coulomb’05, senigallia, italy, sept. 14th 2005 space charge issues in high brightness electron...

COULOMB’05 , Senigallia, Italy, Sept. 14th 2005

Space Charge Issues in High Brightness Electron (Plasma)Beams for X-ray FEL’s

Luca Serafini, INFN-Milan and University of Milan

• Electron beams for X-ray FEL’s are cold relativistic plasmas

propagating through the Linac in laminar flow (up to GeV’s)

• To reach high brightness ( I > kA, n< 1 m) one needs

Many Thanks to: SPARC&PLASMONX Project team

1) Transport the beam through a gentle funnel made byRF and acceleration focusing counteracting space charge# betatron oscillations << 1 # plasma oscillations ~ 1

transverse laminarity

2) # synchrotron oscillations ~ 1/4 (with velocity bunching)longitudinal laminarity


• Reaching the goal brightness is critically dependent on matching the beam

to the invariant envelope condition ( the funnel)

• FODO-like transport is forbidden up to 150 MeV and

not reccommended up to 1 GeV

SPARXino: a 1-1.2 GeV Linac @ LNF to drive aFEL @ 5-10 nm radiation wavelength

1 kA1 kA

1 kA1 kA500 A500 A

• Insensitive to quad misalignment

€

σ IE =1′ γ

2I

IAη 2γ


€

λp = 2πγ′ γ

€

T =1 GeV ; γ f = 2 ⋅103 ; ′ γ = 40 m−1 I =1 kA ; ε th = 5 ⋅10 −7

L.S., J.B. Rosenzweig, PRE 55 (1997) 7565

Cold Relativistic Plasma-Beams in Laminar Flow with time dependent Space Charge Fields

€

η ≅1

Betatron wavelengthBetatron wavelength

photocath. photocath. therm.therm.emittanceemittance

Plasma wavelengthPlasma wavelength(sp. ch. oscillation)(sp. ch. oscillation) norm. amplit.norm. amplit.

of RF focusingof RF focusing

Accelerating gradientAccelerating gradient

Linac lengthLinac length

€

λβ =4πI IA( )

ε th ′ γ 2η

€

th

€

′ γ

€

L = γ f ′ γ

€

IIA

=I

17 kA

€

λp λ β = 0.3# Betatron oscill. ~ 0.3# Betatron oscill. ~ 0.3# Plasma oscill. ~ 1# Plasma oscill. ~ 1# Synchrotron oscill. ~ 1/4# Synchrotron oscill. ~ 1/4

At Linac exitAt Linac exit

€

=2πLacc


QuickTime™ and aCinepak decompressor

are needed to see this picture.

Parmela simulation of SPARC photoinjector up to 150 MeV (velocity bunching with X-band RF cavity)

C. Ronsivalle

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.


Schematic View of the Envelope Schematic View of the Envelope EquationsEquations

(HOMDYN model)(HOMDYN model)

′ σ ′ γ

γ+σ

Ω2 ′ γ 2

γ2

I2I Aσγ3 +

εn,sl2

σ 3γ2

′ ϑ =−Ksol +pϑ ,o

mcβγR2

€

KzRF ϕ( )σ z

€

KzSC

σ z

€

′ ′ σ

€

′ ′ σ z


Emittance Compensation: Emittance Compensation:

Controlled Damping of Plasma Controlled Damping of Plasma OscillationOscillation

Hokuto IijimaHokuto Iijima

L. Serafini, J. B. Rosenzweig, Phys. Rev. E 55 (1997)€

′ γ = 2

σ w

ˆ Ι

3I0γ

€

γ= 8

3

ˆ I

2Ioε th ′ γ

€

σ ' = 0Brillouin FlowBrillouin Flow

100 A ==> 150 MeV


Brief Review of Beam Dinamycs in Photo-Injectors

• The beam generated at the photocathode surface behaves like aSingle Component Relativistic Cold Plasma all the

way up to the injector exit (150 MeV, 1 GeV with compression)

• It is a quasi-laminar beam both in transverse (laminar flow) and longitudinal plane (lack of synchrotron motion)

′ ′ σ + ′ σ ′ γ

γ+σ

Ω2 ′ γ 2

γ2 −I ζ( )

2IAσγ3 =εn,sl

2

σ3γ2 ≈0

γ =γ0+ ′ γ z ′ γ ≡Eacc

mc2′ σ ≡

dσdz

σ ≡ x2 slice ζ =z−βct

Ω2 =eBsol

mc ′ γ

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+ ≈1/8 SW

≈0 TW

⎧ ⎨ ⎩

⎫ ⎬ ⎭

Normalized focusing gradient(solenoid +RF foc.)


ζ

= z - vb

t

σz

Ib

( ζ )r

S.C.R.C.P. or Laminar Plasma-Beam

• Plasma launched at relativistic velocities along the propagation axis with equivalent ionization = 1/γ2 ; plasma confinement provided by external focusing (solenoids, ponderomotive RF focusing, acceleration)

• Spread in plasma frequency along the bunch strong time-dependent space charge effects inter-slice dynamics

r

pr

Per vedere questa immagineoccorre QuickTime™ e un

decompressore Animation.

© M. Serafini

Liouvillian emittance = foil volume

εn ≡ x2 px2 − xpx

2 >>εnsl ≡ x2

ζpx

2ζ

− xpx ζ2

Projected emittance (shadow) >> slice emittance (foil thickness)


0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10Z_[m]

GunLinac

rms beam size [mm]

rms norm. emittance [um]

-0.04

-0.02

0

0.02

0.04

0 0.001 0.002 0.003 0.004 0.005 0.006

z=0.23891

Pr

R [m]

-0.05

0

0.05

0 0.0008 0.0016 0.0024 0.0032 0.004

z=1.5

Pr

R [m]

-0.04

-0.02

0

0.02

0.04

0 0.0008 0.0016 0.0024 0.0032 0.004

z=10

pr_[rad]

R_[m]

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

-0.003 -0.002 -0.001 0 0.001 0.002 0.003

z=0.23891

Rs [m]

Zs-Zb [m]

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

-0.003 -0.002 -0.001 0 0.001 0.002 0.003

Z=10

Rs [m]

Zs-Zb [m]

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

-0.003 -0.002 -0.001 0 0.001 0.002 0.003

z=1.5

Rs [m]

Zs-Zb [m]

Final emittance = 0.4 m

Matching onto the Local Emittance Max.,

Example of an optimized matchingExample of an optimized matching

M. Ferrario et al., “HOMDYN Study For The LCLS RF Photo-Injector”, Proc. of the 2nd ICFA Adv. Acc. Workshop on “The Physics of High Brightness Beams”, UCLA, Nov., 1999, also in SLAC-PUB-8400

QuickTime™ and aAnimation decompressor


QuickTime™ and aAnimation decompressor



Movable Emittance-Movable Emittance-MeterMeter

Measuring Emittance Measuring Emittance Oscillations @ SPARCOscillations @ SPARC

0

1

2

3

4

5

6

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5 3

HBUNCH.OUT

sigma_x_[mm]enx_[um]

Bz_[T]

sigma_x_[mm] Bz_[T]

z_[m]

emittance envelope

0.00.5 1.0 1.5 2.0 2.5 3.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

Emittance

Envelope

Bz field

Z= 170 cmZ= 170 cmZ= 120 cmZ= 120 cmZ= 85 cmZ= 85 cm


0.00.51.01.52.00.500.550.600.650.700.750.80

Projected normalized emittance(mm-mrad)

Rise time (ps)

Bunch Microscopy, Inter-Slice dynamicsBunch Microscopy, Inter-Slice dynamics


Laser Pulse Shaping Experiment:Laser Pulse Shaping Experiment:

a SPARC-BNL/DUV-SLAC/LCLS a SPARC-BNL/DUV-SLAC/LCLS CollaborationCollaboration

The Beer-CanThe Beer-Can

DistributionDistribution


e-beam measurement Q=70 pCGaussian Flat top


e-beam temporal distributionQ=70 pC, after Dazzler optimization


e-beam temporal distribution Q=300 pC


• Inter-slice dynamics brings to projected emittance oscillations which are reversible emittance correction this can be described by a multi-envelope code like HOMDYN the prescription to reach full emittance correction is to match the beam onto the invariant envelope (beam equilibr. mode)

LS and JR, PRE 55 (1997) 2575

S.C.R.C.P. or Laminar Plasma-Beam

σ INV =1′ γ

2I ζ( )IA 1+4Ω2( )γ

• Intra-slice dynamics is affected by space charge field non-linearities (partially reversible, unless wave-breaking is reached) to model intra-slice dynamics we need a multi-particle code (Parmela) the prescription to avoid wave-breaking and irreversible slice emittance growth is to use uniform cylindrical charge density distribution (flat top laser pulses, spatially uniform)


The Blow-Out regime: The Blow-Out regime:

from Pancakes to Waterbagfrom Pancakes to Waterbag

Serafini ==> Luiten ==> RosenzweigSerafini ==> Luiten ==> Rosenzweig

Use any temporally shaped ultra-short pulseLongitudinal expansion of well-chosen shaped radial profile

Uniform ellipsoidal beam created!Linear space-charge fields (3D)€

I r( ) = I0 1− r /a( )2

( )1/ 2

==>==>


• Initial (not-too-optimized) PARMELA study• Standard LCLS injector conditions

– 120 MV/m peak on-axis field

• Beam initial conditions chosen to:– Avoid image charge effects (σb limit)– Produce emittance compensation

• Parameters:– Q=0.33 nC – Initial longit. Gaussian σt =33 fs (cutoff at 3 σ)– Trans. Gaussian with σx =0.77 mm (cutoff at 1.8 σ).

• Final bunch length 1.3 mm (full), 117 A.• At low energy (only) the ellipsoidal beam shape is visible

– Transition to emittance dominated regime destroys shape (it is no longer needed!)

• Initial (not-too-optimized) PARMELA study• Standard LCLS injector conditions

– 120 MV/m peak on-axis field

• Beam initial conditions chosen to:– Avoid image charge effects (σb limit)– Produce emittance compensation

• Parameters:– Q=0.33 nC – Initial longit. Gaussian σt =33 fs (cutoff at 3 σ)– Trans. Gaussian with σx =0.77 mm (cutoff at 1.8 σ).

• Final bunch length 1.3 mm (full), 117 A.• At low energy (only) the ellipsoidal beam shape is visible

– Transition to emittance dominated regime destroys shape (it is no longer needed!)Beam distribution showing ellipsoidal boundary (12.5 MeV)

Initial PARMELA simulation studyInitial PARMELA simulation studyJ.B. Rosenzweig (UCLA)J.B. Rosenzweig (UCLA)

Initial PARMELA simulation studyInitial PARMELA simulation studyJ.B. Rosenzweig (UCLA)J.B. Rosenzweig (UCLA)

Beam distribution at high energy showsBoundary collapse (71.5 MeV)


• Emittance compensation is very good: <0.9 mm-mrad

• Much higher current than standard operation (117 A v. 48 A)

• Extremely small energy spread– Shorter beam

– Approx. linear space charge

• Emittance compensation is very good: <0.9 mm-mrad

• Much higher current than standard operation (117 A v. 48 A)

• Extremely small energy spread– Shorter beam

– Approx. linear space charge

0

0.5

1

1.5

2

2.5

0 200 400 600 800z (cm)

0

0.5

1

1.5

2

2.5

3

0 200 400 600 800

z (cm)

Beam size evolution

RMS emittance evolution Final longitudinal phase space


• Velocity Bunching - Domain of Application : low energy linac section

RF field pushes particles in bunch tail more than in bunch head

Velocity Bunching: a way to increase brightness

• Requires a Spread of absolute velocitiesSpread of absolute velocities on a rectilinear path

T = 5 MeV

T = 25 MeV

€

Lcompr ∝ λ RFγ 3/2

cmp. ballistic bunch.

R56drift ∝ Ldrift γ 2

• Collective effects only in transverse plane (longit. space charge negligible)

• Maximum compressionMaximum compression limited by non linearities of RF field (curvature)


What do we need to perform “Advanced” Velocity Bunching ?

I > 500 A n ~ 1 m

““Advanced”Advanced” Velocity Bunching

• V.B. has been demonstrated at a number of laboratories

Good compression ratio ( C > 10 , I > kA) - No emittance preservation

• None of these systems was designed for optimizing velocity bunchingNone of these systems was designed for optimizing velocity bunching

Yes

10

< 0.3 ps

0.2 nC

CTR

4 S-band

Velocity Bunching

LLNLLLNL

Yes

> 13

0.5 ps (rms)

1 nC

FemotsecondStreak Camera

1 S-band

Velocity Bunching

UTNL-18LUTNL-18L

> 3156Comp. RatioComp. Ratio

BNL-DUVFELBNL-DUVFELUCLAUCLABNL-ATFBNL-ATF

No

0.37 ps(rms)

0.04 nC

zero-phasing method

S-band

Ballistic

0.5 ps(rms)

0.39 ps(rms)Bunch widthBunch width

NoNoSolenoid fieldSolenoid field

0.2 nC0.2 nCChargeCharge

zero-phasing methodCTRMeasurementMeasurement

4 S-bandPWTAcc. StructureAcc. Structure

Velocity BunchingBallisticMethodMethod


To be published on JJAP


Streak Images of Electron BunchStreak Images of Electron Bunch

Injected Phase -70O

Minimum!

200 psec range 50 psec range

Injected Phase -1O


Velocity Bunching @ LLNL - PLEIADES


Velocity bunching conceptVelocity bunching concept

€

H = γ − βr γ 2 −1 −α cosφ€

φ=kz − β rωt + φ0 ; k ≡ ω c

€

γr =1 1− β r2

A quarter of synchrotron oscillation performed inside a RF bucket

Extraction at the resonant (synchronous) velocity (γ=γr)

Injection of a short bunch at =0 (zero field point)

γr

γr

trapped

untrapped

separa

trix

Synchr. Wav.

€

λs ∝λ RFγ 3/2

α

γ

γ

inj.

extr.


Works as well with speed of light RF waves, βr =1

Extraction performed at quasi-resonant velocity (γ )

Injection still at =0 , no bucket but similar pattern of Poincarè lines

Velocity bunching conceptVelocity bunching concept


Compression during acceleration

Velocity Bunching: the very first simulation*

Current scalingwith energy

I/γ = const.0

200

400

600

800

1000

0

20

40

60

80

100

0 2 4 6 8 10

I [A] T [MeV]

Z [m]

Courtesy of D. Yeremian, SLAC

*L.S., M.Ferrario, AIP CP 581 (2001) 87


Average current vs. RF compressor phaseIn SPARC photoinjector

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

-95 -90 -85 -80 -75 -70 -65 -60

RF compressor phase (deg)

Average current (A)

LOW COMPRESSION

MEDIUM COMPRESSION

HIGH COMPRESSION

OVER-COMPRESSION

z = 4 mm

z = 1 mm

Overcompression, Overcompression, i.e.i.e.loss of longitudinal laminarity,loss of longitudinal laminarity,slice mixing, irreversible sp. ch.slice mixing, irreversible sp. ch.emittance growthemittance growth


Limitation: longitudinal emitance Limitation: longitudinal emitance growth induced bygrowth induced by RF curvatureRF curvatureLimitation: longitudinal emitance Limitation: longitudinal emitance growth induced bygrowth induced by RF curvatureRF curvature

InjectionInjection ExtractionExtraction




Parmela simulation of SPARC photoinjector:velocity bunching w/o higher RF harmonic

C. Ronsivalle




Parmela simulation of SPARC photoinjector:velocity bunching with higher RF harmonic

C. Ronsivalle


Current sensitivity for 1° error in RF Current sensitivity for 1° error in RF compressor phase with IV harmonic compressor phase with IV harmonic

cavitycavity

C. Ronsivalle

D.Alesini et al., PAC05

without

with


Three conditions to preserveemittance during velocity bunching

• current growing at the same rate as the beam energy (velocity bunching !, not ballistic)

• (additional external focusing to match onto a parallel envelope (I.E. RFC solution)

• RF compressor accelerating section longer than a plasma wavelength (2-3 m)

• Needs a dedicated well optimized lay-out (presently not available): motivation for SPARC project at LNF

σRFC =1

Ω ′ γ I0

2IAγ0

kpRFC =

Ω ′ γ 2γ

Iγ

=const.


<I> = 860 A

n = 1.5 m

<I> = 450 A

n = 1.0 m


Intra-slice bunch microscopy for<I> = 860 A , n = 1.5 m

Velocity Bunching has almost no effect on Slice Emittance !Velocity Bunching has almost no effect on Slice Emittance !


Velocity Bunching and Magnetic Compression in a FEL Driver: application to Sparxino

See papers THPP019, C. Vaccarezza et al. and MOPP015, V. Fusco et al.

Beam Energy 1.2 GeVPeak current 1-2.5 kAEmittance (average) 2 mEmittance (slice) mEnergy spread(correlated)

0. %

500 MeV

450 A 860 A


€

ρ =I IA

η ′ γ εthγ

⎡

⎣ ⎢

⎤

⎦ ⎥

2

€

σ IE =1′ γ

2I

IAη 2γ

€

γTR =I

′ γ IAηεth

€

γTR ≥1000 I = 450 A

γTR ≥ 3000 I =1200 A

€

σinj = σ IE ′ σ inj = 0

L.S., J.B. Rosenzweig, PRE 55 (1997) 7565

Beam at the Sparxino photoinjector exit (with Velocity Bunching) is still space charge

dominated (cold relativistic plasma)

€

η ≅1LaminarityLaminarityparameterparameter

PhotocathodePhotocathodethermal emittancethermal emittance

Invariant EnvelopeInvariant Envelopenorm. amplit.norm. amplit.of RF focusingof RF focusing

Transition EnergyTransition Energybetween plasmabetween plasmaand gas regimeand gas regime

Beam matching con-Beam matching con-ditions on I. E.ditions on I. E.


QuickTime™ and aGraphics decompressor


See paper THPP019, C. Vaccarezza et al.

Further Magnetic Compression with or w/o additional X-band cavity at compressor entrance

without with


Effects of RF cavity misalignment

See paper MOPP015, V. Fusco et al.

Beam centroid walk-off

Observed negligibleeffect on emittance

No quad used! Only the funnel with

invariant envelope


Conclusions

• The SPARC Project is aiming at producing by 2006 @ LNF

electron beams of unique properties in 6D phase space density

• Investigation on Advanced Velocity Bunching is one of its main

goals, with applications ranging from high brightness beam

production for FEL Drivers to (see PLASMONX Proj.) advanced

plasma acceleration experiments combining fs electron beams with

high intensity (>1020 W/cm2) fs laser beams (plus Thomson X-rays

in spontaneous/coerent regime, i.e. a compact X-ray laser)

• The Sparxino Linac is conceived as a X-FEL Driver based on

Adv. Vel. Bunching: it will be a test bench for the theory of

relativistic cold plasma-beams


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Physics and Applications Physics and Applications of High Brightness Electron of High Brightness Electron

BeamsBeams

Organizers: L. Palumbo (Univ. Roma), J. Rosenzweig (UCLA), L. Serafini (INFN-Milano).


• This solution represents a beam equilibrium mode that turns out to be the transport mode for achieving minimum emittance at the end of the emittance correction process (L.S and J.B.R., PRE 55

(1997) 7565)

• The associated plasma frequency is

• This solution includes (at ) the so-called Brillouin flow (rigid rotation at constant spot-size in a solenoid field)

σBRI =σ INV ′ γ =0( ) =mc

eBsol

I2IAγ

kpINV = 3

Ω ′ γ γ

′ γ =0

Transverse Dynamics of a quasi-laminar plasma beam (constant current)

No slice dependence !


Emittance Oscillations in Beam-Plasmas

• Envelope Oscillations drive emittance oscillations ( )

• Damped Oscillations ( emittance correction) if the beam is transported under two possible equilibrium conditions connected to each other

Brillouin Flow

Invariant Envelope

Δεn ∝σ

Δεn(z) ≅ δσ0

′ γ I I02γ

cosψ( )− 2sinψ( )

ψ ≡ln γ γ0( )/ 2 ; γ =γ0 + ′ γ z

σ INV = 1′ γ

I 2I0γ 14+Ω2( )

σBR =I I0

2γ3Kr


TRACE3D

PARMELA ELEGANT GENESIS

HOMDYN PERSEO

RETAR TREDI ABCI

POISSON-SUPERFISH MAFIA

•0 Matrix 0 Matrix

•I Semi-AnalyticalI Semi-Analytical

•II TrackingII Tracking

•III Self-ConsistentIII Self-Consistent


€

Bn =2I

εn2B

bunch bunch compressorscompressors

RF & magneticRF & magnetic

Pulse ShapingPulse Shaping

New Working New Working PointPoint

How to increase e- BrightnessHow to increase e- Brightness


Brief Review of Beam Dinamycs in Photo-Injectors

• The beam undergoes two regimes along the accelerator, photocathode Linac exit

Single Component Relativistic Cold Plasma (laminar beam or plasma-beam with ionization =

1/γ2 ) Thermal Beam

(gas-beam)• laminarity parameter

€

ρl =I 2IA( )′ γ ηγε th

⎡

⎣ ⎢

⎤

⎦ ⎥

2

ρl >>1

ρl <<1


Typical X-FEL Beam

€

If ε th = 0.3 mm.mrad @ 1 nC

′ γ =50 m−1 ⇔ Eacc=25 MV/m

0 1 2 3 4 5 6

T [GeV]

0.1

1

10

100

00

k

k

Plasma beam confined by focusing channelPotential space charge emittance growth

Gas Beam

ρl

ρl ≅6.7⋅104 Iγ ′ γ

⎡

⎣ ⎢

⎤

⎦ ⎥ 2

coulomb’05, senigallia, italy, sept. 14th 2005 space charge issues in high brightness electron...

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