J. B

. Has

tings

St

anfo

rd L

inea

r Acc

eler

ator

Cen

ter

J. B

. Has

tings

St

anfo

rd L

inea

r Acc

eler

ator

Cen

ter

Linac

Base

d Pho

ton S

ource

s: XF

ELS

Cohe

renc

e Pro

pertie

s Lin

acBa

sed P

hoton

Sou

rces:

XFEL

SCo

here

nce P

rope

rties

Cohe

rent

Sync

hrotr

on R

adiat

ionCo

here

nt Sy

nchr

otron

Rad

iation

σ zσ z

∼λ−1

/3

Power Power

Wav

eleng

thW

avele

ngth

cohe

rent

powe

r

incoh

eren

t pow

er

vacu

um

cham

ber

cutof

f

vacu

um

cham

ber

cutof

f

N

N ≈≈

66 ××1010

99

At e

ntra

nce

to th

e un

dula

tor

E

xpon

entia

lgai

n re

gim

e

S

atur

atio

n(m

axim

um b

unch

ing)

Exce

rpte

d fro

m th

e TE

SLA

Tech

nica

l Des

ign

Rep

ort,

rele

ased

Mar

ch20

01

Mic

robu

nchi

ngth

roug

h SA

SE P

roce

ss

X-FE

L bas

ed on

last

1-km

of ex

isting

SLA

Clin

acX-

FEL b

ased

on la

st 1-

km of

exist

ing S

LAC

linac

LCLS

at S

LAC

LCLS

at S

LAC

LCLS

LCLS

LCLS

1.5-1

5 Å1.5

-15 Å

2 com

pres

sors

2 com

pres

sors

one u

ndula

toron

e und

ulator

Peak

Brig

htne

ss E

nhan

cem

ent F

rom

U

ndul

ator

Rad

iatio

n To

SA

SE#o

f pho

tons

ΩxΩ

yΩ

z

B =

(Ωi-

phas

e sp

ace

area

)

Enha

ncem

ent

Fact

or

# of

ph

oton

sN

l c~

106

Und

ulat

orSA

SE

αΝe

αΝeN

l c

ΩxΩ

y(2πε

x) (2πε

y)

ΩZ

com

pres

sed

∆ω ω⋅

σZ c

=10

−3×1

0ps

∆ ω ω⋅

σZ c

=10

−3×1

00fs

210

210

λ2

()2

B10

2310

3310

10

Nlc: n

umbe

r of e

lect

rons

with

in a

coh

eren

ce le

ngth

l c

Peak

Brill

iance

of F

EL’s

Peak

Brill

iance

of F

EL’s

cour

tesy T

. Shin

take

X-Ra

yX-

Ray

~109

~109

103

by e−

quali

ty,

long u

ndula

tors

103

by e−

quali

ty,

long u

ndula

tors

106

by F

EL ga

in10

6by

FEL

gain

photo

ns

per

phas

e-sp

ace

volum

e pe

r ban

d-wi

dth

photo

ns

per

phas

e-sp

ace

volum

e pe

r ban

d-wi

dth

1 Å

1 Å

•Spo

ntan

eous

und

ulat

or ra

diat

ion

phas

e sp

ace

is th

e in

cohe

rent

sum

of t

he e

lect

ron

phas

e sp

ace,

con

sist

s of

m

any

spat

ial m

odes

•SAS

E: h

ighe

r-ord

er m

odes

hav

e st

rong

er d

iffra

ctio

n +

FEL

gain

is lo

caliz

ed w

ithin

the

elec

trons

sele

ctio

n of

the

fund

amen

tal m

ode

(gai

n gu

idin

g)Fu

lly tr

ansv

erse

ly c

oher

ent e

ven

ε x>

λ/4

π

Tran

sver

se C

oher

ence

x

X’2π

ε x

λ/2

(diff

ract

ion

limit)

Cou

rtesy

of S

. Rei

che

(UC

LA)

Z=25

mZ=

37.5

mZ=

50 m

Z=62

.5 m

Z=75

mZ=

87.5

m

m

Gai

n G

uidi

ng (L

CLS

)

Stat

istic

al fl

uctu

atio

n

T

rans

vers

e co

here

nce

afte

r dou

ble

slit

afte

r cro

ss

Obs

erva

tions

at T

TF F

EL*

01

X [

mm

]

Y [mm] Intensity [arb.units]

0246

X [

mm

]−2

−2

−1

2 0

−2

00

22

* V. A

yvaz

yan

et a

l., P

RL

(200

1); E

ur. P

hys.

J. D

(200

2)

•E(t)

=∑jE

0(t-t j

), t j

is th

e ra

ndom

arr

ival

tim

e of

jth

e-

Tem

pora

l Cha

ract

eris

tics

E 0: w

ave

pack

et o

f a s

ingl

e e-

Nu

λ

ρπλ

σω

uc

Nc

l≈

≈2

bunc

h le

ngth

•Sum

of a

ll pa

cket

s E(

t)

•lc

~ 10

0-10

00 λ

< bu

nch

leng

th

•Due

to n

oise

sta

rt-up

, SAS

E is

a c

haot

ic li

ght t

empo

rally

with

ML

cohe

rent

mod

es (M

Lsp

ikes

in in

tens

ity p

rofil

e)

•Its

long

itudi

nal p

hase

spa

ce is

ML

larg

er th

an F

T lim

it (ro

om fo

r im

prov

emen

t)

•Int

egra

ted

inte

nsity

fluc

tuat

ion

•ML

is N

OT

a co

nsta

nt, d

ecre

ases

due

to in

crea

sing

co

here

nce

in th

e ex

pone

ntia

l gro

wth

, inc

reas

es d

ue to

de

crea

sing

coh

eren

ce a

fter s

atur

atio

n)

LM

II1

=∆

Long

itudi

nal M

odes

leng

th

cohe

renc

elen g

thbu

nch

≈L

M

Man

ipul

atin

g th

e Lo

ngitu

dina

l Ph

ase

Spac

e

•Pr

oduc

e sh

orte

r pul

ses

•Fi

x th

e ce

ntra

l wav

elen

gth

•A

lter t

he lo

ngitu

dina

l coh

eren

ce

Man

ipul

atin

g th

e Lo

ngitu

dina

l Ph

ase

Spac

e

•‘C

ut’ t

he e

lect

ron

beam

: sho

rter b

unch

es•

Self-

Seed

•

Self

seed

with

chi

rped

ele

ctro

n be

am–

Prod

uce

a ch

irped

pho

ton

beam

: use

a

mon

ochr

omat

orto

‘slic

e’ a

smal

l tim

e po

rtion

of

the

the

beam

in e

nerg

y =>

a sh

ort p

ulse

in

time

•Se

ed w

ith a

n ex

tern

al so

urce

Magn

etic B

unch

Com

pres

sion

Magn

etic B

unch

Com

pres

sion

σ z0

σ z0

∆Ε/Ε

∆Ε/Ε

zzσ zσ z

unde

r-co

mpre

ssion

unde

r-co

mpre

ssion

V=

V 0si

n(ωτ

)V

= V 0

sin(

ωτ)

RF A

ccele

ratin

gVo

ltage

RF A

ccele

ratin

gRF

Acc

elera

ting

Volta

geVo

ltage

∆z=

R 56∆

Ε/Ε

∆z=

R 56∆

Ε/Ε

Path

Len

gth-

Ener

gyDe

pend

ent B

eam

line

Path

Len

gth

Path

Len

gth --

Ener

gyEn

ergy

Depe

nden

t Bea

mlin

eDe

pend

ent B

eam

line

…or

over

-co

mpre

ssion

…or

over

-co

mpre

ssion

∆Ε/Ε

∆Ε/Ε

zz

σ E/E

σ E/E

∆Ε/Ε

∆Ε/Ε

zz‘ch

irp’

‘chirp

’

0.55 f

s

Self

Seed

ing,

N=

1

Seed

No

Seed

Self-

seed

ing

optio

n at

the

TESL

A V

UV

FEL

Shor

t pul

ses:

Chi

rped

pul

se sl

icin

g

SASE

FEL

FEL

Am

plifi

er

1stUndulator

2ndUndulator

Out

put

radi

atio

n

Ener

gy-

chirp

ed

elec

tron

bea

m

Inpu

t rad

iatio

n

Freq

uenc

y-c

hirp

ed

radi

atio

n

Elec

tron

bypa

ss Puls

e Sl

icin

gPu

lse

Slic

ing

∆Ε/Ε

≈10

−3

Mon

ochr

omat

or∆Ε

/Ε∆Ε

/Ε

zz‘ch

irp’

‘chirp

’

Mon

ochr

omat

or:

shor

t pul

se li

mit

Mon

ochr

omat

orw

ith s

mal

ler

band

wid

th s

lices

out

sho

rter

pul

seδt

out=

δtin

x δω

mon

o/δω

chirp

But

unc

erta

inty

prin

cipl

e gi

ves

a lim

itδω

mon

ox

δtou

t≥

1/2

For L

CLS

at 8

keV

with

1%

chi

rp, t

hem

inim

um p

ulse

leng

th is

abo

ut 3

.5 fs

fwhm

, usi

ng a

mon

ochr

omat

orre

solu

tion

of 3

.3x1

0-5rm

s.

Out

put p

ulse

fwhm

rms

reso

lutio

nC

ryst

al re

flect

ion

4.1

fs2.

5x10

-5Si

(220

)

4.1

fs5.

7x10

-5Si

(111

)

9 fs

14x1

0-5

Ge(

111)

Mon

ochr

omat

orre

solu

tion

δω/ω

(rm

sx10

-5)

Output pulse fwhm(fs)

Effe

ct o

f sl

icin

g (1

%

chirp

on

120f

s rm

spu

lse)

Effe

ct o

f un

cert

aint

y pr

inci

ple

(E=8

keV

)

50

1020

1525

01020

Som

e pr

actic

al m

onoc

hrom

ator

optio

ns:

Not

e th

at if

the

unce

rtai

nty

prin

cipl

e do

min

ates

, the

n th

e ou

tput

pul

se h

as c

ompl

ete

long

itudi

nal c

oher

ence

For L

CLS,

slice

emitta

nce >

1.8

µmwi

ll not

satur

ate

For L

CLS,

slice

emitta

nce >

1.8

µmwi

ll not

satur

ate

SASE

FEL

is no

t forg

iving

—ins

tead o

f mild

brigh

tness

loss

, pow

er ne

arly

switc

hes O

FFSA

SE F

EL is

not fo

rgivi

ng—

instea

d of m

ild br

ightne

ss lo

ss, p

ower

near

ly sw

itche

s OFF

cour

tesy S

. Reic

he

P=

P 0P

= P 0

ε N=

1.2

µmε N

= 1.

2 µm

P=

P 0/1

00P

= P 0

/100

ε N=

2.0

µmε N

= 2.

0 µm

electr

on be

am mustm

eet b

rightn

ess r

equir

emen

tsele

ctron

beam

mustm

eet b

rightn

ess r

equir

emen

ts

But,

the

FEL

is a

chall

enge

:

End o

f pre

senta

tion

SASE

FEL

Elec

tron B

eam

Requ

ireme

ntsSA

SE F

EL E

lectro

n Bea

m Re

quire

ments

ε Ν<

1 µm

at 1 A

, 15 G

eVε Ν

< 1 µ

m at

1 A, 1

5 GeV

<0.08

% at

I pk

= 4 k

A,

K≈

4, λ u

≈3 c

m, …

<0.08

% at

I pk

= 4 k

A,

K≈

4, λ u

≈3 c

m, …

20L g

> 10

0 m fo

r εΝ

≈1.5

µm

20L g

> 10

0 m fo

r εΝ

≈1.5

µm

Need

to in

creas

e pe

ak cu

rrent,

pre

serve

emi

ttanc

e, an

d ma

intain

sm

all en

ergy

spre

ad, a

ll sim

ultan

eous

lyNe

ed to

incre

ase

peak

curre

nt, p

rese

rve e

mitta

nce,

and

maint

ain

small

ener

gy sp

read

, all s

imult

aneo

usly

AND

prov

ide st

able

oper

ation

AND

prov

ide st

able

oper

ation

trans

verse

emitta

nce:

trans

verse

emitta

nce:

radia

tion w

avele

ngth

radia

tion w

avele

ngth

ener

gy sp

read

:en

ergy

spre

ad:

peak

curre

ntpe

ak cu

rrent

undu

lator

perio

dun

dulat

or pe

riod

beta

functi

onbe

ta fun

ction

undu

lator

‘field

’un

dulat

or ‘fi

eld’

FEL g

ain le

ngth:

FEL g

ain le

ngth:

(~1.5

µm

reali

stic g

oal)

(~1.5

µm

reali

stic g

oal)