heating (suppression of microbunching

instability in bunch compressors), e.g. for FELs-FEL HGHG -FEL EEHG-femtosecond pulse generation (bunch “slicing”)

in storage rings…

A.A. Zholends,M.S. Zolotorev,PRL 76, 6 (1996)

an alternative formula can be found inZ. Huang et al. PRST-AB 7, 074401 (2004)

femtosecond pulse generation at the ALSR.W. Schoenlein et al, SCIENCE, Vol. 287 March 2000

Laser interaction with electron bunch in a resonantly tuned wiggler.

Transverse separation of modulated electrons in dispersive bend of the storage ring

Separation of femtosecond synchrotron radiation at the beamline image plane.

E=1.5 GeV, E=1.2 MeVMu=19 periods, u=16 cm,K=13, L=100 fs, AL=400 J, L=800 nm

electron bunch distribution (as a function of horizontal displacement x and time) at the radiating bend magnet, following inter-action with the laser pulse in the wiggler, and propagation through 1.5 arc sectors of the storage ring

collimation• removal of beam halo, which otherwise causes

background in the detector (el.-magnetic showers or muon production when lost near detector; or synchrotron radiation when passing at large amplitudes) or, for s.c. proton rings, could quench the magnets

• controlled removal (activation of only one area)

• multistage systems frequently employed

• collimators also serve to protect the rest of the accelerator against catastrophic beam losses due to failure (machine protection)

• collimator survival collimator impedance

challenge for many future projects

example: collimator at the SNS high-energy beam-transfer line

beam usually not of ideal shape• beam-gas Coulomb scattering

• beam-gas bremsstrahlung

• Compton scattering off thermal photons

• linac wake fields

• halo from the source or from damping rings

• halo from ring-to-linac transport and bunch compression,…

collimation in linear colliders

Yes, measured beam distribution at the end of the SLAC linac (projection on the x-y plane)!

Is there halo in linear colliders?

let us look at the SLC prediction…

DispersionSpace charge (?) Elastic scattering off residual gasResidual-gas bremsstrahlungTouschek scatteringIntrabeam scatteringDark currentsNonlinear magnetic fields Scattering off thermal photonsScattering off laser fieldIncoherent & nonl. wake fieldsSynchrotron radiation (coherent & incoherent)Ion or electron-cloud effects

More Complete List of Candidate Processes

close to the source, in bendseverywhere

everywhereeverywhere

everywhere

scatteringphoto gun

cavities, linacring, linac

e.g. collimatorsin bends

e- or e+ beams

linac

at the SLC

• muons, SR, showers were all problems

• more and more collimators were added over the years upstream of the final focus

• magnetized toroids were placed between collimators and collision points to reduce the number of muons reaching the detector

• it was difficult to model the halo

schematic of a collimation system for future linearcolliders consisting of spoiler and absorber pairs

scattering off thin spoiler increases beam size on subsequent absorber to prevent damage

collimation is done for different betatron phases and in energy

collimation in storage rings

• beam-gas Coulomb scattering

• beam-gas bremsstrahlung

• Compton scattering off thermal photons

• nonlinear fields (resonances, tune drifts,…)

• space charge

• intrabeam scattering, Touschek effect

• beam-beam interaction

halo generating processes

measurement of beam tailsin LEP-2 (80-100 GeV)using movable collimators

result of Monte-Carlo simulation

beam-gas scattering and thermal-photon scattering

(Courtesy H.. Burkhardt, 1998)

cN

N halo generation rate

density ofresidual gasor of thermalphotons

halo generation by scattering processes

cross section

total cross sectiondepends on limits for ,

Bremsstrahlungelectrons lose energy in inelastic scattering events with theresidual gas (e.g., SLAC-PUB-8012 and references therein)

3/1

22

0

2

0

183ln4

1

where

3

4

3

41

ZA

ZNr

X

kkkXN

A

dk

d

Ae

A

brems

total cross section for energy loss > 1% is 6.5 barn for CO

bB

bremsb

ebrems

LNTk

pN

ZZr

183

lnln3

163/1min

22

remains importantat high energies

k: energy of photon radiatedin bremsstrahlung event

Elastic Coulomb scattering

total cross section

23/82.0 Cel Z

for scattering above minimum angle

3/1min 4.1 where, Za

pae

bB

elb LNTk

pN

scattered electrons:

scattering angle decreases at higher energies

at large amplitudes tail from elastic gas scattering like ~1/y3

TorRauben-heimer,1992

damping ring

Scattering off thermal photonstotal cross section is close to the Thomson cross section=8/(3r0

2)=0.665 barn

density of photons is =2x107 T3/m3; at room temperature =5.3x1014/m3

number of scattered particles: Nb= L Nb

maximum energy loss ymax=x/(1+x), wherex=15.3 [E/TeV] [E/eV] cos2 (/2)

average photon energy E=2.7 kBT (10 meV at 300 K)

this process becomes relevant for beam energies above50 GeV, when the mean relative energy loss in a scatteringevent exceeds 1%

number of photons per radian:

Synchrotron radiation

GeV rad

120

32

5

d

dN

critical energy: ccc EEEc

E ,,

3

, 32.0315

8 and

2

3

energy spread:

2

52

324

55eerms r

emittance growth:5211

35 GeVm102 where Qb

xQx Cl

HEC

tails:2

4

,

/

2, 2

where/28

39 ,

EcCP

EE

e

E

P

dE

dN

c

EE

c

c

at both SLC and LEP the synchrotron radiation was minimized by weakening the last bending magnet closest to the interactionpoint by factor ~10, which reduced the critical energy as well as the number of photons emitted per unit length

in addition radiation masks were installed to absorb photons emittedin the weak bend and in upstream bends

layout of the straight sectionaround IP4 or IP8 in LEP;COLH, COLV, COLZ are masks(Courtesy H.. Burkhardt, 1998)

residual background in LEP arose mainly from multiply scattered photons;reflectivity of soft X-rays is close to 100% for impact below critical angle~30 mrad keV/Ereduced by coating or surface roughening

LEP masks provided complete shielding against direct photons andagainst singly scattered photons:

(Courtesy H.. Burkhardt, 1998)

H. Burkhardt

synchrotron-radiation shields for FCC-ee?

Summary

photo-injectors, space-charge compensation

generation of a flat beamgeneral emittance exchangetransverse-longitudinal emittance exchange

FEL laser seeding and bunch slicing

halo generationcollimation in linear colliders & storage rings