S Semushin and V Malka Review of Scientific Instruments 72 2961 (2001)

Collimated protons accelerated from an overdense gas jet irradiated by a i µm wavelength high-intensity brusque-pulse laser

S. N. Chen, ^1, ^2, ³ M. Vranic,⁴ T. Gangolf,^1, ⁵ E. Boella,⁴ P. Antici,^half-dozen K. Bailly-Grandvaux,⁷ P. Loiseau,⁸ H. Pépin,^{half dozen} G. Revet,^i, ⁱⁱ J. J. Santos,⁷ A. M. Schroer,^five Mikhail Starodubtsev,^two O. Willi,⁵ L. O. Silva,^iv E. d'Humières,⁷ and J. Fuchs^1, ²

South. N. Chen

¹LULI - CNRS, Ecole Polytechnique, CEA: Université Paris-Saclay; UPMC Univ Paris 06: Sorbonne Universités, F-91128 Palaiseau cedex, France

²Establish of Applied Physics, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russian federation

ⁱⁱⁱCalorie-free Stream Labs LLC., Sunnyvale, CA USA

One thousand. Vranic

^ivGoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

T. Gangolf

¹LULI - CNRS, Ecole Polytechnique, CEA: Université Paris-Saclay; UPMC Univ Paris 06: Sorbonne Universités, F-91128 Palaiseau cedex, French republic

⁵Institut für Laser- und Plasmaphysik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany

Due east. Boella

⁴GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

P. Antici

^half-dozenINRS-EMT, 1650, boulevard Lionel-Boulet, J3X 1S2 Varennes (Québec), Canada

Grand. Bailly-Grandvaux

⁷Univ. Bordeaux, CNRS, CEA, CELIA (Heart Light amplification by stimulated emission of radiation Intenses et Applications), UMR 5107, F-33405 Talence, France

P. Loiseau

⁸CEA, DAM, DIF, F-91297 Arpajon, France

H. Pépin

^{half dozen}INRS-EMT, 1650, boulevard Lionel-Boulet, J3X 1S2 Varennes (Québec), Canada

Grand. Revet

^oneLULI - CNRS, Ecole Polytechnique, CEA: Université Paris-Saclay; UPMC Univ Paris 06: Sorbonne Universités, F-91128 Palaiseau cedex, France

²Institute of Applied Physics, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia

J. J. Santos

^viiUniv. Bordeaux, CNRS, CEA, CELIA (Eye Light amplification by stimulated emission of radiation Intenses et Applications), UMR 5107, F-33405 Talence, France

A. K. Schroer

⁵Institut für Light amplification by stimulated emission of radiation- und Plasmaphysik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany

Mikhail Starodubtsev

²Establish of Applied Physics, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia

O. Willi

⁵Institut für Laser- und Plasmaphysik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Frg

L. O. Silva

⁴GoLP/Instituto de Plasmas east Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal

E. d'Humières

⁷Univ. Bordeaux, CNRS, CEA, CELIA (Center Laser Intenses et Applications), UMR 5107, F-33405 Talence, France

J. Fuchs

^aneLULI - CNRS, Ecole Polytechnique, CEA: Université Paris-Saclay; UPMC Univ Paris 06: Sorbonne Universités, F-91128 Palaiseau cedex, French republic

^twoInstitute of Applied Physics, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia

Received 2017 Feb 20; Accustomed 2017 Sep 12.

Abstruse

We accept investigated proton acceleration in the forward direction from a almost-critical density hydrogen gas jet target irradiated by a high intensity (ten¹⁸ West/cm²), short-pulse (five ps) laser with wavelength of 1.054 μm. We observed the signature of the Collisionless Stupor Acceleration machinery, namely quasi-monoenergetic proton beams with small-scale deviation in addition to the more commonly observed electron-sheath driven proton acceleration. The proton energies we obtained were modest (~MeV), but prospects for improvement are offered through further tailoring the gas jet density contour. Also, we observed that this machinery is very robust in producing those beams and thus can exist considered as a future candidate in laser-driven ion sources driven by the upcoming side by side generation of multi-PW most-infrared lasers.

Introduction

Over the past decade, laser-accelerated ion beams^{¹–^iv} have attracted considerable involvement due to their unique characteristics and have already enabled many applications. These include ultrafast radiography^⁵–⁸, and prompt heating of dumbo affair^{⁹–^xi}. However, other scientific (light amplification by stimulated emission of radiation-driven ion fusion)^¹², medical (hadron therapy)^¹³–¹⁵, or more main-stream (like nuclear fuel recycling through Accelerator-Driven-System) applications tin simply be unlocked with farther improvement of the proton beam in terms of flux and maximum energy. Common to all these applications is indeed the need for an ion beam with controllable energy bandwidth, low divergence at the source, and also high repetition rate. The hurdle of a high repetition ion axle tin be addressed easily with the increasing repetition rate of before long bachelor^{^sixteen} and upcoming^¹⁷,¹⁸, laser drivers. Lifting the other two hurdles of bandwidth and deviation is yet more difficult as information technology requires moving away from the most relied upon acceleration method, i.e. the so-called Target Normal Sheath Acceleration (TNSA) mechanism^¹⁹. This machinery is very robust, but information technology intrinsically produces broadband free energy (with 100% spread, unless the number of available ions to accelerate is purposely reduced^²⁰) beams having angular deviation^²¹,²².

Several alternative ion acceleration schemes that would offer the desired improvements in beam parameters have been already proposed and are currently beingness tested. A start scheme relies on radiation-pressure driven dispatch (RPA) of ions in ultra-thin targets^²³. It is rather demanding not only in terms of target thickness, but also in terms of laser parameters. Indeed, for RPA the laser pulse must have ultra-high temporal contrast to not damage the target prior to the main pulse irradiation^²⁴. The laser pulse must also accept ultra-high intensity such that this acceleration mechanism would be dominant with respect to TNSA. For these reasons, with nowadays-twenty-four hours lasers, just the onset of the RPA dispatch mechanism, mixed with TNSA, could be demonstrated^{²⁵–²⁷}, and questions related to the beam quality, namely problems with triggering axle instabilities^²⁸ withal remain.

A second scheme also relies on the laser radiations pressure, but this fourth dimension in thicker targets where it directly puts in motion the ions at the critical density interface at which the laser is stopped. This is the so-called hole-tedious (HB) mechanism^²⁹ that accelerates these front-surface ions^{^xxx}.

In a partially expanded target having nearly-critical density^³¹,³², a tertiary ion acceleration machinery can have place, it is the so-chosen Magnetic Vortex Acceleration mechanism (MVA). As laser light tin can propagate into an expanded target, fast electron currents generated near the target rear surface form a long-living quasistatic magnetic field. This field generates an inductive electric field at the rear plasma-vacuum interface that complements TNSA in providing ion dispatch^³³–³⁵.

Finally, a quaternary ion acceleration mechanism was introduced by Denavit et al.^³⁶, followed past Silva et al.^³⁷ for critically dense targets. Information technology is known as the Collisional Daze Dispatch (CSA) machinery. Information technology is based on the fact that the light amplification by stimulated emission of radiation pulse can induce a collisionless daze wave in a most-critical density target, and the propagating shock tin reflect ions in the target and accelerate them to high energies. Such shock moving ridge is generated by the light amplification by stimulated emission of radiation-accelerated fast electrons injected into the target. It is collisionless since its dissipation mechanism is due to the electrostatic losses. Due to their high energy, the collisional dissipation into these electrons is negligible^³⁸, all the same collisionless processes (i.east. mediated by instabilities and plasma waves) can provide enough energy dissipation^³⁹. Thus, a density steepening (shock) tin can form as the fast electrons overcome the target medium in their propagation^³⁷.

Several numerical studies have been performed to optimize the target and light amplification by stimulated emission of radiation parameters for CSA, and take shown that targets with height densities shut to the critical density with smooth gradients^⁴⁰,⁴¹, represent optimal conditions. CSA was then extended to under-critical density targets by d'Humières et al.^⁴¹. There, the daze wave is not created by the laser, but ions-driven in a down density slope. This low density CSA (LDCSA) scheme was demonstrated experimentally^⁴²,⁴³, to produce low deviation, even so broadband beams since sheath dispatch in the rear end of the target density contour provides additional acceleration.

Light amplification by stimulated emission of radiation-driven CSA protons have significant advantages other than the prospects of low divergence and monoenergetic beams. First, the scaling with the laser energy of CSA is more favorable than that of TNSA, namely, the ion energy scales linearly with laser intensity^⁴⁴, whereas for TNSA it scales with the square root of the laser intensity^⁴⁵. The second point is purely applied since with TNSA or RPA, the solid targets that are used require precise target alignment for each shot, need strict light amplification by stimulated emission of radiation temporal contrast, and produce droppings in the target chamber. With CSA, especially using gas jets equally targets, operation would significantly be easier at upcoming high-repetition charge per unit light amplification by stimulated emission of radiation facilities, eliminating the need for target replacement and realignment. Moreover, using a lower-than-solid density for the target would reduce the amount of droppings generated^⁴⁶. We note that continuous operation of gas jets in high-vacuum chambers take been shown to be possible^⁴⁷, hence eliminating this concern.

The CSA scheme has been clearly demonstrated experimentally using CO₂ lasers^⁴⁸. Indeed, the long wavelength (10.6 µm) of these lasers allows for controlled well-nigh-critical targets to be easily produced. As mentioned to a higher place, the laser-driven CSA mechanism is most efficient in a critically dense plasma where n _eastward ≥γn _cr ^⁴⁹, with north_cr =ε _o m _east ω _{light amplification by stimulated emission of radiation} ²/eastward ² where ω _{light amplification by stimulated emission of radiation} is the angular frequency of the laser, and $γ = \sqrt{1 + a_{0}^{ii}}$ is the relativistic factor for the electrons derived from one-dimensional energy and momentum flux conservation, with $a_{0} = {(I_{50} λ_{50}^{2} / i.37 \times 10^{18} Due west . μ m^{ii} {.cm}^{- 2})}^{1 / ii}$ the normalized laser vector potential, I _L and λ _Fifty being, respectively, the laser intensity and wavelength. In applied units, n _cr[cm⁻³] =one.one ×10 ²¹/λ _L ⁱⁱ[µm]. Since the wavelength of CO₂ lasers is 10.6 μm, the minimum required target density to be overcritical in these conditions is 1 × 10¹⁹ cm⁻³, which is easily created with commercially bachelor gas bottles and a pulsed valve^⁵⁰. Using these targets with high intensity lasers, it was shown that CSA could indeed generate monoenergetic proton beams, i.e. having less than 5% energy bandwidth, of low (<100 mrad) divergence. The major downside is that in exercise CO₂ lasers are limited to irradiances $I_{Fifty} λ_{L}^{two}$ around 10^xix W.µmⁱⁱ/cm².

Well-nigh-infrared (0.eight–1 µm wavelength) lasers exist already at higher irradiances when compared to CO₂ lasers, with $I_{L} λ_{L}^{ii}$ reaching already more than than 10²¹ Due west.µmⁱⁱ/cmⁱⁱ in several facilities world-wide, with prospects for currently congenital facilities to reach I > 10²³ Westward/cm² ^⁵¹. However, the difficulty there with respect to CSA is that college density targets are required, i.e. with densities higher up 10²¹ cm⁻ⁱⁱⁱ (n _cr for a ane µm wavelength laser). This is already possible to reach with foams^⁵²; it becomes nowadays possible with gas jets^⁵³,⁵⁴.

In this article nosotros volition show that using a Hydrogen gas jet with a peak density of 2.vii north _cr, which is irradiated by an intense, short-pulse laser having a wavelength of 1.054 µm, proton beams that display the characteristics of CSA-accelerated beams were observed. With good consistency, the beam displays a quasi-monoenergetic tiptop up to 1 MeV with a very low athwart divergence. The energy of the peak is observed to correlate well with the laser intensity and the target density. The outline of the commodity is as follows. We volition start depict our experimental setup and the measured results. Next, we will nowadays hydrodynamic simulations that bring insight into the target weather, notably suggesting that the target width was affected by the prepulse accompanying the intense light amplification by stimulated emission of radiation pulse. Nosotros volition also present results of particle-in-cell (PIC) simulations of the interaction, which reveal that HB and CSA are both at play, but where CSA, in the conditions of the experiment, produces higher energy ions (hither protons) than HB acceleration. Moreover, the free energy of the ions generated by CSA is found to exist in reasonable agreement with the measured ones. Finally, we will hash out prospects for hereafter comeback of such acceleration technique, still with near-infrared lasers, using tailored gas jets as targets. We note that the recent result of Helle et al.^⁵⁵ exploits besides a loftier density hydrogen gas jet and a well-nigh-infrared (800 nm wavelength) laser for directed proton acceleration. There, the density is increased by the generation of hydrodynamic shocks induced by auxiliary light amplification by stimulated emission of radiation beams and the dispatch is induced by a magnetic vortex. This differs from our results which, when obtained at higher plasma densities, i.e. >2 northward_cr, are rather related to CSA, equally suggested past our simulations.

Experimental Setup

The experiment was performed using the Titan laser at the Jupiter Laser Facility (LLNL, USA), using the experimental setup shown in Fig.i. The curt pulse light amplification by stimulated emission of radiation arm of Titan, focused with an F/three off-axis parabola, irradiated a loftier density gas jet with a maximum of 210 J in five ps with a wavelength of one.054 μm. The laser had a all-time focus of 10 µm (at its total width at half maximum, or FWHM), containing an encircled energy of effectually 35%, thus giving a peak intensity at all-time focus of $I_{Fifty} λ_{Fifty}^{ii}$ = two.ii × x¹⁹ W.µm²/cm², i.e. yielding the parameter a₀ = 4.2. With these parameters, γn _cr = iv.3 × 10²¹ one/cmⁱⁱⁱ, which a priori sets a very high density requirement to efficiently drive CSA.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig1_HTML.jpg

Proton spectrometers were placed, as indicated in Fig.1, on the horizontal plane to measure the proton beam energy and angular distribution. Since we used a pure Hydrogen gas (H₂), the spectrometers were not equipped in a Thomson parabola configuration, i.e. they use a unproblematic magnetic deflection to resolve the proton energies. This allows also to use at the spectrometer entrance a wide slit (horizontally) to resolve, for each spectrometer, the proton beam over ±100 mrad effectually its mean angle of ascertainment. In Fig.1 is shown simply the spectrometer located at 0° with respect to the laser incident axis. Other spectrometers were located at 21°, 43°, and 92° with respect to the aforementioned centrality. As detectors, we used absolutely calibrated^⁵⁶ FujiFilm image plates of type TR.

The nozzle that we used for the gas jet is a Laval blazon design to attain supersonic gas outlet velocity^{^l}. The orifice was rectangular: 1 mm wide and 300 μm long with a throat of 300 × 300 µm² located 3 mm below the opening. Before the experiment, nosotros performed 3D optical (using a He-Ne, 633 nm wavelength laser probe) tomography measurements to narrate the rectangular gas profile in the output of the nozzle using Argon gas. It should exist noted that the difference in gas period constitute past our measurement and others^⁵⁷ between Argon, a monoatomic gas that was used in the test, and Hydrogen (H₂), a diatomic gas, has a deviation of profile and molecular density of less than 1%. This is consistent with calculations that can be made of the gas flow in the exit of the nozzle^⁵⁸, which advise that the differences between Ar and H₂ flows (having respective specific heat ratio 7/5 for for H_ii, and 5/3 for Ar) are minor. Figure2 shows a horizontal cross-section of the measured gas density distribution at 500 μm above the base of the nozzle. We measured, in the range of 10 to 100 confined, that the backing pressure is linearly related to the peak density of the gas jet, which is consistent with other measurements^{⁵⁰,⁵⁹,⁶⁰}. Density profile measurements at higher pressure are difficult, considering the high-density in the jet induces starting time refraction of the optical probe and even, for very high pressures, fully prevents the probe to penetrate the gas jet.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig2_HTML.jpg

3-D tomography of the gas jet. (a) The horizontal cross-department of the gas jet at 500 μm above the nozzle. The colorscale units are in molecular density (molecule/cmⁱⁱⁱ/bar). (b) Vertical and horizontal lineouts of the prototype in (a), which show that the form of the gas jet can be represented every bit a quasi-perfect Gaussian.

Equally shown schematically in Fig.one, the light amplification by stimulated emission of radiation was focused at the ascent edge of the Hydrogen gas jet and along the narrow part of the density profile (see Fig.2a). Since the density profile is Gaussian, we chose a position in this profile for the location of the best focus of the laser, which was placed at 150 μm in front of the location of the peak density. The peak of the laser focus was 500 μm above the gas jet nozzle, i.e. respective to the density profiles shown in Fig.2b.

To produce the high backing pressures needed to obtain near-disquisitional densities in the gas jet, nosotros beginning from a commercially bachelor gas canister (pressurized at 100 bars); then nosotros used a Haskel (world wide web.haskel.com) pneumatic gas compressor able to shrink the gas to 1000 bars, a Clark Cooper EX40 electro-valve (www.clarkcooper.com) that is rated for these high pressures, and loftier pressure pipes and fittings from Swagelok (www.swagelok.com). The gas that we used was Hydrogen (H_ii), which is a diatomic molecule at room temperature; in one case ionized by the laser, the peak ion density during the interaction is double the molecular density that is shown in the measurements of Fig.2. Therefore, by extrapolating our measurements to backing pressures between 150 confined to 900 confined of gas, we conclude that we tin a priori vary the ionized electron density up to ii.7n _cr.

Experimental Results

Before presenting the proton acceleration results, nosotros should notation that the laser pulse that we used to drive the ion dispatch had a pedestal earlier the chief pulse arrives. This pedestal, or prepulse, as measured during the experiment with fast diodes and a h2o-switch prison cell, contains around twenty mJ of energy (at the target chamber middle (TCC), i.eastward. at the location of the short-pulse focus) and is characterized by a brusque ramp (~0.3 ns) preceding a ~1 ns flat plateau. The calibration of the measurement was made past sending a depression-energy, 3 ns duration pulse through the amplifier chain and the compressor, and measuring its energy simultaneously at TCC, and on the diode which measures the prepulse on every shot. Note that these prepulse values are similar to the ones measured in other runs at the aforementioned laser facility by other groups^⁶¹,⁶². Since the prepulse intensity ( $I_{Fifty} λ_{L}^{2} =$ 10^thirteen Westward.µm^two/cm²) is to a higher place the ionization threshold, it modified significantly the gas jet density contour ahead of the main pulse irradiation. This was on one hand benign, since it reduced the thickness of the gas target, which increases the efficiency for CSA, but on the other hand, it had the detrimental outcome to push the disquisitional density interface abroad, i.e. this effectively defocuses the high-intensity light amplification by stimulated emission of radiation pulse arriving on the target interface and thus reduces its ability to drive a strong shock.

The modification of the gas target profile induced past the light amplification by stimulated emission of radiation prepulse is determined by hydrodynamic simulations of the gas jet evolution when it is irradiated by the prepulse. Here we relied on hydrodynamic simulations, to infer the target density profiles at the fourth dimension of the curt-pulse irradiation. Indeed, we could not optically probe the interaction due to the overdense gas jet and would have needed an x-ray source (or a second brusk pulse to create an x-ray burst) to radiograph the gas or plasma. Nevertheless, hydrodynamic simulations in these conditions are well-benchmarked and are able to grasp quantitatively the plasma evolution; such procedure of relying on hydrodynamic simulations has indeed been validated quantitatively many times over the years, equally shown e.g. in refs^{⁴²,⁶³–⁶⁶}. For such simulations, we used the FCI2 hydrodynamic code^⁶⁷ in 2D, modelling the same xy plane as shown in Fig.2a. Fitting the measurements shown in Fig.2, the contour of the gas jet used in the simulation was a Gaussian, as mentioned in the previous section, with a FWHM of 400 µm and using fully ionized Hydrogen with a temperature of 300 K. In the hydrodynamic simulations, the laser propagation from the nearly field (the focusing optics) to the far-field (focus) and later on, is described past a 3D ray-tracing parcel^⁶⁸. We specify a power law that fits the experimental light amplification by stimulated emission of radiation ability of the pre-pulse in guild to get the right light amplification by stimulated emission of radiation free energy. At each time step, the ability is distributed over the rays, then each ray propagates within the plasma and deposits its power via inverse Bremsstrahlung. Then, a not-local electron ship model is used for modeling oestrus fluxes. The focal aeroplane is adequately divers in terms of spatial dimensions, but ray-tracing packages (based on geometrical optics) do not take into account diffraction. This modelling^⁶⁷ is sufficient in many situations for describing plasma heating and is widely used in radiative-hydrodynamics ICF codes that take been well benchmarked^{⁶⁹,⁷⁰}.

In our simulations, the box used was 1.2-mm long and 400-microns wide, we prepare the initial density contour that fits the gas-jet's longitudinal profile (as derived from Fig.2 of the paper), and the initial temperature was set to an arbitrary low temperature. FCI2 being a radiative-hydrodynamics lawmaking designed for describing plasma heating and dynamics, the lower temperature bound used for computing ionization is around 1 eV, leading to a fully ionized plasma in the whole simulation box, even far from the focal spot. But, this has no implications on the fact that plasma heating is localized and on the formation of a blast wave: the plasma is all the same cold far from the focal spot.

The results of the prepulse irradiation of the gas jet are shown in Fig.3 at various times after the prepulse had begun. We observe that it significantly modified the gas jet profile, reducing information technology to well-nigh half its initial thickness after 1 ns. As a outcome, the main light amplification by stimulated emission of radiation pulse will meet the remaining steep and dense gas jet interface while being defocused by ~150 µm. Since the focusing optics of the laser is F/3, the effect of this defocusing results in a reduced intensity at this location of effectually 3 × 10¹⁸ W/cm², a ₀~1. This is estimated by analyzing a gear up of images of the curt-pulse beam, equally focused by the F/3 parabola, taken at various positions around the best focus. The defocusing is seen to follow very well the theoretical gauge for a Gaussian beam, and we observe that a defocus of 150 µm corresponds to a nominal increase of the beam FWHM from 10 µm (at best focus) to ~45 µm. Apart from such superlative laser intensity condition, nosotros also varied (reduced) during the experiment the laser energy or moved the laser focusing signal further to the foot of the gas density profile, hence further reducing the light amplification by stimulated emission of radiation intensity on the critical density interface. These various conditions will be summarized below.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig3_HTML.jpg

Hydrodynamic simulation of the spatial profile of the ion density of the Hydrogen gas jet at various times (as indicated) afterward the starting time of its irradiation by the prepulse of the Titan light amplification by stimulated emission of radiation pulse used during the experiment.

Experimentally, we kickoff performed a serial of shots using the setup shown in Fig.1. While keeping the laser intensity abiding, we varied the bankroll pressure in the gas jet from 170 to 900 bars, which is equivalent to varying the peak electron density in the ionized target gas jet from 0.5due north _cr to 2.sevennorth _cr. The resulting proton spectra measured with the spectrometer oriented at 0° are shown in Fig.4. Note that the 100 keV lower end of the spectrum is the instrumental lower detection limit.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig4_HTML.jpg

A comparison of experimentally measured proton beams generated from the gas jet target in the forward (0°) direction and with different summit density for the gas jet target. (a) Proton spectra measured at 0°. Note that the spectra shown here take not been spectrally deconvolved by the width of the spectrometer slit. The latter is however small compared to the width of the spectral peaks. For case, the spectral meridian measured at 2.5n_cr, which has a width of ΔE/E ~0.16 would have this width reduced to 0.xiii by deconvolving the slit width. Similarly, the spectral peak measured at 1.4n_cr, which has a width of ΔE/E ~0.3 would accept this width reduced to 0.26 past deconvolving the slit width. (b) Divergence of the proton beam as measured continuously along the slit of the spectrometer located at 0°, and at the location of the proton spectral peak that can exist observed in (a). Annotation that exterior the primal centrality (0°), the spectrum has also a similar shape every bit shown in (a), with a spectral peak around the aforementioned value as at 0°, simply with much lower proton number.

As seen in Fig.4, as the density of the gas target was varied from underdense to overdense, the proton spectrum clearly shows that the energy of the pinnacle in the spectrum increased with the target gas density. As well shown in Fig.4 are the angular patterns of these proton beams, all displaying a narrow distribution and well resolved within the credence of the unmarried spectrometer located at 0°. We stress that in all cases, no signal was recorded in the other spectrometers located at larger angles around the bedroom (i.due east. at that place was no point above the noise level). In the instance of overcritical densities, due to the simultaneous observations of a peak in the spectrum, and of a narrow angular distribution for the accelerated beam, we conjecture that the dominant acceleration mechanism could be CSA, as in the example of the CO_ii laser experiments. Every bit volition exist detailed below, nosotros detect that this scenario is supported by the numerical simulations.

A clear spectral peak could non be distinguished in the case of the pinnacle density of 0.fivenorth _cr, although the angular pattern of the axle in this case displayed a narrow profile, even narrower than for higher gas densities: the divergence of this beam is thirteen mrad. This extremely small divergence could be due to the MVA mechanism discussed above, i.east. to a quasi-static magnetic field on the back side of the target formed by the hot electrons accelerated direct past the light amplification by stimulated emission of radiation on the front end side and by the resulting return current^³³. We annotation that experimentally, proton beams with minor divergence have besides been observed before by Willingale et al.^⁷¹ from underdense gas targets accelerated by the TNSA/MVA process.

As the density of the target is increased to one.ivnorthward _cr, the spectrum however conspicuously changes with a significant top in the proton beam spectrum actualization at 0.four MeV (with ΔE/Due east ~0.3). This appears to exist a combination of dispatch mechanisms where there is a quasi-monoenergetic beam on superlative of what appears to exist TNSA accelerated protons at lower energy. When the density of the gas jet target is further increased to two.5n _cr, the peak has shifted to several hundred keV higher in free energy (with ΔE/E ~0.sixteen).

Assuming a like proton beam divergence in the horizontal and vertical directions, nosotros can estimate the proton number in the spectral peaks observed in Fig.4a: using the angular width observed in Fig.4b, both for the spectral summit measured for the plasma density ii.five due north_cr, and the ane measured for the plasma density 1.4 n_cr, we obtain ~ten⁹ protons contained in the peak. This is equivalent, at these proton energies, to ~0.1 mJ of energy carried past the spectrally peaked protons.

The energy that the protons can learn through CSA, HB, and TNSA can be estimated using analytical expressions presented by Wilks et al.^²⁹, Fiuza et al.^⁴⁴ and Stockem-Novo et al.^⁷². For these theoretical studies, the last accelerated proton energy, i.e. acquired as the ions are reflected off the shock^³⁷ or accelerated past the hole-boring potential, tin can exist expressed in terms of $\sqrt{I / n_{i}}$ . For the energy of the ions accelerated past HB, we use one thousand_i(v_hb)²/ii, where m_i is the ion mass and v_hb is the HB ion velocity as expressed in ref.^²⁹, i.e. $v_{h b} = c \sqrt{m_{e} n_{c r} I λ^{two} / ii g_{i} n_{i} 1.37 \times 10^{18}}$ , where λ is in microns and I in W/cmⁱⁱ. Using a number of shots recorded during the experiment with various laser intensities and gas jet densities, the energy of the quasi-monoenergetic proton beam is plotted against the experimental inputs in the expression $\sqrt{I / n_{i}}$ in Fig.5a. The parameter space that we could explore during the experiment was express due to the low number of shots allocated for the campaign. This low shot number and variability in the laser parameters affects our ability to demonstrate reproducibility. Nonetheless, we tin state that, with the limited shots we could get on Titan, the robustness of the procedure generating peaked spectral distribution at high densities was skillful as witnessed by the spectra shown in Figsfour and 5.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig5_HTML.jpg

(a) The proton energy of the quasi-monoenergetic peak recorded in the spectrum for diverse shots (red dots, every bit measured in the experiment) for dissimilar values of the parameter (I/n_i)^ane/2 and every bit compared to the hole-deadening model (Wilks et al.^²⁹) and two CSA models (Fiuza et al.^⁴⁴ & Stockem-Novo et al.^⁷²). The red center signal indicates the energy of the largest population (spectral peak) of protons. The horizontal error bar corresponds to the FWHM of the signal around the spectral summit that is observed. (b) A typical spectrum corresponding to the points encircled in xanthous in (a), which correspond to shots recorded at lower pressures, and which are observed to fall near the curve for the hole-tedious model. (c) A typical spectrum of the other data points, recorded at higher pressures, which are closer to the CSA scalings.

The curve of green dots in Fig.5a, represents the expression presented past Fiuza et al.^⁴⁴ where this expression is dependent on the velocity of the electrostatic stupor created by the hot electrons. The shock velocity is there v _sh,F = (2Mc _southward)/(1 +M ⁱⁱ c _{due south} ²/c ^two) where c _s is the upstream sound speed, c is the speed of light and M ~ $\sqrt{(ane + η) / 0 . 4} {(n_{cr} / {northward}_{i})}^{ane / 2} {a_{0}}^{1 / ii}$ ^³⁷ is the shock Mach number. For our experimental intensities, we took η to be 0.2^⁷³, which is the absorption efficiency at the disquisitional density surface at the (defocused) light amplification by stimulated emission of radiation intensity nosotros used. The blue curve in Fig.5a represents the expression presented in Stockem-Novo et al.^⁷⁰ where their expression is based on the velocity of the adiabatic expansion of a gas; this model looks at a daze driven 3D spherical expansion, i.e. it should atomic number 82 to an underestimate of what we obtain since we work more than in a condition closer to a planar shock driven in the gas jet past the high-intensity laser. Hither, the velocity is $v_{southward h, Due south N} = c \sqrt{Z {grand}_{e} n_{c r} {a_{0}}^{2} / viii m_{i} n_{0}} (i + K_{a d})$ where 1000 _{advertisement} =7/3 for diatomic molecules.

As shown in Fig.5a, we can observe that the experimental information fall either close to the curve respective to HB or to the ones corresponding to CSA. We indeed observed that the information points encircled in the yellow line, close to the HB scaling, have a typical spectrum shown in Fig.5(b) where, on top of an exponentially falling spectrum, there are one or more than minor peaks on a plateau. These data points correspond to shots at a lower density of the gas jet (i.due east. close to n_cr), hence they are higher in the curve because the gas density (northward_i) is lower. In dissimilarity, the other experimental points with a typical spectrum with a strongly pronounced spectral tiptop as found in Fig.4a and too shown in Fig.5c, follow the curves describing CSA. These points accept been obtained at higher gas densities (i.e. >ii n_cr), since they stand for to lower positions in the graph as the factor (I/n_i)^1/2 is smaller. In short, the protons accelerated at high densities, and which brandish a strong spectral top, have higher energy than what is predicted by the hole-tiresome acceleration mechanism and are closer to the CSA trends.

Numerical Simulations

To verify that CSA is indeed the proton acceleration mechanism inducing the potent spectral peaks observed in our experimental conditions at high densities (run across Figs4a and 5c) and to proceeds insight into the actual acceleration processes, nosotros performed particle-in-prison cell (Motion picture) simulations using the lawmaking OSIRIS^⁷⁴ in 2D. The simulation box was 1273 μm long and sixteen μm broad, resolved with 48000 × 600 cells and 8 particles per jail cell. The total simulation time was 20 ps, sampled with a time footstep of Δt =0.06 fs. The initial plasma profile, with peak density of 2.7n _cr, was used for the commencement gear up of simulations, as shown (in blue) in Fig.6, and which corresponds to the modified gas jet target profile equally found by the hydrodynamic simulations shown in Fig.3 for the ane ns duration irradiation of the gas jet past the prepulse. The simulation box is transversely periodic, and the laser is launched from the left-manus wall. The laser is transversely a plane wave, with a temporal envelope of five ps at FWHM. The maximum laser intensity reaches the center of the gas jet (x =0) at t =6.v ps from the beginning of the simulation.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig6_HTML.jpg

(a) The density profiles of the gas jet as calculated by FCI2 (run across Fig.3) and used as the input into the Picture show simulation. Longitudinal density profiles of the gas jet along the laser centrality for two durations of pre-pulse irradiation preceding the main laser pulse (the unperturbed density contour is shown in black). The blue contour corresponds to conditions explored in the present experiment. The red contour corresponds to longer prepulse irradiation that would lead to a shorter density profile. (b) Plasma profiles at t = v.7 ps (0.viii ps before the peak of the main pulse reaches x = 0 mm). Both profiles are obtained for an irradiation by a laser pulse having an intensity characterized by a₀ = four.

In full general, we note that due to the quasi-1D geometry employed in the simulations, nosotros can wait that the proton energies will be overestimated, especially in the case of TNSA protons^⁷⁵. Nosotros underline that multi-dimensional simulations of this setup are beyond the current computational capabilities. Nonetheless, even if one would exist able to perform a full-calibration 3D simulation of the interaction, it would not be possible to guarantee the quantitative agreement in the proton energies between the PIC simulations and experiment, because this result is sensitive to the differences in the thickness of the initial plasma profile. An additional difficulty rises from the fact that the peak plasma density of the gas jet is close to the relativistic critical density, and minor variations in the light amplification by stimulated emission of radiation intensity might change the longitudinal position of the critical density interface. Nonetheless, every bit volition exist detailed below, the picture described by the simulations is found in reasonable understanding with the experimental data, hence allowing us to believe that the physics observed in the simulations is acceptable, and thus emphasizing that daze acceleration as the main acceleration mechanism.

We have tested in the simulation irradiating the gas jet at two laser intensities, namely a ₀ =ane and a ₀ = 4. We chose these two intensities as they stand for to the maximum intensity case (a ₀ = four, i.e. in the plane of best focus of the light amplification by stimulated emission of radiation), or the instance of reduced intensity (a ₀ = 1, resulting from the laser defocus by 150 µm due to the gas jet deformation induced by the prepulse). In both cases, a articulate stupor structure had formed at the target critical density interface irradiated by the laser. The resulting phase space of the accelerated protons for our experimental conditions is illustrated for the ii light amplification by stimulated emission of radiation intensities in Fig.7b and d. We observed that for both laser intensities, the phase space exhibits TNSA accelerated protons, those from hole-boring, as well as CSA accelerated ones which corroborates the fact that we detect several energy distributions, namely several peaks and continuous spectrum. The higher energy CSA accelerated protons led to, as shown in Fig.7a and c, peaks in the spectrum. Here, the TNSA accelerated proton spectrum is not included to highlight the population accelerated by CSA, and its correspondence to the experimentally observed spectral summit respective to a peak density of 2.5 n _cr, which is shown (scarlet bend) in Fig.4a. In the first example the tiptop is close to ane MeV, i.e. consistent with the cherry-red curve measurement shown in Fig.4a, which supports our theorize of the laser beam existence indeed defocused to such a reduced intensity. This is further supported past the fact that the free energy of the protons in the simulation using a ₀ = iv is higher than the i recorded in the experiment.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig7_HTML.jpg

Simulated proton properties obtained with the blueish plasma profile shown in Fig.6 at t = eleven.vii ps. (a) Spectrum of the daze accelerated protons using a laser intensity of a₀ = 1. (b) Corresponding proton longitudinal phase space with a laser intensity of a₀ = 1. (c) Spectrum of the shock accelerated protons using a laser intensity of a₀ = 4. (d) Corresponding proton longitudinal stage space with a laser intensity of a₀ = 4.

Effigyviii shows the temporal evolution of the electron density and allows us to read directly the velocity of the density discontinuities in units of c, the speed of light. This is done for the ii cases of the two density profiles of the gas jet shown in Fig.6 of the paper every bit modified by the ASE of the Titan short-pulse laser (having a ₀ = 1 in both cases). The interaction with the laser prompts a partial expansion backwards of the initially underdense sections of the plasma profiles. One observes that one cannot therefore clearly define a single dispatch velocity from Fig.8, considering of the density gradients in the organisation. However, there are several density discontinuities that propagate into the gas jet. The white line highlights the ascendant i (corresponding ion phase spaces are shown in Figs7b and 9a). The velocity of the maximum density elevation in Fig.8a is v = 0.017c. If we presume the ions reflected from this top would take the velocity v _i = 2five, the ion energy is ~0.54 MeV. The velocity in Fig.8b is somewhat higher, v = 0.024c, so the reflected ions are expected to be around i MeV. Nosotros note that these values are consistent with the spectrum of the reflected ions shown in Figs7a and 9c and which represent to the conditions in which these simulations were run (i.e. to a gas density of ii.5 n _cr).

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig8_HTML.jpg

Electron density evolution as a part of fourth dimension extracted from the PIC simulations. Here, the time is normalized to the laser frequency ω₀, and the propagation length c/ω₀, where c is the speed of low-cal. The initial density profiles correspond, respectively, to the (a) blue, and (b) ruddy profiles shown in Fig.half dozen. The laser normalized intensity is a₀ = ane in both cases. The white dashed lines evidence the hole-boring velocity, and total lines the respective daze velocity.

An external file that holds a picture, illustration, etc. Object name is 41598_2017_12910_Fig9_HTML.jpg

Proton backdrop obtained, for two different laser intensities (as labeled), with the plasma profile corresponding to the crimson profile shown in Fig.6 (i.e. corresponding to a 1.ix ns prepulse) at t = xi.7 ps. (a,b) Proton longitudinal stage space. (c,d) Spectrum of the shock accelerated protons.

We also note that the proton free energy of~0.54 MeV that would effect from the density discontinuity motion seen in Fig.8a is in reasonable agreement with the reddish spectrum shown in Fig.4a, which corresponds to a top density of the gas jet of 2.5n _cr, and a ₀ ~1. Such reasonable correspondence betwixt the simulated and measured proton free energy suggests that reflection of ions on the discontinuity, i.due east. the CSA machinery, observed in the simulations is indeed at play in the experiment.

Moreover, we could clarify in the simulations the velocity of the recessing point at which laser field reflection occurs, i.e. the HB velocity; the results are shown in Tabular arrayane.

Table i

Measured velocities of pigsty-boring (HB) and of the electron discontinuity observed to propagate in the simulations (daze, SH, as illustrated in Fig.eight), for diverse conditions, every bit stated.

	v _hb/c	v _sh/c
a ₀ =one, and using the blue profile of Fig.half dozen (1 ns ASE)	0.013	0.017
a ₀ =1, and using the red profile of Fig.vi (1.9 ns ASE)	0.018	0.024
a ₀ = 4, and using the blue profile of Fig.half dozen (1 ns ASE)	0.049	0.065
a ₀ = iv, and using the cherry profile of Fig.half-dozen (1.9 ns ASE)	0.08	≥0.1 (here we have several density discontinuities in the system with different velocities)

Hence, the simulations clearly demonstrate that, in weather condition of high density (all these simulations are performed with ii.5 due north _cr as the peak density), the dominant electron populations are characterized by a density fasten propagating faster than the hole-boring (and in front of it). This is some other indication that indeed CSA is at play here.

Finally, we take compared these velocities with respect to the measured plasma electron temperature in the simulations to verify that information technology did not impact shock germination, or the shock velocity. The plasma electron temperature (T _e) is hither measured in the upstream region at the time when the hole tiresome starts and the shock is formed. For a ₀ =i, T _e~0.12 MeV (for both the ruby and bluish profiles of Fig.6), yielding a sound speed effectually c _s =0.011 c. Stockem-Novo et al.^⁷² country that for nearly-disquisitional density targets, the shock is launched if v _hb >c _s, which is the case here, referring to the 5 _hb given in Table1. Moreover, every bit v _hb ≪c, we expect that v _sh/v _hb =4/3, which is indeed verified in Tableane. For a ₀ =4, T _e~i MeV (at maximum, i.eastward. at the peak of the light amplification by stimulated emission of radiation irradiation on target), yielding c _s =0.033 c. Again, we verify (see Table1) v _hb >c _s, and that as well v _sh/v _hb~4/3. This further corroborates that stupor acceleration is here at play, with velocities post-obit theoretical scalings.

Conclusions

We take demonstrated the power to accelerate protons through possibly the CSA process with a one.054 μm laser and we accept observed that in that location are certainly trends that should exist emphasized since they greatly touch the efficiency of CSA. Commencement, nosotros should note that the features in the spectrum are controllable by changing the peak density in the gas jet, and tin can be optimized (run across beneath) by reducing its thickness. Indeed, we had observed that as the density of the gas jet increased, then did the peak energy of the quasi-monoenergetic bunch. Furthermore, the minimum required density to find a peaked proton beam was, in our case where we used a laser with wavelength of one.054 μm, above northward _cr =i × 10²¹ 1/cm ³. Thirdly, the angular distribution is likewise sensitive to the gas jet density; nosotros observed that the higher the density, the broader the angular distribution.

Interestingly, the PIC simulations point out to, at high densities, a CSA acceleration machinery since the highest free energy protons are accelerated by a density spike that travels through the target at a velocity higher than the HB one. The experimental data at loftier density are seen also to exist close to existing CSA analytical scalings. This last bespeak could be of interest for assessing focal intensity on target at time to come high-intensity facilities (GIST, APOLLON, ELI, etc.) for which such measurement at the actual target location is still a challenge.

Every bit a perspective, we have explored the upshot of further reducing the thickness of the near-critical density profile in the target. For this, we tested (using the hydrodynamic code) what was the effect of having an fifty-fifty longer prepulse interacting with the gas jet. This is shown in Fig.6a: the red profile shows that when prolonging upward to 1.ix ns the prepulse irradiation (i.e. longer than actually used in the experiment), we tin can indeed shorten fifty-fifty farther the gas jet profile. Of form, this would induce the chief laser pulse to be even more than defocused. This was compensated in the simulations shown in Fig.9 by keeping the laser intensity on the critical density interface at a ₀ = 1 or a ₀ =4. When using this shortened contour and these laser intensities, the resulting proton beam parameters obtained in the Movie simulations are shown in Fig.9. It can be seen that reducing the thickness of the plasma, i.e. the amount of plasma on the back side, tin can indeed ameliorate significantly the concluding proton energy. In the instance with a thicker target (every bit explored in the experiment and shown in Figs6 and 7), the proton free energy is low, simply the spectral bandwidth is small-scale. In the example where the target is thinned out, with also a subtract of 2.v times of the acme target density, we observe that we can obtain much higher final proton energy (meet Fig.9d), simply here with some cost on the bandwidth, which is significantly larger. Testing such reduced width critical density gas jet will exist explored in further experiments, either by changing the prepulse parameters or past using directly thinner gas jets.

Acknowledgements

The authors thank the staff of the Titan Light amplification by stimulated emission of radiation and the Jupiter Light amplification by stimulated emission of radiation facility for their support during the experimental preparation and execution. We thank R. C. Cauble and J.R. Marquès for fruitful discussions, and R. Riquier for the gas jet characterization. This piece of work was partly washed within the LABEX Plas@Par project and supported by Grant No. 11‐IDEX‐0004‐02 and ANR-17-CE30-0026-Pinnacle from Agence Nationale de la Recherche. It has received funding from the European Spousal relationship'south Horizon 2020 inquiry and innovation plan nether grant understanding no 654148 Laserlab-Europe, and was supported in part by the Ministry building of Education and Science of the Russian Federation under Contract No. 14.Z50.31.0007. The use of the Jupiter Laser Facility was supported past the U.Southward. Department of Free energy past Lawrence Livermore National Laboratory nether Contract DE-AC52-07NA27344. This work is supported past FRQNT (nouveaux chercheurs, Grant No. 174726, Squad Grant 2016-PR-189974), NSERC Discovery Grant (Grant No. 435416), ComputeCanada (Chore: pve-323-ac, P. Antici). M.Five. and Fifty.O.S. were supported by the European Research Council (ERC-2010-AdG grant no. 267841). O.Willi acknowledges the DFG Programmes GRK 1203 and SFB/TR18. M. B.-G., J. J. S., and East. d.'H. acknowledge the funding from the project ARIEL (Conseil Regional d'Aquitane); their work was carried out in the framework of the Investments for the Hereafter Programme IdEn Bordeaux LAPHIA (ANR-10-iDEX-03-02). The Film simulations were performed at Fermi/Marconi (Italy) through PRACE resource allotment and at the Accelerates cluster (Lisbon, Portugal).

Writer Contributions

J.F., S.Northward.C. and East.d.H. conceived the projet. S.Northward.C. wrote the manuscript, made Figures 1, 2, 4, and 5 organized and lead the experiment, and analysed the data from the proton spectrometers; One thousand.V. performed the PIC simulations, besides equally their analysis, and made Figures 6, 7, eight and 9; T.Thou. prepared the experiment, laser and diagnostic alignment and characterized the gas nozzles; Due east.B. gave valuable insight in the interpretation of the P. I. C. simulation results and performed postal service-processing of the results; P.A. participated in the experiment; MBG fielded diagnostics during the experiment; P.L. performed the hydrodynamic simulations using FCI2 and made Figure 3; H.P. supervised students and participated in the experiment; G.R. prepared the experiment, laser and diagnostic alignment; J.J.S. supported the experiment and students financially; A.M.South. participated in the experiment and fielded diagnostics; M.S. supervised the information analysis and revised the manuscript; O.W. supervised students and provided financial support, J.F. supervised fielding the experiment, the data analysis and helped write the manuscript. All authors reviewed the manuscript.

Notes

Competing Interests

The authors declare that they have no competing interests.

Footnotes

Publisher'southward notation: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

References

i. Borghesi M, et al. Fast Ion Generation by High-Intensity Laser Irradiation of Solid Targets and Applications. Fusion Sci. Technol. 2006;49:412. doi: 10.13182/FST06-A1159. [CrossRef] [Google Scholar]

two. Fuchs J, et al. Laser acceleration of low emittance, loftier energy ions and applications. C. R. Physique. 2009;10:176–187. doi: ten.1016/j.crhy.2009.03.011. [CrossRef] [Google Scholar]

3. Daido H, Nishiuchi Thou, Pirozhkov AS. Review of laser-driven ion sources and their applications. Rep. Prog. Phys. 2012;75:056401. doi: 10.1088/0034-4885/75/5/056401. [PubMed] [CrossRef] [Google Scholar]

4. Macchi A, Borghesi M, Passoni M. Ion dispatch by superintense light amplification by stimulated emission of radiation-plasma interaction. Rev. Modernistic. Phys. 2013;85:751–793. doi: 10.1103/RevModPhys.85.751. [CrossRef] [Google Scholar]

5. Borghesi K, et al. Electrical field detection in laser-plasma interaction experiments via the proton imaging technique. Phys. Plasmas. 2002;9:2214. doi: x.1063/1.1459457. [CrossRef] [Google Scholar]

6. Romagnani L, et al. Dynamics of Electric Fields Driving the Light amplification by stimulated emission of radiation Acceleration of Multi-MeV Protons. Phys. Rev. Lett. 2005;95:195001. doi: ten.1103/PhysRevLett.95.195001. [PubMed] [CrossRef] [Google Scholar]

vii. Mackinnon AJ, et al. Proton Radiography of a Light amplification by stimulated emission of radiation-Driven Implosion. Phys. Rev. Lett. 2006;97:045001. doi: 10.1103/PhysRevLett.97.045001. [PubMed] [CrossRef] [Google Scholar]

8. Chen SN, et al. Focusing Dynamics of Loftier-Free energy Density, Laser-Driven Ion Beams. Phys. Rev. Lett. 2012;108:055001. doi: 10.1103/PhysRevLett.108.055001. [PubMed] [CrossRef] [Google Scholar]

nine. Patel PK, et al. Isochoric Heating of Solid-Density Matter with an Ultrafast Proton Beam. Phys. Rev. Lett. 2003;91:125004. doi: 10.1103/PhysRevLett.91.125004. [PubMed] [CrossRef] [Google Scholar]

ten. Antici P, et al. Isochoric heating of matter by laser-accelerated high-energy protons. Journal de Physique Four. 2006;133:1077. doi: x.1051/jp4:2006133218. [CrossRef] [Google Scholar]

11. Snavely RA, et al. Physics of Plasmas. 2007;14:092703. doi: ten.1063/one.2774001. [CrossRef] [Google Scholar]

12. Roth 1000, et al. Fast Ignition past Intense Light amplification by stimulated emission of radiation-Accelerated Proton Beams. Phys. Rev. Lett. 2001;86:436. doi: 10.1103/PhysRevLett.86.436. [PubMed] [CrossRef] [Google Scholar]

13. Bulanov SV, et al. Oncological hadrontherapy with laser ion accelerators. Phys. Rev. A. 2002;299:240. [Google Scholar]

xiv. Malka V, et al. Practicability of protontherapy using compact light amplification by stimulated emission of radiation systems. Med. Phys. 2004;31:1587. doi: x.1118/ane.1747751. [PubMed] [CrossRef] [Google Scholar]

15. Linz U, Alonso J. What will it take for laser driven proton accelerators to be applied to tumor therapy? Phys. Rev. Special Topics – Accel. and Beams. 2007;10:094801. doi: 10.1103/PhysRevSTAB.10.094801. [CrossRef] [Google Scholar]

16. Leemans, W. P. et al. The Berkeley Lab Laser Accelerator (BELLA): A 10 GeV laser plasma accelerator, in Advanced Accelerator Concepts: 14th Workshop, edited by S. H. Gold and Chiliad. South. Nusinovich, American Institute of Physics (2010).

17. Papdopoulos DZ, et al. The Apollon x Pow laser: experimental and theoretical investigation of the temporal characteristics. High Power Light amplification by stimulated emission of radiation Science and Engineering science. 2016;4:e34. doi: 10.1017/hpl.2016.34. [CrossRef] [Google Scholar]

18. Mourou K, et al. The future is fibre accelerators. Nat. Phot. 2013;7:258–261. doi: 10.1038/nphoton.2013.75. [CrossRef] [Google Scholar]

19. Wilks SC, et al. Energetic proton generation in ultra-intense light amplification by stimulated emission of radiation–solid interactions. Phys. Plasmas. 2001;8:242. doi: 10.1063/one.1333697. [CrossRef] [Google Scholar]

20. Hegelich M, et al. Laser acceleration of quasi-monoenergetic MeV ion beams. Nature. 2006;431:441–444. doi: 10.1038/nature04400. [PubMed] [CrossRef] [Google Scholar]

21. Snavely RA, et al. Intense Loftier-Free energy Proton Beams from Petawatt-Laser Irradiation of Solids. Phys. Rev. Lett. 2000;85:2945. doi: x.1103/PhysRevLett.85.2945. [PubMed] [CrossRef] [Google Scholar]

22. Bolton PR, et al. Instrumentation for diagnostics and control of laser-accelerated proton (ion) beams. Physica Medica. 2014;xxx:255–270. doi: ten.1016/j.ejmp.2013.09.002. [PubMed] [CrossRef] [Google Scholar]

23. Macchi A, et al. Light amplification by stimulated emission of radiation Acceleration of Ion Bunches at the Front Surface of Overdense Plasmas. Phys. Rev. Lett. 2005;94:165003. doi: x.1103/PhysRevLett.94.165003. [PubMed] [CrossRef] [Google Scholar]

24. Antici P, et al. Energetic protons generated by ultrahigh contrast light amplification by stimulated emission of radiation pulses interacting with ultrathin targets. Physics of Plasmas. 2007;14:030701. doi: ten.1063/ane.2480610. [CrossRef] [Google Scholar]

25. Kar Southward, et al. Ion Acceleration in Multispecies Targets Driven by Intense Laser Radiation Pressure. Phys. Rev. Lett. 2012;109:185006. doi: 10.1103/PhysRevLett.109.185006. [PubMed] [CrossRef] [Google Scholar]

26. Henig A, et al. Radiation-Force per unit area Acceleration of Ion Beams Driven by Circularly Polarized Laser Pulses. Phys. Rev. Lett. 2009;103:245003. doi: ten.1103/PhysRevLett.103.245003. [PubMed] [CrossRef] [Google Scholar]

27. Dollar F, et al. Finite Spot Furnishings on Radiations Force per unit area Acceleration from Intense High-Contrast Laser Interactions with Thin Targets. Phys. Rev. Lett. 2012;108:175005. doi: 10.1103/PhysRevLett.108.175005. [PubMed] [CrossRef] [Google Scholar]

28. Palmer C, et al. Rayleigh-Taylor Instability of an Ultrathin Foil Accelerated by the Radiation Pressure of an Intense Laser. Phys. Rev. Lett. 2012;108:225002. doi: 10.1103/PhysRevLett.108.225002. [PubMed] [CrossRef] [Google Scholar]

29. Wilks South, Kruer WL, Tabak M, Langdon AB. Absorption of Ultra-Intense Light amplification by stimulated emission of radiation Pulses. Phys. Rev. Lett. 1992;69:1383. doi: x.1103/PhysRevLett.69.1383. [PubMed] [CrossRef] [Google Scholar]

30. Sentoku Y, et al. High free energy proton acceleration in interaction of curt laser pulse with dense plasma target. Phys. Plasmas. 2003;10:2009. doi: x.1063/1.1556298. [CrossRef] [Google Scholar]

31. Matsukado Grand, et al. Energetic Protons from a Few-Micron Metallic Foil Evaporated past an Intense Laser Pulse. Phys. Rev. Lett. 2003;91:215001. doi: 10.1103/PhysRevLett.91.215001. [PubMed] [CrossRef] [Google Scholar]

32. Yogo A, et al. Laser ion acceleration via control of the near-disquisitional density target. Phys. Rev. E. 2008;77:016401. doi: x.1103/PhysRevE.77.016401. [PubMed] [CrossRef] [Google Scholar]

33. Bulanov, S. V. & Esirkepov, T. Z. Comment on "Collimated Multi-MeV Ion Beams from High-Intensity Laser Interactions with Underdense Plasma". Phys. Rev. Lett. 98, 049503 (2007); Willingale, 50., et al., Reply. Phys. Rev. Lett. 98, 049504 (2007). [PubMed]

34. Bulanov SS, et al. Generation of GeV protons from 1 PW laser interaction with near critical density targets. Phys. Plasmas. 2010;17:043105. doi: 10.1063/ane.3372840. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

35. Nakamura T, et al. High-Energy Ions from Near-Critical Density Plasmas via Magnetic Vortex Acceleration. Phys. Rev. Lett. 2010;105:135002. doi: 10.1103/PhysRevLett.105.135002. [PubMed] [CrossRef] [Google Scholar]

36. Denavit J. Assimilation of high-intensity subpicosecond lasers on solid density targets. Phys. Rev. Lett. 1992;69:3052. doi: x.1103/PhysRevLett.69.3052. [PubMed] [CrossRef] [Google Scholar]

37. Silva 50, et al. Proton Daze Acceleration in Laser-Plasma Interactions. Phys. Rev. Lett. 2004;92:015002. doi: 10.1103/PhysRevLett.92.015002. [PubMed] [CrossRef] [Google Scholar]

38. Atzeni, S. & Meyer-ter-Vehn, J. The Physics of Inertial Fusion, Clarendon Printing.

39. Moiseev SS, Sagdeev RZ. Collisionless shock waves in a plasma in a weak magnetic field. J. Nucl. Energy, Part C Plasma Phys. 1963;five:43. doi: 10.1088/0368-3281/v/i/309. [CrossRef] [Google Scholar]

40. Moreau JG, d'Humières E, Nuter R, Tikhonchuk VT. Stimulated Raman scattering in the relativistic government in almost-critical plasmas. Phys. Rev. Due east. 2017;95:013208. doi: 10.1103/PhysRevE.95.013208. [PubMed] [CrossRef] [Google Scholar]

41. d'Humières East, et al. Investigation of loftier intensity laser proton acceleration with underdense targets. J. Phys.: Conf. Ser. 2010;244:042023. [Google Scholar]

42. Gauthier G, et al. Investigation of longitudinal proton acceleration in exploded targets irradiated by intense short-pulse laser. Phys. Plasmas. 2014;21:013102. doi: 10.1063/1.4853475. [CrossRef] [Google Scholar]

43. Antici, P. et al. Acceleration of collimated 45 MeV protons past strong collisionless shocks driven in big-calibration slope depression-density plasmas irradiated by a x²⁰ Due west/cm², 1 µm wavelength light amplification by stimulated emission of radiation, submitted; arxiv: 1708.02539. [PMC free commodity] [PubMed]

44. Fiuza F, et al. Laser-Driven Shock Acceleration of Monoenergetic Ion Beams. Phys. Rev. Lett. 2012;109:215001. doi: 10.1103/PhysRevLett.109.215001. [PubMed] [CrossRef] [Google Scholar]

45. Fuchs J, et al. Laser-driven proton scaling laws and new paths towards energy increment. Nat. Phys. 2006;2:48–54. doi: 10.1038/nphys199. [CrossRef] [Google Scholar]

46. Prencipe I, et al. Targets for loftier repetition rate advanced laser facilities: needs, challenges and perspectives. High Ability Laser Science and Engineering. 2017;v:e17. doi: x.1017/hpl.2017.18. [CrossRef] [Google Scholar]

47. Campargue R. Progress in Overexpanded Supersonic Jets and Skimmed Molecular Beams in Free-Jet Zones of Silence. J. Phys. Chem. 1984;88:4466. doi: 10.1021/j150664a004. [CrossRef] [Google Scholar]

48. Palmer, C. et al. Monoenergetic Proton Beams Accelerated by a Radiations Pressure Driven Shock. Phys. Rev. Lett. 106, 014801 (2011); Haberberger, D. et al. Collisionless shocks in laser-produced plasma generate monoenergetic loftier-energy proton beams. Nature Physics 8, 95 (2012); Tresca, O. et al. Spectral Modification of Stupor Accelerated Ions Using a Hydrodynamically Shaped Gas Target. Phys. Rev. Lett. 115, 094802 (2015).

49. Akhiezer AI, Polovin RV. Theory of Wave Movement of an Electron Plasma. Sov. Phys. JETP. 1956;3:696. [Google Scholar]

50. Malka V, et al. Label of neutral density profile in a wide range of pressure level of cylindrical pulsed gas jets. Review of Scientific Instruments. 2000;71:2329. doi: ten.1063/ane.1150619. [CrossRef] [Google Scholar]

51. Danson C, Hillier D, Hopps N, Neely D. Petawatt class lasers worldwide. Loftier Ability Light amplification by stimulated emission of radiation Science and Engineering. 2015;3:e3. doi: 10.1017/hpl.2014.52. [CrossRef] [Google Scholar]

52. Chen SN, et al. Density and temperature label of long-scale length, almost-disquisitional density controlled plasma produced from ultra-depression density plastic foam. Sci. Rep. 2016;vi:21495. doi: x.1038/srep21495. [PMC complimentary article] [PubMed] [CrossRef] [Google Scholar]

53. Chen SN, et al. Proton stopping power measurements using high intensity curt pulse lasers produced proton beams. Nuclear Instrum. and Methods A. 2014;740:105. doi: 10.1016/j.nima.2013.xi.002. [CrossRef] [Google Scholar]

54. Sylla F, et al. Development and characterization of very dumbo submillimetric gas jets for laser-plasma interaction. Rev. of Sci. Instrum. 2012;83:033507. doi: 10.1063/i.3697859. [PubMed] [CrossRef] [Google Scholar]

55. Helle MH, et al. Laser-Accelerated Ions from a Shock-Compressed Gas Foil. Phys Rev Lett. 2016;117:165001. doi: 10.1103/PhysRevLett.117.165001. [PubMed] [CrossRef] [Google Scholar]

56. Mancic A, Fuchs J, Antici P, Audebert P, Gaillard SA. Absolute calibration of photostimulable image plate detectors used as (0.5–20 MeV) high-energy proton detectors. Rev Sci Instrum. 2008;79:073301. doi: 10.1063/1.2949388. [PubMed] [CrossRef] [Google Scholar]

57. Svensson Grand, et al. Supersonic jets of hydrogen and helium for laser wakefield acceleration. Concrete Review Accelerators and Beams. 2016;19:051301. doi: 10.1103/PhysRevAccelBeams.nineteen.051301. [CrossRef] [Google Scholar]

58. Schmid Yard, Veisz L. Supersonic gas jets for laser-plasma experiments. Review of Scientific Instruments. 2012;83:053304. doi: 10.1063/1.4719915. [PubMed] [CrossRef] [Google Scholar]

59. Semushin S, Malka V. High density gas jet nozzle design for laser target production. Review of Scientific Instruments. 2001;72:2961. doi: 10.1063/i.1380393. [CrossRef] [Google Scholar]

threescore. Lemos N, Lopes N, Dias JM, Viola F. Pattern and label of supersonic nozzles for wide focus laser-plasma interactions. Review of Scientific Instruments. 2009;fourscore:103301. doi: 10.1063/1.3233895. [PubMed] [CrossRef] [Google Scholar]

61. Park J, Baldis HA, Chen H. The implementation and information analysis of an interferometer for intense brusk pulse light amplification by stimulated emission of radiation experiments. Loftier Power Laser Scientific discipline and Technology. 2016;iv:e26. doi: 10.1017/hpl.2016.21. [CrossRef] [Google Scholar]

62. Hey DS, et al. Light amplification by stimulated emission of radiation-accelerated proton conversion efficiency thickness scaling. Phys. of Plasmas. 2009;16:123108. doi: x.1063/1.3270079. [CrossRef] [Google Scholar]

63. Aliverdiev A, et al. Hydrodynamics of laser-produced plasma corona measured by optical interferometry. Plasma Phys. Control. Fusion. 2008;fifty:105013. doi: ten.1088/0741-3335/50/ten/105013. [CrossRef] [Google Scholar]

64. Borghesi M, et al. Characterization of laser plasmas for interaction studies: Progress in time-resolved density mapping. Phys. Rev. E. 1996;54:6769. doi: 10.1103/PhysRevE.54.6769. [PubMed] [CrossRef] [Google Scholar]

65. Willi O, Evans RG, Raven A. Time resolved density profiles of laserheated plasmas. Physics of Fluids. 1980;23:2061. doi: ten.1063/1.862893. [CrossRef] [Google Scholar]

66. Börner M, et al. Development of a Nomarski-type multi-frame interferometer equally a time and infinite resolving diagnostics for the gratis electron density of light amplification by stimulated emission of radiation-generated plasma. Review of Scientific Instruments. 2012;83:043501. doi: 10.1063/1.3701366. [PubMed] [CrossRef] [Google Scholar]

67. La fusion thermonucléaire par laser, vol. ii, R. Dautray et al. (Editors), Eyrolles, Paris (1994); Dattolo, E. et al. Status of our understanding and modeling of x-ray coupling efficiency in laser heated hohlraums. Physics of Plasmas eight, 260 (2001).

68. Kaiser TB. Laser ray tracing and ability degradation on an unstructured three-dimensional filigree. Phys. Rev. E. 2000;61:892. doi: 10.1103/PhysRevE.61.895. [PubMed] [CrossRef] [Google Scholar]

69. Marion D, Debayle A, Masson-Laborde P-East, Loiseau P, Casanova Yard. Modeling crossed-beam free energy transfer for inertial confinement fusion. Phys. Plasmas. 2016;23:052705. doi: 10.1063/1.4948489. [CrossRef] [Google Scholar]

70. Masson-Laborde P-E, et al. Laser plasma interaction on rugby hohlraum on the Omega Laser Facility: Comparisons between cylinder, rugby, and elliptical hohlraums. Phys. Plasmas. 2016;23:022703. doi: ten.1063/ane.4941706. [CrossRef] [Google Scholar]

71. Willingale L, et al. Collimated Multi-MeV Ion Beams from Loftier-Intensity Laser Interactions with Underdense Plasma. Phys. Rev. Lett. 2006;96:245002. doi: 10.1103/PhysRevLett.96.245002. [PubMed] [CrossRef] [Google Scholar]

72. Stockem Novo A, Kaluza MC, Fonseca RA, Silva LO. Optimizing laser-driven proton acceleration from overdense targets. Sci. Rep. 2016;vi:29402. doi: 10.1038/srep29402. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

73. Ping Y, et al. Absorption of Short Light amplification by stimulated emission of radiation Pulses on Solid Targets in the Ultrarelativistic Government. Phys. Rev. Lett. 2008;100:085004. doi: 10.1103/PhysRevLett.100.085004. [PubMed] [CrossRef] [Google Scholar]

74. Fonseca RA, et al. OSIRIS: A Three-Dimensional, Fully Relativistic Particle in Cell Lawmaking for Modeling Plasma Based Accelerators. Lecture Notes in Informatics. 2002;2331:342. doi: 10.1007/iii-540-47789-6_36. [CrossRef] [Google Scholar]

75. Brady CS, Arber TD. An ion acceleration machinery in light amplification by stimulated emission of radiation illuminated targets with internal electron density structure. Plasma Phys. Contr. Fusion. 2011;53:015001. doi: x.1088/0741-3335/53/i/015001. [CrossRef] [Google Scholar]

Manufactures from Scientific Reports are provided here courtesy of Nature Publishing Grouping

serlerystoned.blogspot.com

Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5647424/

Serle Rystoned