P l a s m a M o d e l i n g o f W a k e f i e l d s i n E l e c t r o n C l o u d s : T . K a t s o u l e a s , A . Z . G h a l a m , S . L e e , U n i v e r s i t y o f S o u t h e r n C a l i f o r n i a ( U S C ) , W . B . M o r i , C . H u a n g , V . D e c y k , C . R e n U n i v e r s i t y o f C a l i f o r n i a a t L o s A n g e l e s ( U C L A ) W i t h s p e c i a l t h a n k s t o F r a n k Z i m m e r m a n f o r i n v i t i n g m e i n t o t h i s p r o b l e m
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Transcript
Pla
sma
Mod
elin
g of
Wak
efie
lds
in E
lect
ron
Clo
uds:
T. K
atso
ulea
s, A
. Z. G
hala
m, S
. Lee
,U
nive
rsit
y of
Sou
ther
n C
alif
orni
a (U
SC),
W. B
. Mor
i, C
. Hua
ng, V
. Dec
yk, C
. Ren
Uni
vers
ity
of C
alif
orni
a at
Los
Ang
eles
(U
CL
A)
With
spe
cial
than
ks to
Fra
nk Z
imm
erm
an f
or in
vitin
g m
e in
to th
is p
robl
em
Plas
ma
Mod
elin
g of
Ele
ctro
nC
loud
Ins
tabi
lity
•e-
clou
d is
a n
on-n
eutr
al p
lasm
a --
wel
lsu
ited
to p
lasm
a ac
cele
rato
r PI
C m
odel
s
•Pr
evio
us c
loud
mod
el–
no c
olle
ctiv
e in
tera
ctio
n be
twee
n cl
oud
elec
tron
s --
i.e.
, no
wak
e os
cilla
tions
–tr
eat p
lasm
a as
a s
ingl
e ki
ck o
nce
per
orbi
t
–N
ew, r
elat
ivel
y fe
w b
ench
mar
ks
E-1
57
, E-1
62
& E-1
64 C
olla
bo
rati
ons
R. A
ssm
ann,
F.-
J. D
eck
er, P
. Em
ma,
M.
J. Hog
an* , R
.H. I
vers
on,
C. O
’Con
nell
, P.
Kre
jcik
, P. R
aimon
di,
R.H
. Sie
mann
, D. W
alz
Stan
for
d Lin
ear
Ac
cele
rat
or C
enter
B.E
. Blu
e, C
.E.
Clay
ton,
C. H
uang
, C.
Jos
hi* ,
K.A
. Mar
sh,
W.B
. Mor
i, S
. Wan
gU
niv
er
sity
of C
alifo
rni
a at
Los
Ang
ele
s
T. K
atsou
lea
s* , S. L
ee,
P. M
uggl
iU
niv
er
sity
of S
outh
ern
Califo
rnia
• E
xtra
ord
inar
ily h
igh
fie
lds
dev
elo
ped
in b
eam
pla
sma
inte
ract
ion
s
• M
any
qu
esti
on
s re
late
d t
o t
he
app
licab
ility
of
pla
smas
to
hig
h e
ner
gy
acce
lera
tors
an
d c
olli
der
s
Ad
dre
ss t
hes
e q
ues
tio
ns
via
exp
erim
ents
�•
E-1
57:
Fir
st e
xper
imen
t to
stu
dy
Pla
sma
Wak
efie
ld A
ccel
erat
ion
(P
WF
A)
of
elec
tro
ns
ove
r m
eter
sca
le d
ista
nce
s (w
/ LB
NL
)
• P
hys
ics
for
po
sitr
on
bea
m d
rive
rs q
ual
itat
ivel
y d
iffe
ren
t (f
low
-in
vs.
blo
w-o
ut)
� E-1
62
• O
pp
ort
un
ity
for
dra
mat
ical
ly s
ho
rter
bu
nch
es in
th
e F
FT
B in
200
3 w
ith
co
rres
po
nd
ing
ly h
igh
er g
rad
ien
ts (
> G
eV/m
)
� E-1
64
Pla
sma
Wak
efie
ld A
ccel
erat
ion
in M
eter
-lon
g P
lasm
as
UC
LA
Thi
s ta
lk a
ddre
sses
3 q
uest
ions
:
•C
ould
col
lect
ive
effe
cts
in e
lect
ron
clou
ds(i
.e.,
plas
ma
wak
es)
be im
port
ant?
•C
an p
lasm
a m
odel
ing
tool
s be
use
ful f
orm
odel
ing
elec
tron
clo
ud in
stab
ility
?
•D
o re
cent
pos
itron
bea
m-p
lasm
aex
peri
men
ts h
ave
rele
vanc
e to
clo
udph
ysic
s?
Plas
ma
Mod
els
-- O
SIR
IS a
nd Q
uick
PIC
•OS
IRIS
--
fully
exp
licit,
3-D
, Par
ticl
e-in
-ce
ll (P
IC)
-Sol
ve f
ull M
awel
l’s
eqs.
on
a gr
id-M
ovin
g w
indo
w, p
aral
lel,
obje
ct-
orie
nted
Qui
ckP
IC -
- qu
asi-
stat
ic a
ppro
xim
atio
nfo
r ef
fici
ent p
lasm
a w
ake
mod
elin
g
•M
axw
ell’
s eq
uatio
nsfo
r fi
eld
solv
er
•L
oren
tz f
orce
upd
ates
part
icle
’s p
osit
ion
and
mom
entu
m
Par
ticle
pos
ition
s
Lor
entz
For
ce
���� ����� �
zv
ii
,
ρ nm
nm
j,
,,
�
dp dtE
vB
c
���
�
=+
×
�
�
EB
nm
nm
,,
,
∆t
� �� ���� �� ��� ��� ���
Wha
t Is
a Fu
lly E
xplic
it Pa
rtic
le-i
n-ce
ll C
ode?
Typ
ical
sim
ula
tio
n p
aram
eter
s:~1
07 -10
8 p
arti
cles
~1-1
0 G
byt
es~1
04 ti
me
step
s~1
02 -10
3 cp
u h
ou
rs
3-D
OSI
RIS
PIC
Sim
ulat
ion
ofP
arti
cle
Bea
m R
efra
ctio
n
Ref
ract
ion
of a
n E
lect
ron
Bea
m:
Inte
rpla
y B
etw
een
Sim
ulat
ion
& E
xper
imen
t
● 1
to 1
mod
elin
g of
met
er-s
cale
exp
erim
ent i
n 3-
D!
P. M
uggl
i et a
l., N
atur
e 41
1, 2
001
Qui
ckPI
C
•Q
uasi
-sta
tic a
ppro
xim
atio
n·
Froz
en w
akef
ield
ove
r tim
e sc
ale
of th
e bu
nch
leng
th
· =
> β
>> σ
z(v
ery
good
app
roxi
mat
ion!
)
Bea
m
Wak
e
Bas
ic e
quat
ions
for
Qui
ckP
ICU
CL
A
� Qu
asi-
stat
ic o
r fr
oze
n f
ield
Ap
pro
xim
atio
n
(1 c2
∂2
∂t2
−∇
2)A
=4π c
j
(1 c2
∂2
∂t2
−∇
2)φ
=4π
ρ
−∇⊥2A
=4π c
j
−∇⊥2φ
=4π
ρ
� �!"#$$#%&�'( )*+( *, )-#*' ./�&/#
0 #1 &2#1� �!"#$$ #%&�'( )*+
j=
j b+
j e≈
j b=
cρbˆ z
• )ˆ
(//z
A=
A
Loc
al--
φ,Α
at a
ny z
-sli
ce d
epen
don
ly o
n ρ,
j at t
hat s
lice!
φ,A
=ϕ,
A(z
−ct
)
3 &�+(54+' �'( 2�66-)!87
• Ψ
=φ
−A /
/
For
ces
:
plas
ma
:F e
⊥=
−e∇
⊥φ
beam
: F
b⊥
=−e
∇⊥Ψ
2-D
pla
sma
slab B
eam
(3-
D)
Wak
e(3
-D)
1.in
itia
lize
beam
2.so
lve
∇⊥2ϕ
=ρ,
∇⊥2ψ
=ρ e
⇒F p
, ψ3.
push
plas
ma,
stor
eψ
4.st
epsl
aban
dre
peat
2.
5.us
eψ
togi
ants
tep
beam
Qui
ckPI
C lo
op:
Nod
e 3
Nod
e 2
Par
alle
lizat
ion
of Q
uick
PIC
• Q
uick
PIC
is p
aral
leliz
ed u
sing
MP
I.
• In
Qui
ckPI
C d
rive
bea
m is
eve
nly
part
ition
ed a
long
z a
xis;
whi
le u
nifo
rmpl
asm
a is
eve
nly
part
ition
ed a
long
y a
xis.
UC
LA
3D D
eco
mp
osi
tio
n2D
Dec
om
po
siti
on
Nod
e 1 Nod
e 0
9
:;
:
;
Nod
e 0
Nod
e 1
Nod
e 2
Nod
e 3
-300
-200
-100
0
100
200
05
1015
Osi
risQ
uick
pic
(cnd
t)Q
uick
pic
(per
iodi
c)
Logitudinal Wakefield (Mev/m)
X1
(c/ω
p)
Ben
chm
arki
ng Q
uick
PIC
:C
ompa
rison
of w
akef
ield
s be
twee
n O
SIR
IS a
nd Q
uick
PIC
Qu
ickP
IC r
esu
lts
are
slig
htl
y d
iffe
ren
t fr
om
th
at o
f O
SIR
IS (
3D)
UC
LA
Wak
efie
lds
for
E15
7 (m
ildly
non
linea
r ca
se)
Sim
ulat
ions
Par
amet
ers
corr
espo
nd to
SP
S a
nd p
revi
ous
wor
k:
Qui
ckP
IC p
aram
eter
s:64
x64x
64 c
ells
, 4 p
arti
cles
/cel
l, 60
mm
x 6
0mm
x 2
.5m
bo
x
Rum
olo-
Zim
mer
man
Sim
ulat
ion
of E
z w
ake
?
?
Qui
ckPI
C R
esul
ts:
Bea
mC
loud
den
sity
Qui
ckPI
C R
esul
ts:
Lon
gitu
dina
l wak
e vs
. zfr
om Z
imm
erm
an a
nd R
umol
oT
rans
vers
e an
d L
ongi
tudi
nal
wak
es v
s. z
(Fro
m Q
uick
PIC
)Cod
e C
ompa
riso
n
Lo
cate
d in
th
e F
FT
B
e- o
r e+
<>=?A@BCDE
σ
F=CHGIJJ
K =LCM NOP Q
RS TS RU
V WXNYZ [\ XN
VSZ\ WX
JW
R^] "
BCDD @BCD_`J ab
V "
B GcJ
d NYNRe Qf
g WhS Wi QY
ji YNWed WJNYW
kB lXYNXQ\ [iS QRm
n NRhS RU
o WURNi
p8qg Wr
sS WURQXiS`
t liS`W\u YWRXSiS QR
g WhS Wi QYX
s [Jl
B?J
E-1
62 E
xper
imen
tal L
ayo
ut
FF
TB
Tim
e In
teg
rate
d &
Tim
e R
eso
lved
Fo
cusi
ng
of
Po
sitr
on
s
Pla
sma
OF
F
Pla
sma
ON
Tim
e w
ithin
the
bunc
h [p
s]
Horizontal Slice mean r.m.s. [µm]
Tim
e R
eso
lved
“Str
eaks
” o
f C
her
enko
v at
Dif
fere
nt
Pla
sma
Den
siti
es
Qui
ck P
IC S
imul
atio
n of
Bea
m E
volu
tion
in C
loud
Wak
e•
No
exte
rnal
mag
nets
•C
arto
on e
mitt
ance
•N
o sy
nchr
otro
n m
otio
n
(wak
e ef
fect
s is
olat
ed)
•R
ecta
ngul
ar p
ipe.
..
Bea
m &
Clo
ud E
volu
tion
(T
hru
40K
m o
f SP
S)
Bea
m D
ensi
tyC
loud
Den
sity
v wx yz{x |}~ ��� �
� }y�|��}����
��}�}}� }�� ��}}��x ��x y� w�}�
� �� ���� ��� ��� �
� �����������
������� ��� ������� ��� �� ����
Lon
gitu
dina
l For
ce o
n th
e be
am(a
t 2σ
beh
ind
the
cent
er o
f th
e be
am)
Tra
nsve
rse
For
ce o
n th
e be
am(a
t 2σ
beh
ind
the
cent
er o
f th
e be
am)
Bea
m (
Tilt
ed)
E-c
loud
den
sity
Tilt
ed B
eam
Sim
ulat
ion
� �� � ¡� ¢£¤ ¥¦§ ¥
§ £�¨¢©ª£««¨ª
¥ª£¦££§ £§¬ ¨«££¬�«©� �¬ �ª£>®
Bea
m &
Clo
ud E
volu
tion
(T
hru
20K
m o
f SP
S,T
ilted
Bea
m)
Bea
m D
ensi
tyC
loud
Den
sity
� �� � ¡� ¢£¤ ¥¦§ ¥
§ £�¨¢©ª£««¨ª
¥ª£¦££§ £§¬ ¨«££¬�«©� �¬ �ª£ ®
Why
is th
e be
am d
efle
cted
?(c
loud
wak
e +
clo
ud im
age
forc
es!)
•Im
age
forc
es:
+-
- --
----
+++
+ +++
+- -
----
-
F
Bea
m Im
age
Clo
ud Im
age
F
wal
l
F=
q b2 r2
1 γ2≈
0
F≈
q cq b
r2
•C
loud
imag
e m
ay b
e do
min
ant c
ontr
ibut
ion
to c
oher
ent t
une
shif
t:
Tun
e Sh
ift
•Je
i Wei
on
Mon
day
∆ν
∝N
b
1 σ2
1 γ2−
η e
+A
imag
e
Tun
e Sh
ift
•Je
i Wei
on
Mon
day
∆ν
∝N
b
1 σ2
1 γ2−
η e
+A
imag
e
1−
γ2η e
()
Thi
s ta
lk a
ddre
sses
3 q
uest
ions
:•
Cou
ld c
olle
ctiv
e ef
fect
s in
clo
ud w
akef
ield
s(i
.e.,
spac
e ch
arge
of
clou
d on
itse
lf)
beim
port
ant?
•C
an p
lasm
a m
odel
ing
tool
s be
use
ful f
orm
odel
ing
elec
tron
clo
ud in
stab
ility
?
•D
o re
cent
pos
itron
bea
m-p
lasm
aex
peri
men
ts h
ave
rele
vanc
e to
clo
udph
ysic
s?
No
(not
bel
ow 1
09 cm
-3)
Yes
(tim
e-de
pend
ent e
+ w
akes
mea
sure
d)
Yes
(mor
e ph
ysic
s, b
ench
mar
ked
for
relia
bilit
y,e.
g., n
ew c
ontr
ibut
ion
to tu
ne s
hift
foun
d)
It is
pos
sibl
e to
bui
ld a
pow
erfu
l too
l tha
tco
mbi
nes
the
best
of
plas
ma
and
circ
ular
acce
lera
tor
code
s
•N
ext s
teps
–A
dd e
xter
nal m
agne
tic f
ield
s (s
trai
ghtfo
rwar
d)
–A
dd s
ynch
rotr
on m
otio
n(f
airly
str
aigh
tforw
ard)
–A
dd v
aryi
ng p
rofi
le o
f cl
oud
arou
nd r
ing
(str
aigh
tforw
ard)
–Pa
ralle
lize,
ext
end
to th
ousa
nds
of tu
rns
(tim
e sc
ale
of a
larg
e E
-162
run
)
•W
ork
coul
d pr
ocee
d fa
irly
quic
kly
with
“a”
colla
bora
tor’s
vis
it to
US
C
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