Phase Space Manipulation in High-Brightness Electron Beams

Marwan Rihaoui

Lawrence Berkeley National Laboratory Seminar

NGLS talk

June- 27-2011

2

Outline

  Introduction/Motivation.

  The Argonne Wakefield Accelerator.

  “Multi-beam” control of electron beam.

  Phase space exchange between two degrees of freedom.

  Development of a single-shot longitudinal phase space diagnostics.

  Production of a train of picosecond relativistic electron bunches.

  Future plans.

3

Introduction

  Particle accelerators produce and accelerate charged-particles beams up to relativistic energies.

  Accelerators applications include –  Material sciences (electron microscopy

and X-ray in accelerator-based light sources), –  Medical application, –  Nuclear and high-energy physics.

4

Beam & Phase Space: definitions

  A particle is identify by its coordinate and momentum in a 6D phase.

  A beam is a collection of particle confined in space

  Separate to 2D sub-phase space

  Trace space coordinates:

  Trace space coordinates of a particle downstream of an element can be obtained via

{ }ziiyiixiii pzpypxP ,;;;,!

{ }xiipx , { }

yiipy , { }zii pz ,

),,,;,( '' iiiiiii zyyxxX δ≡z

yx

pp

yx ),(' )',( ≡

yxz ppp ,>>

Transverse space Longitudinal space

if XRX =

R: transfer matrix of the element

iX fXR

with z

REFzz

ppp ,−≡δand

5

Statistical representation of a beam

′

′

=

δ

zyyxx

X ==Σ XX~

∑

=

CB

A

′′′′′′′

′′

′′′′′′′

′′

′′′′′′

′′

2

2

2

2

2

2

δ

δ

δ

δ

δ

δ

zzyzyzxzxzzzyzzyxzzxyzyyyyxyxyyyzyyyxyyxxzxyxyxxxxxxzyxxyxxx

∑∑ = Tif RR

  A beam can be represented by its second-order moments arranged as a covariance matrix or “ beam matrix”

  Uncoupled 2D phase spaces ⇒ beam matrix is block diagonal.

  The beam matrix can be propagated using the transfer matrix formalism

iΣ fΣR

6

Emittance and Brightness: figure of merit of a beam

2221xx

ex xppxcm

−=ε

222~

xxxxx ′−′=ε~

22 '2' xxxxx εαγβ =++

zyx

QQBεεε

=Γ

= Beam charge ~

2

~~

2 ','

,xxx

xxxx

εγ

εα

εβ =−==

  Canonical emittance:

  Trace-space emittance (experimentally measurable)

  Normalized Brightness

  Beam’s moment used to parametrize the beam

  Courant-Snyder parameters

7

Goals of research work

  Explore phase space manipulations.

  Multi-beam control of the transverse beam parameters.   Investigate phase space exchange between two degrees of freedom.

  Develop a single shot longitudinal phase space diagnostics and produce a train of picoseconds electron bunches.

7

8

Importance of phase space manipulation: next generation e+/e- linear collider

8

  International Linear Collider requirement (εx, εy, εz) = (8, 0.02, 3000) µm

yββπε xR NNfL

4−+= fR is the repetition frequency. βx and βy are the

twiss parameters . Assume ε= εx = εz

3480 mµ=Γ

  An RF gun at Q=3.2nC gives (εx, εy, εz) = (6,6,13 ) µm

  Redistributing the beam emittances within the 3 degrees of freedom ⇒ suppression of the damping ring (a 3 km circumference ring!)

⇒

9

Importance of phase space manipulation: reducing the size of accelerator-based light sources

  Compact (5 GeV) short-wavelength (λ=1 Å), x-ray free-electron lasers require or

γλπ

ε41

, ≤yx

(εx, εy, εz) = (0.1, 0.1, 10) µm

  An RF gun at Q=1 nC gives (εx, εy, εz) = (1,1,0.1 ) µm

  Only x-ray FEL (LCLS at SLAC) so far operates at 25 GeV

31.0 mµ=Γ⇒

10

Source of high-quality electron beams: the photoinjectors   Principle of operation:

–  1+1/2 cell cavity resonating on TM010,π mode

–  Laser illuminate photocathode on back plate

–  Laser synchronized with e.m. field

rf power from synchronized

klystron   Capabilities

–  e- beam is naturally bunch, –  e- bunch shape controlled

by laser parameters, –  emittances, charge, size

are variable

11

Beam dynamics simulations using Particle-in-Cell codes

  Beam is represented by ensemble of macroparticles.

  To compute space charge force (Fsc) we use the quasi-static approach. 1- Lorentz transformation to rest frame 2- Deposit the charge on 2D or 3D grid 3- Solve Poisson equation ⇒ electric field. 4- Inverse Lorentz transformation to Laboratory frame ⇒ B and E fields. 5- Interpolate E and B field for each of the macro particle position

  ASTRA for 2D cylindrically symmetrical beam low number of macroparticles (between 2000 and 5000).

  IMPACT-T: a fully 3D tracking code, can be run on cluster computers allowing a large number of macroparticles (~ 200,000).

scext FFdtdP

+=External field

12

An example of high-brightness photoinjector The Argonne Wakefield Accelerator (AWA)

  Support advanced accelerator science experiments

  Availability to external user (e.g. NIU)   Chosen for its versatility   Overview

–  5-8 MeV rf gun –  Linac with 8 MV accelerating voltage –  Extensive diagnostics

Constructed as part of my phD work

Gun + solenoids linac solenoid spectrometer

12

13

Simulation of AWA nominal setup

Astra ( blue) VS Impact-T (red)

linac gun linac gun linac gun

linac gun linac gun linac gun

Q=1nC

14

Generic beam diagnostics at AWA

  Transverse beam density monitor

Electron beam Ce:YAG screen

CCD Camera Digitizer

Vacuum Chamber

Lens

Video Signal

Y(pixel)

X(pi

xel)

250mm

mm50

  Integrating Current Monitor: Measure beam charge

  Virtual Cathode: Get laser distribution on the photocathode

15

Generic beam diagnostics at AWA (cont)

  Quadruple Scan Measure emittance –  Vary quadrupole –  Measure spot size downstream

–  Simulated measurements retrieved 22.75/26.37 vs 23.18/25.55 µm

  Spectrometer: Measure beam energy

ppy δη≈

cm4.18=η

iσ

[ ]xxxf kRkRkRkR γαβεσ )()()(2)(~ 21212112112 +−= R

fσ

Ce:YAG

16

“Multi-beam” control of electron beam

  Experiment reveals some interesting physics.   Interaction of multiple beams can be used to shape/control the parameters of a “main” beam

  Multibeams also provide intricate distribution for precisely benchmarking multi-particle simulation algorithms.

  Potential Applications –  Beam focusing. –  Multi-beam-based manipulation of a beam –  Mimicking and optimizing field-array emitter patterns.

  Recent example: –  Halo removal at Tevatron, –  Electron lens at Tevatron.

17

How to generate a multi-beam electron bunch in a photoinjector?

  mask in the laser path ⇒ generation of a multibeamlet distribution

low charge 20 pC

18

Comparison simulation/experiments experiment simulation

Incr

easi

ng B

-fiel

d

Q=1nC

19

Insights from simulations

  Lorentz force integrated over the longitudinal bunch distribution along beamline.   Most of beam-beam interaction occurs within 5 cm from the cathode surface.

20

Emittance Exchange Concept

EEX Initial state Final State

( ) 2222 det xxxxxxx

!"!== #$

( ) 2222 det !!"# ! zzzz $==

T

EXEXf MM 0!! =

=

00

000 0

0

zz

xx

TT

ε

εσ

!

Tu0

="u0

#$u0

#$u0

%u0

&

' (

)

* +

=

00C

BMEX

= T

xx

Tzz

f CCTBBT

00

00

00

ε

εσ

  From now on, we use 4D notations

  Need εxf=εz0 & εzf=εx0

  Coordinates swap between transverse and longitudinal spaces.

EXM

21

zx κ=′Δxκδ =

Deflector Cavity Design and modeling

TM110 mode

kzEeiEcBkxEkxeEE

tiy

tiz

00

00

≈=

≈=−

−

ω

ω

EeVλπ

κ 02

=

  Field in a pillbox cylindrical cavity at zero-crossing

  Cavity normalized strength

  Key element in phase space exchange

Screen

Tail Ref Head

F

F

22

Phase space exchange theory

=

1000100010

01

ξη

ηL

MDL

=

10001000100001

κ

κcavM

ηκ

1−=

  Total transport matrix of the exchanger is

23

Limitations for exact emittance exchange

( )

−+−

−

−−+−

−−

−+−

−+−

=

256

2

2

256

2565656

56

56

12823

12823

12823641281

12823

12823

212823

100

1282364128

1282364128

128230

ηλ

ηλ

ηλ

η

ηλ

ηλλ

ηη

η

ηη

ηλ

ηη

λλ

RLL

RRLLRR

R

LLRLL

M

c

c

cc

0022

02

0022

02

zxxz

zxzx

εεεε

εεεε

Λ+=

Λ+= ( ) ( )( )2562256222

2 2116384

1529zzzz

zx

xc RR ββααββηαλ

+−++

=Λ

  Coupling Terms, can minimized with respect to chirp:

zz

zε

δα −≡

  We need a quadrupole magnets upstream of the exchanger

Deflecting Cavity wavelength

Dispersion

( )zx

xc Rββηαλ

2

2256

22

163841529 +

=Λ

  Exchanger matrix:

  Emittance not perfectly exchanged

for

Λ2

24

10

−

=Δ

x

zz ε

ε10

−

=Δ

z

xx ε

ε

No space charge

Q = 100pC

Choose this region

  Real particle distribution with incoming emittance (ex,ez) = (15.9,3.75)mm

  Space charge does not prevent the minimization of emittance dilution

Limitations for exact emittance exchange

25

Investigation of emittance exchange via start-to-end simulation of AWA   Cathode to exchanger entrance modeled with ASTRA output passed to IMPACT-

T for simulation of exchanger beamline

  Optimized C-S parameters (space charge on)

  Summary of emittance dilutions 54.13;2.10 == xx βα m

26

Measured initial emittance partition

Transverse emittance measured using Quadrupole scan technique

Longitudinal emittance is inferred from the energy spread measurement~8mm

27

Phase space exchange: experimental plans

  AWA can achieved an interesting emittance partition εz

28

20o

Deflecting Cavity

a b

Dipole

YE6 Dipole

QE2

Lc

QE3

Single-shot longitudinal phase space measurement   Map initial (z, d) longitudinal phase space to the transverse plane (x,y)

29

Theoretical background

x

z

E1

E2 E1 > E2 Δx

Δx = ηΔE/E

(E1, z1)

(E2, z2) (E1, z’1)

(E2, z’2)

Δz ≈ R56ΔE/E )()( 1212 zzzzz −−′−′≡Δ

To preserve the relative distance between particles

Δz = 0 R56 = 0

Typically ΔE/E = a few mrad Δx = a few mm’s

QE1 inserted between dipoles

ΔE

Δz

zref

zref - Δz zref + Δz

taEB

tayEE

x

z

ωω

ω

sin

cos

0

0

=

=

0≠yF zy Δ⋅=Δ κ

Tail

Δy Head

Ref

xhx += 0ηδ

κδκ 0560 Rhzy y ++=( )xyz Hxyyx +−

=

2222

2

ηκβγ

ε

xyhhyhxhH yxyxxy 2

11

2222

2/1

2

−+=

−=γ

β

Higher order terms

Determine the resolution

=0

  Goal to map longitudinal phase space to screen

F

F

30

Commissioning of the deflecting cavity

Vertical displacement on screen versus phase of TDC

Calibration procedure for TDC strength

( ) 47.01.153sin75.13 +−= ϕδy )360230(φδ Δ=z

168.1 −= mκ

P= 40 kW

  Developed beam-based calibration procedure to determine cavity deflecting strength

31

Commissioning of the deflecting cavity (cont)

BEAM

Screen Deflecting cavity

Simulation scaling

  Measured deflecting k as a function of input power is in good agreement with numerical simulations.   The cavity was operated up to 800 kW but conditioned to its nominal 2.3 MW power

without problem.

32

Dispersion measurements

Dispersion measurement at YE6 for different QE1 strength

Dispersion versus QE1 strength

QE1=0.0T/m QE1=0.2T/m

QE1=0.4T/m

QE1=0.6T/m

  Beam Based measurement of dispersion is used in order to indirectly tune the R56

QE1=1.4T/m gives R56=0

QE1=0.3T/m

33

Single shot measurement of the LPS

z(mm)

d

Q=1.5nC E =14.6 MeV

17.14.0

−=

=

mm

κ

η

  Using calibration procedure, we can convert the configuration space coordinates into longitudinal coordinate and fractional momentum spread.

34

Generation of train of bunches

  Generate bunch with tunable spacing. 4 pulses generated using a-BBO crystal .

35

QE1=0.2T/m QE1=0.3T/m

QE1=0.4T/m QE1=0.5T/m

Generation of train of bunches measurement

  Evolution of the longitudinal phase space associated to a train of four bunches as a function of the quadrupole QE1.

36

Generation of train of bunches: applications

  Resonant excitation wakefield in dielectric-loaded waveguides

  Production of narrow-band radiation in the Terahertz (THz) regime

z-spacing vs. quadrupole strength Modulated distribution and corresponding spectrum

37

Summary of achievement and future plans   Advanced beam controls in a photoinjector:

–  Developed and tested a technique to use a multi-beam arrangement to control the beam properties via “multi-beam” interaction.

  Emittance Exchange: –  Designed a emittance exchanger beamline and explore limiting effects, –  Installed and commissioned key components of the exchanger –  Verified initial emittance partitions of AWA

  Longitudinal phase space diagnostics: –  Designed, build a single-shot longitudinal phase space diagnostics –  Use the beamline to produce a train of ps electron bunches

  Future Plans: –  Developed longitudinal phase space diagnostics to

•  Explore velocity bunching in photoinjector •  Beam dynamic in beam-driven wakefield accelerators

–  Designed exchanger beamline will be installed at AWA •  Current shaping for enhancing performance of beam-drive wakefield

acceleration

38

Thank you

38

39

  P. Piot, Y. E. Sun, J. G. Power and M. Rihaoui, “Generation of Relativistic Electron Bunches with Arbitrary Current Distribution via Transverse-to-Longitudinal Phase Space Exchange”. Phys. Rev. ST Accel. Beams 14, 022801 (2009) (2011)

  M. Rihaoui, P. Piot, J.G. Power, W. Gai, “Verification of the AWA photoinjector beam parameters required for a transverse-to-longitudinal emittance exchange experiment”. In the Proceeding of Particle Accelerator Conference (PAC’09), Vancouver, Canada (May 2009)

  M. Rihaoui, P. Piot, J.G. Power, W. Gai, “Limiting Effects in the Transverse-to-Longitudinal Emittance Exchange for Low Energy Relativistic Electron Beams”. Proceeding of Particle Accelerator Conference (PAC’09), Vancouver, Canada (May 2009)

  M. Rihaoui, W. Gai, P.Piot, J.G. Power, Z.Yusof, “Measurement and Simulation of Space Charge Effects in a Multi-Beam Electron Bunch from an RF Photoinjector”. Proceeding of Particle Accelerator Conference (PAC’09), Vancouver, Canada (May 2009)

List of publications published or submitted

39

40

  P. Piot, V. Demir, T. Maxwell, M. Rihaoui, J.G. Power, C. Jing, Longitudinal Beam “Diagnostics for the ILC Injectors and Bunch Compressors”. Proceeding of Particle Accelerator Conference (PAC’09), Vancouver, Canada (May 2009)

  M. Rihaoui, P. Piot, J. G. Power, Z. Yusof and W. Gai, “Observation And Simulation Of Space- Charge Effects In A Radio-Frequency Photoinjector Using A Transverse Multi-Beamlet Distribution”. Phys. Rev. ST Accel. Beams 12, 124201 (2009)

  M. Rihaoui, W. Gai, K. J. Kim, P. Piot, J. G. Power and Y. E. Sun, “Beam Dynamics Simulations Of The Transverse-To-Longitudinal Emittance Exchange Proof-Of-Principle Experiment At The Argonne Wakefield Accelerator”. AIP Conf. Proc. 1086, 279 (2009)

  P. Piot, Y. E. Sun and M. Rihaoui, “Production of relativistic electron bunch with tunable current distribution”. AIP Conf. Proc. 1086, 677 (2009)

  M. Rihaoui, W. Gai, P. Piot, J. G. Power and Z. Yusof, “Observation Of Transverse Space Charge Effects In A Multi-Beamlet Electron Bunch Produced In A Photo-Emission Electron Source”. AIP Conf. Proc. 1086, 671 (2009)

List of publications published or submitted

40

41

  M. Rihaoui, C. L. Bohn, P. Piot and J. G. Power, “Impact of transverse irregularities at the photo- cathode on the production of high-charge electron bunches”. In the Proceedings of Particle Accelerator Conference (PAC 07), Albuquerque, New Mexico, 25-29 Jun 2007, pp 4027

  Y.-E Sun, J. G. Power, K.-J. Kim, P. Piot, M. M. Rihaoui, “Design study of a transverse-to- longitudinal emittance exchange proof-of-principle”. Proceedings of the 22nd Particle Accelerator Conference (PAC’07), Albuquerque, New Mexico (25-29 June, 2007)

  G. Power, M. E. Conde, W. Gai, F. Gao, R. Konecny, W. Liu, Z. Yusof, P. Piot, M. Rihaoui, “Pepper-pot based emittance measurement of the AWA photoinjector”. Proceedings of the 22nd Particle Accelerator Conference (PAC’07), Albuquerque, New Mexico (2007)

List of publications published or submitted

41

42

Backup slides

42

43

Magnets modeling

Magnetic Quadrapoles: Perform measurements of B field for the AWA quads Magnetic dipole:   Magnetic field profile and magnets are from RadiaBeam.   Ideal magnetic dipole have hard edge model. We model the magnetic

dipoles with fringe fields using Enge Coefficients

g

zzs

iscB

Bi

iy

y

0

8,,1,)exp(1

11

0

!!"

=+

=!

!

Quad Bz field measurements

Enge Coefficients fit

Safe edges Coil position

Iron bar

N

S

S

N

43

44

Argonne Wakefield Accelerator

rf-waveguide

LPS beamline

spectrometer

YAG3

YAG5

YAG4

YAG1 D1 D2

YAG6 TDC

solenoid

solenoids rf-gun Linac

QE1 QE2 QE3

44

45

Transfer matrix of a realistic system

• Use a realistic model to test for the exchanger validation. • Generate Initial particle distribution of 6 particles with offset in position and momentum with a reference particle X = 0.

•  to get the six phase space R transfer matrix

][

0

XXRYYYRXYXRXYX

eX

X

iiii

iiR

i

Riii

−=−≡

=→

=→

=

=∧

δ

α

i

i

i

i

i

i

iiiiiii

Y

R

R

R

R

eeRRXY

αδ

ααδ

=

=>

===∧∧

6

1

6

1

.

.

.

.

.

.

.

.Reference particle

Probe particles

Ref

Probe

Differece orbit

45

46

RF deflecting Cavity

!!!!

"

#

$$$$

%

&

=

003.1732.0426.191.3

09956.000

0909.39974.00

04262.17294.01

cavM !

!!!!!

"

#

$$$$$$

%

&

=

142

0100

010

02

1

2

ii

i

i

i

LL

LL

M

'''

'

'

4/! 2/! 4/λd1=25cm d2=25c

m

( )!!!!

"

#

$$$$

%

&

=

!!!!!!

"

#

$$$$$$

%

&

==

1631.0427.1909.3

0100

0909.310

0427.173.01

1128

23

2

0100

010

02

1

2

11232

'(((

(

(

c

cc

ddtheory

L

LL

MMMMMM

Md1 Md2 M1 M2 M3

~23cm

k/4

From Don Edwards notes* The transfer matrix for one cell deflecting cavity using pillbox model is:

k/2 k/4

21ddL

c++= !

*Note on rf deflecting cavity can be found at: http://www.nicadd.niu.edu/aard/emittance_exchange/

46

47

!!!!

"

#

$$$$

%

&

'

''

=''

0436.0745.0409.8896.3

0022.00233.02471.02387.0

2355.0896.3015.00015.0

266.04.80858.00010.0

DLCAVDLM

( )

!!!!

"

#

$$$$

%

&

=

!!!!!!!!!

"

#

$$$$$$$$$

%

&

'+'

'

()

*+,

-''+

'

''

'+'

'+'

=

038.0631.03.8909.3

002.0038.02456.0236.0

236.0909.300

2456.03.8041.00

128

23

128

23

128

23641281

128

23

128

23

2128

23

100

128

2364128

128

2364128

128

230

2

56

2

2

2

56

2

565656

56

56

.

/

.

/

.

/

.

.

/

.

//

..

.

..

.

/.

.

//

RLL

RRLL

RR

R

LLRLL

M

c

c

cc

!"

1#=

47

  Matrix inferred from particle tracking

  Matrix analytically derived and evaluated for

  Realistic model reproduce the matrix analytically derived using hard-edge

elements

Transfer matrix of a realistic emittance-exchanger beamline

48

Cavity off Cavity on

48

49 49

Simulations Tools cont…

SUPERFISH used to generate E field

POISSON used to

generate B field

E B

Photo cathode( B = 0)

Magnetic field in the solenoid

Electric field in the rf gun π mode

bucking matching focusing

50