Background pressure effects on MeV protons accelerated via relativistically intense laser-plasma interactions

We present how chamber background pressure affects energetic proton acceleration from an ultra-intense laser incident on a thin liquid target. A high-repetition-rate (100 Hz), 3.5 mJ laser with peak intensity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8 \times 10^{18}\,\text {Wcm}^{-2}$$\end{document}8×1018Wcm-2 impinged on a 450 nm sheet of flowing liquid ethylene glycol. For these parameters, we experimentally demonstrate a threshold in laser-to-proton conversion efficiency at background pressures \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$< 8\,\text {Torr}$$\end{document}<8Torr, wherein the overall energy in ions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>1\,\text {MeV}$$\end{document}>1MeV increases by an order of magnitude. Proton acceleration becomes increasingly efficient at lower background pressures and laser-to-proton conversion efficiency approaches a constant as the vacuum pressure decreases. We present two-dimensional particle-in-cell simulations and a charge neutralization model to support our experimental findings. Our experiment demonstrates that high vacuum is not required for energetic ion acceleration, which relaxes target debris requirements and facilitates applications of high-repetition rate laser-based proton accelerators.


Scientific Reports
| (2020) 10:18245 | https://doi.org/10.1038/s41598-020-75061-1 www.nature.com/scientificreports/ sheath fields. We show proton acceleration becomes increasingly efficient at lower background pressures and laser-to-proton conversion efficiency approaches a constant as the vacuum pressure decreases. Below ∼ 1 Torr , the conversion efficiency is within a few percent of that found at two orders of magnitude lower chamber pressure. A charge neutralization model and two-dimensional PIC simulations show good qualitative agreement with our experimental results. Our demonstration of multi-MeV ion acceleration using liquid targets and variable background pressures is, to our knowledge, the first thorough study of its kind. These results show MeV ion acceleration can readily be achieved with background pressures much higher than previously reported.

Results
Experimental results. Background chamber pressure was reduced from 13.7 Torr in discrete steps, and at each step, a series of shots while changing the position of the laser focus relative to the target were taken. The vacuum chamber setup is shown in Fig. 1. With 3.5 mJ on target, the peak intensity of the laser at best focus was 8 × 10 18 Wcm −2 , well within the relativistic regime of laser-plasma interactions. Figure 2 shows the proton spectra results from performing the intensity scan at six different background pressures. Additional data was collected at 13.7 Torr chamber pressure, but there was no detectable > 1 MeV ions on this scale. We noted no detectable change to the focal spot until the background pressure approached ∼ 80 Torr . The target position was moved along the laser propagation direction in 1.0 µm intervals such that 10 energy spectrum traces were recorded per target position with each trace integrated over 30 laser shots. The spectra were then normalized per shot. Scanning through focus allowed us to establish the peak focus and ensure appropriate prepulse conditions throughout all measurements. The z = 0 position (best focus) was determined by selecting the trace with the highest proton cutoff energy as the zero point. Reduced laser energy and contrast improvements negated proton energy decrease at best focus caused by laser prepulse as seen previously in Morrison et al. 37 . Figure 1. Experimental setup. After focusing, 3.5 mJ of laser energy is focused onto a 450 nm thick liquid target. Variable delay shadowgraphs are recorded using an 80 fs pulse timed to the high intensity pulse. The shadowgraphs reveal a 50-60 µm radius ionization spot (inset).

Figure 2.
Proton energy spectra from a focal scan at different background pressures. The x-axis gives the proton energy in MeV, the y-axis shows the focal position of the target with 0 being set at the peak proton energy, and the color scale gives the proton number (N/MeV/s.r./shot) on a log scale. www.nature.com/scientificreports/ The spectra show a clear enhancement in conversion efficiency to high energy protons when the background pressure decreases (see also Fig. 3) with more than an order of magnitude increase in conversion efficiency as the pressure decreases from 8.4 to 3.0 Torr. Further, we note an asymptotic behavior of the conversion efficiency as the pressure decreases. When going from 0.430 to 0.032 Torr, more than an order of magnitude decrease in chamber pressure, the conversion efficiency is only increased by ∼ 3% . These results indicate that with our parameters, there is less than a 10% difference in conversion efficiency below 0.850 Torr. Sheath field suppression model. To explain the improvement in conversion efficiency as the chamber pressure decreases below 8.4 Torr, we consider the effect of background gas on the accelerating sheath field. In the standard TNSA model, the laser accelerates electrons to MeV energies, which subsequently propagate and circulate through the target. The highest energy electrons move far away from the target region, leaving a positively charged region of the target which the remaining hot electrons turn back towards. These electrons reflux through the target and create a quasi-static electric field that accelerates the ions. The longitudinal spatial extent of this charge separation is estimated as the Debye length given by D = ǫ 0 k B T h /n h e 2 1/2 where k B T h ≃ 0.511 1 + I 2 0 1.37×10 18 Wµm 2 cm −2 1/2 − 1 , is the hot electron temperature in MeV with I being the laser intensity in Wcm −2 , 0 the laser wavelength in μm, ǫ 0 the permittivity of free space, k B the Boltzmann constant, n h the initial hot electron density, and e the fundamental charge unit 38 . The initial hot electron density n h is estimated by considering the number of hot electrons, N h , that exist near the focal spot as n h = N h π( s 2 ) 2 (2 D +d t ) 30 where N h = ηE L /k B T h , s is the FWHM intensity focal spot diameter of the laser, d t is the target thickness, η = (1.2 × 10 −15 (I 2 0 ) 3/4 ) is the laser-to-hot-electron conversion efficiency for intensities between 10 16 and 10 19 Wcm −239, 40 , and E L is the laser pulse energy. Using the laser parameters for our experiment, I avg = 3.0 × 10 18 Wcm −2 ( I peak = 8.0 × 10 18 Wcm −2 ), we find k B T h ≃ 280 keV (600 keV), η ≃ 0.062 (0.13), D ≃ 78 nm (120 nm), and n h ≃ 2.5 × 10 21 cm −3 ( 2.1 × 10 21 cm −3 ).
The majority of hot electrons excited from the initially neutral target are trapped by the positive charge that maintains charge neutrality. These hot electrons recirculate through the target region because of the positive bulk charge, generating the necessary fields for ion acceleration. Without background gas, we estimate the total ion charge number by noting the charge neutrality condition N i = N h , where N i is the number of ions. When considering the vacuum chamber pressure, we note that with a liquid target, a background gas of evaporating liquid (in our case, ethylene glycol) fills a volume around the target. As the hot electrons confined within D from the target overtake the background gas, the resulting electric field will ionize the gas, providing cold electrons that act to cancel the positive charge of the target. Based on these assumptions, we estimate the total charge responsible for accelerating the ions when a background gas is present as eN tot = e(N i − N e,bkg ) where N e,bkg is the number of freed electrons in the background gas. Our model is qualitatively similar to that provided by Batani et al. 41 to explain hot electron expansion velocity in a gas and Sokollik et al. 42 to explain decrease charge from microsphere laser-target interactions, albeit the background pressure used in these works was far from the threshold demonstrated in this work.
The number of freed electrons from the background gas is found by assuming the volume in which background gas ionization occurs to be a cylinder with an effective radius, r s , of the source size of background electrons and a height 2 D , signifying the local extent of the electric field that would ionize the gas, where the factor of two recognizes the gas is present on both sides of the target. Using the ideal gas law, we estimate the number s D k B T bkg with T bkg being the ambient temperature of the gas ( ∼ 300 K ). Based on shadowgraphic images taken during the experiment (Fig. 1), we estimate r s ≃ 55 ± 5 µm , a reasonable assumption based on ion source size reported in literature 43,44 . We can estimate the peak strength of the electric sheath field ( E s ) as E s ∼ k B T h e D 45 . Using this, E s ≃ 3.6−4.8 MVµm −1 , which is similar to that found in simulations here and elsewhere 37 . With this field strength, it is reasonable to assume that over the ionization region, all components of the background gas surrounding the target will be singly ionized on average, suggesting a background electron number N e,bkg = ZN gas , where Z is the sum of all constituent atoms of the molecule. In our model, we assume the background gas nearest the target is ethylene glycol ( C 2 H 6 O 2 ), therefore Z = 10 (see "Methods" for additional considerations). Using the definitions above, we find the total charge of the target when considering background gas to be: The charge found in Eq. (1) is responsible for accelerating ions. As the background pressure increases, the overall target charge decreases, resulting in a reduced conversion efficiency to the laser accelerated ions. The total charge based on this model using our experimental parameters is shown in Fig. 3, where the upper bound assumes the lower bound on intensity ( I avg = 3.0 × 10 18 Wcm −2 ) and the lower bound on electron source size ( r s = 50 µm ) and the lower bound assumes the upper bound on intensity ( I peak = 8.0 × 10 18 Wcm −2 ) and the upper bound on electron source size ( r s = 60 µm ). The model results are co-plotted with the normalized conversion efficiency to target normal ions found experimentally at best focus. Based on the laser parameters used in the work, we expect the background gas to fully neutralize the accelerating fields when the pressure reaches between 5.2 and 12.2 Torr, in reasonable agreement with our experimental data. Our model predicts the total accelerating charge being 99% of its vacuum level at ∼ 50 mTorr , suggesting there should be little difference in conversion efficiency as the pressure decreases beyond this point.
Simulation results. We have performed particle-in-cell (PIC) simulations to model the effects of background pressure on proton acceleration. The simulations were performed using VLPL 46 (Virtual Laser Plasma Lab) in a two-dimensional configuration including a semi-classical ionization model [47][48][49] . Figure 4 shows the proton energy spectra 440 fs after the peak of the pulse reaches the front of the flat-top density of the target. In the vacuum case (left), the ion energy reaches 1.0 MeV, similar to that found experimentally. The difference in experimental cut-off energy and that found in the simulation is likely a result of incorrect pre-plasma conditions or abbreviated acceleration time in the simulation. In the high background pressure case (right), the maximum energy is reduced and the total conversion to protons > 0.5 MeV ( 50% of the peak energy in vacuum) is only ∼ 10% of that found in the vacuum simulation. Simulations also provide supporting evidence for sheath field suppression caused by the background gas. 40 fs after the peak of the pulse reaches the flat-top density region of the target, the peak average value of the x-component of the quasi-static electric sheath field on the rear of the target near the interaction region is approximately twice as high in the vacuum case when compared to the background pressure case (see Supplementary Information).
The sheath field suppression model presented above predicts a greater reduction in conversion efficiency to protons at 50 Torr than found in the simulation; however, we note that the model assumes a three-dimensional background region and an extended region of background gas to neutralize the target. In order to reduce  www.nature.com/scientificreports/ computational costs, our simulations were run in two-dimensions with a smaller transverse extent than what is required by the model. These differences contribute to the discrepancy between the experimental and simulation results.

Discussion
The sheath field suppression model is best used to approximate the pressures at which the background gas limits ion acceleration and does not capture the time dynamics of the accelerating field. Since the highest energy ions are also the earliest ions to gain their energy, these ions are likely least affected by the background gas neutralizing the accelerating field. This observation is consistent with our experimental data in Fig. 2 which shows a cutoff energy that only varies by ∼ 15% across a three order of magnitude scan in pressure where ion acceleration was present. The ions accelerated at later times, and as such the lower energy ions, are more likely to be affected by the target neutralizing. This fact would present itself in the conversion efficiency, making the data presented in Fig. 3 a reasonable comparison. We have experimentally demonstrated MeV level ion acceleration with a mJ class laser at 100 Hz using liquid targets at a background pressure much higher than commonly used. We present a simple charge neutralization model and PIC simulations to support our experimental findings. The data presented in Fig. 2 demonstrates the benefits and capabilities of high repetition rate experiments. Once designed and installed, the data collection took less than 6 h. Each of the subplots in Fig. 2 contains roughly 700 energy spectra traces, with each trace containing 30 laser shots, therefore the data presented in Fig. 2 represents nearly 130,000 relativistic laser-target interactions. Using our experimental parameters, ion acceleration is suppressed at high background pressures ( > 8 Torr ). As the background pressure decreases, there is a slight increase in ion cutoff energy and an asymptotic approach to moderate conversion efficiency. The pressure threshold for ion acceleration is likely system dependent. Scaling the model to higher laser intensities should lead to a stronger sheath field, a larger ionization spot, and a shorter Debye length. Our estimates suggest that at increased laser intensities, ion acceleration suppression occurs at pressures where optical aberrations would interfere with the interaction. This work informs the requirements to achieve proton acceleration which considerably relaxes the background pressures necessary, giving more freedom over experimental choice of target, repetition rate, diagnostics and has potential for cost effective applications.

Experiment. The experiment was conducted using the Red Dragon laser housed within the Extreme Light
Laboratory at Wright Patterson Air Force Base in Dayton, OH. The experimental setup is shown in Fig. 1. The Ti:sapphire laser (800 nm) delivers 3.5 mJ on target with a 40 fs pulse duration into a focal spot size of < 2.0 µm FWHM, reaching an average intensity of 3 × 10 18 Wcm −2 and a peak intensity of 8.0 × 10 18 Wcm −2 . The prepulse contrast of the laser was measured to be at the 10 −6 level on the picosecond-timescale ( ±100 ps ). On the nanosecond-timescale, the prepulse contrast is measured to be better than 10 −10 (detection limited), apart from a pulse replica that exists at −6.1 ns . The ns-pulse replica was below the intensity threshold that would limit ion acceleration at peak focus as was previously seen in Morrison et al. 37 Although the target and laser are capable of operating at 1 kHz, the experiment was run at 100 Hz (250 Hz for 8.4 Torr data) for this study due to radiation exposure safety limits. The laser is focused by a F/1 protected gold coated off axis parabola onto a continuously flowing, 450 nm liquid sheet target 13 at a 45 • angle of incidence. Target thickness was determined by the pressure and flow rate of the high pressure backing lines as well as the impact angle of the liquid microjets. The target has previously been characterized across the background pressures presented in this study using a Filmetrics device as described in Morrison et al. and George et al. 13,37 . A compact magnetic spectrometer which collected ion spectra was located along the rear target normal direction 130 mm from the interaction region. Particles entered into a 0.13 T magnetic field via a 1.0 mm entrance slit and were collected by a linear CCD covered with 508 µm of RP408 plastic scintillator bonded with index matching epoxy. To block scattered light, the CCD was covered with 60 nm of Al deposition. Although the magnetic spectrometer does not distinguish between ion species, calibration of the ion signal using CR-39 and mylar differential filtering suggests that in the energy range of interest ( > 1 MeV ), the measured signal is dominated by protons and heavier ions do not contribute significantly to the measurement 37 .
While operating the laser-target interaction, the lowest achievable background pressure with our setup was 32 mTorr. At pressures below 1 Torr, we varied the chamber pressure by adjusting the vacuum pump aperture. To achieve background pressures above 3 Torr, we backfilled the chamber with air. At low repetition rates, backfilling with air would alter the local background gas significantly, changing the field suppression model presented above. However, using diffusion estimates for the target liquid expanding to a gas then diffusing into air, we estimate that the majority of the local (within ∼ µm of the target surface) background gas is ethylene glycol with our laser repetition rate even when backfilling with air. Even so, assuming a 50/50 mixture of ethylene glycol and air, our model (with Z ≃ 6 ) would predict a cutoff pressure for ion acceleration between ∼ 9 and ∼ 20 Torr , which fits our lower boundary pressure (peak intensity) estimate well. Additionally, at the highest pressures we consider the effects of the protons traveling through a global background gas of air as they make their way to the detector. At the highest pressure presented in this manuscript, the background gas is responsible for down scattering a 1.0 MeV proton to 0.93 ± 0.2 MeV at the magnets and ∼ 0.87 MeV at the detector. Higher proton energies are less affected by the background gas, and as such, we conclude that down scattering in the background gas does not significantly contribute to the substantial reduction in conversion efficiency seen at pressures above ∼ 1 Torr.

Simulation.
Simulations were performed using the particle-in-cell code VLPL. The simulation space was 65 0 × 70 0 with cell sizes 0.02 0 × 0.08 0 in the x × y dimensions, respectively. The target consisted of singly ionized hydrogen, carbon, and oxygen in the constituent ratios of ethylene glycol. The initial electron tempera-Scientific Reports | (2020) 10:18245 | https://doi.org/10.1038/s41598-020-75061-1 www.nature.com/scientificreports/ ture was set to ∼ 2 eV with matching velocity conditions for the ions, and there were initially 8 particle per cell of each species. The target region consisted of a 0.5 0 flat-top density region beginning 15 0 from the left of the simulation box with an initial electron density n e = 60n c , where n c = m e ω 2 0 /4πe 2 is the critical electron density with m e the electron mass and ω 0 the laser angular frequency. Given the contrast of the laser system on the picosecond-timescale, we included a 2 0 exponential profile with a 0.5 0 scale length on the front of the target in the simulation to mimic preplasma conditions and improve laser-to-plasma coupling, while a linear 0.1 0 rear of the target reduces target heating into the lower density region beyond the rear of the target. In the vacuum case, the remainder of the simulation space was empty. In the background plasma case, a neutral gas with atomic constituents of cold ethylene glycol filled the remainder of the simulation space with a particle number determined using the ideal gas law at room temperature to match a 50 Torr chamber environment. A laser with a profile a = a 0 e −(r 2 /σ 2 0 ) sin 2 [πt/(2τ 0 )] linearly polarized in the simulation plane enters the simulation space from the left boundary at a 45 • angle with respect to the target surface, with a 0 = eE 0 /m e ω 0 c , where E 0 is the amplitude of the laser. For our simulation, a 0 = 2 and σ 0 and τ 0 are chosen such that the FWHM intensity spot size is 2.2 µm and the FWHM intensity pulse duration is 42 fs.