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RESEARCH ARTICLE
|
MARCH 02 2021
Enhancing positron production using front surface target
structures
S. Jiang
;
A. Link
;
D. Canning
;
J. A. Fooks
;
P. A. Kempler
;
S. Kerr
;
J. Kim
;
M. Krieger
;
N. S. Lewis
;
R. Wallace
;
G. J. Williams
;
S. Yalamanchili
;
Hui Chen
Appl. Phys. Lett.
118, 094101 (2021)
https://doi.org/10.1063/5.0038222
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Enhancing positron production using front
surface target structures
Cite as: Appl. Phys. Lett.
118
, 094101 (2021);
doi: 10.1063/5.0038222
Submitted: 19 November 2020
.
Accepted: 8 February 2021
.
Published Online: 2 March 2021
S.
Jiang,
1,a)
A.
Link,
1
D.
Canning,
2
J. A.
Fooks,
3
P. A.
Kempler,
4
S.
Kerr,
1
J.
Kim,
5
M.
Krieger,
2
N. S.
Lewis,
6
R.
Wallace,
1
G. J.
Williams,
1
S.
Yalamanchili,
6
and Hui
Chen
1
AFFILIATIONS
1
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
2
Laboratory for Laser Energetics, Rochester, New York 14623, USA
3
General Atomics, San Diego, California 92121, USA
4
California Institute of Technology, Pasadena, California 91125, USA
5
Center for Energy Research, University of California San Diego, San Diego, California 92093, USA
6
California Institute of Technology, Pasadena, California 92093, USA
a)
Author to whom correspondence should be addressed:
jiang8@llnl.gov
ABSTRACT
We report a target design which produced a substantial gain in relativistic electron-positron pair production using high-intensity lasers and
targets with large-scale micro-structures on their surface. Comparing to an unstructured target, a selected Si microwire array target yielded a
near 100% increase in the laser-to-positron conversion efficiency and produced a 10 MeV increase in the average emitted positron energy
under nominally the same experimental conditions. We had established a multi-scale particle-in-cell simulation scheme to simulate both the
laser absorption and the subsequent pair productions in a thick metal target. The experimental results are supported by the simulations dem-
onstrating the performance increase is due to a higher conversion efficiency of laser energy into electrons with kinetic energies greater than
10 MeV due to enhanced direct laser acceleration of electrons enabled by the microwire array.
Published under license by AIP Publishing.
https://doi.org/10.1063/5.0038222
Producing a high-density, relativistic electron-positron pair
plasma in the laboratory could significantly deepen the understanding
of exotic astrophysical objects such as pulsars and quasars, but is
extremely challenging.
1–5
With the advances in high intensity laser
technology, several methods for pair production have been either dem-
onstrated or proposed, with different mechanisms dominating the
physics in different regimes of laser intensity. For example, the
Schwinger mechanism
6
requires an extremely high intensity, above
10
29
W/cm
2
, for spontaneous pair creation from vacuum, whereas
the Breit-Wheeler (BW) mechanism
7
requires about 10
24
W/cm
2
for
avalanche-type discharge.
8,9
These intensities are far beyond the capa-
bility of state-of-the-art lasers (up to 10
22
W/cm
2
).
An alternative method is to inject laser produced high-energy
electrons into high-Z target materials,
4,10–16
with the electrostatic
field of the nucleus involved in the pair production process releas-
ing the constraint on the laser electric field intensity. If a thick
converter target is used, positrons are mainly produced through the
3-step Bethe-Heitler (BH) process.
17
First, relativistic electrons are
generated through a laser plasma interaction (LPI) at the front side
of the target. These electrons then transport through the high-Z
material and produce high-energy photons via Bremsstrahlung
radiation. Propagation of the high-energy photons in the field of
nucleus then creates electron-positron pairs. The key step is to
transfer laser energy into enough high-energy (tens of MeV) elec-
trons, for which, only a moderate intensity laser (
10
20
W/cm
2
)is
needed. Experiments using this type of setup have produced up to
10
12
pairs/shot, which is the highest yield reported to date by use of
lasers.
A key to higher positron yield is the production of hotter elec-
trons. Substantial enhancement in electron energies can be obtained
by manipulating the laser-plasma interaction using a structured tar-
get.
18,19
Specifically, highly ordered silicon microwire arrays facing the
laser pulse enable guiding the relativistic electron beam along the
structured surface and moreover facilitate a direct laser acceleration
mechanism. Such an electron beam can then create a substantial
enhancement in the Bremstrahlung radiation produced by a high-Z
convertor target.
20
The Bremsstrahlung x-rays further interact with
atomic nuclei and create more electron-positron pairs.
Appl. Phys. Lett.
118
, 094101 (2021); doi: 10.1063/5.0038222
118
, 094101-1
Published under license by AIP Publishing
Applied Physics Letters
ARTICLE
scitation.org/journal/apl
02 October 2023 23:40:05
We demonstrate herein experimentally a substantial enhance-
ment in both the yield and the energy of generated positrons using tar-
get structures, which suggests an efficient and inexpensive approach to
improvement of positron sources. Particle-in-cell (PIC) simulations
with the code Chicago
21
have been used to explain the experimental
results and have allowed a direct simulation of the LPI effects on the
positron yield. Moreover, the simulation is in good qualitative agree-
ment with the experimental data.
A schematic diagram of the experimental setup is shown in
Fig. 1(a)
. The structured target was irradiated with the OMEGA EP
laser pulse, with a wavelength of 1.053
l
m, an energy of 500 J, and a
pulse length of approximately 700 fs. Eighty percent of the laser energy
was enclosed in a 35
l
m diameter focal spot as is derived from an on-
shot wavefront and far-field measurement. The peak intensity was esti-
mated to be 4.5
10
20
W/cm
2
according to the measured fluence
map. Prior to the experiment, the structure geometry (spacing and
length) was optimized through PIC simulations of the hot electron
temperature. This geometry, which we call structure 1, is an array of
silicon microwires with 3
l
m diameter, 13
l
mlength,and15
l
mcen-
ter-to-center transverse distance. For reference, we have also shot flat
targets as well as another type of unoptimized structure (structure 2)
that showed detrimental effects on electron energies in simulations.
Structure 2 had 3
l
m diameter, 100
l
mlength,and7
l
m center-to-
center distance. The microwires in the latter target had much longer
lengths than the laser depth-of-focus, and much smaller space in
between them than the laser focal spot size, so they tend to break the
laser pulse during its propagation, resulting in a poor laser intensity at
the critical density surface. Consequently, they led to a low-energy
electron spectrum.
Figures 1(b)
and
1(c)
show scanning electron microscope images
of both target structures used in the experiment. The Si microwire
arrays 100
l
m in height (structure 2) were first grown on a Si
h
111
i
wafer by the vapor-liquid-solid growth method,
22
whereas the shorter
microwire arrays (structure 1) were etched from Si
h
100
i
wafers via
Deep Reactive Ion Etching.
23
The microwires were then embeded in a
30
l
m thick polydimethylsiloxane layer and peeled off of the sub-
strate. This thin polydimethylsiloxane layer was then glued to a 1 mm
thick Au backing layer. In this case, the high-energy electrons gener-
ated and guided by the surface structures would transport through a
thick high-Z material (Au) and induce pair production. The transverse
size of the Au block used in the experiment was also 1 mm. The laser
was directed at normal incidence onto the target and the microwire
arrays were oriented along the laser direction. This configuration has
been shown in the previous work to yield the highest enhancement of
electron energy.
18,19
The positron spectra were measured by an
electron/positron spectrometer on the back side of the target along the
laser direction (which was also the target normal direction).
The experimental positron and electron spectra for three differ-
ent types of targets are shown in
Figs. 2(a)
and
2(b)
. Target structure 1
generated about 50% more positrons than the regular flat target, and
its laser to positron conversion efficiency increased by
97% com-
pared to the flat substrate. The spectrum peak also shifted from
50 MeV for the flat target to
60 MeV for structure 1. Structure 2
showed fewer as well as much lower-energy positrons, in accord with
expectations as the length and spacing of the microwires encumber
the laser focusing. The electron spectrum from structure 2 also showed
the same trend, in agreement with the positron measurements.
However, the electron spectra from flat and from structure 1 were
mutually similar, with both having an electron temperature of about
21 MeV.
Multiple simulations to model the entire process were performed
to elucidate why the measured positron spectrum from structure 1 is
obviously superior, while its electron spectrum is similar to that from
flat target. The simulations used the same laser conditions and target
FIG. 1.
(a) Schematic diagram of the experimental setup. (b) Scanning electron
microscope (SEM) image of the pre-optimized target structure 1. (c) SEM image of
the unoptimized structure 2.
FIG. 2.
Experimentally measured spectra for (a) positrons and (b) electrons.
Different colors indicate the results from different targets under the same laser
conditions.
Applied Physics Letters
ARTICLE
scitation.org/journal/apl
Appl. Phys. Lett.
118
, 094101 (2021); doi: 10.1063/5.0038222
118
, 094101-2
Published under license by AIP Publishing
02 October 2023 23:40:05
geometries as the experiment. We fitted the measured laser fluence
map with two Gaussian functions to maintain the intensity distribu-
tion of the experiment. The OMEGA EP laser had a substantial pre-
pulse that could affect the conversion efficiency from the laser to fast
electrons and would therefore affect the yield and energy of positrons.
The facility has an on-shot prepulse measurement from 3 ns to 1 ns
prior to the main laser pulse. For the prepulse within 1 ns, we assumed
a similar profile to that measured by Dorrer
et al.
on OMEGA EP.
24
The total energy of the prepulse was about 3.5 mJ. Hydrodynamic sim-
ulations with the code HYDRA
25
were used to calculate the preplasma
profile, as shown in
Fig. 3(a)
. The preplasma scale length between rela-
tivistic critical density and critical density is about 2
l
m, and the scale
length below critical density is 10
l
m.
Full 3D PIC simulations to model all physics processes are
impractical with current supercomputers. We instead adopted a two-
stage approach that has been demonstrated on other targets
26,27
to
simulate LPI and transport processes separately. Both stages were per-
formedwiththecodeChicago.
21
The overall simulation process is
illustrated in
Fig. 3(b)
.First,a2DCartesiangeometrywasusedtosim-
ulate the LPI process, with only x and z dimensions modeled in space.
However, the velocity was 3D as all three components
v
x
,
v
y
,and
v
z
were updated at each time step. We could not use a cylindrical geome-
try, because the laser was linearly polarized in the x direction. The elec-
trons were measured at a plane that was 5
l
m inside the target. The
energy, direction, position, and time of each electron macroparticle
have all been recorded. We then processed the laser-generated elec-
trons to get their distribution as a function of energy, angle, transverse
distance, and time. At this point, we assumed a rotational symmetry
along the laser propagation axis for both space and velocity, and con-
verted the distribution to cylindrical coordinates. The transport simu-
lation was performed in a 2D cylindrical geometry. When hot
electrons leave the target, they would create a strong sheath field on
the back side. It is critical to model the sheath field properly to obtain
the correct yield and spectrum. The cylindrical geometry is required to
accurately model the 1
=
r
2
falloffoftheEfield,whereasthe2D
Cartesian geometry would result in a 1
=
r
falloff. The hot electrons
were then re-sampled according to its distribution and injected into a
1 mm thick, 1 mm diameter Au target in a 2D cylindrical geometry.
Positron generation and transport was then simulated both inside and
behind the Au target. To compare with the experimental results, statis-
tics of escaped electrons and positrons were performed at another
extraction plane that was 2 mm from the backside of the target.
The electron spectra generated from the LPI simulations are
shown in
Fig. 3(c)
. The dashed curves are the raw distributions derived
in Cartesian coordinates, and the solid curves are converted distribu-
tions in cylindrical coordinates. Note that the 2D Cartesian simulation
has a virtual dimension in y axis so the electron spectrum has a differ-
ent unit, corresponding to the right y axis in
Fig. 3(c)
.Theelectron
temperatures Te for different portions of the spectra are also labeled in
the plot. After conversion, the temperature for higher-energy-range
FIG. 3.
(a) Initial ion density for 2D Cartesian LPI simulations. (b) Schematic diagram of simulation setups. We have injected the fast electrons derived fro
m LPI simulation to
the following transport simulation after converting the electron source from Cartesian to cylindrical geometry. (c) Electron spectra inside the ta
rget from 2D Cartesian LPI simu-
lations (dashed curves, right y axis) and spectra of injected electron source for 2D cylindrical transport simulations (solid curves, left y axis). (
d) Blue curve (right y axis) shows
the probability of one positron generated by one 0
, monoenergetic electron transporting through a 1 mm thick, 1 mm diameter Au target, without considering any field effects.
The black and red curves (with respect to the left y axis) show injection electron spectra multiplied by the positron generation probability as a funct
ion of energy.
Applied Physics Letters
ARTICLE
scitation.org/journal/apl
Appl. Phys. Lett.
118
, 094101 (2021); doi: 10.1063/5.0038222
118
, 094101-3
Published under license by AIP Publishing
02 October 2023 23:40:05
electrons is maintained at around 20 MeV, which is quite close to the
experimentally measured temperature of 21 MeV. Lower energy elec-
trons have a wider angular distribution and thus tend to be more easily
affected by the conversion. Te decreased by about 3 MeV for electrons
within 25–70 MeV. Comparing structure 1 (red) to flat (black), the
main difference appears at energies above 25 MeV, as structure 1 tends
to produce about an order of magnitude more electrons within this
energy range.
To evaluate the positron yield by different electron spectra, in
Fig. 3(d)
,wehaveplotted
f
ð
E
Þ
P
e
þ
ð
E
Þ
,where
f
(
E
)isthespectrumof
injected electrons [solid curves in
Fig. 3(c)
], and
P
e
þ
ð
E
Þ
is the proba-
bility that one positron could be generated and exit from the 1 mm
thick, 1 mm diameter Au target as one incident electron with energy E
is normally injected.
P
e
þ
ð
E
Þ
(blue curve) was obtained using a Monte
Carlo code MCNP,
28
and the field effects have been ignored. Note that
we cannot directly compare the positron yield from MCNP to the
experimental result as the escaped positron yield and spectra are also
largely affected by the self-generated field. MCNP only provides an
estimation of the positron production capability of different energy
electrons. The positron production probability grows sharply with
energy for incident electrons below
30 MeV and gradually saturates
at high energies. The black and red solid curves indicate the calculated
f
ð
E
Þ
P
e
þ
ð
E
Þ
for flat and structured targets, respectively. Both curves
peak at about 15 MeV. However, electrons within 25–150 MeV from
structure 1 contributed to a great extent to the positron yield, whereas
for the flat target most of the positrons are generated by lower energy
electrons. Overall, the injection spectrum from structure 1 produced
about 30% more positrons than the flat target. Note that this estima-
tion does not consider any field or electron reflux effects that in reality
play an important role.
The Monte Carlo simulation only provides an intuitive view of
the pair production capability of LPI electrons. Understanding the
energy difference in the measured positron spectra requires closer
evaluation of the transport PIC simulations that involve the sheath
field. The comparison of modeled and experimentally measured posi-
tron spectra at target normal (laser direction) is shown in
Fig. 4(a)
.
The simulated spectra agree qualitatively with the experimental data.
In
Fig. 4(b)
, the dark solid curves show the simulated spectra of
escaped electrons at 0
, whereas for comparison the light solid curves
in the background show the corresponding experimental spectra. Both
spectra have a relatively good overlap within the energy range between
40 and 110 MeV. At lower energy, the mismatch is expected, because
the experimentally measured spectra include electrons that are gener-
ated at much later times than those covered by the simulation. The
simulated spectra showed less particles at high energies. However,
according to
Fig. 3(d)
, electrons above 110 MeV would make a negligi-
ble contribution to the positron yield. These high energy electrons
have a small impact on the sheath field as well because their total
charge is low. Therefore, the simulated positron and electron spectra
indicate that the injected electron source from LPI simulation models
the experimental condition reasonably well. For both the flat and the
structure 1 target, the electron spectra measured at the target normal
direction are mutually quite similar, whereas the positron spectra are
obviously different, in accord with experimental observations. In
Fig.
4(b)
, we have also plotted the total electron spectrum (in MeV
–1
)as
the dashed black and red curves. Unlike the spectra at 0
, the total
spectrum from structure 1 clearly shows more high energy electrons,
which explains the large discrepancy in the positron spectra, as for-
ward going positrons are generated by all electrons, not just by the for-
ward going ones.
There are two acceleration mechanisms that are responsible for
the highest energy electrons, including the loop-injected direct acceler-
ation
29
which is associated with any targets having moderate scale
length preplasma, and the structure-guided direct laser acceleration
which occurs only with the structured target.
18,19
We have also found
strong Weibel instabilities
30
near the critical density surface for both
target types, which largely widens the electron divergence. This effect
was dominating so that the usual collimating effect associated with the
front surface micro-wires described in previous work
18,19
did not show
up in the electron spectrum measured at 0
.
The energy of positrons is largely determined by the sheath field
on the back side of the target.
Figure 5
shows the evolution of the
sheath field
E
z
as a function of the longitudinal position z and time t.
Column (a) are the results from the flat target, and column (b) are
from structure 1. Images (a1),(b1) and (a3),(b3) show the
E
z
field at
r
¼
0 and average
E
z
field over the 1 mm diameter disk, respectively,
whereas (a2), (b2) and (a4), (b4) are the corresponding voltages V
calculated by integrating
E
z
over the longitudinal distance z.
V
¼
Ð
z
z
o
E
z
dz
,where
z
0
¼
1 mm indicates the back surface of the target.
These plots allow for an estimate of the accelerating capability of the
sheath field. The images at r
¼
0 indicate that passes of electrons grad-
ually build up the sheath field on the target backside. Comparing the
integrated voltage for flat and structured targets, both the voltage at
FIG. 4.
(a) Positron spectra at 0
from simulations. (b) Electron spectra at 0
(solid
lines, with unit MeV
–1
sr
–1
on the left y axis) and overall electron spectra (dashed
lines, with unit MeV
–1
on the right y axis). Note that the two different spectra plotted
have mutually different units. We have also plotted corresponding experimental
spectra at 0
in the background for comparison.
Applied Physics Letters
ARTICLE
scitation.org/journal/apl
Appl. Phys. Lett.
118
, 094101 (2021); doi: 10.1063/5.0038222
118
, 094101-4
Published under license by AIP Publishing
02 October 2023 23:40:05
r
¼
0 and the average voltage for the structured target are about
10 MV higher than that for flat target, which is consistent with the
measured energy difference between their positron peaks.
The two-stage PIC simulation reproduced the experimental
results, suggesting its potential for further target structure optimization
to control the yield and energy of positrons and other secondary par-
ticles, such as ions that are also greatly influenced by the sheath field.
Optimal target parameters will vary substantially with laser pulse
length, intensity, focal spot size, and the amount of prepulse. As we
have shown, for a given laser condition, the structures can be opti-
mized by performing 2D Cartesian LPI simulations and converting
the electron distributions to cylindrical coordinates. After the conver-
sion, the hot electron temperature and the laser-to-electron conversion
efficiency can both be realistic metrics for estimating the positron
yield. We plan to probe a broader parameter space in future work.
In summary, front surface target structures have been shown
experimentally to substantially enhance the positron yield and energy,
constituting a cost-effective approach to use laser-generated positron
sources for laboratory astrophysics applications. The follow-up simu-
lations explain the entire process of how the laser-plasma interaction
that is manipulated by the target structure affects the yield and energy
of positrons. The agreement between the simulated and experimental
spectra indicates the possibility of further target optimization using
two-stage PIC simulations.
We thank the OMEGA EP team for laser operation and
technical support. This work was performed under the auspices of
the U.S. DOE by LLNL under Contract No. DEAC5207NA27344,
and funded by LDRD (No. 17ERD010). The fabrication of Si
microwire arrays was supported through the Office of Science of
the U.S. Department of Energy under Award No. DE- SC0004993.
Additional support for this work was provided by the Lockheed
Martin Corporation (Award No. 4103810021). We thank the staff
at the Kavli Nanoscience Institute at Caltech for their technical
assistance with fabrication.
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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FIG. 5.
(a1), (b1) Sheath field
E
z
at r
¼
0 as a function of time and longitudinal
position z. (a2), (b2) Corresponding voltage calculated by integrating
E
z
over z.
(a3), (b3) Average
E
z
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(b) is for optimally structured target.
Applied Physics Letters
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Appl. Phys. Lett.
118
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