Max Cornacchia, Paul Emma Stanford Linear Accelerator Center Max Cornacchia, Paul Emma Stanford...
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Transcript of Max Cornacchia, Paul Emma Stanford Linear Accelerator Center Max Cornacchia, Paul Emma Stanford...
Max Cornacchia, Paul EmmaStanford Linear Accelerator CenterMax Cornacchia, Paul Emma
Stanford Linear Accelerator Center
Proposed by M. Cornacchia (Nov. 2001)Proposed by M. Cornacchia (Nov. 2001) Analysis taken from similar Analysis taken from similar x-yx-y coupling coupling
work by W. Spence and P. Emmawork by W. Spence and P. Emma Motivation to reduce transverse and Motivation to reduce transverse and
increase longitudinal emittance increase longitudinal emittance faster faster SASE lasing and less CSR micro-SASE lasing and less CSR micro-bunching in compressorsbunching in compressors
Transverse to Longitudinal Transverse to Longitudinal Emittance ExchangeEmittance Exchange
transverse emittance:transverse emittance:
energy spread:energy spread:
< 1 m at 1 Å, 15 GeV < 1 m at 1 Å, 15 GeV
< 0.05% at Ipk = 4 kA, K 4, u 3 cm, … < 0.05% at Ipk = 4 kA, K 4, u 3 cm, …
We need x < 1 m , but z z
We need x < 1 m , but z z
Can we reduce x at the expense of z ?Can we reduce x at the expense of z ?
RF gun produces x ~ z ~ few mRF gun produces x ~ z ~ few m
SASE FEL needs very bright electron beam…SASE FEL needs very bright electron beam…
< 300 m< 300 m
Emittance Exchange ConceptEmittance Exchange Concept
Electric and magnetic fieldsElectric and magnetic fieldskk
x0
z0
x0
z0
transverse RF in a chicane…transverse RF in a chicane…
Particle at position x in cavity gets acceleration: kx Particle at position x in cavity gets acceleration: kx
Must include magnetic field and calculate emittance in both planes…Must include magnetic field and calculate emittance in both planes…
??
This energy deviation in chicane causes position change: x = This energy deviation in chicane causes position change: x = Choose k to cancel initial position: x kxx kk = 1 = 1 Choose k to cancel initial position: x kxx kk = 1 = 1
Characterize Initial BeamCharacterize Initial BeamInitial uncoupled 44 beam covariance matrix, with = (1+2)/
Initial uncoupled 44 beam covariance matrix, with = (1+2)/
Use z and z to describe longitudinal phase space, same as x and x in transverse
Use z and z to describe longitudinal phase space, same as x and x in transverse
projected emittancesprojected emittances
||RR| = 1| = 1||RR| = 1| = 1
Propagate Beam…Propagate Beam…
Rewrite emittances…Rewrite emittances…
…some details…some details
Introduce Symplectic Condition…Introduce Symplectic Condition…
Final Emittance RelationsFinal Emittance Relations
equal emittances remain equalequal emittances remain equal (i.e., if(i.e., if xx00
= = zz00 thenthen xx = = zz))
equal emittances remain equalequal emittances remain equal (i.e., if(i.e., if xx00
= = zz00 thenthen xx = = zz))
Introduce Transverse RFIntroduce Transverse RF
Effects of Transverse RFEffects of Transverse RF
RR RR
RRkk
RR5656
LL
Chicane with RFChicane with RF
Full System Transport MatrixFull System Transport Matrix
||AA| = 0 | = 0 kk = 1 = 1
Final Emittance RelationsFinal Emittance Relations
Numerical ExampleNumerical Example
non-trivialnon-trivialnon-trivialnon-trivial
get nearly complete emittance exchangeget nearly complete emittance exchangeget nearly complete emittance exchangeget nearly complete emittance exchange
Phase Space Before and After ExchangerPhase Space Before and After Exchanger
x, x before z, before
x = 5 m z = 1 m
x, x after z, after
x = 1 m z = 5 m
bunch is also bunch is also compressed:compressed: zz 18 18 mm
bunch is also bunch is also compressed:compressed: zz 18 18 mm
get large x, xget large x, x
Normalized Phase SpaceNormalized Phase Space
xx, , xx beforebefore zz, , beforebefore
xx = 5 = 5 mm zz = 1 = 1 mm
xx, , xx afterafter zz, , afterafter
xx = 1 = 1 mm zz = 5 = 5 mm
Final Bunch Length and Energy SpreadFinal Bunch Length and Energy Spread
kk = 1, = 1,xx = = zz = 0 = 0kk = 1, = 1,xx = = zz = 0 = 0
22ndnd-order-order xx growth approximated by 2growth approximated by 2ndnd-order dispersion…-order dispersion…22ndnd-order-order xx growth approximated by 2growth approximated by 2ndnd-order dispersion…-order dispersion…
use smalluse small xx
and largeand large use smalluse small xx
and largeand large
zzzz
zzzz
Bunch CompressionBunch Compression
200 200 m m 20 20 mm200 200 m m 20 20 mm
Using Using transverse RF transverse RF (all in last bend)(all in last bend)
Using Using transverse RF transverse RF (all in last bend)(all in last bend)
Use standard Use standard energy ‘chirp’ (2energy ‘chirp’ (2ndnd & 3& 3rdrd bends) bends)
Use standard Use standard energy ‘chirp’ (2energy ‘chirp’ (2ndnd & 3& 3rdrd bends) bends)
RF Deflector (cylindrical)RF Deflector (cylindrical)f = 11.424 GHz2a 11.2 mm (iris diameter)2b 29.1 mm (cell diameter)L 0.376 m (43 cells)Q 5300vg/c 0.0193V0 7 MVP0 14 MW
f = 11.424 GHz2a 11.2 mm (iris diameter)2b 29.1 mm (cell diameter)L 0.376 m (43 cells)Q 5300vg/c 0.0193V0 7 MVP0 14 MW
R. MillerR. Miller
TM11-like modeTM11-like mode
“get aberration-free deflection from this mode”
“get aberration-free deflection from this mode”
(G. Loew, et. al., SLAC, 1963-5)(G. Loew, et. al., SLAC, 1963-5)
(H. Hahn, BNL, 1962-3,
Y. Garauit, Orsay, 1962)
(H. Hahn, BNL, 1962-3,
Y. Garauit, Orsay, 1962)
Cavity ‘Thick-Lens’ EffectCavity ‘Thick-Lens’ Effect
BByy ~ ~ tt
add ‘chirp’ to add ‘chirp’ to compensate compensate ‘thick-lens’‘thick-lens’
ll
initial ‘chirp’initial ‘chirp’
tailtail
headhead
tailtail
headhead
Tracking with Thick-Lens and ChirpTracking with Thick-Lens and Chirpzz 0 0
xx = 5 = 5 mm zz = 1 = 1 mm
xx = 1 = 1 mm zz = 5 = 5 mm
ll = 0.4 m = 0.4 mll = 0.4 m = 0.4 m
same as thin-lens cavity
same as thin-lens cavity
kk
kk
tttt
xxxx
--tron tron oscillations oscillations ~disappear~disappear
--tron tron oscillations oscillations ~disappear~disappear
--tron osc’s tron osc’s started fromstarted from tt errorerror
--tron osc’s tron osc’s started fromstarted from tt errorerror
Unusual System CharacteristicsUnusual System Characteristics
System potentially reduces transverse emittanceSystem potentially reduces transverse emittance Also increases longitudinal emittance, possibly Also increases longitudinal emittance, possibly
damping the CSR instabilitydamping the CSR instability
Bunch length is compressed (all in last bend)Bunch length is compressed (all in last bend)
Moves injector challenge to longitudinal emittanceMoves injector challenge to longitudinal emittance
SummarySummary
Must avoid CSR energy spread increase in 1Must avoid CSR energy spread increase in 1stst bends bends
Scheme may have other uses not yet consideredScheme may have other uses not yet considered