Beam Dynamics in a Spilt SRF-Gun

Beam Dynamics in a Spilt SRF-GunBeam Dynamics in a Spilt SRF-GunM. Ferrario, W. D. Moeller, J. B. Rosenzweig, J. Sekutowicz, M. Ferrario, W. D. Moeller, J. B. Rosenzweig, J. Sekutowicz,

G.TravishG.Travish

INFN, UCLA, DESYINFN, UCLA, DESY

Meeting on “ Superconducting RF Gun Simulations“EUROFEL Work Package 52.-3. June 2005 at BESSY

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Main Advantage: Low RF Power Losses & CW OperationLow RF Power Losses & CW Operation

SUPERCONDUCTING RF PHOTO-SUPERCONDUCTING RF PHOTO-INJECTORSINJECTORS

Main Questions/ConcernsMain Questions/Concerns

• Emittance Compensation ? Emittance Compensation ? • Q degradation due to Magnetic Q degradation due to Magnetic Field ?Field ?• High Peak Field on Cathode ?High Peak Field on Cathode ?• Cathode Materials and QE ?Cathode Materials and QE ?• Laser System ?Laser System ?

Before Cool-DownBefore Cool-Down

B

After Cool-DownAfter Cool-Down

B

Schematic View of the Envelope Schematic View of the Envelope EquationsEquationsHOMDYNHOMDYN

′ σ ′ γ γ

+σ Ω2 ′ γ 2

γ2

I2I Aσγ3 + εn,sl

2

σ 3γ2

′ ϑ =−Ksol +pϑ ,o

mcβγR2

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KzRF ϕ( )σ z

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KzSC

σ z

x

px

Projected Phase Space Slice Phase Spaces

Emittance Oscillations and Growth are driven Emittance Oscillations and Growth are driven by space charge differential defocusing by space charge differential defocusing

in core and tails of the beamin core and tails of the beam

€

′ γ = 2σ w

ˆ Ι 3I0γ

€

γ= 83

ˆ I 2Ioε th ′ γ

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σ ' = 0

Emittance Compensation: Controlled Emittance Compensation: Controlled Damping of Plasma Oscillation (LS-JBR)Damping of Plasma Oscillation (LS-JBR)


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enxT_[um]enxT+_[um]enxCore_[um]enxH-_[um]enxH_[um]enx_[um]enxT_[um]

Z_[m]

Gun Working PointGun Working Point

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enxT_[um]enxT+_[um]enxCore_[um]enxH-_[um]enxH_[um]enx_[um]enxT_[um]

Z_[m]

Linac Working PointLinac Working Point

The emittance compensation occuring in the booster The emittance compensation occuring in the booster when the invariant envelope matching conditions are when the invariant envelope matching conditions are satisfied is actually limited by the head and tail slice satisfied is actually limited by the head and tail slice

behavior behavior

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Homdyn movie

Head and tail slices carry the most pronounced Head and tail slices carry the most pronounced energy spreadenergy spread

ks = qB2mcβγ

Simple Case: Transport in a Long Simple Case: Transport in a Long SolenoidSolenoid

σ'' +ks2σ =K

σ

σeq ξ( ) = K ξ( )ks

σ'' =0 ==> Equilibrium solution ? ==>==> Equilibrium solution ? ==>

0 0.0005 0.001 0.0015 0.002 0.0025metri

0.5

0.6

0.7

0.8

0.9

g K = 2Ig ξ( )Io βγ( )3g(

σ =σ eq+δσ δσ'' +2ks2δσ =0

Small perturbations around the Small perturbations around the equilibrium solutionequilibrium solution

Same Plasma Same Plasma FrequenciesFrequencies

σ ξ( )=σ eq ξ( )+ σ ξ( )−σ eq ξ( )( )cos 2ksz( )σ' ξ( ) =− 2ks σ ξ( ) −σ eq ξ( )( )sin 2ksz( )

Different AmplitudesDifferent Amplitudes

ε z( )= σr2 σr

' 2 − σrσ r' 2 ÷sin 2ksz( )

0 1 2 3 4 5metri

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0

0.5

1

1.5

2

envelopes

0 1 2 3 4 5metri

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20

40

60

80

emi

σr(z)

(z)

Envelope oscillations drive Emittance oscillations

δγγ

=00.5≤g ξ( )≤1

′ σ =0

Bunch with a Linear Bunch with a Linear Energy SpreadEnergy Spread CorrelationCorrelation

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γ+ =γo 1+δγ( )

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γ−=γo 1−δγ( )

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δγ =δγγo

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σ+ =σeq+ +δσ+ cos 2k+z( )

′ σ + = − 2k+δσ+ sin 2k+z( )

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σ−=σeq− +δσ − cos 2k−z( )

′ σ − = − 2k−δσ − sin 2k−z( )

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n =γ2

ko σ eqo 2δσ o +δγ( ) sinΔk2

z ⎛ ⎝ ⎜

⎞ ⎠ ⎟cos k z( ) +δσ o

2 sin Δkz( )

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k =12

k+ + k−( ) = 2ko

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Δk = 2 k− − k+( ) = 2 2koδγ

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δσo = σ c − σ eqo

A Spread in Plasma Frequencies drives A Spread in Plasma Frequencies drives a a BeatingBeating in Emittance Oscillations in Emittance Oscillations

On a longer time scaleOn a longer time scale

increasing the initial envelope offset the emittance evolution is increasing the initial envelope offset the emittance evolution is dominated by the beating term and the original minimum is dominated by the beating term and the original minimum is

recovered only after a longer periodrecovered only after a longer period


Movable Emittance-Movable Emittance-MeterMeter

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HBUNCH.OUT

sigma_x_[mm]enx_[um]

Bz_[T]

sigma_x_[mm] Bz_[T]

z_[m]

emittance envelope

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E0 ∝ λ rf−1 120-140 MV/m==> 52-60 MV/m

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λ1.3 GHz

λ 3 GHz= 2.33

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σ i ∝ λ rf

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Bz ∝ λ rf−1

( )€

Q∝ λ rf 1 nC ==> 2.33 nC

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Q1 nC

Q2.33 nC3 = 0.75

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σ i ∝Q1 / 3

Scaling the LCLS design from S-band to L-bandScaling the LCLS design from S-band to L-band

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charge_scaling

enx_[mmmrad]

Q [nC]

Q^2/3

Q^4/3

TTF VUV-FEL PhotoinjectorTTF VUV-FEL Photoinjector

1.3 GHz, 1.5 cell RF Gun

Main SolenoidBucking Solenoid

Y. KimY. Kim RPPT008 RPPT008 Emittance Damping in TTF2 Booster Linac with Gaussian Longitudinal Laser Beam Profile

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EzBz

z [m]

Splitting Acceleration and Splitting Acceleration and FocusingFocusing

• The Solenoid can be placed downstream the cavity The Solenoid can be placed downstream the cavity • Switching on the solenoid when the cavity is cold Switching on the solenoid when the cavity is cold prevent any trapped magnetic fieldprevent any trapped magnetic field

36 cm

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HBUNCH.OUT

sigma_x_[mm]enx_[um]

sigma_x_[mm]

z_[m]

Q =1 nCQ =1 nCR =1.69 mmR =1.69 mmL =19.8 psL =19.8 psthth = 0.45 mm-mrad = 0.45 mm-mrad

EEpeakpeak = 60 MV/m (Gun) = 60 MV/m (Gun)

EEacc acc = 13 MV/m (Cryo1)= 13 MV/m (Cryo1)B = 3 kG (Solenoid)B = 3 kG (Solenoid)

I = 50 AI = 50 A

E = 120 MeVE = 120 MeV

nn = 0.6 mm-mrad = 0.6 mm-mrad

nn

[mm-mrad][mm-mrad]

Z [m]

HOMDYN Simulation

6 MeV6 MeV

3.3 m

PARMELA PARMELA simulationssimulations

µ-metal shield

solenoid

stainless steelniobiumHe tank

Connection to tuner

RT

2K

≤4K

Coupler port

130 mmR

=125

mm

500 mm

20 mGauss(2G wo )

166 mG 320 mG

Table 1 – SRF gun parameters f MHz] 1300 Epeak at cathode MV/m] 60 < Eacc> MV/m] 32 Bpeak/< Eacc> mT/(MV/

m) 4.47

Epeak/< Eacc> - 1.87 Specification for Qo

- 8*109

Pd at nom. gradient W ~20

L-band SC gun design with coaxial couplerL-band SC gun design with coaxial coupler

SCRF GUN

Scaling with Scaling with γγ

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B ∝ γ

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σr

σ l

∝ γ

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J ∝ γ 3

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σ l ∝ γ −5 3

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σr ∝ γ −2 3

BNL All-Niobium SC GunBNL All-Niobium SC Gun

T. Srinivasan-Rao et al., PAC 2003

1/2 cell, 1.3 GHzMaximum Field: 45 MV/m

Q.E. of Niobium @ 248 nmwith laser cleaningbefore: 2 x 10-7

after: 5 x 10-5

I. Ben-Zvi, Proc. Int. Workshop, Erlangen, 2002

No contamination from cathode particlesNo contamination from cathode particles

2 10-5

4 10-5

6 10-5

8 10-5

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BNL_SCRF_CAT

QE

QE

G [MV/m]

SCRF GUN

Measured

Limited by the available voltageLimited by the available voltage

Measurements at room T Measurements at room T on a dedicated DC on a dedicated DC

systemsystem

Extrapolation to Extrapolation to Higher Field Higher Field

Cs (WF=2 .1 eV)

Is Nb the best superconductor for the photoemission ?

a /pm b /pm c /pm 330 330 330 α / ° β / ° γ / ° 90 90 90

Pb (WF= 4.2 eV) Nb (WF= 4.9 eV)

a /pm b /pm c /pm 495 495 495 α / ° β / ° γ / ° 90 90 90

a /pm b /pm c /pm 614 614 614 α / ° β / ° γ / ° 90 90 90

Very preliminary results measured @ BNL

Quantum Efficiency of Pb

248 nm

213 nm

Puv= ƒ * (Q/ )*(h) = 4 W4 W laser @ 213 nm (V harmonic of 1064 nm laser) can

generate 1nC @ 1MHz nominal beam

1•10- 4

1.5•10-3

Conceptual All Fiber System

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Lots of development in Erbium and Ytterbium doped fiber systemsCommercially available 20W, 2MHz systemsProgress should be very rapid over next 1-2 years

Example: for UV lithographyx7 and x8 of 1.5 µmPicture stolen from Nikon

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sigma_x_[mm]

Z_[m]

Q =0.35 nCQ =0.35 nCR =1. mmR =1. mmL =19.8 psL =19.8 psthth = 0.7 mm-mrad = 0.7 mm-mrad

EEpeakpeak = 60 MV/m (Gun) = 60 MV/m (Gun)

EEacc acc = 11 MV/m (Cryo1)= 11 MV/m (Cryo1)B = 2.9 kG (Solenoid)B = 2.9 kG (Solenoid)

I = 18 AI = 18 A

E = 100 MeVE = 100 MeV

nn = 0.76 mm-mrad = 0.76 mm-mrad

3.2 m

HOMDYN Simulation

nn

[mm-mrad][mm-mrad]

σσxx

[mm][mm]

Z [m]

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Velocity bunching optionVelocity bunching option

CONCLUSIONSCONCLUSIONS

• Emittance compensation by external solenoid is Emittance compensation by external solenoid is possiblepossible• 60 MV/m peak field in SC cavity have been 60 MV/m peak field in SC cavity have been already demonstratedalready demonstrated• Work in progress @ BNL to demonstrate Work in progress @ BNL to demonstrate Pb QE ~10Pb QE ~10-3 -3 @ 200 nm@ 200 nm• Laser System: progress should be very rapid Laser System: progress should be very rapid over next 1-2 yearsover next 1-2 years

The following workshop was approved by ICFA at its meeting Feb 10-11,2005 in Vancouver:

Physics and Applications Physics and Applications of High Brightness Electron Beamsof High Brightness Electron Beams

Erice, Sicily, Italy, October 9-14, 2005Erice, Sicily, Italy, October 9-14, 2005Organizers: L. Palumbo (Univ. Roma), J. Rosenzweig (UCLA), L. Serafini(INFN-Milano).

Documents

Beam Dynamics in a Spilt SRF-Gun