Flat-Beams andFlat-Beams andEmittance ExchangeEmittance Exchange

P. EmmaP. Emma11, Z. Huang, Z. Huang11, K.-J. Kim, K.-J. Kim22, Ph. Piot, Ph. Piot33

June 23, 2006June 23, 2006

Flat-beam gun can produce >100:1 emittance ratioFlat-beam gun can produce >100:1 emittance ratio

Smaller emittance (Smaller emittance (yy) might approach 0.1 ) might approach 0.1 mm

Longitudinal emittance may also approach 0.1 Longitudinal emittance may also approach 0.1 mm

Larger Larger zz is useful to Landau damp is useful to Landau damp -bunching-bunching

Can we exchange Can we exchange zz ↔↔ xx and produce: and produce:

((x x , , y y , , zz) = (0.1 , 0.1 , 10) ) = (0.1 , 0.1 , 10) mm, or better?, or better?[1] [1] SLACSLAC, [2] , [2] ANLANL, [3] , [3] FNALFNAL

transverse emittance:transverse emittance:

energy spread:energy spread:

0.2 0.2 mm at 1 Å, 15 GeV at 1 Å, 15 GeV

0.01%0.01% at at IIpkpk = 4 kA, = 4 kA, KK 3.5, 3.5, uu 3 cm, …3 cm, …

Long. emittance requirement is: Long. emittance requirement is: zz z z 60 60

mm

Can we reduce Can we reduce xx at the expense ofat the expense of zz ? ?

RF gun produces both RF gun produces both xx ~ ~ zz ~ few ~ few mm

FEL needs very bright electron beam…FEL needs very bright electron beam…

Gain Length vs. Gain Length vs. KK of FEL at of FEL at 0.4 0.4 ÅÅ

x,yx,y 1  1 m, m, IIpkpk 3.5 kA, 3.5 kA, 0.01% 0.01%

x,yx,y 0.1  0.1 m, m, IIpkpk 1 kA, 1 kA, 0.01% 0.01%

assume that the beta function in the undulator is optimized to produce the shortest gain length assume that the beta function in the undulator is optimized to produce the shortest gain length

Intrinsic energy spread is Intrinsic energy spread is tootoo small small to be a benefit for x-ray SASE FELto be a benefit for x-ray SASE FEL

Final long. phase space at 14 GeV for initial modulation of 1% at Final long. phase space at 14 GeV for initial modulation of 1% at = = 15 15 mm

heated beam stays coolheated beam stays cool beam blows up with no heaterbeam blows up with no heater

A beam heater is required, which Landau damps A beam heater is required, which Landau damps the CSR/LSC micro-bunching instabilitythe CSR/LSC micro-bunching instability

Very Small Energy Spread is WastedVery Small Energy Spread is Wasted

Ming Xie scalingMing Xie scaling

withoutwithoutheaterheater

withwithheaterheater

LCLS ParametersLCLS Parameters

How cold is the photo-injector beam?How cold is the photo-injector beam?Parmela SimulationParmela Simulation TTF measurementTTF measurement

simulationsimulationmeasuredmeasured

EE

// EE

3 keV3 keV

tt (sec) (sec)

3 keV, accelerated to 14 GeV, and compressed 3 keV, accelerated to 14 GeV, and compressed 36 36 3/143/1410106636 < 36 < 11101055

Too small to be useful in FEL (no effect on FEL gain when <Too small to be useful in FEL (no effect on FEL gain when <11101044))

H. Schlarb, M. HueningH. Schlarb, M. Huening

Generating a Flat BeamGenerating a Flat Beam(Y. Derbenev), (R. Brinkmann, Y. Derbenev, K. Fl(Y. Derbenev), (R. Brinkmann, Y. Derbenev, K. Flöttmann), (D. Edwards …), (Y.-E Sun)öttmann), (D. Edwards …), (Y.-E Sun)

UV lightUV lightrf gunrf gun skew quadsskew quads

experimentexperiment simulationsimulation

X3X3 X4X4 X5X5 X6X6 X7X7 X8X8

xx 0.4 0.4 mm

yy 40 40 mm**

* Ph. Piot, Y.-E Sun, and K.-J. Kim, Phys. Rev. ST Accel. Beams 9, 031001 (2006) * Ph. Piot, Y.-E Sun, and K.-J. Kim, Phys. Rev. ST Accel. Beams 9, 031001 (2006)

booster cavitybooster cavity

Injector Simulation (Injector Simulation (AstraAstra, , Impact-TImpact-T))

2.6-GHz, 1.5-cell RF gun2.6-GHz, 1.5-cell RF gun138 MV/m peak E-field in gun138 MV/m peak E-field in gun8 TESLA SC-cavities at 1.3 GHz (216 MeV)8 TESLA SC-cavities at 1.3 GHz (216 MeV)round-to-flat converter of 3 skew quadsround-to-flat converter of 3 skew quads3D oblate ellipsoid laser pulse3D oblate ellipsoid laser pulse0.6 0.6 m per mm radius thermal emittance m per mm radius thermal emittance 36 MV/m peak E-field in TESLA cavities36 MV/m peak E-field in TESLA cavities300 300 m rms laser spot size on cathodem rms laser spot size on cathode50 50 m rms bunch length (80 fs laser pulse)m rms bunch length (80 fs laser pulse)20 pC bunch charge (34 A)20 pC bunch charge (34 A)

Emittance Levels from SimulationEmittance Levels from Simulation

Thermal 2DThermal 2D: : (0.6 (0.6 m/mm)m/mm)(0.3 mm) (0.3 mm) 0.23 0.23 mm

Transverse 4DTransverse 4D: : (0.23 (0.23 m)m)22 0.053 0.053 mm22

After skew 4DAfter skew 4D: : (9.9 (9.9 m)m)(0.0054 (0.0054 m) m) 0.053 0.053 mm22

Longitudinal 2DLongitudinal 2D: : 0.080 0.080 mm

K.-J. Kim, NIM, A275, 201, (1989)K.-J. Kim, NIM, A275, 201, (1989)

Space-Charge Effects on EmittanceSpace-Charge Effects on EmittanceIs the small longitudinal emittance consistent with the space charge force? Is the small longitudinal emittance consistent with the space charge force?

xx 300 300 m, m, zz 50 50 m, m, II 34 A, 34 A, EE00 138 MV/m, 138 MV/m, 00 45 45°°

zz 0.13 0.13 mm

not so different than not so different than 0.08 0.08 mm seen in simulation seen in simulation

Evolution of Transverse Emittances Along Evolution of Transverse Emittances Along Photo-Injector Beamline (to 216 MeV)Photo-Injector Beamline (to 216 MeV)

acc. cavitiesacc. cavitiesrf gunrf gunskew quadsskew quads

intrinsicintrinsicx,yx,y 0.23 0.23 mm

9.9 9.9 mm9.9 9.9 mm

0.084 0.084 mm0.084 0.084 mm

0.0054 0.0054 mm0.0054 0.0054 mm

coupled valuescoupled values

xx

zz

yy

Longitudinal Distributions After Photo-InjectorLongitudinal Distributions After Photo-Injector

slice energy spreadslice energy spread(rms (rms 4 4101066, 0.9 keV), 0.9 keV)

zz = 0.080 = 0.080 mm

yy = 0.0054 = 0.0054 mm

xx = 9.92 = 9.92 mm

EE00 = 216 MeV = 216 MeV

xxxx

yy

yy

yy

xx

Transverse Distributions After Photo-InjectorTransverse Distributions After Photo-Injector

zz = 0.080 = 0.080 mm

yy = 0.0054 = 0.0054 mm

xx = 9.92 = 9.92 mm

EE00 = 216 MeV = 216 MeV

????

Emittance Exchange Concept (2002)Emittance Exchange Concept (2002)

Electric and magnetic fieldsElectric and magnetic fieldskk

Transverse RF in chicane…Transverse RF in chicane…

Particle at position xx in cavity gets acceleration: kxkx Particle at position xx in cavity gets acceleration: kxkx

Must include magnetic field and calculate emittance in both planesMust include magnetic field and calculate emittance in both planes

This energy deviation in chicane causes position change: xx = = This energy deviation in chicane causes position change: xx = = Choose kk to cancel initial position: xx kxkxx x kk = 1 = 1 Choose kk to cancel initial position: xx kxkxx x kk = 1 = 1

Cornacchia, Emma, PRST AB 5, 084001 (2002) Cornacchia, Emma, PRST AB 5, 084001 (2002)

Improved Emittance Exchanger (2005)Improved Emittance Exchanger (2005)

kkkk

RR11

RRkkRR11

System modified by K.-J. Kim, 2005System modified by K.-J. Kim, 2005

22LL

RR5656 of dog-legof dog-leg

rectangular RF rectangular RF deflecting cavitydeflecting cavity

xx, , zz mapping (ignore mapping (ignore yy coordinate here) coordinate here)

If RF deflector voltage is set to: If RF deflector voltage is set to: kk = = 1/1/

and transverse (bend-plane) and longitudinal and transverse (bend-plane) and longitudinal emittances are completely exchanged.emittances are completely exchanged.

Full Emittance ExchangeFull Emittance Exchange

Emittance Exchange LimitationsEmittance Exchange Limitations4x4 transfer 4x4 transfer matrix is four matrix is four 2x2 blocks2x2 blocks11::

[2][2] Thanks to Bill Spence.Thanks to Bill Spence.

Equal emittances remain equal. Equal emittances remain equal. (If(If xx00

= = zz00 thenthen xx = = z.z.))

Equal, uncoupled emittances Equal, uncoupled emittances cannot be generated from cannot be generated from unequal, uncoupled emittancesunequal, uncoupled emittances33. . (Setting (Setting ||AA| = ½| = ½ produces equal produces equal emittances, but then they are emittances, but then they are highly coupled with highly coupled with 22   0 0.).)[3][3] E. Courant, in “Perspectives in Modern Physics...,” E. Courant, in “Perspectives in Modern Physics...,”

R.E. Marshak, ed., Interscience Publishers, 1966.R.E. Marshak, ed., Interscience Publishers, 1966.

[1][1] K.L. Brown, SLAC-PUB-2370, August 1980. K.L. Brown, SLAC-PUB-2370, August 1980.

22

ParameterParameter symbolsymbol valuevalue unitunit

Electron energyElectron energy EE 216216 MeVMeV

Dipole magnet lengthDipole magnet length LLBB 2020 cmcm

Drift length between dipole magnetsDrift length between dipole magnets LL 11 mm

Bend angle per dipole magnetBend angle per dipole magnet 2020 degdeg

Length of rec. RF cavityLength of rec. RF cavity LLcc 3030 cmcm

Initial horizontal norm. emittanceInitial horizontal norm. emittance xx 9.929.92 mm

Initial longitudinal norm. emittanceInitial longitudinal norm. emittance zz 0.0800.080 mm

Initial rms bunch lengthInitial rms bunch length zzGG 5151 mm

Initial rms slice energy spreadInitial rms slice energy spread EEGG 0.90.9 keVkeV

Initial energy chirp (Initial energy chirp (-z -z slope)slope) hh 6.96.9 mm11

Initial horizontal beta functionInitial horizontal beta function xx 100100 mm

Initial horizontal alpha functionInitial horizontal alpha function xx 00

Emittance Exchanger ParametersEmittance Exchanger Parameters

CSR Suppression with Large Beam SizeCSR Suppression with Large Beam Size

With this large With this large xx and large and large xx, the CSR emittance growth is , the CSR emittance growth is

estimated (1D, estimated (1D, elegantelegant) at ) at 0.08 0.08 mm 0.16 0.16 mm..

x = 100 m

zz

EE//EE

CSR also reduced when CSR also reduced when horizontal beam size horizontal beam size exceeds transverse exceeds transverse coherence length:coherence length:

CSR also reduced when CSR also reduced when horizontal beam size horizontal beam size exceeds transverse exceeds transverse coherence length:coherence length:

Cavity ‘Thick-Lens’ EffectCavity ‘Thick-Lens’ Effect

Thick-lens: Thick-lens: BByy

kickkick, , and then and then xx--offset changesoffset changes

add ‘chirp’ to add ‘chirp’ to compensate: no compensate: no mean mean xx-offset-offset

ll

tailtail

headhead

tailtail

headhead

tailtail

headhead

Thin-lens gives Thin-lens gives no no xx-offset in -offset in cavitycavity

Energy spread is induced in T-cav due to transverse Energy spread is induced in T-cav due to transverse beam extent (beam extent ( = = kxkx))Second-order dispersion is generated in last two bends, Second-order dispersion is generated in last two bends, which dilutes bend plane (which dilutes bend plane (xx) emittance) emittance

The right initial energy chirp minimizes the divergence, The right initial energy chirp minimizes the divergence, , after the last bend, which minimizes emittance growth, after the last bend, which minimizes emittance growth

xx = = 22

x x = = 22

= = kxkx

TcavTcavTcavTcav

xx = = kzkz

Control of Second-Order Dispersive AberrationControl of Second-Order Dispersive Aberration

xx221/21/2 xx221/21/2

The Effect of Initial Chirp The Effect of Initial Chirp Small Small at System Exit at System Exit

much bigger much bigger area increase area increase when large when large

much smaller much smaller area increase area increase when small when small

x

xx

The final divergence, The final divergence, , is decreased by the initial chirp , is decreased by the initial chirp shorter bunch in cavity shorter bunch in cavity less kick, less kick, xx = = kzkz, after cavity..., after cavity...

For large For large (left) and small (left) and small (right), the same (right), the same xx increase increase produces much larger area increase (emittance growth) produces much larger area increase (emittance growth)

when when is large ( is large ( is Twiss parameter, { is Twiss parameter, {1+1+22}/}/, not , not energy)energy)

xx

x

001/21/2 minmin001/21/2

001/21/2

001/21/2

Longitudinal Distributions After Exchanger (no CSR)Longitudinal Distributions After Exchanger (no CSR)

slice energy spreadslice energy spread(rms (rms 6 6101055, 13 keV), 13 keV)

zz = 9.92 = 9.92 mm

yy = 0.0054 = 0.0054 mm

xx = 0.084 = 0.084 mm

EE00 = 216 MeV = 216 MeV

Transverse Distributions After Exchanger (no CSR)Transverse Distributions After Exchanger (no CSR)

xxxx

yy

yy

yy

xx

zz = 9.92 = 9.92 mm

yy = 0.0054 = 0.0054 mm

xx = 0.084 = 0.084 mm

EE00 = 216 MeV = 216 MeV

Transverse phase space (left two plots) and longitudinal phase space Transverse phase space (left two plots) and longitudinal phase space (right two plots) before (top) and after (bottom) emittance exchange. (right two plots) before (top) and after (bottom) emittance exchange.

BEFORE BEFORE EXCHANGEREXCHANGER

AFTER AFTER EXCHANGEREXCHANGER

zz 500 500 m!m!

Operating ParametersOperating Parameters ValueValue UnitsUnits

Bunch chargeBunch charge 2020 pCpC

Laser rms spot sizeLaser rms spot size 300300 mm

Laser rms pulse durationLaser rms pulse duration 8080 fsfs

Peak E-field in rf-gunPeak E-field in rf-gun 138138 MV/mMV/m

Launch phaseLaunch phase 4545 degdeg

Peak E-field in TESLA cavitiesPeak E-field in TESLA cavities 3636 MV/mMV/m

B-field on photocathodeB-field on photocathode 0.1910.191 TT

Cavity off-crest phaseCavity off-crest phase 44 degdeg

Beam ParametersBeam Parameters ValueValue UnitsUnits

Before flat beam transformerBefore flat beam transformer

Transverse emittancesTransverse emittances 4.964.96 mm

Intrinsic transverse emittancesIntrinsic transverse emittances 0.230.23 mm

Longitudinal emittance Longitudinal emittance 0.0710.071 mm

Kinetic energyKinetic energy 215.4215.4 MeVMeV

After transformerAfter transformer

Emittance Emittance xx 9.923 9.923 mm

Emittance Emittance yy 0.0054 0.0054 mm

Longitudinal emittance Longitudinal emittance 0.0800.080 mm

0.230.23 mm

Operating parameters and ‘achieved’ beam parameters at photo-injector end Operating parameters and ‘achieved’ beam parameters at photo-injector end

yx

Flat Beam FEL at 0.4 Flat Beam FEL at 0.4 ÅÅAssume Assume und und = 3 cm= 3 cm, K , K = 1.34,= 1.34, xx 0.16  0.16 m, m, x,yx,y = 20 m = 20 m

IIpkpk 1 kA, 1 kA, 0.024% at 13.6 GeV (hence 0.024% at 13.6 GeV (hence zz 10  10 m)m)

Emittance-exchanged beamEmittance-exchanged beam

Round beamRound beamxx = = yy 0.16 0.16 mm

Round beamRound beamxx = = yy 0.16 0.16 mm

confirmed with Genesis 1.3confirmed with Genesis 1.3Ming Xie, NIMA507, 450 (2003) Ming Xie, NIMA507, 450 (2003)

xx

energy errorenergy errorstartsstarts -osc. -osc.

Unusual System CharacteristicsUnusual System Characteristics

kk

kk

EE//EE

--tron tron oscillations oscillations disappeardisappear

Need Need extremelyextremely stable energy (0.5 stable energy (0.5101066 rms jitter rms jitter 10% 10% xx-beam size jitter)-beam size jitter)

SummarySummarySimulations of flat-beam gun with emittance Simulations of flat-beam gun with emittance exchanger suggest possible levels of:exchanger suggest possible levels of:

zz 9.9 9.9 m, m, yy 0.0054 0.0054 m, m, xx 0.16 0.16 mm

Large Large zz-emittance should Landau-damp micro--emittance should Landau-damp micro-bunching instabilitiesbunching instabilities

Bunch gets longer (50 Bunch gets longer (50 500 500 m) and will need m) and will need to be compressed by to be compressed by 250 to achieve 1 kA250 to achieve 1 kA

CSR needs much closer lookCSR needs much closer look

Sensitivity to energy jitter may be Achilles heelSensitivity to energy jitter may be Achilles heel