Laser-driven ion acceleration via target normal sheath acceleration in the relativistic transparency regime

We present an experimental study investigating laser-driven proton acceleration via target normal sheath acceleration (TNSA) over a target thickness range spanning the typical TNSA-dominant regime (∼1 μm) down to below the onset of relativistic laser-transparency (<40 nm). This is done with a single target material in the form of freely adjustable films of liquid crystals along with high contrast (via plasma mirror) laser interaction (∼2.65 J, 30 fs, I > 1 × 10 21 W cm−2). Thickness dependent maximum proton energies scale well with TNSA models down to the thinnest targets, while those under ∼40 nm indicate the influence of relativistic transparency on TNSA, observed via differences in light transmission, maximum proton energy, and proton beam spatial profile. Oblique laser incidence (45°) allowed the fielding of numerous diagnostics to determine the interaction quality and details: ion energy and spatial distribution was measured along the laser axis and both front and rear target normal directions; these along with reflected and transmitted light measurements on-shot verify TNSA as dominant during high contrast interaction, even for ultra-thin targets. Additionally, 3D particle-in-cell simulations qualitatively support the experimental observations of target-normal-directed proton acceleration from ultra-thin films.


Introduction
A primary research endeavor of ultra-intense laser plasma interaction is efficient secondary radiation production. Selection of various laser and target parameters can cause transfer of laser energy into electron beams [1], x-rays or neutron beams for radiography or remote detection applications [2,3], positron-electron plasmas for fundamental studies related to astrophysics [4], and ion beams, which relate to radiography [5], generation of warm dense matter [6], and cancer therapy [7][8][9][10]. Efforts towards ion beam applications are hastened due to high power, high repetition rate laser facilities currently under development [11][12][13].
The realization of ion beam application goals faces two critical challenges. From a practical perspective, one needs the ability to produce sufficient ion flux through efficient procedures-rapid target insertion, laser operation, and optimized on-line diagnostics. More fundamentally, a thorough understanding of the underlying processes that govern ion acceleration in order to better control aspects such as kinetic energy, particle number, and beam profile is required. For this, increases in laser energy and power have not yielded ion energies necessary to achieve applications like cancer therapy due in part to poor scaling with laser intensity and also to stringent requirements on laser parameters like pulse contrast, which measures the intensity of unwanted but often unavoidable 'pre-pulse' light preceding the main beam relative to that of the peak pulse. While several mechanisms have been identified for ion acceleration [14][15][16][17][18] and multiple reviews have been done to accumulate experiment, simulation, and model descriptions of these [19,20], the optimization of a given mechanism for an application on any particular facility remains difficult. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Target normal sheath acceleration (TNSA) [14,15], involves rear surface layer particles accelerated in the target normal direction up to tens of MeV/nucleon energies by a space-charge electric field set up as fast electrons originating in the front-side pre-plasma are laser-accelerated through the target. TNSA can benefit from pre-pulses-the resulting target pre-plasma is abundant with electrons available for laser acceleration, yielding a larger rear-surface sheath field-but will suffer if the target is sufficiently deformed by these early pulses or if the pre-pulse scale length becomes too long [20,21]. Because of this TNSA is typically maximized for targets robust enough to withstand initial interaction with the laser pre-pulse and main pulse rising edge, typically above several hundred nm. TNSA is nevertheless observed on both short and long pulse systems: current experimental benchmarks for TNSA include 40 MeV protons for ultra-short pulse interaction [22] and 85 MeV for longer pulse lasers [23], both achieved with ∼1 μm thick foils.
Other ion acceleration mechanisms can arise for thinner targets (below 100 nm), but therefore often require intensity contrasts superior to 10 −10 :1 for times at least one ps before the main pulse arrives to preserve target integrity. Sufficiently thin targets can undergo light-sail radiation pressure acceleration [16], where the target receives initial momentum from the laser and then travels along with the pulse to continually gain energy [20]. This process requires irradiation with high intensity, exceptionally spatially homogeneous pulses of circularly polarized light at normal incidence to minimize early target heating and expansion. Other mechanisms can be categorized as enhanced-TNSA [17,18] where an increase in laser penetration due to a relativistic reduction of the plasma frequency (an effect known as relativistic transparency) results a larger volume of electrons being accelerated to generate the sheath field. While these mechanisms may scale more favorably with laser intensity than TNSA [20] they are also difficult to produce in experiments due in part to facility limits but also to interference from plasma instabilities and other complex interactions [24][25][26].
What follows is the first experimental study of ultra-short pulse proton acceleration investigated with oblique laser incidence from the TNSA-dominant thickness regime down to that of relativistic transparency with a single target material. This is enabled first by high contrast (via a plasma mirror) interaction, as superior laser pulse quality is required for successful ion acceleration from ultra-thin targets, and secondly by an in situ target formation system using freely suspended liquid crystal films [27]. This material can be drawn across an aperture in a rigid frame with changes in wiping speed, temperature, and liquid crystal volume to form films several mm in diameter at repetition rates of 0.1 Hz and with thicknesses from 10 nm to several 10 s of μm [28]. Critically, the in situ target formation device forms films to within 2 μm of the same position each formation, removing the necessity for between-shot target alignment and thus allowing rapid data collection. While this ondemand thickness manipulation has been demonstrated as an avenue toward high formation rate plasma mirrors [29], it is utilized here to enable a detailed investigation of the influence of target thickness on ion acceleration mechanisms, including the ultra-thin regime (<40 nm). Furthermore, the low density (∼1 g/ cm 3 ) of liquid crystal used and thin target formation capabilities allowed easy access to the transparency regime.
Ultra-short (τ = 30 fs) pulses of ∼2.65 J were incident on targets at 45°in order to distinguish between laseraxis and target-normal directed acceleration. A single plasma mirror was optional to ascertain differences between moderate(10 −6 :1) and ultra-high (10 −10 :1) contrast. Oblique target incidence also allowed multiple secondary diagnostics to corroborate the target conditions during ultra-thin target proton beam production including ion spatial and energy diagnostics in the front normal, rear normal, and laser axis directions, as well as reflected and transmitted light diagnostics able to measure during laser interaction due to the optical quality of the liquid crystal film surface. The data show efficient acceleration yielding high quality proton beams (beam profile, divergence) in the target-normal direction and ion energy scaling with target thickness in agreement with TNSA models down to the ultra-thin region. Increased laser transparency is observed below the ∼40 nm relativistic skin depth, and the thinnest (∼10 nm) targets exhibit higher average proton energy but larger shotto-shot fluctuations along with changes in proton spatial characteristics including less homogeneity at large angles from target normal.

Experimental setup and apparatus
The experiment was performed on the Draco laser facility at HZDR, which is a 3.5 J, 30 fs, 10 Hz titanium: sapphire based system capable of intensities exceeding 1×10 21 W cm −2 in a 3 μm diameter FWHM focal spot. Figure 1(a) shows a simplified schematic of the primary diagnostic setup, which included an optional single plasma mirror for pulse contrast enhancement. Contrast measurements with and without a plasma mirror are shown in figure 1(b). The optics design focused light onto and then recollected it from the plasma mirror with off-axis parabolas which allowed the setup to be bypassed if desired by moving an additional mirror into the beam-path. The entire plasma mirror optics path had an energy throughput of 80%, resulting in energies between 2.55 and 2.75 J on target. Near-field measurements after plasma mirror reflection were monitored on each shot and did not reveal modulations that would suggest a reduction in final focal spot quality. The plasma mirror substrate had dimensions of 50 mm×95 mm which allowed about 450 few mm spots to be used before it needed to be replaced.
The primary ion diagnostics were multi channel plate Thomson parabola spectrometers (TPS) situated along the laser axis (0°) and target normal (45°) directions, with energy resolution of 0.5-1 MeV from 0 to 30 MeV. Additionally, spatial information of accelerated protons was recorded for a number of shots on radiochromic film (RCF) packs, which could be moved into place on-demand at a distance of 55 mm from the target.
Additional diagnostics were implemented to investigate the reflected and transmitted light upon interaction with the optical quality target surface. This would not only reveal the onset of transparency effects and allow their interaction with ion acceleration to be observed, but also would allow target morphology conditions to be determined at the time of laser interaction. A piece of spectralon (Lambertian scatterer) was used to collect the transmitted beam mode, and a ceramic (MACOR) screen served the same purpose for the reflected light. Two cameras filtered for 1ω and 2ω observed scattered light imaged from the ceramic screen along the same line of sight by using a dichroic mirror. A final diagnostic was a sheet of LANEX, which fluoresces upon impact by energetic electrons, to reveal the spatial distribution of target front-surface electrons ejected in the reflection direction. On some shots a rough electron energy spectrum was obtained using transmission through a wedged aluminum piece in front of the screen.
Liquid crystal films were formed within a linear slide target inserter device (LSTI) [28], as shown in figure 1(c). The 4mm diameter circular aperture was oriented at 45°with respect to the incoming laser axis. 10 μl of the liquid crystal 4-cyano-4'-octylbiphenyl (8CB) was applied to the wiper, which allowed several dozen films to be formed before the chamber needed to be opened for new volume application. A cooled water line pumped by a small chiller unit was installed through the chamber wall to maintain the LSTI frame at the desired temperature for film control, typically around 28.0°C. Film thicknesses were measured on-demand by white light interferometry, which was relayed in from outside the chamber. The LSTI design utilizes the same liquid crystal mesophase surface tension that enables freely suspended film formation to draw films at the front aperture edge within 2 μm of the same position each time, which eliminates the need for target alignment after it is performed on the first film. This alignment, performed with a scattered light imaging system, was verified by observing the accelerated proton energy with on-shot diagnostics as the target was shifted along the incoming laser axis. All data shown here was taken at best focus.

Experimental data and analysis
3.1. TNSA behavior The central experimental result is shown in figure 2(a): maximum proton cutoff energy recorded on the target normal TPS for film thicknesses ranging from >1 μm to 10 nm. Open blue circles indicate the maximum energy observed on the target normal Thomson parabola, and the filled circles are averages of these values with bin size indicated by shaded background region. Pink circles are from RCF stacks and serve to corroborate the Thomson parabola data. While shots without a plasma mirror (triangles) demonstrated predictably decreasing maximum proton energy as film thicknesses decreased below 1 μm, the high contrast data shown here exhibits an overall increase in proton cutoff energy along the target normal direction as thickness decreases down to 300 nm, at which point the cutoff energies plateau. This behavior is in agreement with TNSA scaling law predictions [30][31][32], where maximum proton energy depends on the electron density within the Debye sheath. Assuming that electron density depends on their divergence angle and path length to target rear (i.e. target thickness), a saturation for small thicknesses is expected. The fit shown is calculated using 1D TNSA model [30] with electron temperature scaling [32] and a best fit free parameter a 0 ∼17; this vector potential corresponds to intensity I=6×10 20 W cm −2 , reasonably close to the estimated experimental peak intensity of 10 21 W cm −2 .
Carbon ion (C 6+ ) cutoff energies in the target normal direction exhibit the same target thickness dependence as the protons down to the thinnest targets, with a ratio of proton/carbon cutoff energies whose average remains near 3, shown in figure 2 with error bars. This behavior suggests that both protons and carbon ions gain energy in the same sheath field for each target as thickness is reduced, and in general is in agreement with predictions for TNSA [31].
The high proton energy achieved for ultra-thin targets suggests a high contrast laser interaction, where the target surfaces remain intact before the main pulse arrives. This is supported by observations of the speculardirected optical emission during laser interaction recorded with both 1ω and 2ω filters. Here we expand the measurement of previous target emission studies [33,34] by always using peak laser intensity but with deliberate pulse contrast differences: figure 3 shows representative images of the moderate (no plasma mirror, left) and high contrast laser reflection (right). High contrast results in significantly enhanced reflected light levels and a better-defined spatial mode. Under this condition of unperturbed target surface at the initiation of high intensity laser interaction, 2ω emission becomes visible, with expected spatial modulations due to the strongly intensitydependent generation process. This improved reflection quality indicates a minimally expanded critical surface in the high contrast case [35] and was observed even for ultra-thin targets.
High contrast interaction is further corroborated by the LANEX diagnostic observing electrons ejected in the laser reflection direction during target interaction. Up to 30 nC sr −1 was measured in electron distributions with energies exceeding 9 MeV, obtained by recording the calibrated [36] LANEX fluorescence behind different thicknesses of the Al wedge. This is similar to recent results [37] where electrons ejected in this manner required laser interaction with a sharp density profile originating from high contrast pulse irradiation. Figure 4 shows target normal ion energy traces for various thickness targets (blue lines) for comparison to an average of those laser axis ion spectra observed (red). While all targets have similar spectral shape at low proton energies, the thinnest targets also exhibit increased high energy component suggesting a greater hot electron population. The majority of shots (>90%) at high contrast showed no laser axis ion signal for any thickness, and when present the laser axis energy cutoff and yield were always significantly lower than that observed along target normal for the same shot.
The target normal spatial distribution of proton emission, shown for various thicknesses in figure 5, was of consistently small divergence (<10°) at low and high energy for all thicknesses. This was true even for ultra-thin targets near the transparency threshold with the exception of radial streaking in the low energy ion signal (as in the 4.7 MeV, 6 nm sheet in figure 5). For comparison, the rightmost film is one layer from a moderate contrast, 6500 nm target result, demonstrating significantly larger beam divergence.  . Proton energy spectra in the target normal (blue) and laser axis (red) directions. The latter is averaged over the few shots for which appreciable signal was detected, and as such represents an upper limit for ions in this direction.
The proton acceleration was also measured with RCF film from both the forward and backward target normals for a single target thickness of 36 nm, selected as near the relativistic transparency transition. Figure 6 shows that protons from these two directions are similar in maximum energy, yield, and beam divergence, indicating similarly strong accelerating fields on both surfaces. This is a hallmark of the TNSA mechanism and has been observed previously [38,39] in the case where the target front is sufficiently unperturbed by laser prepulse. A slight offset is observed in the proton emission centroid from exactly the target normal direction: toward the reflected laser in the backward direction and toward the transmitted laser in the forward direction (as indicated by the inset). This angular shift is attributed to an intra-pulse TNSA effect whereby the electron distribution accelerated in the direction of the reflected/transmitted beam will cause a sheath field asymmetry which likewise impacts the proton beam direction [40]. . Radiochromic film (RCF) stacks demonstrating spatial distribution of accelerated protons for different target thicknesses (indicated along top) irradiated with high contrast pulses. Consistency in both beam divergence and overall shape is observed except for ultra-thin films. The rightmost sheet is a representative RCF layer for a moderate contrast shot, demonstrating a higher ion divergence under these conditions.

Transition to transparency
While the energy spectra, spatial distribution, and directionality of the acceleration ions suggests TNSA as the dominant mechanism for low and high contrast shots for thicknesses from 40 nm and above, additional characteristics were observed for ultra-thin targets in the relativistic transparency regime. This state was verified in several ways, but most directly by measuring the laser pulse transmitted through the target. These values are shown in figure 7 as a function of film thickness. Thicknesses above 40 nm exhibit a nearly constant average of ;5% transmission, but those below show both increased average transmission as well as greater shot-to-shot fluctuation.
There is a similar increase in maximum proton energy fluctuations for these ultra-thin targets. Near 10 nm target thickness proton energies ranged from 16 to 26 MeV (see figure 2(a))-despite this the average maximum energy was higher for these thinnest targets. A third observation from the transparency regime was a radial streak pattern outside the primary proton spatial structure visible in the lowest energy RCF layers, as in the top left stack of figure 5. These thinnest targets still showed a high quality reflection during laser interaction, so this burst proton pattern is suspected to originate not from target expansion via pre-pulse but rather from late-time TNSA fields still accelerating particles as the target volume expands after laser interaction.
Although fluctuations in the transmitted light, maximum proton energy, and low-energy spatial distribution were observed for ultra-thin target interaction, none of these effects are seen to correlate strongly with each other, nor with other measured values such as the quality of the reflected or transmitted modes. Additionally, the proton energy only weakly correlates with the±2% laser energy fluctuations on target. Critically, the ratio of proton to carbon 6+ does not fluctuate largely at the thinnest targets ( figure 2(b)), suggesting that rear surface acceleration and hence the target integrity is not affected. As such the source of these fluctuations is believed to be related to underlying laser plasma interaction in this relativistic regime, the details of which will be further studied with particle-in-cell simulations.

Simulations
Simulation efforts for comparison to experimental observations first focused on ion acceleration behavior with thickness: figure 8 shows snapshots in time of the Poynting vector magnitude S, accelerated proton trajectory, and energy spectrum. These fully 3D particle-in-cell simulations were performed using the code large scale plasma (LSP) [41] with 8CB targets using an implicit field solver and particle advance as well as particle tracking. A p-polarized laser pulse (λ=800 nm, τ = 30 fs FWHM sin 2 intensity temporal envelope) with a peak intensity of 1×10 21 W cm −2 is incident at 45°on target, with x as the target normal direction. The target is composed of fully ionized carbon and hydrogen atoms in their stoichiometric ratio in the liquid crystal 8CB, with an electron density of 184 n cr and an initial electron temperature T e = 10 keV. There were 125 particles per species per cell in the 300 nm target simulation, and 8 particles per species per cell in the 30 nm target simulation.
For the 300 nm target, the target normal cell size x 15 D = nm and y z 45 D = D = nm. In the case of the 30 nm target, x 1.5 D = nm in the 150 nm directly around the target, expanding out to 12 nm; y z 12 D = D = nm throughout the grid. In order to maximize vacuum acceleration length while limiting computational cost, the spot size used (1.2 μm, Gaussian FWHM) was smaller than in the experiment to decrease transverse target extent. Additionally, the cells used do not resolve the Debye length (roughly 1 nm); as such the energy-conserving force interpolation of LSP was employed to mitigate numerical heating. These simulations were conducted with a 0.75 Courant timestep. Figures 8(a) and (b) show the strong dependence of laser penetration on target thickness. In figure 8(a) the magnitude of the Poynting vector is plotted at t 20 0 + fs, where t 0 is the time at which the peak of the laser pulse reaches the focus. The laser pulse is largely reflected from the still opaque 300 nm target. Plotting the same quantity at the same point in time in figure 8(b) shows the laser has penetrated through the 30 nm target. The total flux passing through simulation planes at −1.8 and 2.5 μm was recorded for both simulations, allowing measurement of total reflectivity and transmission. The 300 nm target showed 73% reflectivity and 2% transmission, while the 30 nm target showed a marked decrease in reflectivity (61%) and a slight increase in transmission (5%). This is consistent with the trend seen in experiment, where the amount of transmitted light increased substantially around a 30 nm target thickness (see figure 7). Figure 8(c) shows the late-time angular distribution of accelerated protons for t 300 0 + fs for two film thicknesses: the 300 nm target (blue) displays protons directed along target normal in a tight grouping, while the 30 nm target (orange) also shows general target normal acceleration although now with a somewhat broader distribution angle. Dominant proton acceleration in the target normal direction for both thick and relativistically transparent targets are observed, consistent with experimental results. This deviation from true target normal is in a consistent direction with that shown in figure 6, coming from a similar sheath field asymmetry [40].
Finally, figure 8(d) shows the experimental average proton cutoff energies from figure 2(a) in blue with the cutoff energy obtained from the two simulation thicknesses overlaid in red. The simulation cutoff energies fall reasonably close to experimental values and importantly reflect the general experimental trend of highest energies from thinnest targets. The discrepancy seen is most likely due to the simulation laser pulse not properly accounting for the small amount of laser pre-pulse remaining after plasma mirror reflection in the experiment, instead using an idealized pulse shape and beginning with a pre-ionized, initially hot target plasma. A full study of these pre-pulse related effects on the ultra-thin targets is planned to further investigate the ion acceleration fluctuations observed in this regime.  Figure 9 shows maximum proton energy thickness scans taken from numerous literature references, where those with >3 distinct thicknesses and linearly polarized pulses were selected. Here normal incidence data are indicated as triangles, non-normal as circles, and the data presented in this work as stars (also non-normal). Filled points are short pulses (<50 fs) and open are long (>500 fs). In general higher laser energies result in higher maximum proton energies, but the efficiency can vary strongly depending on other laser conditions. Foremost, laser contrast plays an important role in the nature of proton acceleration as thickness is varied: maximized TNSA cutoff energy will occur at that thickness where electron divergence through the target and pre-pulse expansion from imperfect contrast are both minimized [31,52]. Several previous thickness scans [42,45,50,51] therefore exhibit a peak of maximum proton cutoff energy at a certain thickness. If the laser prepulse can be sufficiently suppressed, proton cutoff energies tend to rise slightly or plateau as thickness decreases to 100 nm and below, as seen in [23,26,43,44,[47][48][49]. Those datasets with thicknesses below the transparency regime (∼40 nm) can exhibit a slight increase in proton energy here possibly due to a related enhancement effect. This is true as well of the averaged data presented in this work (black stars), which was also high contrast.

Comparison to literature
The uniqueness of the dataset presented here is then twofold: first, no other data spans the range from few nm to few μm with a single target material, enabling measurement of TNSA over the entire range of thicknesses previously seen as optimum with other laser conditions. The absence of a strong peak confirms the pre-pulse/ electron divergence trade-off described previously. Secondly, this data is the only one to examine non-normal incidence below 100 nm, and the continued increase of cutoff energy in the target normal direction here suggests TNSA as a relevant acceleration mechanism for thicknesses down to the onset of laser transparency. Full characterization of the enhancement regime for targets near 10 nm requires further study with exceptional laser contrast and in particular with a quantity of shots capable of fully mapping the fluctuation regime observed in this experiment, which is only now possible due to laser and solid target technology advancements.

Conclusion
Presented here is a high granularity thickness scan of ultrashort pulse ion acceleration, the first to study oblique incidence interaction from the TNSA regime down below the onset of relativistic transparency, where proton energies are observed beyond 25 MeV with ∼2.65 J, 30 fs pulses. Oblique laser incidence was used to discriminate between target normal and laser axis directed ion acceleration, which was verified with angularly separated ion and optical diagnostics that simultaneously ascertained high contrast laser-target interaction. In particular, the data set presented shows consistent TNSA energies for thicknesses down to ∼100 nm if sufficient contrast can be achieved, providing an avenue toward repeatable, predictable ion acceleration from such targets. Additionally, target normal acceleration in the transparency regime-below 40 nm for the conditions used here-reveal inconsistencies in laser transmission, maximum proton energy, and proton beam spatial profile, the origins of which warrant further simulation and experiment study. In particular, additional experimental control in the form of deliberate pre-pulses that tailor the critical surface and pre-plasma scale length could shed light on further acceleration dynamics.
The large data set allowing a credible statistical evaluation of the acceleration dynamics was able to be collected due to a combination of rapid shot-on-demand, ultra-high contrast laser, diagnostic, and target operation, and serves as an important step towards applications that will require optimized ion acceleration from high repetition rate laser plasma interaction. In particular, the observed proton energy stability in the regime below 100 nm but above the relativistic transparency threshold from consistent laser conditions in combination with the rapid target formation of the LSTI device has achieved the robustness necessary for progress toward applications. Additionally, the low mass of these targets and minimal, optimally directed plasma ejecta of liquid crystal compared to traditional metallic foils both present excellent prospects for lowdebris, high rate laser-target interaction. In this setup, the last remaining cost-intensive consumable is the plasma mirror substrate, which can in principle be replaced with a liquid-crystal based setup [29]. This combination of liquid crystal plasma mirror and target film formation in the 40-100 nm range is hence a credible path toward future application-relevant laser-driven ion sources.