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Da
nie
l M
iha
lcea
Hig
h G
rad
ien
t W
ak
efie
ld A
ccel
erati
on
in
Die
lect
ric-
Load
ed
Str
uct
ure
s
May
5, 2
011
F
erm
ilab
No
rth
ern I
llin
ois
Un
iver
sity
Dep
artm
ent
of
Ph
ysi
cs
•In
tro
du
ctio
n
•W
ak
efie
ld a
ccel
era
tio
n
1. P
lasm
a W
ak
efie
ld A
ccel
era
tors
2. L
ase
r-d
riv
en D
iele
ctri
c S
tru
ctu
res
3. E
lect
ron
bea
m d
riv
en D
iele
ctri
c S
tru
ctu
res
Ou
tlin
e:
3. E
lect
ron
bea
m d
riv
en D
iele
ctri
c S
tru
ctu
res
•D
iele
ctri
c W
ak
efie
ld A
ccel
era
tio
n
1. A
dv
an
tag
es, ea
rly
tim
es
2. H
igh
tra
nsf
orm
er r
ati
o
3. R
ecta
ng
ula
r sl
ab
s (t
heo
ry)
4. V
orp
al
sim
ula
tio
ns
•C
on
clu
sio
ns
Intr
od
uct
ion
Goal:
10 T
eV
Ele
ctr
on
Accele
rato
r
•C
ircu
lar
mac
hin
e. S
ynch
rotr
on r
adia
tion ∝
E4
•L
inea
r ac
cele
rato
r w
ith c
urr
ent
gra
die
nts
of ≈
0.0
5 G
V/m
=>
L >
200 k
m !
Searc
h f
or:
•A
lot
hig
her
fie
ld-g
radie
nts
.
•H
igh b
eam
qual
ity.
•L
ow
cost
.
New
acc
eler
atio
n t
echniq
ues
Intr
od
uct
ion
(2)
Cro
ss s
ecti
on
fo
r e+
e-∝
1/E
2 =
> T
o k
eep
σth
e sa
me
as f
or
E =
1 T
eV
Lu
min
osi
ty m
ust
in
crea
se a
t le
ast
10
0 x
!
yx
fN
Lσ
πσ4
2
=
Ele
ctro
n b
un
ch e
ner
gy n
ot
eno
ug
h. B
eam
qu
alit
y a
lso
cru
cial
.
Sea
rch
fo
r:
•G
ener
ate
low
em
itta
nce
(<
1 µ
m)
hig
h c
har
ge
bea
ms
(>1
nC
).
•C
on
tro
l “c
oll
ecti
ve
effe
cts”
to
mai
nta
in b
eam
qu
alit
y.
•In
crea
se r
epet
itio
n r
ate
(>1
00
Hz)
.
•M
any o
ther
th
ing
s (t
ran
spo
rt l
ine,
bea
m d
iag
no
stic
s, m
ater
ials
, el
ectr
on
ics,
etc
.).
Intr
od
uct
ion
(3)
Ult
ra-h
igh
fie
lds
are
lim
ited
by
th
e E
M p
rop
erti
es
of
the a
ccele
rati
ng s
tru
ctu
re.
Str
uct
ure
M
ax
. F
ield
(M
V/m
)
Su
per
condu
ctin
g5
0
Met
alli
c2
00
Met
alli
c2
00
Die
lect
ric
> 1
03
(~
10
4)
Pla
sma
~ 1
05
Fuse
d s
ilic
a tu
bes
(100 µ
m I
D)
bre
akdow
n o
nse
t at
≈14 G
V/m
!
M.C
. T
hom
son,
et a
l, P
RL
(2008)
Pla
sma W
ak
efie
ld A
ccel
erati
on
Pla
sma w
ak
es
(lin
ear):
•L
ongit
udin
al e
lect
ric
fiel
d
• •W
akes
can
be
exci
ted b
y:
1. E
lect
ron d
rive
bea
m
nEz∝
2. P
hoto
ns
•T
yp
ical
wav
elen
gth
: 50 µ
m
•L
BN
L (
L’O
asis
: 1 G
eV o
ver
3.3
cm
)
Pla
sma
length
= 1
0 c
m
M. J.
Hogan
, et
al,
PR
L (
2005)
Dir
ect
Lase
r A
ccel
erati
on
•C
ross
ed l
aser
bea
ms
(32 m
rad)
to o
bta
in a
lon
git
ud
inal
com
ponen
t.
•E
lect
ric
fiel
d a
mp
litu
de:
1G
V/m
•In
tera
ctio
n r
egio
n:
1.5
mm
•T
he
two l
aser
bea
ms
are
in o
pp
osi
te
phas
e.p
has
e.
lase
r λ
< σ
zN
eed
pre
bu
nch
ing
an
d
com
pre
ssio
n!
LE
AP
Coll
abora
tion
Pro
ble
ms:
•li
mit
ed b
reak
do
wn
th
resh
old
s fo
r la
ser
op
tics
•lo
w i
nte
ract
ion
eff
icie
ncy
Die
lect
ric
Wak
efie
ld A
ccel
erati
on
(D
WA
)
Driv
e b
eam
Test
beam
Die
lectr
ic
c/n
Tra
nsv
erse
sec
tio
n
Vd
riv
e
c/n
Wave-f
ron
t
Ass
um
e:
Vd
rive ≈ ≈≈≈
c (
ult
ra-r
ela
tivis
tic)
In v
acu
um
:
•v
ph
ase
= ω
/kz
= v
dri
ve≈ ≈≈≈
c
•k =
kz
•st
atic
E:
only
rad
ial
com
ponen
t (E
z∝
1/γ
2)
•w
akef
ield
L C
her
enkov r
adia
tion
DW
A (
2)
Sy
nch
ron
ism
con
dit
ion
: O
K f
or
parti
all
y f
ille
d w
avegu
ides
!
Regu
lar
wavegu
ides:
TE
an
d T
M n
orm
al
mod
es
Parti
all
y f
ille
d w
avegu
ides:
Lon
git
ud
inal
Secti
on
Magn
eti
c (
LS
M)
(H f
ield
|| w
ith
die
lectr
ic s
urfa
ce;
Hy
= 0
)
Lon
git
ud
inal
Secti
on
Ele
ctr
ic (
LS
E)
(E f
ield
|| w
ith
die
lectr
ic s
urfa
ce;
Ey
= 0
)
Cau
sali
ty c
on
dit
ion
: w
ak
efi
eld
is
0 i
n f
ron
t of
the c
harge d
istr
ibu
tion
!
zd
zz
Wz
Wnz
nz
z′
′−
⋅′
=∑∫∞
)(
)(
,ρ
ρ(z
)
zz′
z
0,=
nz
W0
,≠
nz
W
DW
A (
3)
x
y
ε εεε ε εεε
Tra
nsvers
e p
rofile
of
the c
urr
ent density (j)
),
()
,(
yx
yx
−=ρ
ρ
()(
)0
,,
,2
,2
=−
==
=
−a
xa
xy
Ly
Lx
xρ
ρρ
ρa
b
xy
zx
mk
EL
xπ ⋅
+=
⇒=
⇒±=
)12(
0,
)co
s()
(x
kx
x
k
k
x
x⋅
=∑λ
ρ
Lx
Dri
ve
ch
arg
e s
ym
me
try s
ets
th
e s
ym
me
try o
f th
e f
ield
s:
“monopoles”
(Ez(y
)=E
z(-
y))
: )si
nh(
)co
s(
)co
sh(
)si
n(
)co
sh(
)co
s(
yk
xk
E
yk
xk
E
yk
xk
E
xx
y
xx
x
xx
z
∝∝∝
“dipoles”
cosh(s
inh)
repla
ced b
y s
inh(c
osh)
x
xy
zL
mk
Ex
⋅+
=⇒
=⇒
±=
)12(
02
,
Vacu
um
regio
nD
iele
ctr
ic r
egio
n []
[]
[] )
(si
n)
cos(
)(
sin
)si
n(
)(
cos
)co
s(
yb
kx
kE
yb
kx
kE
yb
kx
kE
yx
y
yx
x
yx
z
−∝
−∝
−∝
22
2
⊥≡
+k
kk
yx
DW
A (
4)
Lim
it case:
)(o
r
0∞
→→
xx
Lk
[]
0
)(
sin
)(
4
0
2
0
→
−−
⋅+
→
LSE
y
LSM
E
ab
k
ab
a
Eελ
A. T
rem
ain
e a
nd
J.
Ro
se
nzw
eig
, P
R E
, 56
, 7
20
5, (1
99
7)
Driv
e b
eam
= f
lat
beam
!L
x>
> L
y
[]
)(
)(
cos
0,
zvt
vtz
kE
En
LSM
nz
−Θ⋅
−⋅
=1−
=ε
nyk
k
Tran
sform
er
rati
o:
−+
=m
in
max
WWk
→+ max
W
→− min
W
max
imum
acc
eler
atin
g v
olt
age
|max
imum
dec
eler
atin
g v
olt
age|
Th
eore
m:
2≤k
•dri
ve
char
ge
is s
ym
met
ric:
•dri
ve
char
ge
and t
est
char
ge
are
coll
inea
r
)(
)(
00
zz
zz
−=
−ρ
ρ
W0
dri
ve
bunch
ener
gy
kW
0te
st b
unch
ener
gy
when
dri
ve
bunch
is
bro
ught
to r
est
DW
A (
5)
Un
der
qu
ite g
en
eral
ass
um
pti
on
s:
⊥Area
QWz
~λ
σ<<
z
Ult
ra-h
igh
Wz
(>1 G
Vm
)
Str
uct
ure
s w
ith s
mal
l tr
ansv
erse
are
a(<
100µ
m x
100µ
m)
•hig
h q
ual
ity
bea
m
•hig
h e
ner
gy
T
o i
ncr
ease
focu
sab
ilit
y•
hig
h e
ner
gy
•m
ust
be
able
to d
eal
wit
h t
he
ver
y h
igh f
requen
cy r
egim
e (T
Hz)
•m
ater
ials
(b
reak
dow
n)
•b
eam
sta
bil
ity
Use
hig
h b
un
ch
ch
arge (
~ 1
00 n
C)
Argon
ne W
ak
efi
eld
Accele
rato
r (A
WA
)
Few
mm
’s s
truct
ure
s; f
ew 1
0’s
of
GH
z
Com
pari
son
wit
h V
OR
PA
L s
imu
lati
on
s
Theoretical model im
plementation:
•C
ha
rge
is d
ep
osite
d o
n g
rid
to
ma
ke
it
co
mp
atib
le w
ith
PIC
sim
ula
tio
ns
(Im
pa
ct-
T).
•y-c
ha
rge
dis
trib
utio
n is s
ym
me
tric
. N
o
dip
ole
co
ntr
ibu
tio
ns.
htt
p:/
/ww
w.t
xco
rp.c
om
•x-c
ha
rge
dis
trib
utio
n s
imu
late
d b
y t
he
su
pe
rpo
sitio
n o
f 2
0 F
ou
rie
r te
rms.
•z-c
ha
rge
dis
trib
utio
n is g
au
ssia
n w
ith
z0
(ce
nte
r o
f d
rive
ch
arg
e)
= 2
7.5
mm
an
d σ
z=
1.0
mm
.
•L
x=
10
.0 m
m
•a
= 2
.5 m
m a
nd
b =
5.0
mm
Lx
= L
yB
oth
LS
M a
nd
LS
E
Com
pari
son
wit
h V
OR
PA
L s
imu
lati
on
s (2
)
•d
rive
ch
arg
e p
ositio
n:
z =
27
.5 m
m
•fie
lds a
re e
stim
ate
d a
t x =
3.0
mm
an
d y
= 2
.0 m
m
•T
he
ore
tica
l m
od
el ig
no
res d
eca
yin
g m
od
es a
nd
sta
tic f
ield
s.
Com
pari
son
wit
h V
OR
PA
L s
imu
lati
on
s (3
)
•fie
lds a
re e
stim
ate
d a
t z =
18
.6 m
m (≈
8.9
mm
be
hin
d th
e d
rive
ch
arg
e).
•firs
t ro
w:
E-f
ield
s a
s f
un
ctio
ns o
f x a
t fixe
d y
= 0
.04
3 m
m (
ha
lf o
f b
in)
•se
co
nd
ro
w:
E-f
ield
s a
s f
un
ctio
ns o
f y a
t fixe
d x
= 0
.04
3 m
m
Arg
on
ne
Wak
efie
ld A
ccel
erato
r (A
WA
)
Sin
gle
bu
nch
op
erati
on
:
•Q
= 1
-100 n
C (
reac
hed
150 n
C)
•15 M
eV; σ
z=
2.0
mm
; e
x,n
< 2
00 µ
m (
at 1
00 n
C)
•P
eak c
urr
ent:
~10 k
A
Bu
nch
train
op
erati
on
:
•4 b
unch
es x
25 n
C o
r 16 b
unch
es x
5 n
C
•16-6
4 b
unch
es x
50-1
00 (
futu
re)
J. P
ow
er, IC
TA
Work
shop
(2006)
AW
A:
earl
y r
esu
lts
AW
A:
120 k
eV (
1988)
W. G
ai, et
al.
, P
RL
61, (2
756)
1988.
Measu
red
en
ergy
grad
ien
t: >
100 M
eV
/m (
2008)
M. E
. C
onde,
AA
C08
AW
A:
hig
h t
ran
sform
er r
ati
o e
xp
erim
ents
(Coll
ab
ora
tion
: Y
ale
, AN
L,
NIU
)
Non
-coll
inear
bu
nch
es
Incre
ase
tran
sform
er
rati
o
•tr
an
sform
er
rati
o:
~ 1
0
•m
ult
i-b
unch
dri
ve
trai
n
•dri
ve
bunch
sta
bil
ity
•lo
w c
ost
J. L. H
irshfield
S. V
. S
chelk
unov
M. A
. LaP
oin
te
Crit
ical
tilt
an
gle
: ~
70 m
rad
S. S
chel
kuno
v, et al,
PA
C1
1
AW
A:
hig
h t
ran
sform
er r
ati
o e
xp
erim
ents
(2)
Drive:
(R =
5.0
mm
)
Witness:
Rin
g s
ecto
r (r
1 =
4m
m; r2
= 5
mm
; l =
2 m
m)
Transmission:
-drive: 82%
-witness: 38%
Energy gain ≈ ≈≈≈500 keV
Q =
50 n
C
AW
A:
hig
h t
ran
sform
er r
ati
o e
xp
erim
ents
(3)
Tes
t b
eam
Dri
ve
bea
m
Exp
erim
en
tal
ch
all
en
ges:
•S
epar
ate
the
dri
ve
and t
est
bea
ms
in
tran
sver
se p
lane
(las
er, so
lenoid
s, g
un p
has
e).
•S
epar
ate
the
two b
eam
s lo
ngit
udin
ally
(las
er).
•C
ontr
ol
the
tilt
angle
=>
Ali
gnm
ent
is
crit
ical
!
•M
easu
re t
he
ener
gy
shif
t.
AW
A:
hig
h t
ran
sform
er r
ati
o e
xp
erim
ents
(4)
•E
ner
gy
shif
t an
d h
ori
zonta
l kic
k w
ere
mea
sure
d f
or
3 p
has
e del
ays
bet
wee
n d
rive
and w
itnes
s b
eam
s.
•L
arges
t av
erag
e en
ergy
shif
t w
as: ≈
200 k
eV
•E
ner
gy
shif
t an
d h
ori
zonta
l kic
k (
FX)
exce
llen
t
agre
emen
t w
ith t
heo
ry.
•Q
(dri
ve
bea
m)
too l
ow
to d
irec
tly
mea
sure
TR
. S
. S
chel
kunov,
et al,
PA
C11
A b
ett
er
ch
oic
e f
or
the d
riv
e b
eam
: rin
g s
hap
eN
o o
ff-a
xis
beam
AW
A:
rin
g b
eam
s
•tr
an
sform
er
rati
o:
~ 1
0
•m
ult
i-b
unch
dri
ve
trai
n
•d
riv
e b
un
ch
sta
bil
ity
•lo
w c
ost
J. H
irsh
fiel
d, et al,
PR
ST
-AB
(2
00
9)
AW
A:
tria
ngu
lar
shap
ed b
eam
s
Dest
roy
driv
e b
un
ch
sy
mm
etr
y
Incre
ase
tran
sform
er
rati
o k
K i
s m
axim
um
wh
en
th
e d
ecele
rati
ng v
olt
age
is c
on
stan
t acro
ss t
he d
riv
e b
un
ch
.is
con
stan
t acro
ss t
he d
riv
e b
un
ch
.
Sam
e d
ecele
rati
on
Nn
nqn
,,1
12
L=
+=
Acc
elD
ecel
.
q1
q1
-q1/2
q2
q3
–q
2+
q1
q1
–q
2/2
q3
q2
-q
1
q2
–q
1–
q3/2
q4
q4
–q
3+
q2
–q
1q
3–
q2
+ q
1–
q4/2
L
2N
K=
2λ=
d
Exp
erim
en
tal
ch
all
en
ge:
contr
ol
char
ge
rati
os
J. P
ow
er, et al,
PA
C01
Tri
an
gu
lar
shap
ed b
eam
s (2
)
Ram
ped
bea
m o
f 4 b
unch
es
Hig
h t
ransf
orm
er r
atio
(≈
10)
but
low
er
fiel
d g
radie
nt
(≈60 M
V/m
)
1-b
unch
bea
m
Hig
h f
ield
gra
die
nt
(≈200 M
V/m
) b
ut
low
er
tran
sform
er r
atio
(≈
2)
Low
er c
ontr
ibuti
on f
rom
hig
her
ord
er m
odes
Use
of
Fla
tbea
ms
Ferm
ilab
A0 P
hoto
inje
cto
r
ε x/ε
y≈
100 P
iot,
Sun, K
im, P
RS
T-A
B (
2006)
�ε x
= 4
0 µ
m;
ε y=
0.4
µm
�σ
x=
2 m
m; σ
y ≈
10
0 µ
m
�Q
= 0
.5 n
C
Bri
nkm
ann,
Der
ben
ev,
Flo
tman
n,
PR
ST
-AB
(2001)
Pro
of
of
pri
nci
ple
: D
. E
dw
ards,
et al,
PA
C01 (
2001)
•T
he
bea
m m
ainta
ins
its
tran
sver
se s
hap
e over
a
larg
e dis
tance
=>
Hig
her
ener
gy
gai
n f
or
the
wit
nes
s b
eam
.
•C
an o
bta
in l
arge
fiel
d g
radie
nts
.
•In
the
lim
it σ
z<
< λ
=>
Fy
= q
(Ey
+ v
Bx) ≈
0 =
>
no b
eam
bre
ak
-up
.
•M
atch
wel
l w
ith s
lab
-sy
mm
etri
c st
ruct
ure
s.
Ad
va
nta
ges
:
Q =
0.5
nC
∆z
= 6
.7 c
m
NM
L/A
0 (
?):
fla
tbea
ms
Des
ired
bea
m p
ara
met
ers:
•σ
y=
50
µm
; σ
x≈
20σ
yy
M. C
hurc
h, et al,
PA
C07
P. P
iot,
et al,
AA
C8
•ε y≤
1 µ
m;
ε x≈
10
0ε y
•σ
z=
50
µm
•Q
= 3
.0 n
C
Ez≈ ≈≈≈
0.3
GV
/m
Str
uct
ure
pa
ram
eter
s:
�a
= 1
00
µm
�b
= 3
00
µm
�ε
= 4
.0
z
Con
clu
sion
s:
�D
iele
ctr
ic l
oad
ed
wavegu
ides
can
su
stain
ult
ra-h
igh
fie
ld g
rad
ien
ts (
> 1
GV
/m).
�L
ow
ch
arge d
riv
e b
eam
s (~
1n
C)
can
pro
du
ce u
ltra-h
igh
fie
ld g
rad
ien
ts i
f fo
cu
sed
to
the l
evel
of
10’s
of
mic
ron
s.
�F
ield
grad
ien
ts o
f ab
ou
t 100 M
V/m
were
alr
ead
y o
bta
ined
at
AW
A.
�R
ecta
ngu
lar
stru
ctu
res
all
ow
:�
Recta
ngu
lar
stru
ctu
res
all
ow
:
�B
eam
tail
orin
g i
s th
e k
ey
or
hig
h f
ield
grad
ien
ts a
nd
hig
h t
ran
sform
er
rati
o.
•b
eam
focu
sing i
n o
ne
dir
ecti
on
•use
of
flat
bea
ms
•hig
her
ener
gy
gai
n (
longer
str
uct
ure
s)
•li
mit
ed b
eam
bea
k-u
p
•lo
w c
ost
