High Intensity Beam and X-Ray Converter
Target Interactions and Mitigation
Yu-Jiuan Chen, James F. McCarrick, Gary Guethlein,
George J. Caporaso, Frank Chambers, Steven Falabella,
Eugene Lauer, Roger Richardson, Steve Sampayan and John Weir
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
Abstract. Ions extracted from a solid surface or plasma by impact of an high intensity and high
current electron beam can partially neutralize the beam space charge and change the focusing
system. We have investigated ion emission computationally and experimentally. By matching
PIC simulation results with available experimental data, our finding suggests that if a mix of ion
species is available at the emitting surface, protons dominate the backstreaming ion effects, and
that, unless there is surface flashover, ion emission is source limited. We have also investigated
mitigation, such as e-beam cleaning, laser cleaning and ion trapping with a foil barrier. The
temporal behavior of beam spot size with a foil barrier and a focusing scheme to improve foil
barrier performance are discussed.
1 INTRODUCTION
The second axis of the Dual Axis Radiographic Hydrodynamic Test facility
(DARHT-II) [1, 2] will deliver multiple electron pulses to a converter target to
produce x-ray pulses (with spot sizes < 2.1 mm) for flash radiography. Performance of
high resolution x-ray radiography facilities requires high current electron beams to be
focused to a millimeter spot size on an x-ray converter throughout the entire current
pulse. Several effects, such as target plasma created by preceding pulses, and the
backstreaming ion effect [3], may impact the spot size. We have designed the
DARHT-II x-ray converter target to minimize expansion of target plasma into the
incoming beam's path [4, 5, 6]. Thus, the spot size changes from pulse to pulse due to
the charge neutralization effects of the target plasma are small. However, the time
varying focusing forces of backstreaming ions pulled from the desorbed gas at the
target surface or from a pre-existing target plasma plume by the electron beam's strong
electric field could potentially and drastically change the spot size.
We have investigated backstreaming ion emission and mitigation both
computationally and experimentally. In Sec. 2, we show that comparison between PIC
simulation results and the available experimental data indicates that if a mix of species
is available, protons dominate the backstreaming ion effect, and that ion emission may
be source limited. Section 3 shows that we have demonstrated experimentally that
backstreaming ion effects can be minimized by pre-cleaning target surfaces with an
electron beam or a laser. Hughes first suggested the use of a foil to confine
backstreaming ions within a short distance so that the focusing effect is tolerable [7].
We have investigated the foil-barrier scheme experimentally and computationally as
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
240
well;
will discuss
discuss how
how the
the tuning
tuning strategy
strategy
well; the
the results
results will
will be
be discussed
discussed in
in Sec.
Sec. 4.
4. We
We will
for
beam
transport
affects
the
foil-barrier
scheme's
performance
and
how
the
for beam transport affects the foil-barrier scheme’s performance and how the
backstreaming
ions
with
mitigation
affect
the
on-axis
x-ray
dose
in
Sec.
5.
A
summary
backstreaming ions with mitigation affect the on-axis x-ray dose in Sec. 5. A summary
is
is presented
presented in
in Sec.
Sec. 6.
6.
22 ION
FROM FOILS
FOILS
ION EMISSION
EMISSION FROM
ItIt is
solid surfaces
surfaces by
by an
an incoming
incoming DARHT-II
DARHT-II
is aa concern
concern that
that ions
ions desorbed
desorbed from
from solid
beam
accelerated and
and trapped
trapped by
by the
the
beam (18.6
(18.6 MeV,
MeV, 22 kA
kA and
and 2|is)
2µs) and
and subsequently
subsequently accelerated
beam
neutralization to
to the
the beam,
beam,
beam space
space charge
charge potential
potential will
will provide
provide unwanted
unwanted charge
charge neutralization
upsetting
were studied
studied on
on the
the 19.819.8upsetting the
the transport
transport system.
system. These
These ion
ion focusing
focusing effects
effects were
MeV,
[8]. The
beam was
was focused
focused onto
onto aa thin
thin
MeV, 2-kA
2-kA DARHT
DARHT double
double foil
foil experiment
experiment [8].
The beam
foil
by the beam moved
moved both
both
foil to
to minimize
minimize the
the beam
beam scattering. The ions generated by
upstream
upstream and
and downstream to form
form ion channels on the both sides of the foil. The ion
focusing
focusing effects
effects were then observed by measuring the time-varying beam radius on aa
downstream
[9], which had
downstream witness
witness foil.
foil. We have performed a similar experiment [9],
similar
sensitivities
and
operated
at
similar
energy
densities
on
some
of
the same types
similar sensitivities
of
materials,
at
the
6-MeV,
2-kA
ETA-II
facility.
Comparing
PIC
simulation
results
of materials, the
with
data
available
from
these
two
experiments
provides
us
some
understanding
of ion
with data available from
emission.
emission.
Streak X_FWHM (cm) @ 203QSC27
Simulations
20
80
Time (us)
40
Time (ns)
(c)
3
234 A
-a- 309 A
-H 2
ti
20
40
60
Time (ns)
FIGURE 1.
1. The
The ETA-II temporal FWHM beam size on the witness foil when flashover occurred
FIGURE
occurred on
on the
the
quartz foil.
foil. Two
Two experimental
experimental data for two magnetic settings are shown in (a). Simulated temporal
quartz
temporal
beam size
size with
with space-charge-limited
space-charge-limited emission for protons and with space-charge-limited emission for
beam
C+ are
are shown
shown in
in (b) and (c), respectively. Comparison between simulation results with
C+
with the
the experimental
experimental
data indicates
indicates that
that ifif a mix
mix of
of species is available, protons may dominate the backstreaming ion effects.
data
241
The potential species for an ion channel are protons and oxygen from the water
foil surface, carbon, and the foil material itself. The lighter ions have
vapor on the foil
have aa
greater potential to destroy the electron beam’s
beam's final focus since
since they would travel
travel
upstream and downstream at a higher speed and form aa longer ion channel.
channel. The
The ions
ions
from the foil material itself are usually too heavy to have
from
have aa large
large effect
effect on
on the
the beam
beam
spot size during the beam pulse time. One foil material used on the ETA-II
ETA-II double
double foil
foil
experiment for ion emission was quartz. The ETA-II beam impinging on the dielectric
surface created flashover and a rich ion source for space charge limited emission at
surface
at tt ==
Fig. 1 are the temporal profiles of the beam radius on the witness
0. Shown in Fig.
witness foil
foil
from PIC simulations, in which space charge limited protons are
obtained from
are emitted
emitted
from t = 0, and the experimentally measured profiles. The match is
from
is quite
quite good
good and
and is
is
obtained without any additional fitting parameters. The simulated profiles do not
match the data when other heavier ions are used in the simulations (see
(see Fig.1c).
Fig.lc). These
comparisons suggest that if a mix of species is available, protons may dominate the
backstreaming ion effects;
effects; however, simulations where multiple species
species are
are available
available
have not been done, as this requires more sophisticated modeling of the emission
sheath. Given the quality of the match and lacking any direct measurements of the
emitted species, all the simulations presented later in this paper assume only protons
from a surface.
emitted from
DT#1=200A
40
60
Time (ns)
xFWHM(cm)0201SSC27
80
20
100
40
€0
80
100
Time (ns)
120
140
FIGURE 2.
2. Beam
Beam spot
spot temporal
temporal behaviors
behaviors in
DARHT-I (Ref.
FIGURE
in (a)
(a) DARHT-I
(Ref. [10]),
[10]), and
and (b)
(b) ETA-II
ETA-II double
double foil
foil
experiments. The
The DARHT
DARHT data
data show
that there
experiments.
show that
there is
is aa source
source of
of ions
ions even
even at
at relatively
relatively low
low temperatures.
temperatures.
However, the
the ETA-II
ETA-II data
data did
did not
not show
However,
show any
any ion
ion emission
emission effects
effects even
even though
though the
the experiments
experiments had
had
similar sensitivities
sensitivities and
and energy
energy densities
densities on
similar
on some
some materials.
materials.
Typical results
results from
from both
both the
the DARHT
Typical
DARHT and
and ETA-II
ETA-II double
double foil
foil experiments
experiments are
are
shown in
in Figs.
Figs. 2a
2a and
and b.
b. The
The DARHT
shown
DARHT data
data show
show that
that there
there is
is aa source
source of
of ions
ions even
even at
at
relatively low
low temperatures
temperatures [8].
relatively
[8]. However,
However, the
the ETA-II
ETA-II data
data did
did not
not show
show any
any ion
ion
emission effects
effects [9]
emission
[9] even
even though
though the
the experiments
experiments had
had similar
similar sensitivities
sensitivities and
and energy
energy
242
densities
beam energies
energies for
for these
these two
two
densities on
on some
some materials.
materials. Since
Since the
the different
different beam
experiments
does
not
play
a
significant
role
in
any
proposed
ion
production
experiments does not play a significant role in any proposed ion production
mechanism,
has aa shorter
shorter current
current flattop
flattop
mechanism, the
the two
two remaining
remaining differences
differences are
are that
that ETA-II
ETA-II has
(50
ns
rather
than
70
ns),
and
that
the
materials
which
showed
the
strongest
effect
on
(50 ns rather than 70 ns), and that the materials which showed the strongest effect on
DARHT-I
(Ta
and
Ti)
were
not
used
on
ETA-II.
In
order
to
reconcile
the
results,
an
DARHT-I (Ta and Ti) were not used on ETA-II. In order to reconcile the results, an
ion
emission
model
somewhat
more
detailed
than
simple
space
charge
limited
(SCL)
ion emission model somewhat more detailed than simple space charge limited (SCL)
emission
emission isis required.
required.
PIC
for various
species do
do not
not match
match either
either
PIC simulations
simulations assuming
assuming SCL
SCL conditions
conditions for
various species
experiment.
The
resulting
beam
disruption
would
occur
much
sooner
and
be
much
experiment. The resulting beam disruption would occur much sooner and be much
stronger
used in
in [8]
[8] which
which delay
delay the
the onset
onset
stronger than
than what
what is
is observed
observed on
on DARHT-I.
DARHT-I. Models
Models used
of
threshold temperature
temperature can
can match
match
of SCL
SCL emission
emission until
until the
the barrier
barrier material
material reaches
reaches aa threshold
the
A model
model that
that has
has two
two knobs,
knobs, one
one for
for
the onset
onset time
time but
but not
not the
the rate
rate of
of beam
beam disruption.
disruption. A
the
Such aa model
model was
was proposed
proposed
the onset
onset time
time and
and one
one for
for the
the slope,
slope, must
must be
be considered.
considered. Such
in
and
in [11]
[11] and
and has
has been
been used
used in
in this
this paper
paper for PIC simulations of both the ETA-II and
DARHT-I
DARHT-I experiments.
experiments. A
A quick summary of the model is aa follows:
The
simple rate
rate
The desorption
desorption of
of neutral
neutral gas from
from the foil surface is determined by aa simple
equation
that
is
a
strong
function
of
temperature.
The
areal
density
of
neutrals
is
given
equation that is a strong function
of neutrals is given
by
by
dN
(1)
= ν ( N s − N )e− E b / T
dt
where
initial density
density of
of
where N
N isis the
the number
number of
of desorbed neutrals per unit area, Ns is the initial
adsorbates
characterizes
adsorbates on
on the
the surface,
surface, vν is
is a rate
rate coefficient,
coefficient, and Eb
Eb is an energy that characterizes
the
and is
is of
of
the nature
nature of
of the
the adsorption.
adsorption. The
The initial
initial adsorbate density, Ns, is measurable and
15
2
13 -11
the
1013
but is
is aa much
much
the order
order 10
1015 cm"
cm-2.. The
The rate
rate coefficient
coefficient ,, v,
ν, is roughly of order 10
ss" ,, but
less
that controls
controls the
the
less sensitive
sensitive parameter
parameter than
than Eb,
Eb, which is basically a fitting parameter that
onset
exponential temperature
temperature
onset time
time of
of the
the beam
beam disruption
disruption in the experiment. The exponential
dependence results
results in
in behavior
behavior characterized by a threshold temperature
dependence
temperature at
at which
which all
all
of the
the adsorbed
adsorbed gas
gas is
is released.
released. Sample curves for a linear heating rate are shown
of
shown in
in
Fig. 3.
3.
Fig.
o.o
300
400
500
600
T(t), K
700
800
SOO
FIGURE 3.
3. Gas
Gas desorption
desorption model
model given
given linear
linear temperature
temperature rise,
FIGURE
rise,o for
for various
various binding
binding energies.
energies. The
The
temperature threshold
threshold for
for full
full gas
gas desorption
desorption is
is around
around 400
400 –—600
K depending
temperature
600°K
depending on
on the
the binding
binding energy
energy
betweenthe
the adsorbates
adsorbates and
and the
the surface.
surface.
between
243
an ionization
ionization model.
model. The
The two
two extremes
extremes are
are to
to assume
assume that
that
The next ingredient is an
avalanche breakdown occurs immediately
immediately in
in the
the desorbed
desorbed species,
species, aa quite
quite strong
strong
effect, or that only beam impact
impact ionization
ionization occurs,
occurs, which
which isis weak
weak atat these
these electron
electron
quickly enters
enters the
the SCL
SCL regime,
regime, since
since only
only aa small
small
energies. The former assumption quickly
of ions
ions is
is needed
needed to
to reach
reach the
the space
space charge
charge limit.
limit. The
The latter
latter
fraction of aa monolayer of
with aa simple
simple rate
rate equation
equation
assumption is also modeled with
dNti _ σoNJ
dN
NJbb
=
(2)
(2)
dt
dt
qq
NIi is the areal ion
ion density,
density, σa is
is the
the impact
impact ionization
ionization cross
cross section,
section, JJb
is the
the
where N
b is
and qq is
is the
the unit
unit charge.
charge. The
The ion
ion emission
emission current
current isis then
then bound
bound
beam current density, and
aNJb.
cross section
section in
in
by the smaller of the SCL value or the quantity σΝJ
b. The ionization cross
of 66 –- 20
20 MeV
MeV is
is of
of order
order 2.5x10
2.5xlO~-1919 cm
cm22.. The
Thesolution
solution of
ofEqs.
Eqs.(1)
(1)and
and
the energy range of
(2) is proportional to
to the
the product of
of σa and
and the
the areal
areal adsorbate
adsorbate density,
density, which
which includes
includes
the number of monolayers on
on the surface
surface and
and is
is not
not exactly
exactly known.
known. Thus
Thus the
the product
product
σN
<jNs is a second fitting parameter for
for the experimental
experimental data,
data, yielding
yielding the
the slope
slope of
of the
the
beam disruption.
Consider a subset of the DARHT-I
DARHT-I data
data consisting
consisting of
of the
the first
first 50
50 ns
ns of
of the
the flattop
flattop
and compare it to the flattop data from
from ETA-II
ETA-II (see
(see Fig.
Fig. 2).
2). Since
Since the
the curves
curves for
for Ta
Ta and
and
Ti are not available for ETA-II, it becomes clear
clear that 50
50 ns
ns is
is not
not long
long enough
enough to
to
resolve the ion effect above the error bars
bars of
of the
the ETA-II
ETA-II data.
data. Thus
Thus the
the experimental
experimental
data can be matched by
by adjusting
adjusting EEbb to produce
produce an
an onset
onset later
later than
than would
would be
be resolved
resolved
on ETA-II, and then adjusting
adjusting σN
aNss to
to produce
produce the
the correct
correct slope
slope of
of the
the DARHT-I
DARHT-I data
data
thereafter. Figure 4 shows
shows the results of aa simulation
simulation assuming
assuming aa binding
binding energy
energy of
of
0.47 eV and 33 monolayers of adsorbed
adsorbed gas,
gas, using
using the
the nominal
nominal cross
cross section
section given
given
above, compared with the 70
70 ns
ns flattop
flattop of
of the
the DARHT
DARHT data
data (with
(with the
the Ta
Taand
andTi
Ticurves
curves
removed).
20
15
10
20
40
€0
SO
Time (ns)
100
CO
80
100
Time (ns)
FIGURE 4. Comparison of the
the temporal
temporal beam
beam sizes
sizes over
over 70
70 ns
ns flattop
flattop from
from the
the DARHT-I
DARHT-I double-foil
double-foil
experiment (left) and
and from the simulation
simulation using
using the
the gas
gas desorption/ionization
desorption/ionization model
model and
and assuming
assuming 33
monolayers of adsorbed
adsorbed gas
gas and
and aa binding
binding energy
energy of
of 0.47
0.47 eV
eV (right).
(right). The
The agreement
agreement between
between the
the these
these
results
results suggests
suggests that
that the
the ion
ion emission
emission in
in the
the experiment
experiment is
is source
source limited.
limited.
40
244
As mentioned earlier, the simulations presented here only involve one species of
ions, namely protons; however, it is unlikely that simulations with multiple SCL
species can match simultaneously the rapid beam disruption shown in Fig. 1 and the
slow disruption shown in Fig. 2. Although the simple model given by Eqs. 1 and 2
glosses over the mix of physics giving rise to gas desorption, it does serve to reconcile
the available experimental data and gives a rough quantification of emission current,
showing that it is source limited. It is possible that surface cleaning will be sufficient
to avoid this type of emission from the barrier surface.
3 SURFACE CLEANING
As discussed in the previous section, without a pre-existing plasma created on the
target surface, the spot disruption on the6-MeV, 2-KA ETA-II beam due to the
backstreaming ions was weak during its flattop. To simulate the DARHT-II beamtarget interactions, backstreaming ion emission and surface cleaning were studied on
the ETA-II/SNOWTRON double pulse facility [12]. First, plasma was created by
striking the 1-MeV, 2-kA Snowtron beam on one side of a foil. The better
characterized ETA-II beam entered from the other side to probe the beam-target
interactions. Typically five diagnostics were taken for each shot. Backstreaming ions
were collected by a Faraday cup at the ETA-II side. On-axis x-ray dose generated by
the ETA-II beam was measured through a pair of apertures along a path that included
the SNOWTRON cathode. The ETA-II x-ray spots at 10 ns before and 15 ns after the
center of the flattop were recorded by imaging the optical transition radiation from the
target. The time integrated SNOWTRON beam spot was taken by an optical framing
camera.
Figure 5 presents a set of results for e-beam cleaning of a 3-mil graphite foil. The
first column presents the SNOWTRON beam images if the SNOWTRON was fired.
The first and the last rows present the nominal data when the SNOWTRON beam was
not fired and no plasma created. Note that no ion signals were detected by the Faraday
cup for the nominal cases. Rows 2-4 present data for various SNOWTRON spot sizes.
The calculated peak foil temperature based on energy deposition is given at the side of
each row. The separation between the SNOWTRON beam and the ETA-II beam was 2
(is for this set of data. The second column presents the ion signals detected by Faraday
cup. The total ion charge collected by the cup is also shown with each Faraday cup
data. The SNOWTRON beam spot sizes for Rows 2 and 3 were the same. However,
for the pre-cleaned case, SNOWTRON was fired twice with a 1-second separation.
The Faraday cup signal indicates that the first pulse cleaned the foil surface and
reduced ion emission. The third column gives the on-axis x-ray doses generated by the
ETA-II beam. The last two columns give the ETA-II beam images 10 ns before and 15
ns after the center of beam flattop. These data show that e-beam cleaning preserved the
beam spot size and on-axis x-ray dose. Comparing Rows 4 and 5 suggests that ion
emission due to gas desorption occurs around 400°C, which agrees with observations
on ion emission in an IVA diode reported in Ref. [13].
245
SNOWTHCN
Faraday
cup
On-axis
dose
ETA,
10nsBC
ETAf
15ns AC
ETA only |
FIGURE 5.
5. Faraday
Faraday cup's
cup’s ion signals, beam spot sizes and x-ray forward doses for the electron beam
FIGURE
cleaning experiment.
experiment. The
The SNOWTRON
SNOWTRON beam
beam with various spot sizes was used to create the target
cleaning
plasma. ItIt was
was also
also used
used to
to pre-clean
pre-clean the
the graphite
graphite foil
foil surface
surface in the "preclean"
“preclean” case. The SNOWTRON
plasma.
beam images
images with
with beam
beam sizes
sizes and
and estimated
estimated graphite temperatures, ion signals collected by Faraday
beam
cup, the
the forward
forward on-axis
on-axis x-ray
x-ray doses
doses generated
generated by
by the
the ETA-II
ETA-II beam,
beam, ETA-II beam images at 10 ns
cup,
before and
and 15
15 ns
ns after
after the
the center
center of
of the
the beam
beam flattop
flattop are
are shown
shown in
in columns
columns from
from the
the left
left to
to the
the right.
right. The
The
before
data show
show that
that e-beam
e-beam cleaning
cleaning preserved
preserved the
the beam
beam spot size and on-axis
on-axis x-ray
x-ray dose. Comparing Rows
data
o
and 55 suggests
suggests that
that ion emission due to gas desorption occurs around 400
C, which agrees with
44 and
400°C,
observations
on
ion
emission
in
an
IVA
diode
reported
in
Ref.
[13].
observations on ion emission in IVA
reported
246
Streak camera
10 iis after center
Faraday eup
No cleaning pulses
3G85SOD4 - Fdse Color
(to)
9 cleaning pulses
same spot as last shot
9 clein ling pulses
on fresh spot
(4)
ETA oiuj (no laser)
Same spot as (c)
(e)
20535CG7 - raise C
100 cleaning pulses
on fresh spot
30S35CH - Fa
FIGURE
FIGURE 6.
6. The
The ETA-II
ETA-II beam
beam spot
spot sizes
sizes corresponding to the
the number
number of pre-cleaning laser pulses. A
60-mJ NdiYAG
Nd:YAG laser
laser was
was used
used for
for pre-cleaning
pre-cleaning a 6-mil
6-mil graphite
graphite foil
foil and for
for generating the
the surface
surface
60-mJ
plasma. The
The separation
separation between
between firings
firings of
of the
the laser
laser pulse
pulse for
for creating
creating surface
surface plasma
plasma and
and the
the ETA-II
ETA-II
plasma.
beam was
was 22 |is.
µs. The
The separation
separation between
between the
the last
last laser
laser cleaning
cleaning pulse
pulse and
and the
the ETA-II
ETA-II beam
beam is
is about
about 1
beam
sec. Firing
Firing 99 or
or more
more pre-cleaning
pre-cleaning pulses
pulses can minimize beam
beam disruption.
sec.
We have also investigated using a pulsed laser to pre-clean graphite foil.
foil. A 6-mil
We
foil, which was
was backed
backed with
with a 10-mil
10-mil quartz
quartz foil
foil serving
serving as a Cherenkov
Cherenkov
graphite foil,
foil, was
was used
used as
as a target.
target. A
A 60-mJ
60-mJ NdiYAG
Nd:YAG laser
laser at 1.06
1.06 jim
µm was
was used
used to
to preprewitness foil,
clean the
the graphite. Since the backstreaming
backstreaming ions'
ions’ spot size disruption effects
effects on the
clean
ETA-II beam
beam is weak without a pre-existing plasma, the laser was also used to create
ETA-II
plasma on the
the graphite foil
foil surface
surface at 2 (is
µs before
before the ETA-II beam was fired.
fired. Without
plasma
pre-cleaning, the
the beam
beam blew
blew up
up rapidly
rapidly in
in the
the presence
presence of
of ions
ions and
and formed
formed a large
large halo
halo
pre-cleaning,
247
(shown in Fig. 6a). The image of the halo is barely visible because the x-ray intensity
created by the halo was small. The laser spot used for pre-cleaning and e-beam
disruption was about 5 mm in diameter. We found that the ETA-II spot was preserved
if the separation between the last laser cleaning pulse and the ETA-II beam is around 1
second. Firing 9 or more laser pulses on a foil with a prior cleaning history (Fig. 6b),
or 100 pulses on a foil with no prior cleaning history (Fig. 6e), can effectively preserve
the beam spot size through the entire beam flattop. Presumably those laser pulses have
cleaned the graphite surface. Note that the data presented in the "ETA only" case was
taken when the ETA-II beam was impinging on an old spot used by the shot
corresponding to the data in Fig. 6c. The surface had been cleaned by both the 9 laser
cleaning pulses and the e-beam, and hence, the data in Fig. 6d represents the best
possible beam spot behavior for the ETA-II beam.
4 FOIL BARRIER AND ION TRANSIENT BEHAVIOR
Mitigation of backstreaming ion effects with a foil-barrier was demonstrated on the
ETA-II/SNOWTRON double pulse facility [14]. When plasma is created by the
SNOWTRON beam 600 ns prior to the ETA pulse, the focus of the ETA-II beam was
destroyed within 20 ns if a foil-barrier was not used. However, if a grounded foil was
placed 1 cm in front of the ETA-II side of the target, the spot size was preserved
through the entire ETA-II flattop.
While the use of a grounded foil to stop backstreaming ions has been successful,
some time-dependent focusing remains. Consider that the ions are emitted from the
grounded target surface and are impeded by the grounded foil barrier. Since the
transverse electric field of the beam is sufficiently large to cause surface flashover and
to lead to unpredictable or at least unreliable behavior, both surfaces are grounded as a
requirement. The region between the two ground planes has a strong potential well due
to the beam space charge. If the geometry were one dimensional - a slab of charge
between two sheets - it is clear that the region would act, under ideal circumstances, as
a trap for the ions, and that the target and the barrier foil act as turning points for ions
born at zero energy. What is not as obvious is that, due to the two dimensional nature
of the system and, to a lesser extent, time dependence of the beam current, the trapping
effect is "robust", and that ideal conditions such as zero emission energy are not
necessary. The result is that ion charge accumulates between the target and barrier, and
moves towards a steady-state configuration of complete neutralization of the electron
beam. The stability of such an equilibrium and the existence of a physical path towards
it are not addressed in this paper. What is important is that at the start of a beam pulse,
there are no ions (i.e., a neutralization fraction,/, of 0) and that the system evolves
with time towards / = 1. The spatial profile of the neutralization evolves as well. The
effect of this dynamic evolution on the beam focus (and resulting X-ray spot size) is
the concern.
PIC simulations of a baseline DARHT-II target/barrier system have been performed
to study the evolution of the system. The simulation transports a K-V electron beam
from the downstream side of the foil barrier to the target. The phase space is chosen to
produce a 1 mm edge radius beam at a waist on the target surface, at a full current of 2
248
kA,
emittance of
of 44 cm-mrad,
cm-mrad,
kA, an
an energy
energy of
of 18.4
18.4 MeV,
MeV, and
and an
an un-normalized
un-normalized edge
edge emittance
when
no
ions
are
present.
The
beam
current
is
given
a
5
ns
rise
time
from
zero
at the
the
when no ions are present. The beam current is given a 5 ns rise time from zero at
start
of
the
simulation
(t
=
0),
so
that
the
beam
radius
is
somewhat
smaller
initially
start of the simulation (t = 0), so that the beam radius is somewhat smaller initially
(about
target is
is assumed
assumed to
to emit
emit
(about 0.8
0.8 mm)
mm) than
than at
at the
the full-current
full-current value.
value. The
The target
backstreaming
ions
under
space
charge
limited
conditions,
from
an
area
corresponding
backstreaming ions under space charge limited conditions, from an area corresponding
to
space charge
charge and
and current
current effects
effects are
are
to the
the nominal
nominal beam
beam focus.
focus. Self-consistent
Self-consistent space
included.
Since
only
the
trap
region
from
the
foil
barrier
to
the
target
is
simulated,
included. Since only the trap region from the foil barrier to the target is simulated,
emittance
and the
the upstream
upstream portion
portion of
of the
the
emittance growth
growth due
due to
to scattering
scattering by
by the
the foil
foil barrier
barrier and
barrier
foil-focusing
are
not
included
in
the
simulations.
The
foil
barrier
and
the
target
barrier foil-focusing are not included in the simulations. The foil barrier and the target
are
(also at
at ground)
ground) is
is 55 cm
cm in
in radius.
radius.
are 44 cm
cm apart
apart and
and the
the beam
beam pipe
pipe (also
Figure
7
shows
the
evolution
of
the
beam
size
on
the
target,
as an
an r.
r. m.
m. s.
s. value
value in
in
Figure 7 shows the evolution of the beam size on the target, as
the
density averaged
averaged over
over the
the emitting
emitting surface.
surface.
the X
X transverse
transverse plane,
plane, and
and the
the ion
ion current
current density
For
twice the
the xXrms
size. We consider the
For aa uniform
uniform beam,
beam, the
the edge
edge radius
radius would
would be
be twice
rms size. We consider the
curves
curves will
will be
be discussed
discussed later.
later. The
The beam
beam size
size
curves labeled
labeled "No
“No bias"
bias” first;
first; the
the other
other curves
(Fig.
fast initial
initial growth
growth followed
followed by
by smaller
smaller (±10%)
(±10%)
(Fig. 7a)
7a) is
is characterized
characterized by
by aa period
period of
of fast
variations
mm. The
The initial
initial growth
growth corresponds
corresponds to
to an
an early
early
variations about
about aa rough
rough value
value of
of 0.5
0.5 mm.
spike
(Fig. 7b)
7b) as
as the
the beam
beam current
current rises
rises to
to its
its flattop
flattop value,
value,
spike in
in the
the ion
ion emission
emission current
current (Fig.
producing
focus the
the electron
electron beam.
beam. The
The subsequent
subsequent
producing aa "belch"
“belch” of
of ions
ions that
that over
over focus
variations
are
characteristic
of
electron
beam/backstreaming
ion
behavior.
As
the beam
beam
variations are characteristic of electron beam/backstreaming ion behavior. As the
is
over
focused
and
the
size
on
the
target
grows,
the
space
charge
limited
ion
current
is over focused and the size on the target grows, the space charge limited ion current
drops.
leads
drops. The
The beam
beam experiences less over focusing, and the spot size shrinks, which leads
to
increase
in
the
axial
electric
field,
and
therefore
the
ion
current,
and
so
forth.
The
to increase in the axial electric field, and therefore the ion current, and so forth. The
initial
current
spike
in
the
graph
diminishes
the
fact
that,
at
later
times,
the
ion
current
initial current
is
MA/m22.. The
The very
very gradual
gradual
is experiencing
experiencing roughly 50% variation, between 2 and 33 MA/m
decaying
"fill time”
time" of the trap is much
much
decaying ion
ion current curve shows that the effective
effective “fill
longer
z/y(3zz phase
phase
longer than
than the
the beam
beam pulse. Figure 8 shows four snapshots of the ion z/γβ
space,
slow filling of
of the
the trap.
trap.
space, taken
taken at 5, 25, 50, and 80 ns, which also show the slow
(b)lon Emission
Emission Current
Current
(b)Ion
7
0.6
6
0.5
5
Jion (A/mm 2 )
r.m.s. radius (mm)
(a)Spot
(a)Spot Size
Size on
on Target
Target
0.7
0.4
0.3
0.2
3
2
No Bias
50 kV
0.1
4
No Bias
50 kV
100 kV
1
100 kV
0
0.0
0
10
20
Time
Time (ns)
(ns)
0
30
10
20
Time (ns)
(ns)
Time
30
FIGURE
target, as
as r.r. m.
m. s.s. value
value in
in the
the X
X plane,
plane,and
and
FIGURE 7.
7. Temporal
Temporal behaviors of (a) beam spot size on the target,
(b) ion
ion emission
emission current
current averaged over the emitting surface in a baseline DARHT-II
(b)
DARHT-II target/barrier
target/barrier
system with
with aa 4-cm
4-cm foil-target
foil-target separation and a 5-cm radius beam pipe. The
system
The nominal
nominal xx^
for the
the 18.418.4rms for
MeV and
and 2-kA
2-kA beam
beam without
without ions is 0.5 mm.
MeV
249
The
degrees of
of freedom
freedom for
for the
the ions.
ions.
The robust
robust nature
nature of
of the
the trap
trap stems
stems from
from the
the radial
radial degrees
An
ion velocity,
velocity, but
but rather
rather pure
pure radial
radial
An axial
axial turning
turning point
point does
does not
not correspond
correspond to
to zero
zero ion
motion.
accumulation of
of positive
positive charge
charge
motion. As
As ions
ions decelerate
decelerate near
near the
the foil
foil barrier,
barrier, the
the accumulation
(which
exceeds
the
beam
density
at
the
barrier,
although
to
a
lesser
extent
than
at the
the
(which exceeds the beam density at the barrier, although to a lesser extent than at
effective
A-K
gap
near
the
target)
deflects
subsequent
ions
radially,
so
that
v
can
be
effective A-K gap near the target) deflects
so that vzz can be
zero
even
though
the
potential
is
not
zero.
Also,
during
the
ion
"belch"
phase,
the
zero even though the potential
“belch” phase, the
potential
even before
before any
any
potential well
well is
is deepening
deepening as the beam current rises. Therefore, even
reflection
accelerating
reflection has
has taken
taken place,
place, the
the ions
ions are not all experiencing the same accelerating
conditions.
conditions.
FIGURE8.8. Snapshots
Snapshots of
of the
the z-yp
z-γβzz ion phase space in the nominal DARHT-II
FIGURE
DARHT-II target/barrier
target/barrier system.
system.
The long
long fill
fill time
time of
of the
the trap
trap and the transient behavior may not lend themselves
The
themselves to
to
“clean” performance
performance of
of the target system from a radiographic standpoint.
aa "clean"
standpoint. As
As shown
shown
in Fig.
Fig. 7a,
7a, while
while the
the foil
foil barrier
barrier scheme
scheme does
does minimize
minimize beam
in
beam disruption
disruption reasonably
reasonably
well,
the
time
integrated
spot
size
is
better
preserved
by
the
foil
well, the time integrated spot size is better preserved by the foil barrier
barrier scheme
scheme for
for aa
long
pulse
beam
than
for
a
short
pulse
beam.
A
possible
route
around
such
behavior
long pulse beam than for a short pulse beam. A possible route around such behavior is
is
to open
open the
the trap.
trap. Under
Under ideal
ideal circumstances
circumstances one
one would
to
would use
use aa dielectric
dielectric rather
rather than
than aa
conducting foil
foil barrier,
barrier, but
but this
this idea
idea fails
fails in
in practice
practice due
conducting
due to
to surface
surface flashover,
flashover, as
as
mentioned
earlier
[9].
Another
possibility
is
to
employ
a
bias
voltage
so
mentioned earlier [9]. Another possibility is to employ a bias voltage so that
that the
the ions
ions
are not
not emitted
emitted at
at zero
zero energy.
energy. Bias
Bias schemes
schemes have
have been
are
been investigated
investigated in
in the
the past
past [15,
[15,
16], where
where the
the bias
bias voltage
voltage is
is used
used to
to trap
trap the
the ions.
ions. In
In the
the present
present case,
16],
case, however,
however, the
the
bias voltage
voltage isis of
of opposite
opposite polarity
polarity to
to intentionally
intentionally drive
bias
drive the
the target/barrier
target/barrier system
system like
like
an ion
ion diode.
diode. How
How to
to maintain
maintain such
an
such aa bias
bias on
on aa target
target being
being struck
struck by
by aa high-intensity
high-intensity
electron
beam
is
not
clear.
However,
one
can
gloss
over
such
electron beam is not clear. However, one can gloss over such difficulties
difficulties in
in aa
simulation
to
see
if
the
idea
has
merit.
The
answer
is
that
it
does
not,
in
fact,
solve
simulation to see if the idea has merit. The answer is that it does not, in fact, solve all
all
theproblems.
problems.
the
250
PIC simulations have been performed using a geometry and beam conditions
similar to those above, but now the target is assumed to not fill the beam pipe. It is a
conducting disk a few beam radii in size, held at positive voltage with respect to the
beam pipe and the foil barrier. The foil barrier is assumed to be a perfect absorber of
ions that reach it. Runs have been done at bias voltages of 50 and 100 kV. The ion
emission current and resulting beam spot sizes are the additional curves shown in Fig.
8. The ions now have sufficient energy so that they all strike the barrier; thus the
system does settle into a rough steady-state with nearly fixed emission current.
However, the initial beam spot transient is not eliminated and some of the oscillatory
behavior as the beam over- and re-focuses on the target remains. At 100 kV, most of
the latter is eliminated. However, it is not clear that this is a sufficient benefit to
counter the implementation difficulties of the bias voltage.
5 FOIL-BARRIER AND FOCUSING SCHEME
Performance of the foil-barrier scheme for spot size preservation requires
minimizing the backstreaming ions' focusing effects to a tolerable level. The scaling
law for the ion channel's disruption length LD [17] is given as LD = (ny^2I0/fl)l/2a,
where / and I0 is the beam current and Alfven current, respectively, / is the ion
neutralization fraction, and a is the beam radius. This scaling law indicates that the
suitable foil-target separation depends on the overall beam envelope inside the ion trap
region, and that the final spot size is sensitive to the beam radius and ions'
neutralization fraction. For a single pulse machine, the foil can be placed closely to the
target to minimize the spot size sensitivity. However, the spot size on a closely placed
foil will be too small to be practical for a multi-pulse machine since the foil may not
survive the impact of multiple beam pulses. Instead of shortening the foil-target
separation, the foil-barrier's performance can also be improved without sacrificing the
final spot size and the x-ray dose by using a different focusing scheme to obtain a
larger beam envelope in the ion trap region. This results in weaker ion focusing forces
and a larger beam spot on the foil, which is preferable for foil survivability.
We have investigated computationally several tuning schemes with various foil
locations to achieve a larger spot size on the foil barrier without sacrificing the
nominal spot size on the target. The DARHT-II target configuration is used again. For
the results presented in this section, the nominal focal length is 32 cm. The DARHT-II
beam near the x-ray converter is 18.4 MeV, 2 kA with a 1-mm radius (0.7-mm r.m.s.).
The particle simulations, mentioned in the previous section, indicate that the charge
neutralization fraction of those trapped ions near the end of DARHT-II 4th pulse is a
function of the distance normalized to the foil-target separation (z/L). To allow a fast
parameter study of various focusing schemes, an envelope equation is solved by using
a fit for the simulated charge neutralization fraction. Foil focusing effects and lens'
aberrations are not modeled by the envelope equation. The spherical aberration and
chromatic aberration of the solenoid lens are irrelevant to this section's discussion.
The foil focusing effects are insignificant due to the small beam size near the foil. Our
particle simulations indicate that the spot size changes due to the foil focusing effects
are only a few percent.
251
1,0
1J 1
1
SL3
10
i
i.3
10
FIGURE
envelopes in
traps with
with various
various foil-target
foil-target separations
separations
FIGURE 9.
9. The
The r.
r. m.
m. s.
s. beam
beam envelopes
envelopes
in the
the foil-barrier
foil-barrier traps
traps
with
various
foil-target
separations
Figure
envelopes (curves)
Figure 99 shows
shows the
the r.
r. m.
m. s.
s. beam
beam envelopes
(curves) with
with aa foil
foil (vertical
(vertical dashes)
dashes)
placed
at
4,
3.5,
3,
2.5,
2
or
0
cm
in
front
of
the
target
surface.
The
surface. The beam
is focused
focused
placed at 4, 3.5, 3, 2.5, 2 or 0 cm in front of the target surface.
beam is
is
focused
beyond
Fig. 9b.
The
beyond the
the target
target front
front surface
surface in
in Fig.
Fig. 9a
9a and
and on
on the
the front
front surface
surface in
in Fig.
Fig.
9b. The
The
focusing
focusing scheme
scheme used
used for
for Fig.
Fig. 9a
9a is
is better
better for
for aa multi-pulse
multi-pulse machine
machine since
since the
the foil
foil can
can
be placed further
size on
further upstream
upstream from
from the
the target,
target, and
and hence,
hence, the
the beam
beam size
size
on the
the foil
foil is
is
larger
larger for
for better foil
foil
survivability. Comparison
foil survivability.
Comparison between
between the
the envelope
envelope curve
curve
corresponding
corresponding to
to aaa 3-cm
3-cm
corresponding to
to aa 4-cm
4-cm separation
separation in
in Fig.
Fig. 9a
9a and
and that
that corresponding
corresponding
to
3-cm
separation
separation in
in Fig.
Fig. 9b
9b suggests
suggests that,
that, when
when the
the final
final beam
beam spot
spot size
size is
is similar
similar after
after beam
beam
traveling through
through the
the ion
ion trap,
trap, the
the resulting
resulting beam
divergence is
similar. Therefore,
beam divergence
divergence
is also
also similar.
similar.
Therefore,
the forward
forward x-ray
with the
the same
same spot
spot sizes
sizes but
but using
using different
different
the
forward
x-ray doses
doses created
created by
by beams
beams with
focusing
focusing schemes
separations should
should be
be similar.
similar.
The beam
beam divergence
divergence
focusing
schemes and
and target-foil
target-foil separations
similar. The
divergence
at
the x-ray
x-ray converter
envelopes in
in Fig.
Fig. 9a
9a is
is shown
shown as
as aaa function
function
at the
converter corresponding
corresponding to
to the
the envelopes
of
the
foil-target
separation
in
Fig.
10.
The
envelope
slope
(R’),
thermal
of the foil-target
foil-target separation in Fig. 10. The envelope
spread
(θ
of
envelope slope
slope (R’),
(/?'), thermal
thermal spread
spread (θ
(0ththth)))
and
the
effective
divergence
are
plotted.
Since
the
effective
divergence
for
various
effective divergence
divergence are plotted.
and the effective
plotted. Since
Since the effective divergence
divergence for
for various
foil-target
foil-target separations
small compared
compared with
with the
the scattering
scattering angle
angle accumulated
accumulated
foil-target
separations remains
remains small
in
1-mm Ta
effects of
convergent beam
beam hitting
hitting the
the x-ray
x-ray converter
converter on
on
in aa 1-mm
Ta target,
target, the
the effects
effects
of aa convergent
the
forward
x-ray
dose
should
not
be
an
issue.
forward x-ray dose should not be an issue.
the forward
0.1
E
US
0.025
g
0
E*
g -04125
5
-OJD5
-04175
FIGURE 10.
The beam
beam divergence
divergence at
at the
the x-ray
x-ray converter
converter
when
an
underfocusing
scheme
isisused.
used.
FIGURE
10. The
converter when
whenan
anunderfocusing
underfocusing scheme
schemeis
used.
252
4 SUMMARY
It is a concern that ions desorbed from solid surfaces by an incoming electron beam,
and subsequently accelerated and trapped by the beam space charge potential, will
provide unwanted charge neutralization to the beam, upsetting the transport system.
We have investigated these ion focusing effects computationally and experimentally.
Our finding suggests that if a mix of ion species is available at the emitting surface,
protons dominate the backstreaming ion effects, and that, unless there is surface
flashover or other pre-existing plasma, ion emission is source limited. While the
mechanisms of ion emission from either a solid surface or plasma are still not
understood, ion emission can be minimized by cleaning the surface with an electron
beam or several laser pulses. The unwanted ion focusing effects can also be minimized
by using a grounded foil to trap ions in a small region. However, the beam radius will
exhibit some transient behavior due to the trapped ions' long fill time in the
longitudinal phase space. Finally, the foil-barrier's performance in terms of spot size
sensitivity to beam parameters and foil survivability can be improved by using a
focusing scheme which provides a large beam envelope with a fast convergence in the
trap region.
ACKNOWLEDGMENTS
This work was performed under the auspices of the U.S. Department of Energy by
University of California Lawrence Livermore National Laboratory under contract No.
W-7405-Eng-48.
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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