Paul EmmaStanford Linear Accelerator Center

July 2, 2002

Paul EmmaStanford Linear Accelerator Center

July 2, 2002

High Brightness Electron Beam Magnetic Compression:

Physics and Compressor Design

High Brightness Electron Beam Magnetic Compression:

Physics and Compressor Design

“Any fool with four dipoles can compress a bunch”

—anonymous

“Any fool with four dipoles can compress a bunch”

—anonymous

OK, but there may be a few details to consider…OK, but there may be a few details to consider…

Magnetic Bunch CompressionMagnetic Bunch Compression

z0z0

zzzz

under-compressionunder-compression

V = V0sin()V = V0sin()

RF AcceleratingRF AcceleratingVoltageVoltage

RF AcceleratingRF AcceleratingVoltageVoltage

z = R56z = R56

Path Length-EnergyPath Length-EnergyDependent BeamlineDependent BeamlinePath Length-EnergyPath Length-EnergyDependent BeamlineDependent Beamline

…or over-compression

…or over-compression

zz

E/EE/E

zz

‘chirp’‘chirp’

TESLA XFEL at DESYTESLA XFEL at DESY

X-FEL Integrated into linear colliderX-FEL Integrated into linear collider

0.85-60 Å0.85-60 Å

3 compressors3 compressors

X-FEL based on last 1-km of existing SLAC linacX-FEL based on last 1-km of existing SLAC linac

LCLS at SLACLCLS at SLAC

LCLSLCLSLCLSLCLS

1.5-15 Å1.5-15 Å

2 compressors2 compressors

eV

z

eV0

Single-Stage Bunch CompressionSingle-Stage Bunch Compression

final bunch length and energy spread…final bunch length and energy spread…

bunch length stability with RF phase jitter…bunch length stability with RF phase jitter… T. RaubenheimerT. Raubenheimer

‘chirp’

t0t0

t0t0 t1t1

late arrival,higher energy,

less chirp

late arrival,higher energy,

less chirp

longer bunch,less wake,more chirp

longer bunch,less wake,more chirp

t2t2

Two-Stage Compression Used for StabilityTwo-Stage Compression Used for Stability

System can be optimized for stability against timing & charge jitterSystem can be optimized for stability against timing & charge jitter

~same bunch length~same bunch length

Types of CompressorsTypes of Compressors

wigglerwiggler

FODO-cell arcFODO-cell arcTT

SLC RTL,SLC arcsNLC BC2

SLC RTL,SLC arcsNLC BC2

LEUTL,… LCLS, TTF-BC1,2,TESLA-BC1

LEUTL,… LCLS, TTF-BC1,2,TESLA-BC1

TESLA-BC2,3TESLA-BC2,3

But T566 > 0 in all cases…But T566 > 0 in all cases…

(bunch head at z < 0)(bunch head at z < 0)

> 0> 0

reverse signreverse sign

< 0< 0

simple, achromaticsimple, achromatic

< 0< 0

achromatic, cancellation?achromatic, cancellation?

LTLT

4-dipole chicane4-dipole chicane

LBLB

LcLc

For chicane or wiggler (any ‘non-focusing’ compressor), the path length...For chicane or wiggler (any ‘non-focusing’ compressor), the path length...For chicane or wiggler (any ‘non-focusing’ compressor), the path length...For chicane or wiggler (any ‘non-focusing’ compressor), the path length...

Now add 2Now add 2ndnd order term of sinusoidal rf accelerating voltage... order term of sinusoidal rf accelerating voltage...Now add 2Now add 2ndnd order term of sinusoidal rf accelerating voltage... order term of sinusoidal rf accelerating voltage...

For a uniform temporal distribution [For a uniform temporal distribution [zz0044 = (9/5) = (9/5)zz00

44] and] and zz0000 = 0 = 0 ... ...For a uniform temporal distribution [For a uniform temporal distribution [zz0044 = (9/5) = (9/5)zz00

44] and] and zz0000 = 0 = 0 ... ...

22ndnd Order Compression Limitations Order Compression Limitations

r T566/R56r T566/R56

For chicane and accelerating phase, RF curvature and For chicane and accelerating phase, RF curvature and TT566566 always add, always add, limiting the minimum bunch length ...limiting the minimum bunch length ...For chicane and accelerating phase, RF curvature and For chicane and accelerating phase, RF curvature and TT566566 always add, always add, limiting the minimum bunch length ...limiting the minimum bunch length ...

eV

z

e

eV

z

e

rr TT566566//RR5656rr TT566566//RR5656

Decelerating phase can be used to compensate Decelerating phase can be used to compensate TT566566, but not , but not practical in low energy compressors (used in NLC and TESLA)...practical in low energy compressors (used in NLC and TESLA)...Decelerating phase can be used to compensate Decelerating phase can be used to compensate TT566566, but not , but not practical in low energy compressors (used in NLC and TESLA)...practical in low energy compressors (used in NLC and TESLA)...

e

linear2nd-order

R56 /m

z /

m

1 40° x =

Slope Slope linearizedlinearized

x = s/4

Harmonic RF used to Linearize CompressionHarmonic RF used to Linearize CompressionRF curvature and 2nd-order compression cause current spikesRF curvature and 2nd-order compression cause current spikes

Harmonic RF at decelerating phase corrects 2nd-order and allows unchanged z-distributionHarmonic RF at decelerating phase corrects 2nd-order and allows unchanged z-distribution

avoid!avoid!

0

2 25660 2 3

562

11 1

2

1

sz z i

xs x

TE E

ReV

0

2 25660 2 3

562

11 1

2

1

sz z i

xs x

TE E

ReV

0.5-m X-band section for LCLS (22 MV, 11.4 GHz)

0.5-m X-band section for LCLS (22 MV, 11.4 GHz)

3rd harmonic used at TTF/TESLA4th harmonic used at LCLS3rd harmonic used at TTF/TESLA4th harmonic used at LCLS

m

m

eV

z

e

eV

z

e

Reverse-Sign R56 to Linearize CompressionReverse-Sign R56 to Linearize Compression

eV

z

e

eV

z

e

TESLA-BCarc example 70°

TESLA-BCarc example 70°

chicane or wigglerchicane or wiggler

R56 < 0R56 < 0

FODO-cell arcFODO-cell arc

R56 > 0R56 > 0

SLACSLAC S-Band: S-Band:ss00 1.32 mm 1.32 mmaa 11.6 mm 11.6 mm

ss < ~6 mm < ~6 mm

SLACSLAC S-Band: S-Band:ss00 1.32 mm 1.32 mmaa 11.6 mm 11.6 mm

ss < ~6 mm < ~6 mm

Wakefield induced slope (–)Wakefield induced slope (–)Wakefield induced slope (–)Wakefield induced slope (–)RF slope (+ for chicane)RF slope (+ for chicane)RF slope (+ for chicane)RF slope (+ for chicane)

For a For a uniformuniform ss-distribution (-distribution (ss = 2 = 233ss)...)...For a For a uniformuniform ss-distribution (-distribution (ss = 2 = 233ss)...)...

Induced voltage along bunch:Induced voltage along bunch:Induced voltage along bunch:Induced voltage along bunch:

Longitudinal Geometric WakefieldsLongitudinal Geometric WakefieldsVV

(( ss)/

MV

/nC

/m)/

MV

/nC

/m

ss//ssFWFW

1 mm1 mm

500 500 mm

250 250 mm

100 100 mm 50 50 mm 25 25 mm

s

Longitudinal point-wake:Longitudinal point-wake:Longitudinal point-wake:Longitudinal point-wake:

K. BaneK. Bane

LL 550 m, 550 m,N N 6.2 6.2101099,,z z 75 75 m,m,EE = 14 GeV = 14 GeV

LCLSLCLS Example of Wakefield Use Example of Wakefield Usewakefield ‘OFF’wakefield ‘OFF’

wakefield ‘ON’wakefield ‘ON’

for uniform for uniform distributiondistributionfor uniform for uniform distributiondistribution

wake-induced wake-induced energy spreadenergy spreadwake-induced wake-induced energy spreadenergy spread

headhead

0.26 %0.26 %

headhead

< 0.02 %< 0.02 %

end of LCLS linacend of LCLS linac

Wake cancels energy chirp after compression (weaker chicane, less CSR),

Wake cancels energy chirp after compression (weaker chicane, less CSR),

but also forms current spikes during compression,

but also forms current spikes during compression,

Advantages and Disadvantages of WakefieldAdvantages and Disadvantages of Wakefield

…and transverse wakes may dilute emittance of long bunch

…and transverse wakes may dilute emittance of long bunch

Best of both: use SC-L-band before compression and S- or C-band after ?

Best of both: use SC-L-band before compression and S- or C-band after ?

Synchrotron RadiationSynchrotron Radiation

zz

1/3

Pow

erPo

wer

WavelengthWavelength

coherent power

incoherent power

vacuum chamber cutoff

vacuum chamber cutoff

N N 10 101010

Incoherent synchrotron radiation (ISR) increases at high energies - dilutes ‘slice’ emittance...

Incoherent synchrotron radiation (ISR) increases at high energies - dilutes ‘slice’ emittance...

For, symmetric beta-functions, the effect is minimum when...

For, symmetric beta-functions, the effect is minimum when...

And substituting R56 for ... And substituting R56 for ...

Total chicane length, L, set by tolerable N (e.g., /0 1%)…Total chicane length, L, set by tolerable N (e.g., /0 1%)…

LCLS BC2 (E = 4.50 GeV, |R56| = 22 mm) needs L 6.4 mLCLS BC1 (E = 0.25 GeV, |R56| = 36 mm) needs L 0.06 m

LCLS BC2 (E = 4.50 GeV, |R56| = 22 mm) needs L 6.4 mLCLS BC1 (E = 0.25 GeV, |R56| = 36 mm) needs L 0.06 m

ISR Emittance Growth for ChicaneISR Emittance Growth for Chicane

xx

LL

LBLB

LL

T. RaubenheimerT. Raubenheimer

x = Rx = R1616((ss))E/EE/E

bend-plane emittance growthbend-plane emittance growth

ee––RR

Coherent Synchrotron Radiation (CSR)Coherent Synchrotron Radiation (CSR)

zz

coherent radiation coherent radiation forforzz

overtaking length:overtaking length: L L00 (24 (24zzRR22))1/31/3

ssxx

Powerful radiation generates energy spread in bends Powerful radiation generates energy spread in bends

Causes bend-plane emittance growth (short bunch worse) Causes bend-plane emittance growth (short bunch worse)

Energy spread breaks achromatic system Energy spread breaks achromatic system

LL00

CSR wake is strong at very small scales ( m)CSR wake is strong at very small scales ( m)

B1B1 B2B2 B3B3 B4B4

xx 1.52 1.52 mm

Projected Emittance GrowthProjected Emittance GrowthB1B1 B2B2 B3B3 B4B4

0.021%0.021%

0.043%0.043% Berlin Workshop Case

Berlin Workshop Case

x/m

rad

z /mm

Now rematch incoming beamNow rematch incoming beam

optopt 1.37 m 1.37 m

optopt 1.101.10optopt 1.37 m 1.37 m

optopt 1.101.10

1.52 1.52 mm

00 = 1.00 = 1.00 mmCSRCSR 0.145 0.145 mm

Projected Emittance growth reduced by Projected Emittance growth reduced by -matching-matching

slice centroids after CSR

slice centroids after CSR

optopt

optopt

optopt

optopt

1.15 1.15 mm

00 = 1.00 = 1.00 mmCSRCSR 0.145 0.145 mm

xx 244 mm 244 mm

xx 107 mm 107 mmI

RR5656 = = 21 mm21 mm RR5656 = = 4 mm4 mm

Double-Chicane Emittance Growth CancellationDouble-Chicane Emittance Growth Cancellation

ss 50 50 mm

ss 200 200 mm

ss 20 20 mm EE00 =

5 G

eV =

5 G

eV

CSR Emittance Growth Reduced in CSR Emittance Growth Reduced in DoubleDouble-Chicane-Chicane

xx 1.01 1.01 mmxx 1.01 1.01 mm

projected emittance growth is greatly reduced using double-projected emittance growth is greatly reduced using double-chicane, however, microbunching can be more severechicane, however, microbunching can be more severe

projected emittance growth is greatly reduced using double-projected emittance growth is greatly reduced using double-chicane, however, microbunching can be more severechicane, however, microbunching can be more severe

single-chicanesingle-chicanesingle-chicanesingle-chicane

double-chicanedouble-chicanedouble-chicanedouble-chicane

CSR Microbunching* in LCLSCSR Microbunching* in LCLS

SC-wiggler SC-wiggler damps damps

bunchingbunching 33101055

Super-conducting wiggler prior to BC increases uncorrelated E-spread ()Super-conducting wiggler prior to BC increases uncorrelated E-spread ()

R. CarrR. Carr

energy profileenergy profile long. spacelong. space temporal profiletemporal profile

micro-bunching

micro-bunching

33101066

230 fsec230 fsec

CSR can amplify small current modulations:

CSR can amplify small current modulations:

* First observed by M. Borland (ANL) in LCLS Elegant tracking* First observed by M. Borland (ANL) in LCLS Elegant tracking

EE/E/E00 = 3 = 3101066

xx00 = 0 = 0

‘‘cold’ beamcold’ beam

CSR Microbunching Gain in LCLS BC2CSR Microbunching Gain in LCLS BC2

add 2% current & energy modulation

add 2% current & energy modulation

after compressor

after compressor

CSR Microbunching AnimationCSR Microbunching Animation

E/E0E/E0

f(s)f(s)

xx

LCLS BC2 CSR Microbunching Gain vs. LCLS BC2 CSR Microbunching Gain vs.

“theory”: S. Heifets et al., SLAC-PUB-9165, March 2002“theory”: S. Heifets et al., SLAC-PUB-9165, March 2002

Initial modulation wavelength prior to compressor

Initial modulation wavelength prior to compressor

Micr

obun

chin

g G

ain

Micr

obun

chin

g G

ain

‘cold’ beam‘cold’ beamx=1 mx=1 m

x=1 m, =3105x=1 m, =3105

see also E. Saldin, Jan. 02, and Z. Huang, April 02

…Energy Profile also modulated…Energy Profile also modulated

energy profile

current profile Next set of bends will magnify this again…

‘slice’ effects

Next set of bends will magnify this again…

‘slice’ effects

E/E vs. z

xx = 1 = 1 mm

curves: Z. Huang et al., PRSTAB April 2002points: 1D tracking code

LCLS BC1/BC2 Compound Gain CurveLCLS BC1/BC2 Compound Gain Curve

wavelength at entrance to BC2wavelength at entrance to BC2wavelength at entrance to BC2wavelength at entrance to BC2

Com

poun

d G

ain

Com

poun

d G

ain

= 3= 3101066

SC-wiggler: SC-wiggler: = 3= 3101055

Microbunching is damped by Microbunching is damped by xx-emittance -emittance or uncorrelated energy spread for or uncorrelated energy spread for

wavelengths less than…wavelengths less than…

Microbunching is damped by Microbunching is damped by xx-emittance -emittance or uncorrelated energy spread for or uncorrelated energy spread for

wavelengths less than…wavelengths less than…

Damping by Emittance and Energy SpreadDamping by Emittance and Energy Spread

E. SchneidmillerE. Schneidmiller, et al. (no compression), et al. (no compression)E. SchneidmillerE. Schneidmiller, et al. (no compression), et al. (no compression)

To reduce microbunching…To reduce microbunching… long bends, long bends, LLbb

large large xx oror xx

large uncorrelated energy spread, large uncorrelated energy spread, uu

To reduce microbunching…To reduce microbunching… long bends, long bends, LLbb

large large xx oror xx

large uncorrelated energy spread, large uncorrelated energy spread, uu

Dipole Field QualityDipole Field Quality

Quadrupole field component at radius r0Quadrupole field component at radius r0

Sextupole field component at radius r0

Sextupole field component at radius r0

Large beam size in chicane — need constant bend field over wide apertureLarge beam size in chicane — need constant bend field over wide aperture

LCLS BC2 B2 & B3 bends:|b1/b0| < 0.01 %|b2/b0| < 0.05 %

LCLS BC2 B2 & B3 bends:|b1/b0| < 0.01 %|b2/b0| < 0.05 %

at r0 = 2 cmat r0 = 2 cm

…causes dispersion error and beta-mismatch…causes dispersion error and beta-mismatch

…causes 2nd-order dispersion, with chromatic and geometric aberrations…causes 2nd-order dispersion, with chromatic and geometric aberrations

|b1/b0| is correctable…|b1/b0| is correctable…

x /2x /2

‘‘Tweaker’ quadrupoles allow dispersion correctionTweaker’ quadrupoles allow dispersion correction

with two quads…correct and (), orthogonallywith two quads…correct and (), orthogonally

LEUTL chicane (ANL)LEUTL chicane (ANL)

M. BorlandM. Borland

relative bunch length (z)relative bunch length (z)

BPM ()BPM ()

Feedback SystemsFeedback Systems

, V, V

Feedback at each compressor, plus charge-feedback at gun……needs work (algorithm, diagnostics, full-system simulations)Feedback at each compressor, plus charge-feedback at gun……needs work (algorithm, diagnostics, full-system simulations)

tolerances:~ 0.1 deg-S~0.1% V/V

tolerances:~ 0.1 deg-S~0.1% V/V

Final CommentsFinal Comments

Many details need attention so that brightness is increased, not decreased after compression

Compression system design should be well integrated into entire machine Stability Emittance preservation Diagnostics

Feedback systems may be critical Progress made at SLC only after feedback

systems up and running

Many details need attention so that brightness is increased, not decreased after compression

Compression system design should be well integrated into entire machine Stability Emittance preservation Diagnostics

Feedback systems may be critical Progress made at SLC only after feedback

systems up and running