# Forward-looking insights in laser-generated ultra-intense $\gamma$-ray and
neutron sources for nuclear application and science

M. M. Günther<EMAIL_ADDRESS>GSI-Helmholtzzentrum für Schwerionenforschung
GmbH, Planckstraße 1, 64291 Darmstadt, Germany  O. N. Rosmej  GSI-
Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291
Darmstadt, Germany  Goethe-Universität Frankfurt am Main, Max-von-Laue-Str.1,
60438 Frankfurt am Main, Germany  Helmholtz Forschungsakademie Hessen für FAIR
(HFHF), Campus Frankfurt am Main, Germany  P. Tavana  Goethe-Universität
Frankfurt am Main, Max-von-Laue-Str.1, 60438 Frankfurt am Main, Germany  M.
Gyrdymov  Goethe-Universität Frankfurt am Main, Max-von-Laue-Str.1, 60438
Frankfurt am Main, Germany  A. Skobliakov  Institute for Theoretical and
Experimental Physics named by A.I. Alikhanov of NRC <<Kurchatov Institute>>,
B. Cheremuschkinskaya 25, 117218 Moscow, Russia  A. Kantsyrev  Institute for
Theoretical and Experimental Physics named by A.I. Alikhanov of NRC
<<Kurchatov Institute>>, B. Cheremuschkinskaya 25, 117218 Moscow, Russia  S.
Zähter  GSI-Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1,
64291 Darmstadt, Germany  Goethe-Universität Frankfurt am Main, Max-von-Laue-
Str.1, 60438 Frankfurt am Main, Germany  N. G. Borisenko  P. N. Lebedev
Physical Institute, RAS, Leninsky Prospekt 53, 119991 Moscow, Russia  A.
Pukhov  Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Gebäude
25.32 Etage 01, 40225 Düsseldorf, Germany  N. E. Andreev  Joint Institute for
High Temperatures, RAS, Izhorskaya st. 13, Bldg. 2, 125412 Moscow, Russia
Moscow Institute of Physics and Technology (State University), Institutskiy
Pereulok 9, 141700 Dolgoprudny Moscow region, Russia

###### Abstract

##  I Abstract

Ultra-intense MeV photon and neutron beams are indispensable tools in many
research fields such as nuclear, atomic and material science as well as in
medical and biophysical applications. For applications in laboratory nuclear
astrophysics, neutron fluxes in excess of 1021 n/(cm2 s) are required. Such
ultra-high fluxes are unattainable with existing conventional reactor- and
accelerator-based facilities. Currently discussed concepts for generating
high-flux neutron beams are based on ultra-high power multi-petawatt lasers
operating around 1023 W/cm2 intensities. Here, we present an efficient concept
for generating $\gamma$ and neutron beams based on enhanced production of
direct laser accelerated electrons in relativistic laser interactions with a
long-scale near critical density plasma at 1019 W/cm2 intensity. Experimental
insights in the laser-driven generation of ultra-intense, well-directed multi-
MeV beams of photons more than 1012 ph/sr and an ultra-high intense neutron
source with greater than 6$\times$1010 neutrons per shot are presented. More
than 1.4% laser-to-gamma conversion efficiency above 10 MeV and 0.05% laser-
to-neutron conversion efficiency were recorded, already at moderate
relativistic laser intensities and ps pulse duration. This approach promises a
strong boost of the diagnostic potential of existing kJ PW laser systems used
for Inertial Confinement Fusion (ICF) research.

##  II Introduction

Ultra-intense $\gamma$ and neutron beams are of interest in laboratory
astrophysics Reifarth2014 ; Gyuerky2019 ; Nunes2020 , high energy density
plasma physics Miquel2013 ; Moses2016 ; LePape2010 ; Morace2014 ; Glenzer2012
; Frenje2013  and applications e.g. in biology, medicine and material science
Thirolf2014 ; Arai2009 ; Tanaka2020 ; Krasny2018 ; Habs2011 ; Koester2012 ;
Mor2015 .

High-brilliant $\gamma$ beams open possibilities for selective excitation of
atomic nucleus states for investigation of photo-disintegration reactions in
nuclear astrophysics Lan2018  as well as efficient production of radioisotopes
for medical diagnostics and radio-oncological therapeutics, such as scandium,
copper and platinum isotopes Ma2019 ; Lovless2019 ; Luo2016 ; Koester2012 ;
Habs2011 . Also, studies of nuclear resonance fluorescence (NRF) are
attractive for the development of isotope selective radiographic imaging
techniques Pruet2006 .

Neutron sources are indispensable tools for approving astrophysical
nucleosynthesis theories, where the production of bulk heavy nuclei beyond
iron (Fe) is attributed to the slow (s) and rapid (r) neutron capture
processes. Nuclear reaction cross sections for nuclear structure physics
studies can be accessed by means of conventional neutron sources based on
electron accelerators Altstadt2007 , nuclear fission reactors like high-flux
neutron reactor of the Institut Laue-Langevin (ILL) ILL , and spallation
sources Taylor2007 . The ILL reactor (1015 n/(cm2 s)) ILL  and the upcoming
European Spallation Source (ESS) with 1016 n/(cm2 s) Garoby2018  are examples
for the highest peak-fluxes of the existing neutron sources. For most
applications, especially in nuclear astrophysics, fast neutrons have to be
moderated to the epithermal neutron energy range which decreases the effective
neutron flux on target. For nuclear astrophysical studies the so-called Time-
Of-Flight (TOF) facilities are preferable to reach suitable conditions for
neutron energy distribution. For example the LANSCE facility of the Los Alamos
National Laboratory in the USA provides neutron peak-fluxes of 1015 n/(cm2 s)
as well as an integrated neutron flux of 105 n/(cm2 s) in the nuclear
astrophysical relevant neutron energy range between 10 – 100 keV Nowicki2017 .
Currently, quasi-stellar beam conditions for nuclear astrophysical
investigations are available at the Frankfurt Neutron Source of the Stern
Gerlach Zentrum (FRANZ) with an integrated neutron flux of 6$\times$106 n/(cm2
s) in the energy range of 10 – 100 keV on target Alzubaidi2016 ; Reifarth2014
.

Investigation of the r-process for nucleosynthesis of heavy isotopes takes
place along the chain of short-lived isotopes where the neutron capture time
is shorter than the time of the $\beta^{-}$–decay Thielemann2011 ;
Reifarth2014 . For r-process studies, nuclear quantities such as $\beta$-decay
properties, masses and neutron capture rates for nuclei far from the so-called
valley of stability are of key importance and are still an experimental
challenge Horowitz2019 . One example for a suitable initial isotope for the
investigation of multi-neutron capture events in the r-process chain, but also
in the s-process scheme is the stable 96Zr isotope Sonnabend2004 ; Chen2019 .
Chen et al. Chen2019  have shown in simulations that for multiple neutron
capture processes, a neutron peak-flux of 1024 n/(cm2 s) is required to ensure
the neutron capture time ($\approx$1 s) shorter than the 97-102Zr isotope
half-lives. The neutron capture time is determined by the product of the
neutron peak-flux and the capture cross section. Therefore, especially for
laboratory nuclear astrophysical studies the development of neutron sources
with high neutron-fluxes and neutron energies from tens of keV to several
hundreds of keV are of great importance. Recent theoretical studies of the
neutron capture cascade using laser-driven neutron sources have shown the
feasibility for neutron capture nucleosynthesis in the laboratory Hill2021 .

An alternative way for the generation of high-fluence and high-flux $\gamma$
and neutron beams in compact facilities is based on high-power lasers in
relativistic laser-plasma interactions. Upcoming high-brilliance and high-
intensity $\gamma$ beam facilities like the Variable-Energy Gamma Ray system
(VEGA) at ELI-NP will produce tunable and narrow $\gamma$ beams via Compton
backscattering of 100 TW laser pulses on relativistic electrons with energies
above 700 MeV Tanaka2020 . The planned upgrade of the high intense
$\gamma$-ray source, HI$\gamma$S-2, will provide up to 20 MeV $\gamma$ beams
via Compton backscattering in a conventional accelerator based free electron
laser (FEL) structure Higs . Also in construction is the Gamma Factory
facility at CERN that provides $\gamma$ beams with energies of several
hundreds of MeV generated via the excitation of highly ionized relativistic
heavy ions by lasers Krasny2018 . Such facilities allow for a renaissance in
photo-nuclear research field. A review to a prospective possible pathway to
reach peak neutron-fluxes of 1021–1024 n/(cm2 s) applicable for investigating
nucleosynthesis in the laboratory is reported using ultra-high power (multi-
PW) lasers with intensities up to around 1023 W/cm2 Chen2019 .

In general, two principal laser-plasma based methods are being pursued to
generate $\gamma$ beams in the MeV regime. On the one hand, we consider the
electron acceleration via the laser-driven plasma wake field based on the
relativistic laser pulse interaction with a gas target (under dense plasma) at
several tens of femtosecond pulse duration Hooker2013 . The interaction of the
GeV quasi mono-energetic electrons with the contra-propagating laser pulse
Phuoc2012 ; Cipiccia2011  leads to the generation of narrow band beams of
Compton backscattered photons Yu2016  with energies at $\gamma_{\text{e}}^{2}$
of the laser photon energy, where
$\gamma_{\text{e}}=\frac{1}{\sqrt{1-(\frac{v_{\text{e}}}{c})^{2}}}$ is the
electron Lorentz factor. On the other hand, by interaction of relativistic
laser pulses with high-$Z$ solid targets, electrons can be ponderomotively
accelerated in the low-dense pre-plasma region in front of the target
Norreys1999 ; Palaniyappan2018 . Relativistic electrons are then decelerated
in a high-$Z$ sample producing continuous MeV-bremsstrahlung radiation
Giulietti2008 ; Schumaker2014 ; Ain2018 . Concepts for producing multi-MeV
highly brilliant photon beams from MeV-betatron emission of trapped GeV-
electrons were theoretically discussed for the next generation of ultra-high
intense lasers Zhu2020 ; Benedetti2018 ; Zhu2016 ; Ridgers2012 . Such single
laser schemes allow to investigate quantum electrodynamic (QED) effects and
QED plasmas Zhu2016 ; Ridgers2012 . Additionally, simulation studies
considering a counter propagating multi-PW laser scheme for two-side
irradiation have shown promising results in the production of enhanced
electron-positron plasma density for strong-field QED investigations Luo2015 .

Currently, besides neutron generation in inertial fusion processes Glenzer2012
; Frenje2013 , there are several other scenarios for the laser-based
production of neutrons via nuclear reactions: Accelerated deuterons interact
with heavy or light isotopes resulting in compound nucleus excitations or
direct reactions. In the latter case, neutrons with energies of the half of
the deuteron energies are produced Roth2013 . The highest reaction cross
sections are achieved at deuteron energies above 10 MeV. The neutron yield is
peaked in a forward direction and the neutron beam has a sub-nanosecond pulse
duration. For an efficient laser-driven acceleration of deuterons ultra-high-
contrast and ultra-high-intense PW-class laser systems are demanded Roth2013 ;
Jung2013 . In the proton induced reactions, a compound nucleus is excited. The
interaction of protons with light isotopes results in a flat neutron spectrum.
This is different from the interaction of protons with heavy isotopes, where
the neutron spectrum peaks at low energies. The realization of a laser driven
spallation neutron source needs several tens of MeV proton energies. State-of-
the-art research on these neutron production concepts are presented in
Roth2013 ; Petrov2013 ; Kleinschmidt2018 .

In the case of photo-nuclear reactions, compound nucleus excitations take
place. The neutron spectrum can be described by a Maxwellian-like distribution
function with a mean kinetic energy up to several MeV and an isotropic angular
distribution. Depending on the neutron generation process, the neutron source
properties differ from each other in the energy distribution, the
directionality and the pulse duration. Compared to the proton/deuteron induced
neutron generation processes, the pulse duration of the gamma-driven neutrons
is much shorter Pomerantz2014 ; Jiao2017  due to the relativistic feature of
the electron beam generating $\gamma$-rays. Nowadays, the high-yield laser-
driven $\gamma$ and neutron-beam production schemes are based on applications
of high-intensity multi-petawatt-class laser systems, where the current state-
of-the-art research is discussed in Pomerantz2014 ; Jiao2017 .

In this work, we present a forward-looking experimental scheme for generating
ultra-intense $\gamma$ and neutron beams at moderate relativistic laser
intensities with high robustness and set record values of boosted $\gamma$ and
neutron fluences. We make feasible an effective laser-driven MeV-gamma and
neutron production scheme via the laser pulse interaction with sub-millimeter
thick aerogel polymer foam target systems. Laser energy-to-gamma/neutron
conversion efficiencies of $\approx$2%/0.05% are reached, already at moderate
relativistic laser intensities. For example, it allows the approach to direct
nuclear astrophysical investigations in the laboratory. In addition, it
promises a high diagnostic potential for existing kJ PW laser systems used for
inertial confinement nuclear fusion research.

##  III Results

###  III.1 Experiment

Laser driven electron beams are excellent tools for the generation of ultra-
short and bright sources of particles and radiation. Experimental results on
enhanced laser driven beam generation in the multi-MeV energy range in
interaction of sub-ps laser pulses of relativistic intensities with sub-mm
thick low-density polymer foams promise a strong increase of the diagnostic
potential of high-energy sub-PW and kJ PW-class laser systems Willingale2018 ;
Rosmej2019 ; Rosmej2020 .

In the experiment, a high energy sub-picosecond laser pulse of relativistic
intensity interacts with a pre-ionized polymer foam of near critical electron
density (NCD), where super-ponderomotive electrons are produced via the direct
laser acceleration (DLA)-process in the presence of strong quasi-static
electric and magnetic fields Pukhov1999 ; Pukhov2003 . A radial electrostatic
field is created by ponderomotive expulsion of background plasma electrons
caused by a relativistic laser pulse. At the same time, the current of
accelerated electrons generates an azimuthal magnetic field Pukhov2003 . A
relativistic electron trapped in the channel experiences transverse betatron
oscillations and gains the energy efficiently from the laser pulse when the
frequency of the betatron oscillations becomes in resonance with the Doppler
shifted laser frequency Pukhov2003 .

The DLA works efficiently in NCD plasmas and with a picoseconds laser pulse
duration. Different from the laser wake field acceleration (LWFA), the DLA
does not generate electrons at very high energies, rather, it produces ample
amounts of electrons with Maxwell-Boltzmann-like distributions carrying $\mu$C
of charge Pukhov1999 ; Pugachev2016 ; Pugachev2019 . The interaction of a high
number DLA-accelerated electrons with high-$Z$ materials causes an ultra-high
fluence of MeV-radiation that can trigger nuclear reactions resulting into
neutron production.

The effective temperature of the DLA accelerated electrons exceeds more than
one order of magnitude the ponderomotive potential and their energies extend
up to 100 MeV, already at moderate relativistic laser intensities Rosmej2019 ;
Rosmej2020 . The reason for this behavior is a long acceleration path in a NCD
plasma ensured by pre-ionized sub-mm thick foams and a relatively long sub-ps
laser pulse duration. This differs from the case of the so-called multilayer
targets where a low-density (“near-critical”) layer of a few-micron thickness
is added on the illuminated side of a thin, high-density layer. Such kind of a
target was used in the last decade for proton acceleration at ultra-
relativistic intensities and sub 100-fs pulses Sagattoni2012 ; Bin2018 ;
WMa2019 . In Bin2018 , the generation of hot electrons from a double layer
target irradiated by a laser pulse with an intensity of 2$\times$1020 W/cm2
was reported. The target was consisted of a several micrometers thin NCD
plasma slab (0.5 $n_{\text{cr}}$) and an over-dense foil. The measured
effective electron temperature was 8 MeV, which is only twice higher than the
ponderomotive potential.

Figure 1: Experimental set-up. Top view of the diagnostic set-ups used for
irradiation of aerogel-foams (CHO) at 1019 W/cm2 (20 J in focal spot) laser
intensity and conventional foils at ultra-relativistic intensity of $\sim$1021
W/cm2 (40 J in focal spot). An imaging plate (IP) behind 6 mm thick steel
cylinder was used to measure an angular distribution of electrons with
energies above 7.5 MeV. Nuclear activation plates consisting of different
materials were placed at the front of cylinder at 5∘ and 15∘ to the laser
axis. Three 0.99 T magnetic spectrometer measured the energy distribution of
accelerated electrons at 0∘, 15∘ and 45∘ to the laser axis. Figure 2:
Electron spectra. Electron spectra in values of the fluence per electron
energy as function of electron energy registered at three different angles
(0∘, 15∘, 45∘) to the laser direction: a Spectra measured in interaction of a
laser pulse with 1019 W/cm2 intensity and 20 J in the FWHM of the focal spot
with aerogel foam (CHO) target stacked together with a gold (Au) foil of 10
$\mu$m thickness (setup 1a, blue) and with 1 mm thick gold converter (setup
1b, red). b Result of the cylinder stack diagnostic for the angular
distribution of super-ponderomotive electrons with energies above 7.5 MeV
measured in a single shot onto aerogel+thin foil (left) and aerogel+1mm-thick
converter (right). c Spectra measured in interaction of a laser pulse with
1021 W/cm2 and 40 J in FWHM of the focal spot with 10 $\mu$m titanium (Ti)
foil and (d) with 1 mm-thick gold converter.

The present experiment was performed at the high-energy laser facility PHELIX
Bagnaud2010 . We investigated the electron acceleration with the focus on
$\gamma$ and neutron production in the interaction of DLA electrons with
high-$Z$ materials using two different peak laser intensities ($\sim$1019
W/cm2 and $\sim$1021 W/cm2). These different intensity regimes were achieved
by different focusing systems Rosmej2020 . Polymer aerogel-foams with a mean
density of 2 mg/cm3 and sub-millimeter thickness Borisenko2007  were used for
the production of a NCD-plasma via the mechanism of super-sonic ionization
Rosmej2019 ; Guskov2011  by sending a well-controlled nanosecond-pulse before
the main relativistic pulse. A fully ionized plasma corresponds to
0.64$\times$1021 cm-3 electron density or 0.64 $n_{\text{cr}}$
($n_{\text{cr}}=$1021 cm-3). Measurements of the plasma density inside the
ringholder after ionization by a super-sonic wave is a big challenge. At the
same time, Particle-In-Cell(PIC) simulations performed for a step-like density
profile with $n_{\text{cr}}$ and 0.5 $n_{\text{cr}}$ Pugachev2016 ;
Pugachev2019  as well as for a partially ramped density profile in order to
account for plasma expansion toward the main laser pulse Rosmej2019  showed a
very similar overall behavior of the energy and angular distributions of
super-ponderomotive electrons.

Compared to NCD-plasmas generated by laser irradiation of conventional foils,
the DLA path in 300–400 $\mu$m thick foams is strongly enhanced, which results
in an increased propagation length of the laser main pulse through the NCD-
plasma and allows to produce a high charge of electrons with energies far
above the ponderomotive potential Rosmej2019 . A schematic of the experimental
setup is presented in Fig. 1. Here, the energy distribution of the DLA-
electrons was measured by means of magnet spectrometers. A steel cylinder was
used to map the angular distribution of the electron beam. The high-current,
well-directed, super-ponderomotive electrons produced in the NCD plasma pass
through a high-$Z$ converter generating bremsstrahlung. $\gamma$-rays together
with some fraction of relativistic electrons that escape the converter,
propagated 23 cm in vacuum and triggered nuclear reactions in the activation
detectors consisting of gold (Au), tantalum (Ta), indium (In) and chromium
(Cr).

For further discussion, we introduce the convention for the designations of
the four principal laser-target setups used in the experiment, which will be
applied in the following: setup 1a (1019 W/cm2 onto foam+thin foil), setup 1b
(1019 W/cm2 onto foam+1mm thick foil), setup 2a (1021 W/cm2 onto thin foil),
setup 2b (1021 W/cm2 onto 1mm thick foil).

###  III.2 Electron spectra

In the experiment, spectra of super-ponderomotive electrons were measured by
means of magnetic spectrometers at three different angles to the laser axis
(see Fig. 1). In the case of the setup 1a and 1b, we observe a strong
dependence of the electron energies on the angle between the electron beam
propagation direction and the laser direction, which is presented in Fig. 2a.
The experimental graphs are shown for the electron spectra measured at 0∘, 15∘
and 45∘ to the laser axis for setup 1a (blue) and setup 1b (red). The main
fraction of relativistic electrons is accelerated along the laser axis (0∘) up
to energies of 100 MeV (Fig. 2a). The difference in the spectra between the
setup 1a and 1b is caused by propagation of electrons through 1 mm thick Au-
convertor in the 1b-case. This thickness corresponds to the mean free path of
electrons with $E\leq$8 MeV.

The electron energy distribution was approximated by a Maxwellian-like
distribution function with one or two effective temperatures $T_{\text{hot}}$.
In the case of setup 1a, the electron spectrum measured at 0∘ was described by
an exponential function with $T_{\text{hot,1}}=$(12.1$\pm$1.4) MeV and
$T_{\text{hot,2}}=$(26.5$\pm$3.4) MeV, both exceeding the ponderomotive
potential at 1019 W/cm2 more than one order of magnitude. With increasing the
observation angle, the temperature and the number of accelerated electrons
drop down to $T_{\text{hot,1}}=$(8.1$\pm$1.2) MeV
($T_{\text{hot,2}}=$(15.8$\pm$1.7) MeV) at 15∘ and further to
$T_{\text{hot,1}}=$(1.9$\pm$0.1) MeV ($T_{\text{hot,2}}=$(7.3$\pm$1.2) MeV) at
45∘. Electron spectra measured in the case of setup 1b show the same tendency.
The difference between 1a and 1b is seen only below 15 MeV for electrons that
undergo significant energy loss in the 1 mm thick Au-converter (see Fig.2a).

In direct shots on thin metallic foils at ultra-relativistic laser intensity
of 1021 W/cm2 (setup 2a), the electron energy distribution was approximated
with $T_{\text{hot}}$=(9.9$\pm$2.2) MeV (Fig. 2c) for measurements at 0∘ and
15∘ to the laser axis and the maximum of the detected electron energy reached
50 MeV, which is twice lower than in the case 1a and 1b. In shots onto 1 mm
thick converter (setup 2b), the effective temperature and the maximum of the
detected energy of escaping electrons are 4 MeV and 40 MeV correspondingly
(Fig. 2d). The dependence of the electron energy distribution from angle to
the laser axis is observed only at 45∘, which indicates a rather divergent
electron beam. In shots with 1021 W/cm2 laser intensity, 100 $\mu$m entrance
slit was used (see Methods, Electron diagnostics). This resulted into
comparable level of the electron signal and the background caused by the
bremsstrahlung radiation from the Au-converter and, as a consequence, rather
noisy electron spectra.

Measurements using cylinder diagnostic (see Methods) showed that the electron
beam generated via DLA process in NCD plasma is well-collimated. Fig. 2b
presents results of 120∘\- cylinder diagnostic for setups 1a and 1b. The
Imaging Plate (IP) signals are caused by electrons with energies above 7.5
MeV, which are capable to trigger nuclear reactions in activation samples. The
measurements show that in the first case, the relativistic DLA electrons with
energies above 7.5 MeV propagate within a half angle of 13∘ to the laser axis
(0.16 sr solid angle), while in the setup 1b within 20∘ (0.38 sr) due to
electron scattering in 1 mm thick foil. From shot-to-shot deviation of the
electron beam position from the laser axis was not larger than 5∘. This result
is in contrast to the stochastic beam pointing reported by Willingale et al.
Willingale2018 .

###  III.3 MeV $\gamma$ beam

For the characterization of the bremsstrahlung spectrum generated by super
ponderomotive electrons in high-$Z$ samples, we used a nuclear activation-
based diagnostic, which is sensitive to more than 7.5 MeV photon energies,
similar to that described in Guenther2011 . In the present work, the samples
composed of elementary Au, Ta, In and Cr were stacked together and placed at a
distance of 23 cm in forward direction at 5∘ and 15∘ to the laser axis (Fig.
1).

After each laser shot, the nuclear activated samples were analyzed by a low-
background spectroscopy using 60% high purity germanium (HPGe) detector
systems to identify the reaction channels leading to the isotopes of interest
and to determine reaction yields of the activated isotopes in every sample
(see below, methods nuclear diagnostics). The high-energy bremsstrahlung
spectrum was evaluated according to the analysis process described in Methods.

Figure 3 shows the energy dependent bremsstrahlung fluences detected at 5∘ to
the laser axis for the different laser intensities and target systems (setup:
1a, 1b, 2a, and 2b). In the case of setup 1b, the photon spectrum follows an
exponential dependence on energy with an effective temperature of
(12.7$\pm$2.1) MeV. The measured number of photons reaches
(4.9$\pm$2.1)$\times$109 per 1.5$\times$1.5 cm2 area of the activation sample
stack or (1.2$\pm$0.5)1012 ph/sr. We would like to point out, that only in
interaction of 1019 W/cm2 laser pulse with a foam layer stacked together with
1mm thick Au-converter (1b), photo-neutron disintegrations up to
197Au($\gamma$,5n)192Au with maximum of the reaction cross section at 50 MeV
(see below) were observed (blue dots at 50 MeV, Fig. 3).

Figure 3: MeV-bremsstrahlung. MeV-bremsstrahlung fluence in dependence on
energies from different laser-target setups described in the legend, where
used combined aerogel (CHO) with two different thick gold (Au) targets (data
as blue and yellow dots) as well as thin and thick metal targets, only (data
as magenta and purple triangles). The error bars represent the accuracy of
reaction yield and the width of nuclear resonance used for spectral
reconstruction (see Methods). Dashed lines are thermal exponential fits on the
experimental data. Figure 4:  Simulated angular distribution. GEANT4
simulations of the angular distribution of electrons and photons above 7.5 MeV
after the laser pulse interaction with an aerogel-foam (CHO) target combined
with a 1 mm thick converter (Au). The angular distributions are shown using
the same color scale in arbitrary unit. The half divergence angle of the
electron beam is 17∘, where the photons are distributed within the half
divergence angle of 10.5∘. The white curves represent the line-out (dashed
lines) of the colored distribution in the range of the horizontal angle in
degree (∘).

In the case of direct irradiation of a high-$Z$ converter with ultra-
relativistic laser intensity (setup 2b), a 10 times lower fluence of
(1.2$\pm$0.5)1011 ph/sr with a twice lower effective temperature of
(5.3$\pm$2.0) MeV was recorded compared to 1b (see Fig. 3). Here, only
($\gamma$,3n)-reactions in Au and Ta with maximum of the reaction cross
section at $\sim$30 MeV were registered.

The difference in the photon fluences and effective temperatures in 1b- and
2b- cases can be explained by higher electron energy and directionality of the
relativistic electron beam generated in the interaction of 1019 W/cm2 (20 J)
laser pulse with pre-ionized sub-mm thick foam targets compared to shots with
an ultra-relativistic intensity of 1021 W/cm2 (40 J) onto Au-converter (see
Fig. 2a and 2d).

The bremsstrahlung spectra measured by means of the nuclear activation method
in setup 1b and 2b consist of a primary gamma-beam with energies above 10 MeV
(threshold of photo-nuclear reactions), generated by laser-accelerated
electrons in the Au-converter, and a secondary $\gamma$-beam, produced by
above 10 MeV electrons that emerge the converter (see Fig. 1, experimental
setup) and hit the activation stack. The acceptance angle of the activation
sample stack is of 4.3 msr, only. This is a small part of solid angles covered
by the relativistic electron and $\gamma$ beams. In the case of 1b, the
divergence angle of electrons was defined experimentally (Fig. 2b), the
divergence angle of the $\gamma$ beam with energies above 10 MeV generated in
the converter was unknown.

In order to solve this problem, the GEANT4 Monte Carlo code Agostinelli2003
was used to simulate the relativistic electron transport through a 1 mm thick
converter (setup 1b) and the generation of the primary $\gamma$ beam. In
GEANT4, the following physical processes were involved in simulations of the
relativistic electron beam interaction with high-$Z$ converter and activation
plates: collisional and radiative energy loss, e-e+ pair production, gamma
driven nuclear reactions in the region of Giant Dipole Resonance (GDR). In
simulations, ShieldingLEND G4Manual  physics list was applied which represents
Low Energy Nuclear Data (LEND) with a set of low energy nuclear interaction
processes. Electro-nuclear reactions in GEANT4 are handled by the classes
G4ElectroNuclearProcess and G4PositronNuclearProcess G4Manual . The
experimental geometry together with the measured energy and angular
distributions of the DLA-electrons in the case of setup 1a were used as input
parameters. A converter plate was considered as cold solid matter, since the
laser energy was fully absorbed in the foam Rosmej2020  and the laser didn’t
hit the converter. The benchmarking was done by comparing measured and
simulated isotope yields (see below, methods nuclear diagnostics). Simulations
resulted in a half divergence angle of 17∘ (0.27 sr) for electrons above 10
MeV and 10.5∘ (0.11 sr) for $\gamma$ of the same energy (see Fig. 4). This
means that in the case of setup 1b, 1.6% of electrons and 4% of primary gammas
generated in 1mm Au converter interact with the activation samples and trigger
nuclear reactions. In addition, in the sample placed at 15∘, a more than one
order of magnitude lower activity was measured, which also indicates a highly
directed MeV-bremsstrahlung beam. The differences between the measured (0.38
sr, Fig. 2b) and the simulated (0.27 sr) electron divergence cones can be
explained by a strong increase of the IP-response produced by electrons with
energies below 1 MeV Bonnet2013  compared to those above 1 MeV. The beam of
DLA-electrons passes a 1 mm thick Au-converter and produces the MeV-
bremsstrahlung radiation with 0.11 sr divergence angle. A high fraction of the
relativistic electrons escapes the converter (Fig. 2, setup case 1b) with 0.27
sr divergence, propagate 23 cm in vacuum and produce additional gamma-
radiation in the activation samples. According to GEANT4 simulations, 65% of
the total gamma-fluence originates in the converter and 35% in the activation
stack. Under consideration, that 1.2$\times$1012 ph/sr are produced in two
different ways described above, we obtain the total photon number with
energies greater than 10 MeV: 1.2$\times$1012 ph/sr $\times$ (0.65$\times$0.11
sr + 0.35$\times$0.27 sr) = 2$\times$1011. Taking into account the effective
temperature of (12.7$\pm$2.1) MeV and laser energy of 20 J, we end up with an
ultra-high conversion efficiency of the laser energy into above 10 MeV gammas
of (1.4$\pm$0.3)%. Compared to the present work, a concept of a non-linear
Compton backscattering scheme driven by a PW short laser pulse at more than
5$\times$1021 W/cm2 in a NCD plasma coupled with a plasma mirror was recently
discussed in Huang2019 . The described simulation studies show a broad-band
spectrum that contains more than 1011 photons with energies above 10 MeV with
less than 1% laser-to-$\gamma$ energy conversion efficiency.

Figure 5: Protons. a Proton number in arbitrary units as a function of proton
energy. Yellow dots are proton number evaluated in case of laser interaction
with aerogel-foams combined with thin metal foils at 1019 W/cm2 intensity
(setup 1a), while the magenta dots describe proton number obtained in laser
interactions with thin metal foils at 1021 W/cm2 laser intensity (setup 2a).
Error bars represent the accuracy of reaction yield and the width of nuclear
resonance used for spectral reconstruction. The dashed curves demonstrate the
different slopes of proton spectra. PIC-simulated proton spectrum is shown as
blue solid line. b IP signal produced by electrons above 7.5 MeV directed
along the laser axis (FWHM range, black dashed circle) with positions of
activation samples for detection of (p,xn)-reactions and expected direction of
TNSA-accelerated proton beam (foil-target normal was +10∘ to laser direction).
The half protons divergence angle of 6∘\- 7∘ was estimated assuming a Gaussian
angular distribution at the target normal and taking into account proton
induced reaction yields measured at 5∘ and 15∘ (black dotted circle). c
Momentum diagram of protons from 3D PIC simulation (VLPL code). Transversal
and longitudinal momenta are shown as normalized values, where the colors
display the proton energies. Dashed lines indicate the half divergence angle
ranges at 5∘ and 10∘.

###  III.4 Accelerated protons

In laser interactions with thin foil targets at 1021 W/cm2 laser intensity
(setup 2a) and with combined foam and thin foil target systems at 1019 W/cm2
(setup 1a), we observed proton induced nuclear reactions in the GDR region.
These reactions lead to compound nucleus excitations in Au and Cr activation
samples and generation of mercury (Hg) and manganese (Mn) isotopes. The
reaction cross sections and corresponding proton energy ranges of the GDRs are
shown below in the methods section. In the case of proton-induced reactions,
there are no competing photo-nuclear channels that lead to the same isotope if
starting from the same natural stable mother isotopes.

In the case where the activation stack was oriented to laser with Au-sample
(Cr is at rear), we observed following proton-driven nuclear reactions:
197Au(p,n)${}^{197\text{m}}$Hg with a maximum of the cross section at 12 MeV
proton energy, 197Au(p,3n)${}^{195\text{m}}$Hg at 28 MeV and 54Cr(p,3n)52Mn at
37 MeV. For the opposite sequence of samples (Cr is at front), we identified
the reaction channel 52Cr(p,n)52Mn at 14 MeV. The gamma spectra of the
different sequenced activation stacks are shown in the methods section (see
below).

The proton number within the width of each GDR was deduced from the reaction
yield of the corresponding isotope by deconvolution with the reaction cross
sections (see below, methods nuclear diagnostics). The proton number per
sample measured in the GDR region centered at 14 MeV with the resonance width
of 8 MeV and at 37 MeV with the resonance width of 20 MeV are
(1.38$\pm$0.62)$\times$109 and (1.48$\pm$0.80)$\times$109 for the setup 1a. In
the case of setup 2a, the proton number reached (1.62$\pm$0.41)$\times$1010 at
14 MeV and (3.74$\pm$1.03)$\times$108 at 37 MeV proton energy. Compared to
setup 2a at 1021 W/cm2 and laser pulse energy of 40 J, the proton number in
setup 1a at 1019 W/cm2 with 20 J laser energy reaches a 4 times higher value
in the upper cut-off region of proton energy. This behavior allows for
enhanced nuclear reaction yields over a wide range of proton energies.

Figure 5a shows normalized proton number in dependence on the energy obtained
for setups 1a (yellow) and 2a (magenta). In the case of interaction of 1021
W/cm2 laser pulse with a thin foil (setup 2a), experimental data were fitted
by an exponential function with an effective temperature of 5-6 MeV. This
protons spectral properties are characteristic for the target normal sheath
acceleration (TNSA) mechanism Borghesi2014 ; Robson2007 . The important
feature of the proton spectrum evaluated for setup 1a is a very flat slope
(Fig. 5a, yellow dashed line), which results into a high proton number at
energies above 20 MeV. The dark blue curve in Fig. 5a presents the result of
the 3D PIC simulation performed by means of the virtual laser plasma
laboratory (VLPL) code Pukhov1999JPP  for the experimental conditions
discussed above. The slope of the simulated proton spectrum is in a good
agreement with the experiment.

Another important feature of the proton beam in the case of setup 1a is its
low divergence. We measured a 500 times higher 52Mn isotope yields produced in
the activation stack (Cr-front) placed at 5∘ to laser axis compared to those
measured at 15∘. In these shots, the target normal was counterclockwise
rotated by 10∘ to laser direction (Fig. 5b). The half protons divergence angle
of 6∘\- 7∘ was estimated assuming a Gaussian angular distribution of the
proton beam centered at the target normal and taking into account proton
driven reaction yields measured at 5∘ and 15∘.

This is in a good agreement with 3D PIC results. According to the simulations
(setup 1a), the 20 J laser pulse is absorbed in the foam before it reaches the
foil Rosmej2020 . A large space charge of super-ponderomotive electrons
accelerated in the NCD-plasma reaches the rear side of the foil, which stays
cold. The simulations show that energetic electrons spread out along the foil
rear side generating a very planar electrostatic field. This field accelerates
a highly collimated ion beam. Result of simulations is presented in the
diagram of the longitudinal and transversal proton momenta (Fig. 5c), which is
characteristic for a highly collimated proton beam with a 5∘-7∘ half of
divergence angle.

###  III.5 Neutrons

Enhanced neutron fluences were observed in laser pulse interactions with foam
target systems at moderate relativistic laser intensities. Here, in the setup
1a, neutron generation was dominated by protons, while in the setup 1b the
neutrons are dominantly generated by photo-nuclear reactions.

In both cases, the generation of neutrons was investigated via a well-
established indium activation method (e.g. Zankl1981 ), which can be applied
for fast and epithermal/slow neutrons. In the experiment, elementary indium
with a purity of 99.999 % in the natural isotope abundance of 115In (95.7 %)
and 113In (4.3 %) was used. We focused on the decay channels of activated
indium isotopes that were reached via neutron induced reactions. In this
procedure, an input of $\gamma$-driven nuclear reactions leading to the same
indium isotope type was taken into account (see below, methods nuclear
diagnostics).

In the study of reactions triggered by epithermal neutrons, the strong nuclear
resonance with a reaction cross section of 104 barn at 1 eV for the neutron
capture reaction 115In(n,$\gamma$)${}^{116\text{m}}$In was considered. Fast
neutrons were investigated by the pure neutron activation channel
115In(n,n’)${}^{115\text{m}}$In with 0.343 barn at 2.5 MeV and the activation
channels 113In(n,n’)${}^{113\text{m}}$In with 0.2 barn at 2.5 MeV as well as
the 113In(n,2n)${}^{112\text{m}}$In reaction with 1.5 barn at 14 MeV initial
neutron energy. The reaction channels 115In(n,2n)${}^{114\text{m}}$In and
113In(n,$\gamma$)${}^{114\text{m}}$In are not useful because the daughter
isotope becomes the same for fast and slow neutrons.

The neutrons were produced within the activation sample placed at a distance
of 23 cm to the laser interaction point, which covers a solid angle of 4.3
msr. According to GEANT4 simulations, a contribution of background neutrons to
the nuclear activation of In isotopes was not higher than 30%.

In the case of setup 1b only, we observed a significant yield of
${}^{112\text{m}}$In and ${}^{114\text{m}}$In isomers produced by fast
neutrons generated in $\gamma$-driven nuclear reactions triggered by a high
number of above 10 MeV photons (Fig. 3, setup 1b). Such reactions lead to the
production of neutrons, which are evaporated with high kinetic energy from an
excited compound nucleus.

Figure 6 shows the neutron number per activation sample evaluated using the
indium isotope yields after subtraction of the $\gamma$-driven channels. The
energy distribution of neutrons evaporated from excited states of compound
nucleus can be described by a Maxwellian-like function Bertulani2009 . The
neutron number per energy width of the corresponding GDR was determined by
weighting the reaction yields with the cross sections EXFOR  for each
reaction. As described in the methods, the mean neutron energy
$E_{\text{mean}}$ was evaluated by an isotope relation equation using the
experimentally measured reaction yields of indium isotopes produced by
epithermal as well as fast neutrons starting from the same mother isotope
similar it was shown in Zankl1981 . The total neutron numbers were obtained by
fitting the measured neutron spectra with a Maxwellian-like distribution
function $N(E/(\pi E_{\text{{mean}}}))^{1/2}\exp(-E/E_{\text{{mean}}})$ using
the known $E_{\text{mean}}$, where $E$ is the neutron kinetic energy. The
dashed curves in Fig. 6 present such neutron distribution functions for each
scenario.

Figure 6: Neutrons. Number of neutrons in different Giant Dipol Resonance
(GDR) regions measured in the activation sample with 4.3 msr acceptance angle
for different laser-target setups described in the legend. The error bars
represent the accuracy of reaction yield and the width of nuclear resonance
used for spectral reconstruction (see Methods). The mean neutron energies
$E_{\text{mean}}$ are evaluated from the activation method (see methods) and
used to build a Maxwellian-like energy distribution of neutrons (dashed
lines).

In the case of setup 1b (Fig. 6, blue dots), the enhanced neutron production
centered at fast neutrons is explained by a higher effective temperature and
fluence of the MeV-bremsstrahlung (see Fig. 3). In this case, we observe
neutron activations in indium around 14 MeV neutron energy.

In the setup 1a and 2a, using thin foils, neutrons were produced by proton
induced nuclear reactions. Only in the case of setup 1a, we observed a high
number of ${}^{\text{116m}}$In generated in interactions with epithermal/slow
neutrons (see below, methods nuclear diagnostics) and ${}^{112\text{m}}$In
activations at 14 MeV neutron energy. This behavior is a consequence of the
flat slope of the proton spectrum, which leads to a high proton number at
energies greater than 20 MeV responsible for fast neutron production. The
neutron spectrum in the case of 1a can be explained by a combined Maxwellian-
like distribution with an additional exponential part describing the high
energy tail of the neutron spectrum Bertulani2009 ; Gadioli1976 ; Batenkov2007
. Here, the process of precompound excitation in proton induced nuclear
reactions is taking into account, where the step after the nuclear reaction
leads to the probability to emit a nucleon (neutron) immediately before the
compound nucleus state Gruppelaar1986 ; Gadioli1992 ; Koning1999 . Such
probability increases with the proton energy. Therefore the flat slope of the
proton spectrum obtained in the setup case 1a, favors the probability for
precompound excitations. Neutrons emitted from the precompound state have the
most energy but very few in number compared to the statistical evaporated
neutrons from compound state, which means a small contribution to the neutron
energy distribution Gadioli1976 ; Batenkov2007 . The observed reaction yields
in In fit well with GEANT4 simulations (see below, methods).

In addition to the indium isomer activation, we observed neutron capture
reactions in the Au sample (197Au(n,$\gamma$)${}^{198\text{m}}$Au) induced by
epithermal neutrons at 5 eV, where a strong resonance with a cross section of
2.8$\times$104 barn was excited. The highest yield of ${}^{198\text{m}}$Au was
observed for the laser-target setup 1a, where the mean kinetic energy of
neutrons generated in proton driven nuclear reactions was of 0.5–1 MeV. The
stable Au isotope represents a waiting point within the nuclear astrophysical
r-process heavy element nucleosynthesis. Within the experimental accuracy, the
${}^{198\text{m}}$Au yield reached in the present work is in a good agreement
with the theoretical study by Hill et al. Hill2021 .

|  $p$-driven(this work) |  |  $\gamma$-driven(this work) |  | ion-drivenRoth2013 ; Jung2013  |  | ion-drivenKleinschmidt2018  |  |  $\gamma$-drivenPomerantz2014
---|---|---|---|---|---|---|---|---|---
laser intensity $I_{\text{laser}}$ |  $\sim$1019 $\frac{\text{W}}{\text{cm}^{2}}$ |  |  $\sim$1019 $\frac{\text{W}}{\text{cm}^{2}}$ |  | 5$\times$1020$\frac{\text{W}}{\text{cm}^{2}}$ |  | 2$\times$1020$\frac{\text{W}}{\text{cm}^{2}}$ |  | 2$\times$1020$\frac{\text{W}}{\text{cm}^{2}}$
focused energy $E_{\text{laser}}$ | 20 J |  | 20 J |  | 52 J |  | 60 J |  | 20J – 30J
target system | CHO foam |  | CHO foam |  | CD2 foil |  | CD2 foil |  | CH foil
neutron production | (p,$xn$) |  | ($\gamma$,$xn$) |  | ($d$,$n$) |  | ($d$,$n$) |  | ($\gamma$,$xn$)
primaries ($>$10 MeV) |  $\sim$3$\times$1011, proton |  | 3$\times$1011, $e^{-}$ |  |  $>$1011, $d$ |  | N/A, $d$ |  | N/A, $e^{-}$
laser-primary conversion eff. | – |  | 10 % |  | 0.5 % |  | N/A |  | N/A
laser-$\gamma$ conversion eff. | – |  | 1.4 % ($>$10 MeV) |  | – |  | – |  | N/A
total neutron number | 6.2$\times$1010 |  | 1.4$\times$1010 |  | 7.2$\times$109 |  | 6.5$\times$1010 |  | 1.2$\times$109
neutron direction | isotropic |  | isotropic |  | 16 % directed |  | 10 % directed |  | isotropic
mean neutron energy | 500 keV – 1 MeV |  | 2 MeV |  |  $>$10 MeV directed |  |  $>$10 MeV directed |  |  $\sim$1 MeV
|  |  |  |  | 2–4 MeV isotropic |  | 2–4 MeV isotropic |  |
laser-neutron conversion eff. | 0.05 % |  | 0.02 % |  | 0.01 % |  | 0.07 % |  | 0.001 %
neutrons per laser energy | 3.1$\times$109 n/J |  | 7$\times$108 n/J |  | 1.3$\times$108 n/J |  | 1.07$\times$109 n/J |  | 6$\times$107 n/J
Table 1: Conversion efficiencies. Results from presented work in case of
$\gamma$-neutron production and proton-driven neutron generation are shown in
comparison with previous experiments, where records of neutron generation via
laser accelerated deuterons interacting with beryllium catcher Roth2013 ;
Jung2013 ; Kleinschmidt2018  as well as via the electron acceleration to
bremsstrahlung to neutron scheme Pomerantz2014  were reported.

Summarizing the results, we suggest an universal approach for a strongly
enhanced laser-based generation of ultra-high neutron fluence triggered by
gammas and/or protons using foam-foil target systems. Keeping the laser
parameters constant and varying the target systems one can create two neutron
production schemes:

1\. In the case of aerogel-foam targets combined with 10$\mu$m Au foils, the
neutron generation is dominated by proton induced nuclear reactions. The
neutron number evaluated from the proton-driven nuclear reactions in the
sample with 4.3 msr acceptance angle reaches (6.7$\pm$0.8)$\times$109 per
shot, while the mean neutron kinetic energy was of 0.5 – 1 MeV. Triggered by
all accelerated protons propagating in the solid angle of 0.04 sr the neutron
number reaches (6.2$\pm$0.5)$\times$1010 per laser shot.

2\. Using aerogel-foams stacked with high-$Z$ converters (setup 1b), the
neutron generation via photo-nuclear reactions in the sample is caused by high
fluence electrons and $\gamma$’s with energies above 10 MeV. The evaluated
neutron number is of (3.6$\pm$0.6)$\times$108 per shot and a mean neutron
kinetic energy of 2 MeV. The number of neutrons triggered by all initial
electrons and photons above 10 MeV propagating in 0.27 sr and 0.11 sr solid
angles (Fig. 6) reaches (1.4$\pm$0.2)$\times$1010 per laser shot.

The high nuclear reaction yield in the case of aerogel targets and the
corresponding total fluence and temperature of $\gamma$ photons as well as
mean kinetic energy of neutrons is realized by the strong enhancement of the
number and the energy of super-ponderomotive electrons compared to shots onto
foils at ultra-relativistic intensity.

In Tab. 1, the results of the present work are shown in comparison with
previous experiments on laser-driven neutron sources, where record values were
reported in two independent neutron production schemes described by Roth et
al. and Jung et al. Roth2013 ; Jung2013 , Kleinschmidt et al. Kleinschmidt2018
, and by Pomerantz et al. Pomerantz2014 . In the present work, using the
combination of low density foams with thin or thick metallic foils, two
neutron generation schemes were realized: one via pure $\gamma$ induced
nuclear reactions and another one, via proton dominated nuclear reactions,
which results in a high neutron fluence.

In setup 1b, a high current beam of super-ponderomotive electrons boosts the
production of MeV-bremsstrahlung radiation by propagation through a high-$Z$
converter. In this scheme, a record conversion efficiency of laser energy into
energy of more than 10 MeV $\gamma$-rays of (1.4$\pm$0.3) % was achieved. The
measured 1.4$\times$1010 neutrons with 2 MeV mean energy correspond to 0.02 %
laser-to-neutron conversion efficiency. In Pomerantz2014 , super-ponderomotive
electron beams were used to trigger neutron production in Cu-converter. The
relativistic electrons were generated at 5$\times$1020 W/cm2 laser intensity
and 90 J laser energy on target in interaction with underdense CH-plasma. For
comparison with the presented results we assume a similar laser energy in the
focal spot of 20–30 J. The number of registered neutrons and the corresponding
conversion efficiency were more than 10 times lower than in our case (see Tab.
1).

The more efficient neutron production scheme can be realized via proton and
deuteron induced nuclear reactions. In our experiment, using foam+thin foil
(setup 1a), we observed enhance generation of protons in the GDR region above
20 MeV and measured 6.2$\times$1010 neutrons with 0.5–1 MeV mean energy. The
laser-to-neutron conversion efficiency of 0.05 % exceeds results reported in
Roth2013 ; Jung2013  and is close to those obtained at the PHELIX-laser by
Kleinschmidt et al. Kleinschmidt2018  using deuteron induced nuclear
reactions. Note that in all experiments, results were obtained at higher laser
energies and at 10–50 times higher laser intensities than in our case.

An additional advantage of our approach realized via proton beams, is the
generation of a high number of neutrons with moderate kinetic energies, which
can be applied in experiements on laboratory astrophysics. Confirmation of
this is the observation of the high yield of ${}^{198\text{m}}$Au produced in
the neutron capture process.

In summary, the interaction of a sub-ps laser pulse of moderate relativistic
intensity with sub-mm long polymer foams combined with thin and thick high-$Z$
foils results into the highest number of generated neutrons per Joule laser
energy compared to the schemes presented in Tab. 1. This concept promises a
strong boost of neutron production on kJ PW-class laser systems.

##  IV Discussion

In this work, we presented a prospective way for producing well-directed high
intense multi-MeV $\gamma$ beams and ultra-high fluence neutron sources at
moderate relativistic laser intensities of 1019 W/cm2 and 20 J energy within
the focal spot. Our approach is based on the DLA-process in long-scale NCD
plasmas, where the super-ponderomotive electrons with energies up to 100 MeV
are produced. The charge carried by electrons with more than 10 MeV
propagating in the 0.16 sr solid angle reaches 50–100 nC what corresponds to
10% of the conversion efficiency. This high-current well-directed electron
beam is the basis for the generation of proton- and $\gamma$-sources
applicable for the discussed nuclear research.

Ultra-high intense, highly directed MeV $\gamma$ beams with fluences greater
than 1012 ph/sr above 10 MeV photon energy and effective temperatures of 13
MeV were detected. The conversion efficiency from laser energy into above 10
MeV-photons reached (1.4$\pm$0.3) %. This provides a basis for the preparation
of a narrow band $\gamma$ beam, suitable for nuclear photonics applications
Thirolf2014 ; Guenther2018 .

The presented experimental technique allows to choose the generated neutron
behavior by varying the target system. Depending on the application needs, the
laser driven neutron source of ultra-high fast neutrons can be provided via
photo-nuclear reactions with a laser energy conversion efficiency of 0.02 %.
Higher laser to neutron conversion efficiency of 0.05% was achieved via proton
induced neutron generation already at moderate relativistic laser intensities
and ps pulse duration, where the averaged neutron energies are in a suitable
range for nuclear physics applications without moderation processes. The
experimental top yields, realized in the present work at 1019 W/cm2 laser
intensities and 20 J laser energy, reached more than 1010 neutrons per laser
shot in the photon-driven as well as greater than 6$\times$1010 per shot in
the proton-driven scheme. The shape of the neutron spectra evaluated in this
work for (p,n)-reactions is very similar to those simulated in Chen2019  and
discussed for investigation of multiple neutron capture processes in Zr.

GEANT4 Monte Carlo simulations were performed to optimize the neutron
production for PHELIX parameters (1019 W/cm2, $E_{\text{FWHM}}$= 20 J, setup
1b). After placing the Au converter direct to the foam rear-side and
increasing the converter thickness up to 5–7 mm, a record neutron fluence of
2$\times$1011 cm-2 and 1022 cm-2 s-1 flux estimated for $\sim$20 ps neutron
pulse duration was achieved. From Particle-In-Cell (PIC) simulation studies we
expect a more than one order of magnitude higher relativistic electron number
with energies above 7.5 MeV by increasing the laser energy from 20 J to 200 J.
This results in a corresponding enhancement of the neutron fluence and flux.

Current developments in the laser technology toward higher laser pulse
energies and higher repetition rates (one shot per minute) will allow for
investigation of multi neutron capture processes in laboratory conditions.
Parts of the field for astrophysical nucleosynthesis Burbidge1957 ; Cowan1985
, such as the investigation of the r-process important for the heavy element
synthesis in solar or explosive scenarios become accessible. Especially, the
investigation of multi/single neutron capture rates on heavy radioactive or
unstable elements is a current challenge and not experimentally accessible in
conventionally nuclear physics facilities.

One of the upcoming facilities using radioactive heavy ions is the Facility
for Antiproton and Ion Research (FAIR) in Darmstadt, Germany Lederer2016 ;
Ji2016 . The two most limitations for the feasibility of such nuclear
astrophysical studies are: 1. the separation of the heavy ion facilities from
reactor or accelerator based neutron sources, and 2. too low neutron fluxes
reached by conventional neutron sources. A suitable way that allows such
important r-process studies is the combination of laser-driven ultra-high flux
neutron sources with future heavy ion facilities like FAIR. Our prospective
insights on neutron generation in relativistic laser interactions with long-
scale NCD plasmas show a suitable and realistic way to reach conditions for
nuclear astrophysical laboratory science using existing high-energy sub-PW
laser systems as well as kJ PW-class laser facilities.

Figure 7:  Gamma spectrum. Results of the gamma spectroscopy of the activated
samples: (a) and (c) at 5∘ (blue and orange spectra), (b) and (d) 15∘ (red
spectra) for the laser-target setup scenarios. The black spectrum in each
panel represents the detector back ground spectrum. Blue and orange colors are
used for different sequences of activation plates in the stack. The unequal
count rate of the back ground between the panels (a),(c) and (b),(d) is caused
by the differently HPGe detector stations with its own back ground shielding.
Results are shown after subtraction of the detector background. An important
indicator for signal differences between 5∘ and 15∘ is the pulse height of the
annihilation line at 511 keV, because the most activated isotopes are
$\beta^{+}$-emitter. Figure 8:  Cross section. (a) and (b) present the nuclear
reaction cross sections for the observed gamma, proton and neutron induced
reactions. (c) show the measured reaction yields together with simulated by
means of GEANT4. The error bars represent the total error of the reaction
yields, where the main uncertainty is caused by the geometrical detector
efficiency error and the error of the counting statistics. In panel (d) on the
left, the pure neutron induced reaction yields are shown for the laser-target
setups (these numbers are obtained from the total measured yields after
subtraction of yield of the corresponding gamma induced reactions leading to
the same isotope). The key reaction products are used for neutron number
reconstruction.

##  V Methods

###  V.1 Laser and target system

The experiment was performed at the Petawatt High-Energy Laser for heavy Ion
eXperiments (PHELIX) at GSI in Darmstadt, Germany. The Nd:Glas laser amplifier
system delivered a s-polarized beam with a central wavelength of 1053 nm and a
highest main pulse to nanosecond pre-pulse contrast of more than 1011. The
pulse length was (0.75$\pm$0.25) ps. The laser pulse was focused by an off-
axis copper parabolic mirror on the target under $\approx$7∘ to target normal.
To conduct a moderate relativistic intense laser pulse of (1 –
2.5)$\times$1019 W/cm2 a (90$\pm$10) J pulse was focused by a focal length of
150 cm on the target, where the FWHM of the elliptical focal spot size was
(12$\pm$2)$\mu$m$\times$(18$\pm$2)$\mu$m. 22 % of the laser pulse energy is
contained in the FWHM of the focal spot which results in an energy of
(20$\pm$2) J on the target. The high intensity laser pulse of 1021 W/cm2 was
produced via a 180 J pulse focused by a parabolic mirror with a focal length
of 40 cm. The FWHM of the elliptical focal size was
(2.7$\pm$0.2)$\mu$m$\times$(3.2$\pm$0.2)$\mu$m, where the laser pulse energy
within the FWHM was (38$\pm$2) J. The long focal length was used in laser
shots on aerogel-foam target systems and the short focal length was used in
shots on foil targets. To realize a NCD plasma a well-defined long pre-pulse
with 1.5 ns pulse duration irradiated the foam target system by a delay of 2 –
3 ns before the main pulse, where the intensity of the pre-pulse was about
5$\times$1013 W/cm2 and the pulse energy was 1 – 3 J Rosmej2019 . For the
generation of a sub-mm NCD plasma a plastic aerogel target made from
triacetate cellulose, C12H16O8, with a volume density of 2 mg/cm3 and a
thickness between 300 $\mu$m and 400 $\mu$m was used Borisenko2007 . A fully
ionized plasma corresponds to 0.64$\times$1021 cm-3 electron density or 0.64
$n_{\text{cr}}$ ($n_{\text{cr}}=$1021 cm-3). As foil targets, 10 $\mu$m thick
pure metallic foils (Au, Ti) and 1 mm thick pure Au targets were used.

###  V.2 Electron diagnostics

The electron spectrometers were realized using a homogeneous magnetic field of
0.99 T created by two parallel positioned flat neodymium permanent magnets.
Calibrated imaging plates (IP) from BASF Tanaka2005 ; Rusby2015  were used as
detectors. The spectral resolution was optimized by numerical simulations that
consider the measured two dimensional magnetic field distribution and an
entrance slit with a size of 300 $\mu$m (width) $\times$1 mm (height). The
experimental error in the detection of the electrons was not higher than 2%,
which allows for a precise spectral measurement in the electron energy range
between 1.75 MeV to 100 MeV. To increase the signal-to-noise ratio and to
reduce the MeV-bremsstrahlung background, each spectrometer was shielded by a
CuW collimator placed in front of the entrance hole. The spectrometers were
positioned in laser forward direction at a distance of 405 mm at 0∘, 15∘ and
45∘ in the horizontal plane perpendicular to the laser polarization direction.
Furthermore, a stack of three steel cylinders with a thickness each of 3 mm
and a radius of 200 mm were placed in a distance of 230 mm from the laser
interaction target. Between the steel cylinder, IPs were fixed to measure the
angular distribution of the electron beam in horizontal as well as vertical
directions for two different energy ranges above 3 MeV and above 7.5 MeV.

###  V.3 Nuclear diagnostics for MeV bremsstrahlung and neutrons

After each laser shot, the nuclear activated samples were analyzed by a low
back ground $\gamma$-spectroscopy using 60 % high purity germanium (HPGe)
detector systems to identify the reaction channels of the isotopes of interest
(Fig. 7). A stack of pure (more than 99%) elemental Au, Ta, Cr and In plates
was used as an activation detector system, where their natural isotope
abundance provide different nuclear reaction thresholds (see Fig. 8a). The
reaction yield of the activated isotopes in the sample is shown in Fig. 8c,d.
In the activation samples, multi-neutron disintegration reactions were
observed, triggered by MeV-photons and particles (Fig. 8a,b). The size of each
plate was 15 mm$\times$15 mm$\times$1 mm, while the thickness of the indium
foil was of 0.25 mm. The activation detector stacks were placed in a distance
of 230 mm at two different angular positions with respect to the laser axis
(5∘ and 15∘). The main uncertainty in determination of the reaction yield is
caused by the geometrical detector efficiency error, where the geometry and
self absorption processes of $\gamma$ decay lines within the activation
samples are considered by the error of the counting statistics of the HPGe
detector. The nuclear reaction yield of each $i$-th reaction $Y_{\text{i}}$ is
the convolution of the initial photon or particle spectrum
$N_{\gamma\text{,p}}(E^{\prime})$ with the energy dependent reaction cross
section $\sigma_{\text{i}}(E^{\prime})$ (see Fig. 8a,b):
$Y_{\text{i}}=N_{\text{T}}\int_{E_{\text{th}}}^{\infty}N_{\gamma\text{,p}}(E^{\prime})\sigma_{\text{i}}(E^{\prime})dE^{\prime}$,
where $N_{\text{T}}$ is the surface atomic number density of each sample. The
photon or particle spectrum was deconvolved by weighting the reaction yield
with the reaction cross section within each energy bin $dE^{\prime}$ of the
reaction $i$ with the reaction threshold $E_{\text{th}}$. The error in the
determination of the initial photon or particle spectrum is the combination of
the error of the reaction yield and the width of the corresponding nuclear
resonance of the nuclear reaction (Fig. 8a,b). All uncertainties are shown as
the error bars of the experimental results presented in the corresponding
diagrams in this work. The nuclear reaction cross sections were taken from the
EXFOR data base EXFOR  and evaluated by the Talys nuclear reaction code
Koning2012 .

In the following, the indium activation method is described for the neutron
fluence measurement. Reaction channels induced by MeV-photons leading to the
same In isotopes with respect to the neutron induced reactions were also
considered. The contribution of these reactions is determined by weighting the
experimental MeV-bremsstrahlung spectrum (see Fig. 3) with the cross sections
(Fig. 8a,b) of the corresponding reaction channels:
113In($\gamma$,$\gamma$’)${}^{113\text{m}}$In,
113In($\gamma$,n)${}^{112\text{m}}$In,
115In($\gamma$,$\gamma$’)${}^{115\text{m}}$In,
115In($\gamma$,n)${}^{114\text{m}}$In, 115In($\gamma$,2n)${}^{113\text{m}}$In,
115In($\gamma$,3n)${}^{112\text{m}}$In. The total $\gamma$ induced reaction
yields of the activated indium isotopes are shown in the right panel of Fig.
8d. For the setups with foam target systems (1a, 1b) the contribution of the
$\gamma$ induced indium isotopes ${}^{113\text{m}}$In, ${}^{112\text{m}}$In
and ${}^{114\text{m}}$In are compared to the same neutron-induced isotopes.
However, the $\gamma$ induced contribution into production of
${}^{115\text{m}}$In is more than one order of magnitude lower compared to the
neutron induced contribution. The neutron induced reaction yields shown in the
left panel of Fig. 8d are determined by subtraction of the corresponding
yields of $\gamma$ induced In isotopes from the measured total reaction
yields. It has to be noted that the high value of the ${}^{114\text{m}}$In
yield is reached via the epithermal neutron capture reactions and the fast
neutron scattering processes.

To evaluate a neutron energy distribution, following neutron energy ranges are
considered: 1 eV, 2.5 MeV and 14 MeV. This corresponds to three key reaction
channels taken into account for the reconstruction of the neutron number:
115In(n,$\gamma$)${}^{116\text{m}}$In, 115In(n,n’)${}^{115\text{m}}$In and
113In(n,2n)${}^{112\text{m}}$In. The indium isomers ${}^{113\text{m}}$In from
reactions 113In(n,n’)${}^{113\text{m}}$In,
115In($\gamma$,2n)${}^{113\text{m}}$In and
113In($\gamma$,$\gamma$’)${}^{113\text{m}}$In, are not used: first, because of
the high natural abundance of the stable mother isotope 115In and second,
because of the high fluence of $\gamma$’s in the corresponding energy range,
where the ${}^{113\text{m}}$In is produced via $\gamma$ induced reactions.
Also not used for the reconstruction of neutron numbers is the
${}^{114\text{m}}$In isomer that is produced via the reaction
115In(n,2n)${}^{114\text{m}}$In, because of the activation of
${}^{114\text{m}}$In is: first, dominated by $\gamma$ induced reactions
115In($\gamma$,n)${}^{114\text{m}}$In (high $\gamma$ fluence at 14 MeV, high
abundance of 115In) and second, by the neutron capture reaction
113In(n,$\gamma$)${}^{114\text{m}}$In with a high reaction cross section of
104 barn in the epithermal neutrons.

For setup 1a, the simulated reaction yield is exemplary shown in Fig. 8d
(black stars). The GEANT4 simulation is in a well agreement with the
experimental yields of indium isomers (yellow dots in Fig. 8d). The simulation
considers reactions generated within the sample stack placed at 5∘ and 23 cm
distance from laser interaction point. The ${}^{116\text{m}}$In isomers can be
also generated by neutron scattering processes on environmental materials.
Additional GEANT4 simulations of the background neutron number caused by the
target chamber environment resulted into less than 30% contribution to the
measured indium isomer yields, what is inside the experimental accuracy.

In the present work, the mean neutron kinetic energy is determined by an
advanced isotope relation equation, where the basic idea is taken from
Zankl1981 . Starting from the 115In mother isotope, the daughter isotopes
${}^{116\text{m}}$In activated by thermal/epithermal neutrons and the
${}^{115\text{m}}$In activated by fast neutrons are generated. The resonance,
excited in the reaction channel 115In(n,n’)${}^{115\text{m}}$In is centered in
the fast neutron region and overlaps the cross section region of the reaction
channel 115In(n,$\gamma$)${}^{116\text{m}}$In (Fig. 2 in Zankl1981 ).
Therefore, the cross section ratio of the ${}^{116\text{m}}$In production to
the cross section range of ${}^{115\text{m}}$In production is related to the
isotope yield ratio of ${}^{116\text{m}}$In to ${}^{115\text{m}}$In:
$\frac{\sigma_{{}^{\text{116m}}\text{In}}}{\sigma_{{}^{\text{115m}}\text{In}}}=\frac{Y_{{}^{\text{116m}}\text{In}}}{Y_{{}^{\text{115m}}\text{In}}}$.
The reaction yield of ${}^{116\text{m}}$In and ${}^{115\text{m}}$In are known
from the experiment. Then, the relation equation allows to determine the cross
section ratio and therefore the neutron energy where the ${}^{116\text{m}}$In
isotopes are produced covered by the resonance range for ${}^{115\text{m}}$In
production at ${\sigma_{{}^{\text{115m}}\text{In}}}=$0.35 barn. This
determined cross section range corresponds to the mean kinetic energy
$E_{\text{mean}}$ of the initial neutrons.

##  VI Data availability

The authors declare that the data supporting the findings of this study are
available within the paper.

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##  VIII Acknowledgements

The presented results were obtained in the experiment P176 performed in the
framework of FAIR Phase-0 at the PHELIX laser facility at the GSI
Helmholtzzentrum für Schwerionenforschung GmbH in Darmstadt, Germany. We thank
the PHELIX team for the support. The research of N.E.A was supported by The
Ministry of Science and Higher Education of the Russian Federation (Agreement
with Joint Institute for High Temperatures RAS No 075-15-2020-785 dated
September 23, 2020).

##  IX Author contributions

M.M.G. was writing the manuscript and conceived the scheme. M.M.G and P.T.
evaluated the results from the nuclear diagnostics. M.M.G., and M.G. performed
the illustration of the results. A.S. and A.K. were performing GEANT4
simulations. A.P. and N.E.A. provided theoretical support. N.G.B. fabricated
the aerogel-foam targets and provided related target information. O.N.R., S.Z.
and M.G. evaluated the results from the electron diagnostics and performed
illustrations. The experimental studies were performed by M.M.G., O.N.R.,
P.T., M.G. and S.Z.. All authors discussed the results, commented on the
manuscript, and agreed on the contents.

##  X Competing interests

The authors declare no competing interests.