Self-Consistent Simulation of Transport and Energy Deposition of Intense Laser-Accelerated Proton Beams in Solid-Density Matter

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

Recent developments in ultrashort and intense laser systems have enabled the generation of short and brilliant proton sources, which are valuable for studying plasmas under extreme conditions in high-energy-density physics. However, developing sensors for the energy selection, focusing, transport, and detection of these sources remains challenging. This work presents a novel and simple design for an isochronous magnetic selector capable of angular and energy selection of proton sources, significantly reducing temporal spread compared to the current state of the art. The isochronous selector separates the beam based on ion energy, making it a potential component in new energy spectrum sensors for ions. Analytical estimations and Monte Carlo simulations validate the proposed configuration. Due to its low temporal spread, this selector is also useful for studying extreme states of matter, such as proton stopping power in warm dense matter, where short plasma stagnation time (<100 ps) is a critical factor. The proposed selector can also be employed at higher proton energies, achieving final time spreads of a few picoseconds. This has important implications for sensing technologies in the study of coherent energy deposition in biology and medical physics.

A laser parameter study on enhancing proton generation from microtube foil targets

The interaction of an intense laser with a solid foil target can drive [Formula: see text] TV/m electric fields, accelerating ions to MeV energies. In this study, we experimentally observe that structured targets can dramatically enhance proton acceleration in the target normal sheath acceleration regime. At the Texas Petawatt Laser facility, we compared proton acceleration from a [Formula: see text] flat Ag foil, to a fixed microtube structure 3D printed on the front side of the same foil type. A pulse length (140-450 fs) and intensity ((4-10) [Formula: see text] W/cm[Formula: see text]) study found an optimum laser configuration (140 fs, 4 [Formula: see text] W/cm[Formula: see text]), in which microtube targets increase the proton cutoff energy by 50% and the yield of highly energetic protons ([Formula: see text] MeV) by a factor of 8[Formula: see text]. When the laser intensity reaches [Formula: see text] W/cm[Formula: see text], the prepulse shutters the microtubes with an overcritical plasma, damping their performance. 2D particle-in-cell simulations are performed, with and without the preplasma profile imported, to better understand the coupling of laser energy to the microtube targets. The simulations are in qualitative agreement with the experimental results, and show that the prepulse is necessary to account for when the laser intensity is sufficiently high.

Proton stopping measurements at low velocity in warm dense carbon

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Charged particle interaction and energy dissipation in plasma is fundamentally interesting. Here the authors study proton stopping in laser-produced plasma for the moderate to strong coupling with electrons.

Transport of an intense proton beam from a cone-structured target through plastic foam with unique proton source modeling

Laser-accelerated proton beams are applicable to several research areas within high-energy density science, including warm dense matter generation, proton radiography, and inertial confinement fusion, which all involve transport of the beam through matter. We report on experimental measurements of intense proton beam transport through plastic foam blocks. The intense proton beam was accelerated by the 10ps, 700J OMEGA EP laser irradiating a curved foil target, and focused by an attached hollow cone. The protons then entered the foam block of density 0.38g/cm^{3} and thickness 0.55 or 1.00mm. At the rear of the foam block, a Cu layer revealed the cross section of the intense beam via proton- and hot electron-induced Cu-K_{α} emission. Images of x-ray emission show a bright spot on the rear Cu film indicative of a forward-directed beam without major breakup. 2D fluid-PIC simulations of the transport were conducted using a unique multi-injection source model incorporating energy-dependent beam divergence. Along with postprocessed calculations of the Cu-K_{α} emission profile, simulations showed that protons retain their ballistic transport through the foam and are able to heat the foam up to several keV in temperature. The total experimental emission profile for the 1.0mm foam agrees qualitatively with the simulated profile, suggesting that the protons indeed retain their beamlike qualities.

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

Observation of a high degree of stopping for laser-accelerated intense proton beams in dense ionized matter

Intense particle beams generated from the interaction of ultrahigh intensity lasers with sample foils provide options in radiography, high-yield neutron sources, high-energy-density-matter generation, and ion fast ignition. An accurate understanding of beam transportation behavior in dense matter is crucial for all these applications. Here we report the experimental evidence on one order of magnitude enhancement of intense laser-accelerated proton beam stopping in dense ionized matter, in comparison with the current-widely used models describing individual ion stopping in matter. Supported by particle-in-cell (PIC) simulations, we attribute the enhancement to the strong decelerating electric field approaching 1 GV/m that can be created by the beam-driven return current. This collective effect plays the dominant role in the stopping of laser-accelerated intense proton beams in dense ionized matter. This finding is essential for the optimum design of ion driven fast ignition and inertial confinement fusion.

A detailed understanding of particle stopping in matter is essential for nuclear fusion and high energy density science. Here, the authors report one order of magnitude enhancement of intense laser-accelerated proton beam stopping in dense ionized matter in comparison with currently used models describing ion stopping in matter.

Uniform warm dense matter formed by direct laser heating in the presence of external magnetic fields

With the recent realization of kilotesla quasistatic magnetic fields, the interaction of a laser with magnetized solids enters an unexplored new regime. In particular, a circularly polarized (CP) laser pulse may propagate in a highly magnetized plasma of any high density without encountering cutoff reflection in the whistler mode. With this, we propose a scheme for producing uniform warm dense matter (WDM) by direct laser heating with a CP laser irradiating onto the target along the magnetic field. It is shown by particle-in-cell simulations, which include advanced ionization dynamics and collision dynamics, moderately intense right-hand CP laser light at 10^{15}W/cm^{2} can propagate in solid aluminum and heat it efficiently to the 100 eV level within picoseconds. By using two laser pulses irradiating from two sides of a thin solid target, uniform heating to WDM can be achieved. This provides a controllable way to create WDM at different temperatures.

Focussing Protons from a Kilojoule Laser for Intense Beam Heating using Proximal Target Structures

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4 × 10¹⁸ W/cm², producing proton beams with 3 MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. The beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100 eV.

Transport of intense particle beams in large-scale plasmas

Transport of particle beams in plasmas is widely employed in fundamental research, industry, and medicine. Due to the high inertia of ion beams, their transport in plasmas is usually assumed to be stable. Here we report the focusing and flapping of intense slab proton beams transporting through large-scale plasmas by using a recently developed kinetic particle-in-cell simulation code. The beam self-focusing effect in the simulation is prominent and agrees well with previous experiments and theories. Moreover, the beam can curve and flap like turbulence as the beam density increases. Simulation and analysis indicate that the self-generated magnetic fields, produced by movement of collisional plasmas, are the dominant driver of such behaviors. By analyzing the spatial growth rate of magnetic energy and energy deposition of injected proton beams, it is found that the focusing and flapping are significantly determined by the injected beam densities and energies. In addition, a remarkable nonlinear beam energy loss is observed. Our research might find application in inertial confinement fusion and also might be of interest to the laboratory astrophysics community.

Particle-in-cell simulation of transport and energy deposition of intense proton beams in solid-state materials

A particle-in-cell (PIC) simulation code is used to investigate the transport and energy deposition of an intense proton beam in solid-state material. This code is able to simulate close particle interactions by using a Monte Carlo binary collision model. Such a model takes into account all related interactions between the incident protons and material particles, e.g., proton-nucleus, proton-bound-electron, and proton-free-electron collisions. This code also includes a Monte Carlo model for the collisional ionization and electron-ion recombination as well as the depression of the ionization potential by shielding of surrounding particles. Moreover, for intense proton beams, in order to include collective electromagnetic effects, significantly speed up the simulation, and simultaneously avoid numerical instabilities, an approach that combines the PIC method with a reduced model of high-density plasma based on Ohm's law is used. Simulation results indicate that the collective electromagnetic effects have a significant influence on the transport and energy deposition of proton beams. The Ohmic electric field would increase the stopping power and leads to a shortened range of proton beams in solid. The magnetic field would localize the energy deposition by collimating proton beams, which would otherwise be deflected by the collisions with nuclei.

Anomalous material-dependent transport of focused, laser-driven proton beams

Intense lasers can accelerate protons in sufficient numbers and energy that the resulting beam can heat materials to exotic warm (10 s of eV temperature) states. Here we show with experimental data that a laser-driven proton beam focused onto a target heated it in a localized spot with size strongly dependent upon material and as small as 35 μm radius. Simulations indicate that cold stopping power values cannot model the intense proton beam transport in solid targets well enough to match the large differences observed. In the experiment a 74 J, 670 fs laser drove a focusing proton beam that transported through different thicknesses of solid Mylar, Al, Cu or Au, eventually heating a rear, thin, Au witness layer. The XUV emission seen from the rear of the Au indicated a clear dependence of proton beam transport upon atomic number, Z, of the transport layer: a larger and brighter emission spot was measured after proton transport through the lower Z foils even with equal mass density for supposed equivalent proton stopping range. Beam transport dynamics pertaining to the observed heated spot were investigated numerically with a particle-in-cell (PIC) code. In simulations protons moving through an Al transport layer result in higher Au temperature responsible for higher Au radiant emittance compared to a Cu transport case. The inferred finding that proton stopping varies with temperature in different materials, considerably changing the beam heating profile, can guide applications seeking to controllably heat targets with intense proton beams.

Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.

Experimental evidence for the enhanced and reduced stopping regimes for protons propagating through hot plasmas

Our understanding of the dynamics of ion collisional energy loss in a plasma is still not complete, in part due to the difficulty and lack of high-quality experimental measurements. These measurements are crucial to benchmark existing models. Here, we show that such a measurement is possible using high-flux proton beams accelerated by high intensity short pulse lasers, where there is a high number of particles in a picosecond pulse, which is ideal for measurements in quickly expanding plasmas. By reducing the energy bandwidth of the protons using a passive selector, we have made proton stopping measurements in partially ionized Argon and fully ionized Hydrogen plasmas with electron temperatures of hundreds of eV and densities in the range 1020-1021 cm-3. In the first case, we have observed, consistently with previous reports, enhanced stopping of protons when compared to stopping power in non-ionized gas. In the second case, we have observed for the first time the regime of reduced stopping, which is theoretically predicted in such hot and fully ionized plasma. The versatility of these tunable short-pulse laser based ion sources, where the ion type and energy can be changed at will, could open up the possibility for a variety of ion stopping power measurements in plasmas so long as they are well characterized in terms of temperature and density. In turn, these measurements will allow tests of the validity of existing theoretical models.

Monte Carlo approach to calculate proton stopping in warm dense matter within particle-in-cell simulations

A Monte Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. This approach is based on multiple electron-electron, electron-ion, and ion-ion binary collision and accounts for both the free and the bound electrons in the plasmas. This approach enables one to calculate the stopping of particles in a more natural manner than existing theoretical treatment. In the low-temperature limit, when "all" electrons are bound to the nucleus, the stopping power coincides with the predictions from the Bethe-Bloch formula and is consistent with the data from the National Institute of Standard and Technology database. At higher temperatures, some of the bound electrons are ionized, and this increases the stopping power in the plasmas, as demonstrated by A. B. Zylstra et al. [Phys. Rev. Lett. 114, 215002 (2015)]PRLTAO0031-900710.1103/PhysRevLett.114.215002. At even higher temperatures, the degree of ionization reaches a maximum and thus decreases the stopping power due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.

Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of ∼15 MeV passing through a WDP of beryllium with an electronic density around the solid value n_{e}≈3×10^{23}cm^{-3} and with temperature around ∼40 eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.215002]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.