Collective Effects in the Driver of the Wisconsin Free-Electron

Laser (WiFEL)

Robert Bosch, Kevin Kleman and the WiFEL teamSynchrotron Radiation Center

University of Wisconsin-MadisonJuhao Wu

SLAC National Accelerator Laboratory

September 27, 2010

OutlineI. The Wisconsin FEL

II. Two-stage compressionA. Macroscopic effects

B. Microbunching

C. Beam spreader

III. Single-stage compression

IV. Shot noise

V. Using CSR to remove chirp

VI. CSR effect in recirculating linac driver

VII. Summary

WiFEL is a planned user facility with 3 FELs driven by a 1.7 GeV e-beam and 3 FELs at 2.2 GeV.

• A superconducting photoinjector and linac provide 200-pC parabolic bunches with peak current of 50 A.

• Magnetic bunch compression in-creases the current to 1 kA for the FELs.

• Collective effects in the driver must be considered.

Scientific Demand for a VUV/Soft Xray FEL

• Diffraction, VUV/X-ray light; e.g., for coherent imaging at nanometer-scale

• Highest energy-resolution beamlines• Tool for advanced nanotechnology patterning

• Subpicosecond pulses for pump-probe experiments;

e.g., for femtochemistry• High flux for resonant inelastic X-ray scattering

(photon in, photon out)• Coherent synchrotron radiation in the infrared from

bunches as a whole

UW FEL Layout

Supercon

duct

ing

elect

ron

linea

r acc

elera

tor

Bunch

com

press

or 1

Supercon

ducti

ng

elect

ron

gun

Bunch

com

press

or 2

Supercon

duct

ing

electr

on

l inear

acc

elera

tor

Supercon

duct

ing

electr

on

l inear

acc

elera

tor w

ith

third

harm

onic

cavit

ies

Supercon

duct

ing

electr

on

l inear

acc

elera

tor

Undulato

rs

Mono

chro

mato

rs

Experim

ental

Areas

2.2 G

eV

1.7 G

eV

Beam s

witchy

ard w

ith R

F sepa

rato

rs

1

2

3

5

64

5 Oct

ober 2

007

Ken Jaco

bs

The FEL design fits in a field that is owned by the University of Wisconsin, across the street from SRC.

UV Hall

1.7 GeV

Seed lasers

Undulators180 – 550 eV

20 – 180 eV

4.6 – 40 eV

Master laser oscillator

Fiber link synchronization

Injector laser

Pump lasersEnd stations

Ebeam switch

2.2 GeV

Seed lasers Undulators

80 – 550 eV

250 – 750 eV

300 – 900 eV

SRF Linac SRF LinacInjector

X-ray Hall

Pump lasersEnd

stations

Ebeam dump

RF power

supplies

Fib

er link

synch

ronization

•All undulators operate simultaneously at repetition rate up to 1 MHz each.

•Total number of undulators set by budget.

•Synchronization to ~10 fs.

UW FEL Layout

Courtesy Bill Graves

Figure courtesy of R. Legg

200-MHz superconducting rf gun

Superconducting Linac

• Linac is based on CW superconducting modules.

•CW SRF is currently in use at Jlab, SNS, Stanford, Daresbury, Rossendorf, BESSY

CW SRF linac at Rossendorf

Magnetic Bunch Compression:

Injectors Make 10’s Amps but FEL Need Kiloamps

Initial design: 2-stage bunch compressor with chicanes at 215 MeV and 485 MeV. Factor-of-twenty compression

gives 1 kA output current.

1.7

GeV

= -17.8°

Injector3 Modules

= 9° = 50.6°

L215 Modules

BC1R56 =

-87 mm

BC2R56 =

-18 mm3.9 GHz Cavities (10)36.3 MV, 180°

215

MeV

L1 2 Modules 48

5 M

eV

Gun 4 M

eV

251.

3 M

eV

BC1 compresses by a factor of 8, while BC2 compresses by a factor of 2.5

Lattice functions plotted from 4 MeV to 1.7 GeV

Compression of a parabolic bunch without collective effects. 100,000 particles are tracked by ELEGANT.

4 MeV BC1 entrance

BC1 exit BC2 entrance

BC2 exit 1.7 GeV

Tail

Longitudinal wakefields affect the compression.

• The ELEGANT code simulates the effects.• An approximate analytic model provides fast

1. Estimate of the minimum initial bunch length that

can be compressed without an upright tail.

2. Trial-and-error compensation of wakes

by adjusting rf parameters.

3. Jitter estimates.

4. Microbunching gain.

Analytic model

• The bunch is frozen outside of the chicanes.• Longitudinal impedances act upon frozen

bunches.• Longitudinal impedances within the chicanes are

represented by effective impedances. Emittance effects are included in the effective impedances.

Longitudinal Impedance Formulas

Longitudinal space charge (LSC)

Linac geometric impedance

Steady-state coherent synchrotron radiation (CSR) in magnets

Coherent edge radiation (CER) downstream of magnets

bb

b

krK

kr

kr

iZkZ 12

0LSC 1)(

12/1

cell2

0LINAC )1(1)(

kga

Li

ka

iZkZ

)4/(58.0163.1)( 3/23/10CSR kiZkZ

3/13/2

20

CER

)2/,min(ln

2)( dLZkZ

Effective impedances from beginning of bunch compressor BC1

before BC1

between BC1 and BC2

after BC2, up to 1.7 GeV

initial wavelength of modulation

Tracking simulations show that macroscopic wake effects upon the 1.7-GeV bunch are approximated by resistive impedances.

LiTrack with resistors ELEGANT with coherent radiation

Trapezoidal bunch

Gaussian bunch

Parabolic bunch

Upright bunch tails in phase space at 1.7 GeV are predicted by formulas for resistive impedances.

LiTrack with resistors ELEGANT with coherent radiation

Trapezoidal bunch

Gaussian bunch

Parabolic bunch

Fast 1-D compressor adjustment for design optimization with CSR/CER and wakes of the injector, harmonic cavities, and linacs for 200-pC parabolic bunches

ELEGANT simulation (slow)

LiTrack with coherent radiation approximated by resistors (fast)

4 MeV BC1 entrance

BC1 exit BC2 entrance

BC2 exit 1.7 GeV

ELEGANT simulation of the adjusted compression.

Microbunching

• Input current and energy modulations at the entrance of BC1 cause output modulations at 1.7 GeV.

• Formulas for the growth of modulations are obtained.

• ELEGANT tracking of 4 million particles agrees with the formulas.

• Evaluation of the formulas is much faster than tracking simulations.

Analytic modeling (curves) and ELEGANT simulations (dots) predict microbunching gain for a trapezoidal bunch.

Trapezoidal bunch with3-keV Gaussian energydistribution and 1-micronnormalized emittance

Trapezoidal bunch with10-keV laser-heater energy distribution and1-micron normalized emittance

Analytic modeling (curves) and ELEGANT simulations (dots) predict microbunching gain for low emittance.

Trapezoidal bunch with3-keV Gaussian energydistribution and 0.1-micronnormalized emittance

Analytic modeling (curves) also approximates ELEGANT simulations of a parabolic bunch (dots).

Parabolic bunch with3-keV Gaussian energydistribution and 1-micronnormalized emittance

Parabolic bunch with10-keV laser-heater energy distribution and 1-micron normalized emittance

Analytic modeling (curves) approximates ELEGANT simulations of a parabolic bunch (dots) that is heated by 10-keV in a laser-heater simulation.

Parabolic bunch heated by 10 keV in a laser heater simulation. Normalized emittance is 1 micron

3-keV initial Gaussianenergy distribution

After 10-keV heating in a laser heater simulation

The effect of the beam spreader upon microbunching gain for a 3-keV Gaussian energy distribution. Solid lines and dots are analytic and simulated gain from the chicane entrance through the beam spreader; dashed lines and open dots are gain without a beam spreader. (a) Original spreader design with R56 = 950 microns. (b) Revised spreader design with R56 = 38.5 microns.

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-2

100

102

104

106

108

gain

(a)

(I/I)out /(E/E)in(E/E)out /(E/E)in(I/I)out /(I/I)in(E/E)out /(I/I)in

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-2

100

102

104

106

108

gain

(b)

(I/I)out /(E/E)in(E/E)out /(E/E)in(I/I)out /(I/I)in(E/E)out /(I/I)in

Single-stage factor-of-twenty bunch compressor, with rf parameters optimized for 200-pC parabolic bunches. In comparison with 2-stage compression, the required harmonic-cavity voltage is much larger, and the dechirping phase in the final linac is larger.

1.7

GeV

= -18.5°

Injector5 Modules

= 40°

L115 Modules

BC1R56 = -100 mm

3.9 GHz Cavities (10)45 MV, 180°

400

MeV

Gun 4 M

eV

445

MeV

RF parameters of the 1-stage compressor adjusted for coherent radiation and wakes of the injector and linac L1, for 200-pC parabolic bunches. The output of a low-R56 beam spreader is shown.

-0.05 0.00 0.05z [mm]

-0.40

0.00

0.40

E/E

[%

]

-0.05 0.00 0.05z [mm]

0

1000

2000

curr

ent [

A]

Tail

The effect of the beam spreader upon microbunching gain for a 3-keV Gaussian energy distribution. Solid lines and dots are analytic and simulated gain from the chicane entrance through the beam spreader; dashed lines and open dots are gain without a beam spreader. (a) Original spreader design with R56 = 950 microns. (b) Revised spreader design with R56 = 38.5 microns.

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-3

10-1

101

103

105

107

gain

(a)

(I/I)out /(E/E)in(E/E)out /(E/E)in(I/I)out /(I/I)in(E/E)out /(I/I)in

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-3

10-1

101

103

105

107

gain

(b)

(I/I)out /(E/E)in(E/E)out /(E/E)in(I/I)out /(I/I)in(E/E)out /(I/I)in

The microbunching gain is more than an order of magnitude lower with single-stage compression than with two-stage compression.

With a low-R56 spreader, the microbunching is not increased.

Single-stage compression with a low-R56 spreader provides the best FEL performance since a colder bunch can be compressed. Laser-heating may not be required.

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-6

10-4

10-2

100

rela

tive

mod

ulat

ion (I/I)out original design

(I/I)out low-R56 spreader(E/E)out original design(E/E)out low-R56 spreader

(a)

0.0 0.1 0.2 0.3 0.4 0.50 [mm]

10-6

10-4

10-2

100

rela

tive

mod

ulat

ion (I/I)out original design

(I/I)out low-R56 spreader(E/E)out original design(E/E)out low-R56 spreader

(b)

Current and energy modulations at the FEL from shot noise, according to an analytical calculation that assumes linear gain for an initially parabolic bunch with 3-keV Gaussian energy spread. (a) Two-stage bunch compressor. (b) One-stage bunch compressor. The one-stage compressor with low-R56 spreader satisfies the FEL requirements that modulations with wavelengths shorter than the bunch should be smaller than 10% for current and 3x10-4 for energy modulations.

The lower microbunching gain with single stage compression and a low-R56 spreader is confirmed by the following simulations that approximate the amplified shot noise for an initial energy spread of 3 keV.

Amplified shot noise for two-stage compression followed by a beam spreader with R56 = 950 microns.

Amplified shot noise for two-stage compression followed by a beam spreader with R56 = 40 microns.

Amplified shot noise for single-stage compression followed by a beam spreader with R56 = 950 microns.

Amplified shot noise for single-stage compression followed by a beam spreader with R56 = 40 microns.

A beneficial application of collective effects:

In the WiFEL single-stage compressor, the compressed bunch is accelerated 40 degrees off-crest to remove its energy chirp. Since this requires 30% more RF accelerating voltage than on-crest acceleration, an alternative method of removing the bunch’s energy chirp may be cost-effective.

The wake of coherent synchrotron radiation (CSR) is one alternative method for removing the bunch chirp.

An analytic model predicts that a short bending magnet reduces the chirp of a rectangular bunch (in V/s) by –NqZ0/πtb2, where N is the bunch population, q is the electron charge, Z0 is the impedance of free space, and tb is the bunch length in seconds.

The magnets should be separated by a distance exceeding ctb/(1-cosӨ), where c is the speed of light and Ө is the angle of deflection in a bending magnet.

About 15 bending magnets are predicted to give a dechirped WiFEL bunch with on-crest acceleration of the compressed bunch.

Removing the chirp of a bunch with the wake of CSR. This chicane dechirper cell contains 8 short bending magnets.

Longitudinal phase space at the exit of the beam spreader for on-crest acceleration after single-stage compression. (a) No dechirping cells. (b)Two dechirping cells (16 bending magnets) at beam energy of 400 MeV. (c) Two dechirping cells at 1.7 GeV.

Simulations of shot noise show increased microbunching from thedechirping chicanes’ R56 = -1 mm, for a bunch that is not heated by alaser heater. The FEL requirements are marginally satisfied withouta laser heater, with initial energy spread of 3 keV.

Dechirping by off-crest acceleration,no dechirping chicanes

Dechirping by 4 dechirping chicanesat beam energy of 400 MeV

Dechirping by 4 dechirping chicanesat beam energy of 1700 MeV

Removing the chirp of a bunch with the wake of CSR. This isochronous arc dechirper contains 3 bending magnets.

Longitudinal phase space at the exit of the beam spreader for on-crest acceleration after single-stage compression.(a)No dechirping arcs. (b) Four dechirping arcs (12 bending magnets)at beam energy of 400 MeV. (c) Four dechirping arcs at 1.7 GeV.

Simulations of shot noise show little increase in microbunching from theisochronous dechirping arcs, for a bunch that is not heated by a laser heater.The FEL requirements are satisfied without a laser heater.

Dechirping by off-crest acceleration,no dechirping arcs

Dechirping by 4 isochronous arcsat beam energy of 400 MeV

Dechirping by 4 isochronous arcsat beam energy of 1700 MeV

CSR is also important in a recirculating-linac FEL driver. Lattice functions for a 1.7-GeV design with two 3-magnet isochronous arcs on each end, followed by a chicane for bunch compression.

Parameters for good compression with CSR effects have been found by trial-and-error tracking with the ELEGANT code. Here, a 200-pC bunch with initial length of 450 um compresses well with a linac phase of 17.2 degrees.

Q = 200 pC, initial length of 450 um, continued

Q = 200 pC, initial length of 450 um, continued

Q = 200 pC, initial length of 450 um, continued

Summary• Collective effects must be considered in the WiFEL driver

• Longitudinal wakes were modeled with longitudinal impedances before and after each stage of compression.

• Resistive impedances in the longitudinal LiTrack code approximate macroscopic CSR/CER effects. This allows fast adjustment of rf parameters to compensate longitudinal wakes.

• Microbunching analytic model agrees with simulations. Microbunching gain is minimized with single-stage compression followed by a beam spreader with R56 << 1 mm. Shot noise simulations suggest that a laser heater will not be required in this case. With a cold bunch, we expect better FEL performance.

• The compressed bunch may be dechirped with the wake of CSR. This reduces the expense for superconducting RF cavities.

• In a recirculating-linac design, CSR effects have been studied by tracking with ELEGANT. Trial and error has been used to find parameters for good compression in a chicane downstream of the recirculating linac.