# A Platform for Ultra-fast Proton Probing of Matter in Extreme Conditions

Luca Volpe  Alberto Perez  Teresa Cebriano RamírezAddress of corresp
<EMAIL_ADDRESS>Carlos Sánchez Sánchez  Sofia Malko  Alessandro Curcio
Berkhahoum Kebladj  Samia Khetari  Centro de Laseres Pulsados, Building M5,
Science Park, Calle Adaja 8, 37185 Villamayor, Salamanca, Spain  ETSI
Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid,
Spain  Department of Fundamental Physics, University of Salamanca, 37008
Salamanca, Spain  Princeton Plasma Physics Laboratory, 100 Stellarator Road,
Princeton, NJ 08536, USA.

###### Abstract

Recent developments of Ultra Short and Intense laser system paved the way for
the generation of short and brilliant proton sources that can be used to study
plasmas at extreme conditions in the context of High Energy Density Physics.
Energy selection, focusing and transport of such sources is still a challenge
that is not completely solved. Here we present a novel and simple design for a
isochrone magnet capable of angular and energy selection of proton sources by
reducing the temporal spread. The isochrone selector is demanded for studying
proton stopping power in Warm Dense Matter close to the Bragg peak (proton
energy below 1 MeV) where the reduced investigated masses imply a short plasma
stagnation time ($<$ 100 ps). The proposed selector can also be used at higher
proton energy by pushing the final time spread at the level of few ps.
Analytical estimations and Monte Carlo simulations are presented to validate
the proposed configurations.

###### keywords:

Ions, protons, laser-plasma charged particle acceleration, magnetic transport,
WDM, HED

##  1 Introduction

The advent of PW-class CEP laser systems in the last decades broke ground for
the acceleration of ultra-short and brilliant proton bunches. The latter have
been used to probe matter in extreme conditions such as the Warm Dense Matter
generated via isochoric heating (via laser, X-ray, electrons and ions) which
is relevant for of High Energy Density Physics, laboratory Astrophysics,
Planetology and, especially, for Laser fusion 10, 32, 18, 24. High energy
density (HED) plasmas, including Warm Dense Matter (WDM), are important and
fascinating states of matter that can be now easily generated by lasers or by
laser-driven secondary sources such as X-rays 31, electrons or ions 21. The
sub-ps dynamics of such states is important to understand the mechanism of the
electron-electron and electron-ion thermalisation far from the equilibrium.
Laser-Driven Proton Sources (LDPS) can be used to study Ion Stopping Power
(ISP) in HED and WDM as well as to be used for radiography 15, 27 and/or
deflectometry 14. Ultra-short Laser-driven proton bunches are becoming
relevant also in the context of biology and medical physics where the effects
of fast dose deposition in tissues is now under investigation. In addition,
recently emerging experimental stations offer combinations of intense solid-
state lasers with the 4th generation of X-ray Free Electron Lasers 30 sources,
that are capable to provide highly brilliant photon sources in the keV region.
A new generation of experiments is now possible, where fast-heated plasma
states can be investigated by using fast laser-driven electron or proton
sources. Highly brilliant proton beams are routinely generated via Target
Normal Sheath Acceleration (TNSA) 29 mechanism with exponential energy
spectrum ranging up to few tens of MeV’s and duration of the order of few ps.
Numerical simulations suggest the possibility of improvements in the quality
of such sources in terms of maximum energy and energy spread. This can be
accomplished by increasing the laser intensity as well as improving the pulse
temporal contrast and the beam spatial quality. Conventional accelerators can
provide proton sources with high brightness, low energy spread and very small
divergence. However, LDPS are still relevant due to some peculiar
characteristics like: i) ultra-short pulse duration ($\sim$ ps) ii) High
Repetition Rate (HRR) capability (up to 1 KHz) and iii) Small size i.e Table
Top Machines (Few meters dimension and low cost). Indeed, LDPS are extremely
short 6, being able to provide an almost instantaneous ($<$ ps) dose, not
comparable with other proton sources. Such dose can be comparable with
standard doses in HRR operation. Finally, the reduced dimension of laser
systems compared with standard accelerators are improving day by day. Indeed,
laser companies are now able to provide compact hundreds of TW scale laser
systems occupying a few meters area. These systems can work at 10s of shots
per second and technological development is promisingly increasing the HRR up
to 100 shots per second. Smaller laser systems can reach tens of TW with
higher repetition rates up to 1 kHz, see for example the Silos system of ELI-
ALPS (7 fs, 30 mJ, 1 KHz). LDPS can be used to investigate plasma states at
unprecedented short time scales. Reducing the pulse duration of the “driver”
below the hydrodynamic time scale of matter (i.e. below 1 nanosecond) permits
to heat the matter isochorically; at the same time acceleration of short
charged particle beams 1 with lasers offers the possibility to perform “pump
and probe” experiments in which the same laser is used to generate the plasma
sample and accelerate the proton probe. However, many of these experiments
require quasi monoenergetic and short proton pulses while TNSA mechanism
generates proton beams with a broadband energy spectrum. Therefore additional
beam manipulations, such as energy selection or spatial focusing is needed.
Energy selection and beam collimation can be done by using special
configuration of permanent magnets: dipoles, quadrupoles, etc. Unfortunately,
such manipulation has a cost in terms of final proton pulse duration that
increase proportionally to the size of the magnetic device. In this line of
research several developments are already underway. The most relevant examples
are ELI-MAIA ion transport system at Eli beamline in Czech Republic 18, 5 and
the pair of pulsed solenoids established at Draco system at HZDR in Dresden
Germany 13. Other smaller-size systems were also developed for dedicated
experiments 4, 26. All the above-mentioned approaches can provide MeV-energy
proton beams with time duration of the order of $\mu$\- seconds or in the best
case can go down to hundreds of ns. For several applications this is not
representing a limitation. However, as stated before, the new opened
experimental possibilities, by using $\mu$m-size and ps-time plasmas, require
shorter proton/ion bunches down to few picoseconds and, for biological
applications, is interesting to go even further down to sub-picosecond time
duration to investigate coherent absorption processes. The ion time spread due
to transportation is more important for proton energies below the MeV level,
for example a proton beam with central energy of 1 MeV and energy spread of
100 keV increase the temporal length at an approximated rate of 70 ps/cm.
Recently, at the Centro de Laseres Pulsados (CLPU) an experimental campaign
has been conducted to measure proton stopping power in Warm Dense Plasmas. In
such experiment the Ti:sa 30 fs 200 TW systems at CLPU was used to both
generate the WDM and the proton beam whose energy loss was measured after
passing through the laser-driven WDM sample 16. The novel experimental
approach has improved time and energy resolution guiding new experimental
activities focused on micrometric size and picosecond and sub-picosecond time
plasmas with implications in several interesting fields of science among which
Inertial Confinement Fusion (ICF) 10, 32 and ion-driven fast ignition 24, 7. A
precise knowledge of ion stopping in WDM is also essential for understanding
proton transport in matter 12 and proton isochoric heating 21, 19. Such
experiments have applications for studying the structure 17, the equation-of-
state 22 and the transport properties of dense plasmas 8, like conductivity
22, 20 and thermal equilibrium 28 of WDM samples. Other applications include
plasma diagnostics using ion beams 15, 27. Developing ultra-short proton
pulses was mainly driven from Ion stopping power in WDM experiments even if
there are at least two more important applications of such pulses. The first
is Proton Fast Ignition approach to Inertial fusion 24 where the requested
duration of the proton beams falls below 20 ps. This can be reached only by
developing a complex time-compressor transport line 9. The second application
is related to the use of short proton pulses in the context of the “fast dose
deposition” 23 approach to cancer therapy in Medicine, that is an emerging
field of investigation. In the above mentioned experiment 16 a compact
magnetic selector 2 has been used to manipulate the energy-space properties of
a laser-driven sources sent to a laser generated WDM sample. The final
temporal duration of the selected proton beam was about 400 ps (@ the WDM
sample) a bit longer than the characteristic WDM stagnation time with the
central energy of the proton beam fixed to 500 keV $\pm$ 25 keV. The magnetic
device was 6 cm long and the total distance between proton source and the WDM
sample was around 8 cm. The compact magnetic selector was made by a dipole
magnet with a system of pinholes and slits at the entrance to control the
proton divergence, and at the exit to control the energy band that could be
reduced at the expense of the total number of selected protons. A new and
optimised version of the selector can help to reduce the temporal stretch but
going below 100 ps requires a different approach.

Here, we proposed a simple way to perform a consistent reduction of the proton
pulse duration, by using an isochrone ion selector, down to few 10s of ps @
energies $<$ 1 MeV. The selected proton pulses could be used for experiments
that require high temporal and spectral resolution, like ultrashort pump-probe
experiments and proton isochoric heating. Another relevant application is
certainly proton/ion stopping power studies in WDM with an unprecedent energy
resolution very close to the Bragg peak region (region where the proton energy
is comparable with the thermal energy of the WDM electrons) where most of the
theoretical predictions are in contradiction. Ultrashort LDPS will open a new
horizon for applications in the field of biology and medical physics for the
study of fast dose deposition in proton therapy.

##  2 Design

We assume here that proton sources are generated with the conventional TNSA
mechanism with a characteristic broadband energy spectrum and divergence. The
magnetic selector Fig. 1 is composed by three main parts: i) a first
collimator, ii) an isochrone magnetic transporter and iii) a final energy
selector. The collimator is composed by two slits (Fig. 1, lower inset) placed
close to the proton source. It can discriminate protons according to their
divergence. Although introducing losses, this stage reduces the angular
dispersion of the proton pulse, which in turn reduces the temporal dispersion
at the exit of the magnet. The collimated protons enter into the magnetic
transporter made by a dipole (upper left figure), where a constant magnetic
field disperses different proton energies, while maintaining the temporal
dispersion. Finally, the energy selector, made by a exchangeable and movable
pinhole, allows only the exit of protons whit certain energies (upper right
inset). The designed magnetic selector permits to obtain a final collimated
proton pulse extremely narrow both in energy and time. According to Fig.1 the
system has four adjustable parameters: the distance between the
slits($d_{slits}$), the angle between the proton pulse and the side of the
magnet ($\theta$), and the position($p_{pinh}$) and radius ($r_{pinh}$) of the
pinhole. The first parameter changes the temporal dispersion of the output
pulse ($\Delta T$), and it is usually set to the minimum. It also changes the
angular dispersion at the exit and is often significantly narrow (1 - 3 mrad).
The last three parameters control the central energy ($E_{c}$) and the energy
dispersion ($\Delta E$) of the output beam, and they are selected according to
experimental requirements.

Figure 1: Scheme of the proposed device. Lower and upper right inset are
zoomed pictured of the slit system and the final pinhole respectively. Angles
$\theta$ and $\varphi$ are complementary.

###  2.1 Temporal selection

The dynamics of a moving charged particle inside a constant magnetic field is
ruled by the Lorentz force $\vec{F}_{L}=q\;(\vec{v}\times\vec{B})$, where $q$
and $\vec{v}$ are the particle charge and velocity respectively, and $\vec{B}$
is the magnetic field. Since Lorentz force is always perpendicular to the
speed, it causes particles to describe circular orbits, being the cyclotron
radius $R_{c}=mv/qB$, where $m$ is the mass of the particle. Considering non
relativistic protons with energy $E_{c}=mv^{2}/2$, the cyclotron radius can be
written as:

$R_{c}=\frac{\sqrt{2m}}{q}\frac{\sqrt{E_{c}}}{B}$ (1)

As a consequence, at a constant field, the radius of the proton trajectories
depends only on the energy of the protons. If the limits of the dipole have
been set as shown in Fig. 1, the total distance that the proton travels inside
the dipole is $D=2\theta R_{c}$, where $\theta$ is the angle between the
proton initial speed and the magnet side. The whole Time of Flight (ToF) of
this part of the trajectory $t_{dipole}$ is:

$t_{dipole}=D/v=\frac{2m}{qB}\theta$ (2)

Notice that it does not depend on the energy of the protons, but it does on
the angle $\theta$. This implies that the only temporal dispersion produced
inside the dipole is caused by the angular dispersion and not by the energy
dispersion. Therefore, if the entrance angle of the protons is limited to
$\theta\pm\alpha$ (as shown in Fig. 1, lower insert), the temporal dispersion
$\Delta t_{\alpha}$ that affects the proton pulse is:

$\Delta t_{\alpha}=\frac{4m}{qB}\alpha$ (3)

To achieve a small temporal dispersion, therefore, a small acceptance angle is
critical, and this is the reason why the slits system before the dipole is
necessary. However, this system requires that protons travel some distance in
free space, with increased temporal dispersion due to the differences in
kinetic energies. The distance between the source and the first slit
($d_{source}$) is meant to be as close as practically possible, while the
distance between the slits depends on the needed acceptance angle:

$d_{slits}=\frac{h}{\tan(\alpha)}$ (4)

The time dispersion caused by this First Flight ($\Delta t_{\text{ff}}$),
assuming a divergence angle $\alpha$ very small, is:

$\displaystyle\Delta t_{\text{ff}}=$
$\displaystyle(d_{slits}(\alpha)+d_{source})\sqrt{\frac{m}{2}}\times$ (5)
$\displaystyle\times$ $\displaystyle\left[\frac{1}{\sqrt{E_{c}-\Delta
E})}-\frac{1}{\sqrt{E_{c}+\Delta E})}\right]$

Those two effects (time dispersion due to angular dispersion $\Delta
t_{\alpha}$ and due to first flight $\Delta t_{\text{ff}}$) have opposite
dependencies on the acceptance angle. Maintaining the same central energy and
energy dispersion, it is possible to change the acceptance angle $\alpha$ by
changing the distance between slits $d_{slits}$, but increasing the acceptance
angle reduces the temporal dispersion of the first flight and increases the
dispersion due to the angular dispersion, and viceversa. The total temporal
dispersion due to both combined effects can be described as follow:

$\Delta t(\alpha,E_{c},\Delta E)=\sqrt{\Delta t_{\text{ff}}^{2}+\Delta
t_{\alpha}^{2}}$ (6)

###  2.2 Energy selection

To control the spectrum of the exiting protons ($E_{c}\pm\Delta E$), a final
pinhole is placed. The expression of the pinholes position ($p_{pinh}$) and
radius ($r_{pinh}$) are:

$\displaystyle p_{pinh}$
$\displaystyle=k_{E}\,\sin(\theta)\left(\sqrt{E_{c}+\Delta
E}+\sqrt{E_{c}-\Delta E}\right)$ (7) $\displaystyle r_{pinh}$
$\displaystyle=k_{E}\,\sin(\theta)\left(\sqrt{E_{c}+\Delta
E}-\sqrt{E_{c}-\Delta E}\right)$ (8)

where $k_{E}=\sqrt{2m}/(qB)$. It is also useful to express the same equations
with the central energy and energy dispersion as a function of the position
and radius of the pinhole so they can be checked during the experiment.

$E_{c}=\frac{(p_{pinh}^{2}+r_{pinh}^{2})}{4k_{E}^{2}\sin^{2}(\theta)}\;;\;\;\;\Delta
E=\frac{p_{pinh}\cdot r_{pinh}}{2k_{E}^{2}\sin^{2}(\theta)}$ (9)

Another useful expression is the maximum proton energy that a dipole can
operate as a function of the length of the dipole $L$ and the angle $\theta$:

$\displaystyle E_{MAX}=\frac{L^{2}}{4k_{E}^{2}\sin^{2}(\theta)}$ (10)
$\displaystyle E_{MAX}[MeV]\approx\frac{1.2\times
10^{-5}}{\sin^{2}(\theta)}\;B[T]\;L^{2}[mm]$ (11)

Considering a typical case, a dipole of L = 20 cm, $B$ = 1 T, and $\theta$ =
30∘, the maximum energy that this device can operates is 1.9 MeV. In theory,
any dipole can operate at any energy if the angle $\theta$ is small enough,
regardless of its length. In practice, a tiny angle makes the dipole harder to
align, so a compromise is recommended. Assuming a fixed central energy and
energy dispersion, it is possible to numerically calculate the acceptance
angle that achieves the smallest temporal dispersion, which typically lies
between 0.5 and 2 mrad. The total temporal dispersion achieved on these
configurations is also illustrated in Fig. 2. We can see that the time
dispersion decrease as the relation $\Delta E/E_{c}$ also decreases. To better
evaluate the selector performance we can compare the time spread of a proton
beam with the same parameters as in 2. Targeting energy of 500 keV $\pm$ 25
keV, and assuming a distance between the source and the first slit
$d_{source}$ of 3 mm, we can obtain a proton pulse, at the exit of the
selector, with a final duration of around 70 ps, which is $\sim$ 6 times
smaller than the one obtained with the previous selector ($\simeq$ 400 ps).
The graph in Fig.2 shows that, for 500 keV central energy, an even shorter
proton pulses ($\sim$ 50 ps) can be obtained by reducing the energy bandwidth
down to 15 keV (this is possible by reducing the number of selected particle
or by reducing the proton source size). Another operation regime, i.e. with
sub-picosecond proton pulses ($<$ 1 ps), can also be obtained by considering
higher proton energy of 15 MeV with few keVs of energy spread, this will open
new possibilities related to fast proton imaging and/or deflectometry.
According to eq.11, in order reach 15 MeV of selected energy the selector
configuration must be adapted by enlarging the total size L up to 300 mm and
by reducing the angle with respect the normal $\theta=15^{\circ}$.

Figure 2: Time dispersion as a function of the energy dispersion.for different
central energies

###  2.3 Transmission coefficient

Energy Selection is directly dependent on the spatial extension of the used
pinholes which imply a strong reduction of the total number of the selected
protons. To estimate the transmission coefficient we have to take into account
three different elements: i) the source size, ii) the solid angle of
acceptance, and the central energy. Firstly, we know that the source is not
exactly punctual, but a disc with a radius of few hundreds of um (here we use
150 $\mu m$ approximately 16). This dimension is significantly larger than the
slits aperture typically used in this device ($\sim 10\;\mu m$), so it is
necessary to count what portion of the disc actually has some fire angle. To
do this we assume that the emission is homogeneous on all the disc surfaces.
Secondly, the combination of the slits system and final pinhole only leaves a
narrow solid angle of acceptance for the protons, which only allows the
protons with very small divergence to pass. It is possible to geometrically
calculate this solid angle for a given energy, and later, integrate which
proportion of the protons are emitted in this angle. Finally, this acceptance
solid angle is different from energy to energy, being zero far from the
central energy and maximum at it. To better quantify the transmission
coefficient of the device in our range of interest (i.e. $E_{c}\pm\Delta E$),
we have to integrate it over all that range.

The calculated transmission coefficient is represented as a function of energy
dispersion and for different central energies in Fig. 3. Here we can see that,
once more, the transmission decrease with the relation $\Delta E/E_{c}$. It is
then essential to make a compromise at the time to design an application,
because configuring the device in order to achieve a narrow energy bandwidth
implies that the proton flux will be reduced.

Figure 3: Time dispersion as a function of the energy dispersion.for different
central energies Figure 4: 2D results proton particle transport in the
isochrone magnetic selector

##  3 Simulations

In order to probe those concepts, a simulation has been carried out by
tracking individual protons along its path through the device using a
dedicated code. The code has been made using Python programming language and
Numpy, Scipy, Numba and Matplotlib libraries. The method used consist of
particle tracking of individual protons along its trajectory by using the
Lorentz force and Runge-Kutta method.

For the simulation, the distance between the source and the first slit is
$d_{source}$ = 2 mm, the distance between slits has been set at 7.6 mm, and
the slit space is 8 $\mu m$. The dipole has a magnetic field of B = 1 T, the
angle between the dipole side and the proton beam $\theta$ has been set at
63∘, and the dipole has a length of 15 cm. The pinhole has been placed at a
distance of $p_{pinh}$ = 9.14 cm, and has a radius of 2.3 mm, aimed to the
energy range of 1 MeV $\pm$ 50 keV. The input proton beam has the typical TNSA
angular and energetic distribution of a laser pulse hitting an Al foil target.
The interaction area has been estimated as a 75 $\mu m$ radius circular source
and 30∘ FWHM angular distribution. Only protons with energy of 500 $\pm$ 50
keV has been simulated to save resources.

The results of the simulation can bee seen in Fig. 4, where it is show the
trajectory of the simulated proton beam (left), the comparison between the
energy dispersion and temporal dispersion at the source and at the end (right
upper and right lower respectively). As we can see, it is possible to obtain
extremely monochromatic and narrow pulses at the exit of the device.

Figure 5: VisedX intial conditions for the MCNP6 simulation. The A zone is the
output region of the proton beam and the inset is the proton energy
distribution

By way of comparison , trajectories, spot and final energy distribution have
been simulated by MCNP6 software (based on Monte Carlo method) which includes
routines for tracking charged particles through magnetic fields by direct
integration methods 3.

The following parameters have been considered to describe the geometrical set
up for MCNP6 simulations: the dimensions of the rectangular cell that forms
the dipole are 20 cm length (Z dimension), 5 cm width (X dimension) and 0.6 cm
height (Y dimension). The magnet is tilted 30 degrees with respect to the
vertical axis (clockwise sense). Furthermore, the energy of the proton source
has been set within the range 500 $\pm$ 25 keV ( Fig.5 inset, represents the
proton initial distribution as a function of the energy). Spatially the
initial beam represents a Dirac delta without width. In addition, no
divergence was considered for these simulations.

The proton source was placed at 4.5 mm from the closest point of the magnet
and the magnetic B-field modulus has been established as 1 Tesla, with
direction normal to the magnet surface. The results of the trajectories are
obtained by means of FMESH superimposed MESH tally B type FLUX 25 that allows
to solve the problem over the system geometry.

The results are shown in Fig.6 a) and b) that represent the trajectories as a
function of the energy and the projection of the flux over the magnet surface,
respectively. The lower energy protons find the exit at 9.95 $\pm$ 0.02 cm
from the input point (at 0.4 $\pm$ 0.02 cm from the magnet bottom corner in
the simulation) and the higher energy ones at 10.50 $\pm$ 0.02 cm. These
parameters match with expression (7) that results in 10.23 cm which is
approximately the midpoint between the two values mentioned above.

Other outcome of MCNP6 simulations is the spot shape at the exit of the magnet
in which, the particle distribution at different energies along the z-axis can
be observed (Fig. 7 a)). Figures (7 b) and c)) represent the normalized
projections of the spot over the axes of Fig. 7 a) (profiles). In these
simulations it can be observed the extension of the proton beam in Z, while in
Y dimension remains sharped. Using the expression (8) with the MCNP6 applied
parameters, the value of ($r_{pinh}$) corresponds to 0.26 cm. This value fits
with the half of FWHM in Fig.7 c) (spot profile projection in Z) making
evident the spatial selection of particles as a function of their energy.

(Fig. 7)

Figure 6: a) MCNP6 proton trajectories as a function of the energy. b)
Projection of the proton flux over the magnet surface Figure 7: a) Spot at the
exit of the magnet. b) and c) are the vertical and horizontal profiles,
respectively

##  4 Discussion and conclusions

A novel and simple design has been proposed for a isochrone magnetic selector
capable of angular and energy selection for laser-driven proton pulses by
minimizing their temporal duration. The proposed device can finally select
proton beams with central energies of hundreds of keV and tens of keV
bandwidth and transport them up to the sample maintaining the temporal
duration below 100s of ps, which is the required temporal duration to probe
micrometeric size laser-driven Warm Dense Matter. A preliminary parametric
study is presented by comparing the performances with a previous magnetic
selector used in a recent experiment. The comparison shows a consistent and
relevant reduction x6 of the final proton pulse duration. A full Monte Carlo
simulation has been performed by using the MCNP6 code 11 consolidating the
results.

## Acknowledgements

The authors acknowledge the financial support of the Junta de Castilla y León
grant no. CLP263P20.

## References

  * 1 F. Albert, M.E. Couprie, A. Debus, M.C. Downer, J. Faure, A. Flacco, L.A. Gizzi, T. Grismayer, A. Huebl, C. Joshi, M. Labat, W.P. Leemans, A.R. Maier, S.P.D. Mangles, P. Mason, F. Mathieu, P. Muggli, M. Nishiuchi, J. Osterhoff, P.P. Rajeev, U. Schramm, J. Schreiber, A.G.R Thomas, J.L. Vay, M. Vranic, and K. Zeil.  2020 roadmap on plasma accelerators.  New Journal of Physics, 23(3):031101, 2021.
  * 2 J.I. Apiñaniz, S. Malko, R. Fedosejevs, W. Cayzac, X. Vaisseau, D. De Luis, G. Gatti, C McGuffey., M. Bailly-Grandvaux, K. Bhutwala, V. Ospina-Bohórquez, J. Balboa, J. J. Santos, D. Batani, F.N. Beg, L. Roso, J.A. Pérez-Hernández, and L. Volpe.  A quasi-monoenergetic short time duration compact proton source for probing high energy density states of matter.  Sci. rep, 11, 2020.
  * 3 J. Bull.  Magnetic field tracking features in mcnp6.  Technical report, LA-UR-11-00872, Los Alamos National Laboratory, 2011\.
  * 4 S. Chen, M. Gauthier, D.P. Higginson, S. Dorard, F. Mangia, R. Riquier, S. Atzeni, J.R. Marquès, and J. Fuchs.  Monochromatic short pulse laser produced ion beam using a compact passive magnetic device.  Review of Scientific Instruments, 85:043504–043504, 04 2014.
  * 5 G.A.P Cirrone, G. Petringa, R. Catalano, F. Schillaci F, L. Allegra, A. Amato, R. Avolio, M. Costa, G. Cuttone, A. Fajstavr, G. Gallo, L. Giuffrida, M. Guarrera, G. Korn, G. Larosa, R. Leanza, E. Lo Vecchio, G. Messina, G. Milluzzo, V. Olsovcova, S. Pulvirenti, J. Pipek, F. Romano, D. Rizzo, A.D. Russo, S. Salamone, V. Scuderi, A. Velyhan, S. Vinciguerra, M. Zakova, E. Zappalà, and D. Margarone.  ELIMED-ELIMAIA: The first open user irradiation beamline for laser-plasma-accelerated ion beams.  Frontiers in Physics, 8, 2020.
  * 6 B. Dromey, M. Coughlan, L. Senje, M. Taylor, S. Kuschel, B. Villagomez-Bernabe, R. Stefanuik, G. Nersisyan, L. Stella, J. Kohanoff, M. Borghesi, F. Currell, D. Riley, D. Jung, C.G. Wahlström, C.L.S. Lewis, and M. Zepf.  Picosecond metrology of laser-driven proton bursts.  Nature Communications, 7:10642, 2016.
  * 7 J.C. Fernández, B.J. Albright, F.N. Beg, M.E. Foord, B.M. Hegelich, J.J. Honrubia, M. Roth, R.B. Stephens, and L. Yin.  Fast ignition with laser-driven proton and ion beams.  Nuclear Fusion, 54(5):054006, 2014.
  * 8 P.E. Grabowski, S.B. Hansen, M.S. Murillo, L.G. Stanton, F.R. Graziani, A.B. Zylstra, S.D. Baalrud, P. Arnault, A.D. Baczewski, L.X. Benedict, C. Blancard, O. Čertík, J. Clérouin, L.A. Collins, S. Copeland, A.A. Correa, J. Dai, J. Daligault, M.P. Desjarlais, M.W.C. Dharma-wardana, G. Faussurier, J. Haack, T. Haxhimali, A. Hayes-Sterbenz, Y. Hou, S.X. Hu, D. Jensen, G. Jungman, G. Kagan, D. Kang, J.D. Kress, Q. Ma, M. Marciante, E. Meyer, R.E. Rudd, D. Saumon, L. Shulenburger, R.L. Singleton, T. Sjostrom, L.J. Stanek, C.E. Starrett, C. Ticknor, S. Valaitis, J. Venzke, and A. White.  Review of the first charged-particle transport coefficient comparison workshop.  High Energy Density Physics, 37:100905, 2020.
  * 9 A. He, F. Willeke, L. H. Yu, L. Yang, T. Shaftan, G. Wang, Y. Li, Y. Hidaka, and J. Qiang.  Design of low energy bunch compressors with space charge effects.  Phys. Rev. ST Accel. Beams, 18:014201, 2015.
  * 10 O.A. Hurricane, P.T. Springer, P.K. Patel, D.A. Callahan, K. Baker, D.T. Casey, L. Divol, T. Döppner, D. E. Hinkel, M. Hohenberger, L.F. Berzak Hopkins, C. Jarrott, A. Kritcher, S. Le Pape, S. Maclaren, L. Masse, A. Pak, J. Ralph, C. Thomas, P. Volegov, and A. Zylstra.  Approaching a burning plasma on the NIF.  Physics of Plasmas, 26(5):052704, 2019.
  * 11 C.J. Josey, A.R. Clark, J.A. Kulesza, E.J. Pearson, and M.E. Rising.  MCNP® Code Version 6.3.0 Verification & Validation Testing.  Technical Report LA-UR-22-32951, Rev. 1, Los Alamos National Laboratory, Los Alamos, NM, USA, 2022.
  * 12 J. Kim, B. Qiao, C. McGuffey, M. S. Wei, P. E. Grabowski, and F. N. Beg.  Self-consistent simulation of transport and energy deposition of intense laser-accelerated proton beams in solid-density matter.  Phys. Rev. Lett., 115:054801, 2015.
  * 13 F. Kroll, F.E. Brack, C. Bernert, S. Bock, E. Bodenstein, K. Brüchner, T. Cowan, L. Gaus, R. Gebhardt, U. Helbig, L. Karsch, T. Kluge, S. Kraft, M. Krause, E. Lessmann, U. Masood, S. Meister, J. Metzkes-Ng, A. Nossula, and E. Beyreuther.  Tumour irradiation in mice with a laser-accelerated proton beam.  Nature Physics, 18:316–322, 2022.
  * 14 C. K. Li, F. H. Séguin, J. R. Rygg, J. A. Frenje, M. Manuel, R. D. Petrasso, R. Betti, J. Delettrez, J. P. Knauer, F. Marshall, D. D. Meyerhofer, D. Shvarts, V. A. Smalyuk, C. Stoeckl, O. L. Landen, R. P. J. Town, C. A. Back, and J. D. Kilkenny.  Monoenergetic-proton-radiography measurements of implosion dynamics in direct-drive inertial-confinement fusion.  Phys. Rev. Lett., 100:225001, 2008.
  * 15 A. J. Mackinnon, P. K. Patel, M. Borghesi, R. C. Clarke, R. R. Freeman, H. Habara, S. P. Hatchett, D. Hey, D. G. Hicks, S. Kar, M. H. Key, J. A. King, K. Lancaster, D. Neely, A. Nikkro, P. A. Norreys, M. M. Notley, T. W. Phillips, L. Romagnani, R. A. Snavely, R. B. Stephens, and R. P. J. Town.  Proton radiography of a laser-driven implosion.  Phys. Rev. Lett., 97:045001, 2006.
  * 16 S. Malko, W. Cayzac, V. Ospina-Bohórquez, K. Bhutwala, M. Bailly-Grandvaux, C. McGuffey, R. Fedosejevs, X. Vaisseau, An. Tauschwitz, J.I.Apiñaniz, D. De Luis Blanco, G. Gatti, M. Huault, J.A. Perez Hernandez, S.X. Hu, A.J. White, L.A. Collins, K. Nichols, P. Neumayer, G. Faussurier, J. Vorberger, G. Prestopino, C. Verona, J.J. Santos, D. Batani, F.N. Beg, L. Roso, and L. Volpe.  Proton stopping measurements at low velocity in warm dense carbon.  Nature Communications, 13:2893, 2022.
  * 17 A. Mančić, A. Lévy, M. Harmand, M. Nakatsutsumi, P. Antici, P. Audebert, P. Combis, S. Fourmaux, S. Mazevet, O. Peyrusse, V. Recoules, P. Renaudin, J. Robiche, F. Dorchies, and J. Fuchs.  Picosecond short-range disordering in isochorically heated aluminum at solid density.  Phys. Rev. Lett., 104:035002, Jan 2010.
  * 18 D. Margarone, G. A. P. Cirrone, G. Cuttone, A. Amico, L. Andò, M. Borghesi, S.V. Bulanov, S. Stepan, D. Chatain, A. Fajstavr, L. Giuffrida, F. Grepl, S. Kar, J. Krasa, D. Kramer, G. Larosa, R. Leanza, T. Levato, M. Maggiore, L. Manti, G. Milluzzo, B. Odlozilik, V. Olsovcova, J.P. Perin, J. Pipek, J. Psikal, G. Petringa, J. Ridky, F. Romano, B. Rus, A. Russo, F. Schillaci, V. Scuderi, A. Velyhan, R. Versaci, T. Wiste, M. Zakova Martina, and G. Korn.  ELIMAIA: A laser-driven ion accelerator for multidisciplinary applications.  Quantum Beam Science, 2(2), 2018.
  * 19 C. McGuffey, J. Kim, M. S. Wei, P. M. Nilson, S. N. Chen, J. Fuchs, P. Fitzsimmons, M.E. Foord, D. Mariscal, H.S. McLean, P.K. Patel, R.B. Stephens, and F.N. Beg.  Focussing protons from a kilojoule laser for intense beam heating using proximal target structures.  Sci. rep, 10, 2020.
  * 20 A. McKelvey, G. Kemp, P. Sterne, A. Fernandez, R. Shepherd, M. Marinak, A. Link, G. Collins, H. Sio, J. King, R. Freeman, R. Hua, C. McGuffey, J. Kim, F. Beg, and Y. Ping.  Thermal conductivity measurements of proton-heated warm dense aluminum.  Nature Communications, 7:7015, 2017.
  * 21 P. K. Patel, A. J. Mackinnon, M. H. Key, T. E. Cowan, M. E. Foord, M. Allen, D.F. Price, H. Ruhl, P.T. Springer, and R. Stephens.  Isochoric heating of solid-density matter with an ultrafast proton beam.  Phys. Rev. Lett., 91:125004, 2003.
  * 22 Y. Ping, H.D. Whitley, A. McKelvey, G.E. Kemp, P.A. Sterne, R. Shepherd, M. Marinak, R. Hua, F.N. Beg, and J.H. Eggert.  Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating.  Phys. Rev. E, 100:043204, Oct 2019.
  * 23 S. Raschke, S. Spickermann, T. Toncian, M. Swantusch, J. Boeker, U. Giesen, G. Iliakis, O. Willi, and F. Boege.  Ultra-short laser-accelerated proton pulses have similar dna-damaging effectiveness but produce less immediate nitroxidative stress than conventional proton beams.  Sci. rep, 6, 2016.
  * 24 M. Roth, T. E. Cowan, M.H. Key, S.P. Hatchett, C. Brown, W. Fountain, J. Johnson, D.M. Pennington, R.A. Snavely, S.C. Wilks, K. Yasuike, H. Ruhl, F. Pegoraro, S.V. Bulanov, E.M. Campbell, M.D. Perry, and H. Powell.  Fast ignition by intense laser-accelerated proton beams.  Phys. Rev. Lett., 86:436–439, 2001.
  * 25 A.L. Swift, E.A. McKigney, R.C. Schirato, A.P. Robinson, and B.A. Temple.  A verification of MCNP6 FMESH tally capabilities.  2015\.
  * 26 J. Teng, Y.Q. Gu, J. Chen, B. Zhu, B. Zhang, T.K. Zhang, F. Tan, W. Hong, B.H. Zhang, and X.Q. Wang.  Magnetic quadrupoles lens for hot spot proton imaging in inertial confinement fusion.  Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 826:15–20, 2016\.
  * 27 L. Volpe, D. Batani, B. Vauzour, Ph. Nicolai, J.J. Santos, C. Regan, A. Morace, F. Dorchies, C. Fourment, S. Hulin, F. Perez, S. Baton, K. Lancaster, M. Galimberti, R. Heathcote, M. Tolley, Ch. Spindloe, P. Koester, L. Labate, L.A. Gizzi, C. Benedetti, A. Sgattoni, M. Richetta, J. Pasley, F. Beg, S. Chawla, D. P. Higginson, and A.G. MacPhee.  Proton radiography of laser-driven imploding target in cylindrical geometry.  Physics of Plasmas, 18(1):012704, 2011.
  * 28 T.G. White, J. Vorberger, C.R. Brown, B.J. Crowley, Davis P., S.H. Glenzer, J.W. Harris, Le Pape S. Hochhaus, D.C. and, T. Ma, C.D. Murphy, L.K. Neumayer, P. Pattison, S. Richardson, D.O. Gericke, and G. Gregori.  Observation of inhibited electron-ion coupling in strongly heated graphite.  Sci. rep, 2, 2012.
  * 29 S.C. Wilks, A.B. Langdon, T.E. Cowan, M. Roth, M. Singh, S. Hatchett, M.H. Key, D. Pennington, A. MacKinnon, and R.A. Snavely.  Energetic proton generation in ultra-intense laser–solid interactions.  Physics of Plasmas, 8(2):542–549, 2001.
  * 30 U. Zastrau, K. Appel, C. Baehtz, O. Baehr, L. Batchelor, A. Berghäuser, M. Banjafar, E. Brambrink, V. Cerantola, T.E. Cowan, H. Damker, S. Dietrich, S. Di Dio Cafiso, J. Dreyer, H.O. Engel, T. Feldmann, S. Findeisen, M. Foese, D. Fulla-Marsa, S. Göde, M. Hassan, J. Hauser, T. Herrmannsdörfer, H. Höppner, J. Kaa, P. Kaever, K. Knöfel, Z. Konôpková, A. Laso García, H.P. Liermann, J. Mainberger, M. Makita, E.C. Martens, E.E. McBride, D. Möller, M. Nakatsutsumi, A. Pelka, C. Plueckthun, C. Prescher, T.R. Preston, M. Röper, A. Schmidt, W. Seidel, J.P. Schwinkendorf, M.O. Schoelmerich, U. Schramm, A. Schropp, C. Strohm, K. Sukharnikov, P. Talkovski, I. Thorpe, M. Toncian, T. Toncian, L. Wollenweber, S. Yamamoto, and T. Tschentscher.  The High Energy Density Scientific Instrument at the European XFEL.  Journal of Synchrotron Radiation, 28(5):1393–1416, 2021.
  * 31 A. B. Zylstra, J.A. Frenje, P.E. Grabowski, C.K. Li, G.W. Collins, P. Fitzsimmons, S. Glenzer, F. Graziani, S.B. Hansen, S.X Hu, M. Gatu Johnson, P Keiter, H. Reynolds, J.R. Rygg, F. H. Séguin, and R.D. Petrasso R. D.  Measurement of charged-particle stopping in warm dense plasma.  Phys. Rev. Lett., 114:215002, 2015.
  * 32 A.B. Zylstra, O.A. Hurricane, D. A. Callahan, A.L. Kritcher, J.E. Ralph, H. Robey, J.S. Ross, C.V. Young, K.L. Baker, D.T. Casey, T. Döppner, L. Divol, M. Hohenberger, S. Le Pape, A. Pak, P. K. Patel, R. Tommasini, S. Ali, P. Amendt, L.J. Atherton, B. Bachmann, D.S. Bailey, L.R. Benedetti, L.F. Berzak Hopkins, R. Betti, S. Bhandarkar, J. Biener, R.M. Bionta, N. Birge, E.J. Bond, D.K. Bradley, T. Braun, T.M. Briggs, M.W. Bruhn, P.M. Celliers, B. Chang, T.D. Chapman, H. Chen, C.M. Choate, A.R. Christopherson, D.S. Clark, J.W. Crippen, E.L. Dewald, T.R. Dittrich, M.J. Edwards, W.A. Farmer, J.E. Field, D.N. Fittinghoff, J.A. Frenje, J.A. Gaffney, M. Gatu Johnson, S.H. Glenzer, G.P. Grim, S.W. Haan, K.D. Hahn, G.N. Hall, B.A. Hammel, J.A. Harte, E.P. Hartouni, J.E. Heebner, V.J. Hernandez, H. W. Herrmann, M.C. Herrmann, D. Hinkel, D.D.M. Ho, J.P. Holder, W.W. Hsing, H.Huang, K.D. Humbird, N. Izumi, L.C. Jarrott, J. Jeet, O.S. Jones, G.D. Kerbel, S.M. Kerr, S.F. Khan, J. Kilkenny, Y.H. Kim, H.G. Kleinrath, V.G. Kleinrath, C. Kong, J.M. Koning, J.J. Kroll, M. Kruse, B. Kustowski, O.L. Landen, S. Langer, D. Larson, N. Lemos, J.D. Lindl, T. Ma, M.J. MacDonald, B.J. MacGowan, A.J. Mackinnon, S.A. Maclaren, A.G. MacPhee, M.M. Marinak, D.A. Mariscal, E. Marley, L.P. Masse, K.D. Meaney, N.B Meezan, P. Michel, M. Millot, J.L. Milovich, J.D. Moody, A.S. Moore, J.W. Morton, T. Murphy, K. Newman, J.M.G. Di Nicola, A. Nikroo, R.C. Nora, M.V. Patel, L. Pelz, J.L. Peterson, Y. Ping, B.B. Pollock, M. Ratledge, N.G. Rice, H.G. Rinderknecht, M.D. Rosen, M. Rubery, J.D. Salmonson, J.D. Sater, S. Schiaffino, D.J. Schlossberg, M.B. Schneider, C.R. Schroeder, H.A. Scott, S.M. Sepke, K. Sequoia, M. Sherlock, S. Shin, V.A. Smalyuk, B.K. Spears, P.T. Springer, M. Stadermann, S. Stoupin, D.J. Strozzi, L.J. Suter, C.A. Thomas, R.P.J. Town, E.R. Tubman, P.L. Volegov, C.R. Weber, K. Widmann, C. Wild, C.H Wilde, B.M. Van Wonterghem, D.T. Woods, B.N. Woodworth, M. Yamaguchi, S.T. Yang, and G.B. Zimmerman.  Burning plasma achieved in inertial fusion.  Nature, 601:542–548, 2022.