Modeling of lonization Physics with the PIC Code
OSIRIS
S. Deng l, F. Tsung 2, S. Lee \ Wei Lu2, W.B. Mori2, T. Katsouleas \ P. Muggli l
B.E. Blue 2, C.E.Clayton 2, C. O'Connell3, E. Dodd 2, F.-J. Decker3, C. Huang 2,
M. J. Hogan3, R. Hemker 2, R.H. Iverson 3,C. Joshi2, C. Ren 2,
P. Raimondi3, S. Wang 2, D. Walz 3
1. University of Southern California, Los Angeles, CA 90089
2. University of California at Los Angeles, Los Angeles CA 90095
S.Stanford Linear Accelerator Center, Stanford, CA 94025
Abstract. When considering intense particle or laser beams propagating in dense plasma or gas, ionization
plays an important role. Impact ionization and tunnel ionization may create new plasma electrons, altering the
physics of wakefield accelerators, causing blue shifts in laser spectra, creating and modifying instabilities, etc.
Here we describe the addition of an impact ionization package into the 3-D, object-oriented, fully parallel PIC
code OSIRIS. We apply the simulation tool to simulate the parameters of the upcoming El64 Plasma Wakefield
Accelerator experiment at the Stanford Linear Accelerator Center (SLAC). We find that impact ionization is
dominated by the plasma electrons moving in the wake rather than the 30 GeV drive beam electrons. Impact
ionization leads to a significant number of trapped electrons accelerated from rest in the wake.
Motivation
Ionization is important in plasma sources for plasma-based accelerators. With shorter electron
beams and higher intensity laser beams becoming available, simulating and understanding the
physical effect of ionization becomes more and more important for nearly every plasma source
except fully ionized hydrogen. In the upcoming El64 Plasma Wakefield Accelerator experiment
at SLAC, a short (.1 mm) but high current electron bunch is proposed to drive plasma wakefields
in a partially ionized Li plasma. To achieve the optimal wake amplitude, a high-density plasma
and gas (exceeding 1015 cm ~3) is required. lonization by the electron beam or plasma electrons
may not be ignored in this case.
In this paper, we introduce the algorithm of adding an ionization package (focused on impact
ionization only at this stage) into the 3-D object-oriented fully parallel PIC code OSIRIS[1].
Simulation results of the creation of new electrons, electron trapping and simulation for El64 are
also presented. Adding tunnel ionization and benchmarking the results with XOOPIC will be
discussed in future publications.
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
219
Impact ionization
ionization module
module
Impact
module
Impact
ionization
Figure
shows
simple
module
for
Collisions are
are implemented
implemented in
in OSIRIS
OSIRIS
Figure
impact
ionization.
Collisions
are
implemented
in
OSIRIS
Figure 111 shows
shows aaa simple
simple module
module for
for impact
impact ionization.
ionization. Collisions
with
Monte
Carlo
collision
(MCC) package
package
including the
the null
null collision
collision method
method [2].
[2]. For
For the
the
with
the
null
collision
method
[2].
For
the
with aaa Monte
Monte Carlo
Carlo collision
collision (MCC)
(MCC)
package including
including
MCC,
the
probability
for
a
particle
to
ionize
the
gas
is:
MCC,
the
probability
for
a
particle
to
ionize
the
gas
is:
MCC, the probability for a particle to ionize the gas is:
P
σ
Pi
Pii =
= nngga(Vi)IVilAt
σ(v
(vii)|v
)|vii|¨W
|¨W
(1)
(1)
(1)
Here,
velocity
of
the
incident
particle.
We
Here,
is
gas
density,
aσ is
is
gas
cross-section, vvYIii is
is the
the velocity
velocity of
of the
the iiith
incident particle.
particle. We
We
th incident
Here, nnnggg is
is gas
gas density,
density, σ
is gas
gas cross-section,
cross-section,
is
the
th
compare
random
if
Random
(0,1)<P
ionization
compare
number
between
and 111 with
with this
this probability,
probability, if
if Random
Random (0,1)<P
(0,l)<Pi,
ionization
ii,, ionization
compare aaa random
random number
number between
between 00
0 and
and
with
this
probability,
does
electron
and
neutralizing
ion.
does
occur,
decreases
the
gas
density
and creates
creates aaa new
new electron
electron and
and neutralizing
neutralizing ion.
ion.
does occur,
occur, decreases
decreases the
the gas
gas density
density and
and
creates
new
v’
v
FIGURE 1. Simple model for impact ionization: Particles injected into gas may ionize the gas and create
FIGURE
Particles
injected
into gas
gas may
may ionize
ionize the
the gas
gas and
and create
create new
new electrons
electrons and
and ions.
ions.
FIGURE 1.
1. Simple
Simple model
model for
for impact
impact ionization:
ionization:
Particles
injected
into
new
electrons
and ions.
The
The Osiris
Osiris PIC
PIC code
code
Osiris
independent,
Osiris
is
3D fully
fully relativistic
relativistic PIC
PIC code.
code. ItIt consists
consists of
of modules.
modules. Each
Each module
module isis independent,
independent,
Osiris is
is aa 3D
and
and
can exchange
exchange information
information with
with other
other modules.
modules. This
This structure
structure enables
enables us
us to
to very
very easily
easily add
add aaa
and can
new
module
gas species,
new gas
module can interact with other modules
realize
new
for aa gas
species, and
and this
this new
gas module
modules to
to realize
realize
new module
module for
ionization.
ionization.
ionization.
Simulation
Simulation Results
Results
A. Test
problem with
A.
Test problem
with 2D
2D Cartesian
Cartesian Geometry
Geometry
-2.50
-2.50
-2.50
-1.25
-1.25
-1.25
0.00
0.00
x2
x2
x2
x2
Plasma
center
Plasma
and gas
gas come
come into
into aa moving
moving window
window from
from the
the right
right side.
side. The
The beam
beam stays
stays atat the
the center
center
Plasma and
of
of the
the simulation
simulation window.
of
the
simulation
window. Simulation
Simulation parameters
parameters are:
are: simulation
simulation box
box 18*6c/ω
18*6c/copp,, grid
grid 180*60,
180*60, 999
particles
=19/ωp. We
can
particles per
per cell,
particles
per
cell, dt=0.07/ω
dt=0.07/cOp,
We set
set plasma
plasma density
density to
to be
be uniform,
uniform, and
and the
the gas
gas can
can
pp, ttmax
max=19/cOp.
be
be fully
fully ionized.
ionized.
be
fully
ionized.
We
both electron
We simulate
simulate both
We
simulate
electron beam
beam and
and positron
positron beams;
beams; the
the comparison
comparison is
is shown
shown in
in Fig.
Fig. 2:
2:
1.25
1.25
0.00
1.25
2.50
2.50
2.50
00
55
10
10
15
15
0
x1
x1
-3.5
-3.5
-3.0
-3.0
-2.5
-2.0
-1.5
-2.5
-2.0
-1.5
Phasespace_x2x1
Phasespace_x2x1
5
10
15
15
x1
-1.0
-1.0
-0.5
-0.5
0.0
0.0
-2.5
(a)
(a)
-2.0
-1.5
Phasespace_x2x1
-1.0
-0.5
-0.5
(b)
(b)
FIGURE 2.
2. Real
Real space
space density
density of
FIGURE
both
cases,
FIGURE
2.
Real
space
density
of newly
newly created
created electrons
electrons for
for (a)
(a) electron
electron beam,
beam, (b)
(b) positron
positron beam.
beam. In
In both
both cases,
cases,
new electrons
electrons are
are created,
created, but
electrons are
are sucked
sucked to
to the
the center
center of
of the
the
beam.
new
but for
for the
the positron
positron beam,
beam, the
the new
new created
created electrons
the beam.
beam.
new
electrons
are
created,
220
shows the
the wavelength
wavelength changing
changing after
after ionization
ionizationisisturned
turnedon.
on.The
Thewavelength
wavelengthofofwake
wake
Figure 33 shows
Figure 3 shows the wavelength changing after ionization is turned on. The wavelength of wake
shorter because
because the
the new
new created
created electrons
electrons increase
increasethe
theplasma
plasmadensity.
density.
field becomes shorter
field becomes shorter because the new created electrons increase the plasma density.
0.00
0.00
0.00
0.00
1.25
1.25
2.50
2.50
2.50
2.50
x2
x2
1.25
x2
x2
1.25
3.75
3.75
5.00
5.00
3.75
3.75
5.00
5.00
0
5
0
-0.4
-0.4
5
-0.2
-0.2
10
x1 10
x1
0.0
0.0
E1_field
E1_field
15
15
0.2
0.2
0
5
0
0.4
0.4
5
-0.4
-0.4
-0.2
-0.2
10
x1 10
x1
15
15
0.0
0.0
E1_field
E1_field
0.2
0.2
(a)
(b)
(a)
(b)
(a)
(b)
FIGURE
3.
Comparison
of
longitudinal
electrical
field
between
(a)
with
FIGURE
3.
Comparison
of
longitudinal
electrical
field
between
(a)
with
ionizationand
and(b)
(b)without
withoutionization.
ionization.
FIGURE 3. Comparison of longitudinal electrical field between (a) withionization
ionization
and
(b)
without
ionization.
B.
B.
Electron
trapping
in
3D
simulation
B. Electron
Electrontrapping
trappingin
inaaa 3D
3D simulation
simulation
-2
-2
-2
-2
-1-1
-1
-1
p1
p1
p1
p1
It
ItItis
isispredicted
predicted
that
when
born
at
the
proper
phase,
the
newcreated
createdelectrons
electronscan
canbe
betrapped
trappedby
by
predictedthat
thatwhen
whenborn
bornat
atthe
theproper
properphase,
phase,the
thenew
new
created
electrons
can
be
trapped
by
the
the
excited
plasma
wake.
We
simulate
3D
case
in
which
new
created
electronsare
areobserved
observedto
to
theexcited
excitedplasma
plasmawake.
wake.We
Wesimulate
simulateaaa3D
3Dcase
casein
inwhich
which new
new created
created electrons
electrons
are
observed
to
gain
gain
more
energy
than
background
plasma
electrons
as
Fig.444shows.
shows.
gainmore
moreenergy
energythan
thanbackground
backgroundplasma
plasmaelectrons
electronsas
asFig.
Fig.
shows.
0 0
00
11
1 1
0 0
55
x1x1
1010
00
1515
-6-6 -6-6 -5-5 -5-5 -4-4 -4-4 -3-3 -3-3 -2-2 -2-2 -1-1 -1-1 0 0
Phasespace_p1x1
Phasespace_p1x1
55
x1
x1
10
10
15
15
-6.00
-5.50
-5.00
-4.50
-4.00
-3.50
--3.00
-2.50
-2.00
-1.50
--1.00
-0.50
0.00
-6.00
-5.50
-5.00
4.50
-4.00
-3.50
3.00
-2.50
-2.00
-1.50
1.00
-0.50
0.00
Phasespace_p1x1
Phasespace_p1x1
(a)
(a)
(a)
(b)
(b)
(b)
FIGURE
FIGURE4.
Phasespace
spaceP1X1
P1X1of
of (a)
(a)background
background plasma
plasma and
and (b)
(b)
newly created
created
electrons.
The
electrons
FIGURE
4.4.Phase
Phase
space
P1X1
of
(a)
background
plasma
and
(b) newly
newly
created electrons.
electrons. The
The electrons
electronswith
with
normalized
normalizedmomenta
momentaP1=p
P1=p
0.4have
have been
been trapped
trapped and
and accelerated
accelerated
by
the
wave.
Note
that
momentum
zz/mc
z/mc>
normalized
momenta
Pl=p
/mc
>>0.4
0.4
have
been
trapped
and
accelerated by
by the
the wave.
wave. Note
Note that
that momentum
momentum
increasesdownward
downwardin
theseplots.
plots.
increases
increases
downward
ininthese
these
plots.
C. Modeling
Modelingthe
theE164
E164
experiment
C.
C.
Modeling
the
El
64experiment
experiment
Theparameters
parameters of
of the
the upcoming
upcoming E164
E164 Plasma
Plasma Wakefield
Wakefield Experiment
Experiment
and
corresponding
The
The
parameters
of
the
upcoming
El64
Plasma
Wakefield
Experiment and
and corresponding
corresponding
simulationsare
areshown
shownin
thetable
table111below.
below.This
Thissimulation
simulationuses
uses
2D
cylindrical
coordinate.
simulations
simulations
are
shown
ininthe
the
table
below.
This
simulation
uses2D
2Dcylindrical
cylindricalcoordinate.
coordinate.
Table1.
Table
Table
1.1.
Physicalparameters
parameters
Physical
Physical
parameters
-3 -3)
-33-3)
nplasma
(cm
ngas
(cm
N
Vz z
Vr r
beam
3)
nnpplasma
(cm
nngas(CHr
(cm
))
EEEbeam
N
VCT
Va
gas
lasnia(cm"
)
N 10
r
beam
Z
1515
1616
5*10
3*10
30Gev 2*1010
100µµmm 25
25µµmm
5*10
3*10
30Gev
5*1015
3*1016
30Gev 2*10
2*101U 100
lOOum
25um
221
dt
dt
dt
.022/ωωpp
.022/
.022/a>p
Simulation
paramenters
Simulation
Simulationparamenters
paramenters
Grids size
max
ttmax
Grids
Gridssize
size
tmax
22/ωωpp
z:400c/ω
ω
r:200c/ω
ω
22/
22/Q)p z:400c/
z:400c/Cdppp |r:200c/
r:200c/Cdpp p
0
1
1
x2
x2
0
2
3
2
3
0
5
10
15
0
5
x1
-1.5
-1.3
-1.0
-0.8
-0.5
E1_field_x
10
15
x1
-0.3
0.0
0.3
0.5
-1.5
-1.3
(a)(a)
-1.0
-0.8
-0.5
E1_field_x
-0.3
0.0
0.3
0.5
(b)
(b)
FIGURE
The
longitudinalelectron
electronfield
fieldofofthe
thewake
wake(a)
(a)without
withoutionization,
ionization,(b)
(b)with
withionization.
ionization. There
There isis little
little
FIGURE
5. 5.
The
longitudinal
difference
between
them.
difference
between
them.
this
experiment,the
thelaser-ionized
laser-ionizedLiLivapor
vaporplasma
plasmaisisnot
notfully
fullypre-ionized
pre-ionizedby
bythe
thelaser.
laser. The
The
In In
this
experiment,
remaining
neutralgas
gasdensity
densityisisnominally
nominallysix
sixtimes
timesthe
theionized
ionizeddensity.
density.
remaining
neutral
study
effectofofimpact
impactionization
ionizationofofthe
thegas
gason
onthe
theexperiment,
experiment,we
wemodel
modelseveral
several cases.
cases.
ToTostudy
thetheeffect
First,weweexamine
examinethe
theeffect
effectofofthe
theimpact
impactionization
ionizationdue
duetotoboth
both the
the beam
beam (primary)
(primary) and
and the
the
First,
blownoutoutplasma
plasma(secondary
(secondaryionization).
ionization). We
Wefind
findthat
thatthe
thefractional
fractional ionization
ionization from
from impact
impact
blown
ionizationofofthetheneutral
neutralgas
gasis isupuptoto4%,
4%,corresponding
correspondingtotoananincrease
increaseininplasma
plasma density
density of
of
ionization
15
0.24*10
cm3.-3.The
Theeffect
effectofofthis
thisdensity
densityononthe
theelectric
electricfield
fieldofofthe
thewake
wakeisisminimal
minimal (Fig
(Fig 5).
5).
0.24*
1015 cm"
Includingionization
ionizationininthe
themodel
modelincreases
increasesthe
thewake
wakewavelength
wavelength by
by 1.4%
1.4% and
and decreases
decreases the
the
Including
amplitude
9%atat3 3D z . zThe
. Thespike
spikeelectric
electricfield
fieldisisdecreased
decreasedby
by36%.
36%.However,
However, the
the spike
spike value
value
amplitude
byby9%
useful
accelerationexperiments
experimentssince
sinceititcontains
containsvery
verylittle
littleenergy.
energy.Next,
Next,we
weisolate
isolate the
the
is is
notnot
useful
forforacceleration
sourceofofthetheionization
ionizationininthe
themodeled
modeledexperiment
experimentby
byincluding
including the
the primary
primary or
or secondary
secondary
source
ionization
processonly.
only.We
Wefind
findthat
thatplasma
plasmaionization
ionizationdominates
dominatesbeam
beamionization
ionization by
by aa factor
factor of
of
ionization
process
order
400.
This
is
because
the
cross-section
for
ionization
of
gas
is
peaked
near
10
eV
and
drops
order 400. This is because the cross-section for ionization of gas is peaked near 10 eV and drops
sharplyasasenergy
energyincreases
increases[3].
[3]. We
Wealso
alsoestimated
estimatedthe
thenumber
numberofoftrapped
trappedelectrons
electrons after
after 1.65
1.65
sharply
mm
of
propagation.
Less
than
0.01%
electrons
are
trapped.
This
number
will
increase
as
new
mm of propagation. Less than 0.01% electrons are trapped. This number will increase as new
electrons
continuallycreated
createdand
andtrapped
trappedover
overthe
the30
30cm
cmdesign
designlength.
length.
electrons
arearecontinually
Summary
Summary
We added impact ionization into the code OSIRIS, and presented 2D and 3D simulation
We added impact ionization into the code OSIRIS, and presented 2D and 3D simulation
results. In both cases, we see the creation of new electrons, change of wake wavelength and
results.
In both cases, we see the creation of new electrons, change of wake wavelength and
trapping of newly created electron. Also, we conclude that impact ionization will occur but may
trapping
of newly created electron. Also, we conclude that impact ionization will occur but may
have little effect on the wakes in experiment E164. Because of the lower cross-section at higher
have
little
effect on the wakes in experiment El64. Because of the lower cross-section at higher
energy, plasma ionization dominates beam impact ionization.
energy, plasma ionization dominates beam impact ionization.
Acknowledgments
Acknowledgments
The authors gratefully acknowledged the help from David L. Bruhwiler. This work is
The authors gratefully acknowledged the help from David L. Bruhwiler. This work is
222
supported by U.S. Department of Energy, under Contracts USDOE DE-FG03-92ER40745, NSFPHY-0078715, DE-FC02-01ER41192, DE-FG03-92ER40727, DE-FC02-01ER41179, PHY0078508.
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code for modeling plasma based accelerators, IEEE Particle Accelerator Conference 5 , 3672-3674 (1999).
2. V. Vahedi and M. Surendra, Comput. Phys. Commun. 87, 199(1995)
3. David L. Bruhwiler, Rodolfo E. Giacone, Physical Review Special Topics, vol. 4, pp. 101302 (2001)
223