Paul Emma Stanford Linear Accelerator Center July 2, 2002 High Brightness Electron Beam Magnetic Compression: Physics and Compressor Design
Jan 16, 2016
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