The scaling of proton energies in ultrashort pulse laser plasma acceleration

This paper presents a systematic investigation of an ultrashort pulse laser acceleration of protons that yields unprecedented maximum proton energies of 17 MeV at a table-top Ti:sapphire laser power level of 100 TW. For plain few-micron-thick foil targets, a linear scaling of the maximum proton energy with laser power is observed and this is attributed to the short acceleration period close to the target rear surface. Although excellent laser pulse contrast was available, slight deformations of the target rear were found to lead to a predictable shift of the direction of the energetic proton emission away from the target normal that could be used for better discrimination of the low-energy part of the spectrum.


Introduction
In recent years, a number of applications of laser-accelerated ion pulses have been realized or proposed that make use of their unique properties. The high beam-optical quality [1] of particle beams accelerated from the rear side of a laser-irradiated thin foil and the inherent synchronization suggest their use as probes for electric fields in laser-driven inertial confinement fusion [2] and in relativistic laser plasma research [3,4]. Here, the large energy bandwidth of the non-relativistic particles even allows for improved time mapping by the correlation between time-of-flight and energy. The high charge of the pulses combined with the excellent transverse emittance further motivates the injection of laser-accelerated bunches into synchrotrons after an appropriate phase rotation has been performed [5,6].
Medical applications, especially in radiation therapy [7], could also take advantage of the broader energy bandwidth, provided that it can be reproducibly matched to the energy loss in a macroscopic target volume. Radiation therapy, however, requires proton energies of up to 250 MeV at a dose rate of a few Gy per minute, and thus a pulse repetition rate of the order of 1 Hz. Although the radiation doses available in single pulses seem promising for use in this field, the average achievable current, and thus the pulse repetition rate, still has to be improved. The crucial and still unresolved issue, however, for most applications is the increase in maximum particle energy. At present, the maximum proton energies achieved with highenergy high-power lasers operating in single pulse mode range between 50 and 60 MeV (for references, see section 3), while with table-top lasers that, in contrast, operate with repetition rates of 10 Hz, energies of only around a few MeV have been reported.
With the recent development of 100 TW class Ti:sapphire lasers with ultrashort pulses with pulse lengths around 30 fs, introduced in section 2, the hope is to bridge the hitherto huge discrepancy in the achievable maximum ion energies between single-shot and table-top laser systems [8,9]. Systematic studies can now be performed and scaling laws for the most established ion acceleration regime, the target normal sheath acceleration (TNSA) [10], are to be deduced with ultrashort pulses for the identification of feasible routes toward high proton energies at reasonable pulse repetition rates.
In this work, we aim for a simple and robust approach that, following the systematic studies presented in sections 3 and 4, can be developed into a stable proton source operating at high repetition rates. Thus, micron-thick plain metal foils were used as targets that can later be operated, e.g. in tape targets, although more complex structured or mass-limited targets are promising candidates for further improvement of the spectral quality [11] and of the maximum energies [12]. With the 150 TW laser Draco (Dresden laser acceleration source), recently installed at the research center Dresden-Rossendorf (FZD), we were able to demonstrate the highest proton energies observed so far with a 10 Hz repetition rate table-top laser system, and could show a strong deviation from the well-known square-root scaling of the proton energy with laser power to a linear scaling. After a revision of the existing analytical models for the scaling of maximum energies, we derive that the measurement can be well explained in the frame of these models, a fact that has not been discussed so far to our knowledge. Furthermore, we present in section 4 that the detection of the maximum proton energy can be complicated by a preplasma-induced deformation of the foil, even for state-of-the-art laser pulse contrast. This effect is experimentally well known [13] for 10 TW class lasers and can be qualitatively explained analytically as well as in two-dimensional (2D) particle-in-cell (PIC) simulations for the parameters of the experiment. As the experimental results strongly rely on the laser 3 parameters on the target, the following section is devoted to a detailed technical description of the experiment, which may serve as a reference for the emerging class of 100 TW lasers.

Experimental setup
The experiments were performed with the ultrashort pulse 150 TW laser system Draco, recently installed at the research center Dresden-Rossendorf. Based on the Pulsar design of Amplitude Technologies (France) [14], the chirped pulse amplification Ti:sapphire system consists of a regenerative amplifier and three stages of multipass amplifiers capable of delivering up to 6 J pulse energy at a pulse repetition rate of 10 Hz. Cryogenic cooling in the last amplifier ensures a stable beam profile for single pulse operation, as well as for variable pumping power, and thus variable beam energy. Spectral gain narrowing in the amplifier chain is pre-compensated for by an accousto-optic filter inside the cavity of the regenerative amplifier (Mazzler, Fastlite). Active control of spectral losses allows for a full amplification bandwidth of up to 80 nm and thus pulse durations of below 25 fs after compression. An independent second programmable acoustooptic filter (Dazzler), controlling the spectral phase of the pulse, is used in combination with a SPIDER (APE) diagnostic of the compressed pulse for the pre-compensation of higher order dispersion effects in the chain. Following compression, wavefront corrections are performed with a large aperture deformable mirror imaged onto a wavefront sensor (Phasics) and potential pulse-front tilts are interferometrically monitored and minimized over the full aperture [15].
For the first series of experiments discussed here, the laser pulse is transported into a dedicated target area with an overall efficiency (compared to the energy level directly behind the last amplifier) of about 60%. The wavefront corrected beam of about 90-100 mm diameter is tightly focused using an off-axis parabolic mirror with a focal length of 250 mm to a spot size of about 3 µm diameter (full-width at half-maximum, FWHM). About 80% of the laser energy can be concentrated inside the focal spot, as shown by the enlarged image in figure 1. Hence, peak intensities exceeding 10 21 W cm −2 are readily achieved on the target. The parameters, which have routinely been achieved on the target for experiments, are listed in table 1 and compared with the design parameters of the system. Special measures are taken to optimize the temporal pulse contrast of the system. By means of two saturable absorbers, one cleaning the short energy boosted oscillator pulse at a pulse duration of a few ps and the other installed behind the regenerative amplifier, the amplified spontaneous emission (ASE) background from both cavities is significantly suppressed. Measurements with a high dynamic range third-order autocorrelator (Sequoia, Amplitude Technologies), depicted in figure 2, show that a level pulse contrast ratio of few 10 −10 can be achieved over several 100 ps before the intensity starts to increase about 30 ps ahead of the main pulse. On the ns time scale, the ASE pedestal as well as prepulses leaking out of the regenerative amplifier or originating from cross-talk in the multipass amplifiers are measured with a fast photodiode (rise time of 1 ns) using calibrated absorption filters and a fast oscilloscope. The ASE signal begins to become measurable about 3.5 ns before the main pulse and reaches an energy contrast which, integrated over 100 fs (time resolution of the third-order autocorrelator), is consistent with the intensity contrast measurement for a few 100 ps. This is achieved by means of two pulse cleaning Pockels cells, one of which also protects the laser front-end against target back reflections.
As sketched in figure 3, thin metal foil targets are irradiated with p-polarized light at an incident angle of φ = 45 • . Positioning in the focal plane is continuously monitored between where the dynamic range in the wings is increased by multiple exposure techniques using calibrated attenuators. The diameter (FWHM) of the spot amounts to 3.2 µm in the horizontal and 2.8 µm in the vertical, respectively, which is due to a slight ellipticity in the incoming beam. The horizontal line out illustrates that 80% of the laser energy can be found inside the focal spot.
consecutive laser shots by backside imaging, as well as front-side imaging of the focal spot of an alignment laser beam exactly copropagating with the high-power beam, resulting in an alignment precision for the focus depth of 10 µm. Proton pulses emitted from the target rear side under the target normal direction are detected using stacks of radiochromic film (RCF) dosimetry media and under the target normal using a Thomson parabola spectrometer with an entrance aperture of 0.25 µsr. With RCF the spatial distribution of the proton fluence can be measured. Moreover, stacking of many RCF slices provides a coarse energy resolution due to the range-energy relationship of the stopping power. From the RCF data, the proton spectrum can be reconstructed, and since the complete proton beam can be recorded, a calculation of the conversion efficiency of laser to total proton energy is possible [16]. In this study, stacks of GafChromic EBT films covered with 13 µm Al foil are used. The RCF stacks are mounted on a motorized wheel in order to irradiate at least eight stacks before opening the target chamber becomes necessary. For the detection of the proton spectra with higher spectral resolution and to distinguish different ion species, a Thomson parabola spectrometer consisting of parallel magnetic (560 mT) and electric fields (3.7 × 10 5 V m −1 ) is used. The parabolic ion traces are recorded using a multi-channel plate with the phosphor anode imaged to a 12-bit CCD camera in order to provide online analysis of the obtained ion spectra in the energy range of 1-30 MeV.

Proton energy scaling
Over the last decade, maximum proton energies well above 10 MeV could only be observed when high-power high-energy lasers were applied for the irradiation of thin foils, as summarized by the open circles in figure 4. At the same time, maximum energies reached with short pulse Table 1. Comparison of the design parameters of the 150 TW Draco system and those reproducibly achieved during the first experimental campaign. All parameters refer to conditions on target. The intensity is derived using a focal spot diameter (FWHM) of 3 µm. Contrast is given as the power ratio with reference to the maximum pulse power, as discussed below. lasers were generally limited to only a few MeV, as illustrated by the colored diamonds where the color represents the typical ranges of pulse durations of such lasers of τ l = 30, . . . , 100 fs. While for the aforementioned long-pulse high-power lasers with τ l 100 fs, a clear scaling of the maximum proton energies with the square root of the laser power could be established experimentally [8], no obvious dependence could be obtained from the short pulse laser data, this having been partly due to the fact that these sub-10 TW lasers were operating close to the MeV proton energy threshold. As reported in the following, this situation has changed with the recent advent of 100 TW class ultrashort pulse lasers (τ l ∼ 30 fs).
The red squares in figure 4 represent the results from our systematic studies where the laser energy has been varied while keeping its pulse duration and focusing parameters constant. Maximum proton energies of up to 17 MeV have been reached and have thus considerably extended the energy range accessible with compact ultrashort pulse laser systems. Moreover, the scaling of the maximum proton energy with laser power has been found to significantly deviate from the well-established square-root scaling. This novel scaling regime, exhibiting a faster linear scaling with laser power for ultrashort laser pulses, can be basically understood as a consequence of the 3D field distribution in the vicinity of the target rear surface. For the sake of simplicity, the analytical model of Schreiber et al [9] will be used in a novel interpretation to illustrate the transition between the two regimes.
The model is based on the assumption that a relativistic laser pulse of pulse duration τ l accelerates N e electrons from the target front side to an average energy E e . The total number of electrons is determined by the efficieny η of the conversion of laser energy E l into electron energy N e E e = ηE l . The electron bunch of length τ l c leaves the target rear side spread to a circular area of radius R = r l + d tanϑ, where r l denotes the radius of the laser focal spot, d the thickness of the irradiated thin foil and ϑ the half-angle of the propagation cone. As a consequence, a positive surface charge Qe/(π R 2 ) is induced at the rear side of the target. It leads to the on-axis potential distribution where ζ = z/R stands for the normalized propagation direction normal to the foil. Electrons of average energy E e are forced to turn around at a distance ζ t = E e /E ∞ assuming ζ t 1.
The equation of the equilibrium number of electrons outside of the foil with the induced surface   (9) represents a 5 J experiment at Janusp [26], and the dotted diamonds (10) show the results of an energy scan applying up to 10 J on the target and at LULI [8]. Open circles (11,12,13,14) stand for single shot experiments at the glass laser facilities LLNL NovaPW [27], RAL Vulcan [28], Los Alamos Trident [29,30] and Phelix GSI [6]. Marked circles represent recent energy scans ranging up to 300 J performed at Vulcan and Trident [29,31]. The color code of the experimental points corresponds to the different pulse duration regimes given in the legend for the curves following equation ( the potential corresponds to the hot electron Debye length λ D and the surface field is consistent with the one resulting from the established plasma expansion model [10]. The energy of a laser-accelerated proton is now deduced from the potential caused by the induced surface charge at the actual position of the proton ζ to E p (ζ ) = −e (r = 0, ζ ) = −E ∞ (1 + ζ − 1 + ζ 2 ). The size of the surface charge thus influences the energy gain of protons close to the surface (ζ = z/R < 1). For a quantitative analysis of the maximum energy E max that a proton can reach, integration of the equation of motion up to the duration of the laser pulse leads to an implicit function [9] that can be approximated by The reference time τ 0 = R/v ∞ = R/(2E ∞ /m p ) 1/2 is used to emphasize the time the proton remains in the vicinity of the accelerating surface charge. It directly follows that for acceleration times and thus pulse durations shorter than twice the reference time τ 0 , the scaling of the maximum proton energy with laser power is dominantly linear. This situation applies for the Draco data presented in figure 4, where for P l ∼ 100 TW the reference time amounts to τ 0 ∼ 20 fs and the pulse duration to τ l = 30 fs. Using the measured focal radius of r l = 1.7 µm and a well-established propagation angle of ϑ = 10 • , and assuming a conversion efficiency of η = 20%, our experimental data are well described by equation (3), where the red solid line in figure 4 corresponds to a target thickness of d = 2 µm and the dashed line to d = 5 µm. A set of solid curves is additionally displayed for slightly longer (color-coded) pulse durations to guide the eye. For higher powers of ultrashort pulses, the influence of the source size diminishes as the reference time τ 0 decreases, leading to the curvature of the red line. The same holds true for longer laser pulses, thus increasing acceleration times. For all cases the scaling converges to the square-root scaling for τ l 2τ 0 . The corresponding dotted line in figure 4 therefore represents an upper limit of the proton energy for a given laser power, provided that the conversion efficiency is assumed to be constant. As it is not the intention of this paper to discuss the absolute proton energies achievable with long pulse lasers, but only the scaling behavior in relation to the short pulse case, the increase of the absorption efficiency to up to 50% [8], being well established for this laser class, has been ignored in all the curves of figure 4.
We are aware of the fact that the model strongly simplifies the acceleration dynamics, especially with regard to the 1D plasma expansion model [8,10]. However, as it has been successfully used to describe maximum energies and pulse duration dependencies in the past and nicely describes the principle behavior of our experimental findings, we feel that it can be used to discuss the efficiency of modern ultrashort pulse laser systems for proton acceleration. Keeping for the present discussion conversion efficiency and electron divergence constant, optimum use of the laser power can be made when (τ l /τ 0 ) ∼ 2.5 [32], which for the Draco parameters discussed here would correspond to P l ∼ 1 PW. It thus turns out (red curve in figure 4) that ultrashort laser pulses can be efficiently used for the acceleration of protons in the TNSA regime when (a) the laser pulse is focused tightly and (b) the laser power is well above a few 100 TW. For the laser energies at present available at Draco (3-4 J), optimum conditions As electrons are believed to penetrate the target foil with a divergence angle ϑ ∼ 10 • , maintaining condition (a), i.e. a small source size at the target rear, not only requires tight focusing but also thin foils of the order of d ∼ 1 µm. However, as discussed in the following section, at a laser power level of 100 TW, excellent pulse contrast is required to be able to take advantage of such foil thicknesses. Figure 5 shows maximum proton energies as a function of the foil thickness and the foil material for nearly identical laser parameters. Again, the general trend can be nicely reproduced by the red line in the figure representing the Schreiber model (equation (3)) for the same parameters that are used in figure 4. Furthermore, no significant changes are observed at the 100 TW level when different target materials are used. Especially for the case of the semiconductor silicon, this finding allows for a more complex target design based on straightforward wafer preparation technologies.

Proton acceleration from foil targets distorted by shock waves
Although Thomson parabola spectrometers provide an excellent energy resolution, absolute proton numbers as well as the energy-dependent beam divergence above about 1 MeV can be best determined with stacked RCF films. As this information is of particular importance for the design of beam transport systems and thus for most applications, images of representative shots were recorded. In these shots, a systematic deviation of the emission angle of the most energetic protons from the target normal was found for the 2-µm-thick foil targets, as illustrated by the raw RCF images presented in figure 3. Consequently, in these shots, the small acceptance angle of the online spectrometer did not cover the full energy range.
For two characteristic shots on foils of different thicknesses (2 and 5 µm titanium foil), this deflection is analyzed in figure 6. The centroid derived from the angular distribution is plotted for proton energies corresponding to the stopping power in the particular RCF stack layers as Dashed lines indicate the corresponding spot edges in the horizontal cut of the angular proton emission distribution. The edges illustrate an energy-dependent beam divergence of the order of 10 • -20 • , which is slightly reduced for thicker foils, as well. For a set of more than 30 consecutive shots, this behavior was reproduced with the deflection of the most energetic protons exhibiting a fluctuation of about ±5 • . This general behavior also holds true when the angle of incidence φ (or the foil orientation, respectively) is slightly rotated, allowing for the optimization of the online detection system. For such an optimized angle, higher proton energies, consistent with the RCF stack measurements, are recorded (not explicitly shown). Further, for this condition, only highest carbon and oxygen ion charge states are observed in the Thomson parabola spectrometer.
These findings can be explained by a scheme first discussed by the group at the Lund laser facility in 2005 [13,33]. The ns ASE pedestal of an ultrashort laser pulse with sufficient intensity (≈10 12 W cm −2 ) can form a preplasma at the front surface of the target. As the preplasma expands into vacuum, it launches a cold and plastic shock wave with a velocity of the order of µm ns −1 . The shock front breaks through the rear surface of the foil and results in a significant deformation (several µm) of this surface (sketched in the left part of figure 7). As long as the rear surface remains intact and the ion density gradient remains steep, effective proton acceleration in the TNSA scheme occurs during the time the ultrashort laser pulse is interacting with the target foil. At higher ASE intensities, the maximum proton energy can be limited due to a longer plasma scale length [25,34]. The deformed target geometry finally determines the emission direction of the energetic proton pulse. When the main laser pulse impinges on Figure 7. Schematic overview of the proton acceleration from a foil target after shock wave deformation. (Left) An ASE pedestal with a duration of a few ns generates a cold ablation plasma, which expands and launches a shock wave into the target foil. The shock front breaks through and deforms the rear surface while the plasma scale length remains small. (Right) The main part of the ultrashort laser pulse interacts with the deformed foil at oblique incidence, generating hot electrons, which are asymmetrically distributed at the rear surface. The most energetic protons stem from a small area with a local target normal shifted toward the laser axis. Protons with less energy originate from a larger area with an average target normal more parallel to the global target normal. the target, electrons are asymmetrically distributed along the target rear surface (sketched in the right part of figure 7). At the position where the laser hits the deformed target, the highest field gradients are created. Hydrogen and heavier ions are completely field ionized and protons are accelerated to the highest energies. Protons originating from this area are steered toward the laser axis (θ < 0 • ) according to the local deformation. Since lower energetic protons stem from a larger region, they experience on average less deflection, as can be seen in figure 6. Less deformation, and hence less deflection, is also expected for the thicker target foils. Moreover, the magnitude of the rear side deformation influences the divergence of the proton emission, which is reduced for the thicker target in figure 6, as well.

Modeling of the target deformation
In order to model the shape of the target deformation, we apply a simple analytical model, which employs the quasi-two-dimensional scheme presented by Lundh et al in [13] for the characterization of the shock wave ballistics. The deformation amplitude depends on the velocity of the shock front v s driving through the target and the deformation velocity v d of the target rear surface after shock break-through. From mass and momentum conservation, v s = c 0 ( √ 1 + x + 1)/2 and v d = c 0 ( √ 1 + x − 1)/α are derived. Here the parameter x equals x = (4α/ρ 0 c 2 0 )I 2/3 , where I is the ASE intensity of the laser, ρ 0 the density, c 0 the speed of sound and α a material-specific parameter. For our experimental conditions (I = 5 × 10 12 W cm −2 , Ti foil with ρ 0 = 4.53 g cm −3 , c 0 = 5.24 µm ns −1 , α = 1.02 and d = 2 µm), v s = 7.8 µm ns −1 and v d = 5.7 µm ns −1 can be derived. For an estimated ASE duration of τ ASE = 1.8 ns, we obtain a  [25], where the velocity of the perturbation front is estimated from the dependence of the optimum thickness on the prepulse duration. Although the ASE intensity at this experiment is considerably lower than for the present case, this velocity is of the same magnitude as the shock velocities derived with the model. This confirms that even for very thin foils of only 2 µm, which turned out to be the optimal thickness for the 100 TW Draco laser parameters, the target rear surface remains intact, although the calculated deformation is larger than the foil thickness. We further assume that the angular distribution of the emitted protons follows the shape of the generated Debye sheath [1]. The protons start perpendicular to the target surface and, in this picture, are subsequently deflected to pass perpendicular to the isosurface of the Debye sheath. The sheath is thus modeled as a superposition of a Gaussian-shaped target foil f (x) = A exp(−x 2 /2σ 2 ) and a different Gaussian sheath in a static situation and the angular distribution calculated accordingly (see figure 8 (top)).
The width of the Gaussian target shape 2σ can be fixed for the given deformation amplitude A using the experimental observable of the maximum deflection angle θ = 14 • of the centroids (figure 6), assuming that the most energetic protons originate from the point on the foil where the laser pulse is arriving at the deformed target.
Taking tan φ = f (x)/x and tan θ as the derivation of f (x), this leads to the relation σ = A/ tan φ tan θ exp(tan θ/tan φ) = 16 µm. The maximum of the Gaussian-shaped plasma sheath is set to the same position. A sheath amplitude of 1 µm (typical Debye length of the order of a wavelength) is used and the width of 9 µm is adjusted to match the maximum emission angles observed on the RCF stack layers. Angular proton distributions are evaluated corresponding to different sizes of proton sources and their centroid is determined and compared to the measured data, as depicted in the lower panel of figure 8. The shape of the model curve fits the RCF stack data surprisingly well. Although from this model the target shape cannot be predicted unambiguously because neither temporal plasma sheath evolution nor realistic field gradients are included, the proton source sizes for individual energy classes can be deduced indirectly. For a target thickness of d = 2 µm, a laser focal spot radius of r L = 1.6 µm and a half opening angle of the hot electron spread in the foil of ϑ = 10 • , the source size of the most energetic protons can be estimated as 2(r L + d tan θ) = 4 µm. This compares well to the model prediction (see figure 8). The obtained linear dependence between source size and proton energy reproduces the tendency published in [35] where the source size is measured with foil targets with microgrooved rear side.  figure 6. Independently, the com of the proton emission distributions obtained from a 2D PIC simulation as a function of the proton energy is included.

Particle-in-cell (PIC) simulation
In order to validate the simplified treatment of the sheath in the previous discussion, the interaction of the main pulse with the same predeformed target is simulated using the 2D PIC code PICLS [36]. The simulation box was set to 200 µm × 200 µm with 79 cells per micron. To save computation time, the electron density of the titanium foil is reduced to 100 n c , starting with a fully preionized neutral plasma of 1 µm titanium ions covered with a 50 nm proton layer at the rear surface. For the target deformation due to the ASE, we assume a similar Gaussian shape of 35 µm width at FWHM and 9 µm amplitude. Figure 9(d) shows the ion charge density profile before the main laser pulse hits the target. The laser pulse, having a Gaussian spatial and temporal profile with a waist of 7 µm and duration of 30 fs at FWHM, enters the simulation box from the left at 45 • with respect to the target. The laser is focused to the center of the Gaussian; hence it hits the deformed target off-center, see figure 9(a).  c)) (normalized to E a = 10E 0 (a), E b = 1E 0 (b) and E c = 0.1E 0 (c)) and ion charge density distribution ((d)-(f)) at the time the laser pulse maximum hits the target ((a) and (d)) and 100 fs ((b) and (e)) and 335 fs ((c) and (f)) later. (a) The laser main pulse is seen to hit the target at 45 • incidence (yellow arrow), being partly reflected. ((b) and (c)) The reflected pulse leaves the simulation box to the left, while the electron Debye sheath creates an electric field at the front and rear target surface. This sheath field is not symmetric, leading to asymmetric acceleration of ions ((e) and (f)), with the fastest ions shifted toward the laser direction. The low-energy protons are stemming from the distant wings where the target preformation, and hence sheath asymmetry, is negligible. Figure 9 shows the temporal evolution of the electric field strength ((a)-(c)) and ion charge density ((d)-(f)). It is seen that the laser hitting the target off-center (a) indeed creates an asymmetric electric field distribution ((b) and (c)). The Debye sheath tip is seen to move normal to the predeformed target surface at the location where the laser hits. As this is where the high-energy ions originate from, they are also moving in that direction ((d)-(f)).
Similar to the previous analytical discussion, the centroid of the angular proton emission distribution for different proton energies is evaluated and included in figure 8. Although the exact curvature does not reproduce the recorded data perfectly, in the PIC simulation the deflection angle for the most energetic ions is reproduced. Thus, the PIC simulation that considers the temporal plasma expansion also supports the assumption that the shape of the target foil is indeed imprinted in the shape of the field gradients.

Conclusions
In summary, it was possible to demonstrate that with state-of-the-art 100 TW class ultrashort pulse lasers and micron-thick foil targets, proton pulses can be effectively accelerated to energies up to 17 MeV in the established TNSA regime. The observed linear scaling with laser power suggests that already with 500 TW class lasers, the present maximum proton energy limit of about 50 MeV reached with high-energy lasers could be realized. Only plain foil targets and non-destructive laser pulse cleaning techniques (i.e. no plasma mirrors) were used, so that for the first time applications making use of full 10 Hz operation can be envisioned. In principle, the approach can be extended also to micro-coated dot targets, demonstrated to narrow the energy bandwidth at low energies [11]. Small deflections of the proton pulses induced by target deformation in the remaining ASE level were observed and investigated because of their importance for the determination of the proton energy scaling. The target deformation was shown to be predictable by analytical modeling as well as PIC simulations. They appear stable and may potentially be included in the design of proton beam delivery optics.
Above an energy level of 4 MeV, a laser to proton energy conversion efficiency of about 0.5% could be deduced from RCF stack measurements (i.e. a proton pulse energy of 6 mJ), whereas for energies above 10 MeV a typical dose of 2.5 Gy was detected on an area of a few square centimeters. Thus, systematic radiobiological experiments, requiring radiation doses of an order of one to tens of Gy at short irradiation times on minute scales, are well within reach.
Although TNSA scaling laws appear to be well investigated, for ultrashort pulses and intensities in the range of 10 21 W cm −2 it is seen that more detailed experimental studies are required. For a full understanding of the achievable proton and ion energies, this would include further study of laser absorption, and interferometric studies of the extension of the sheath field, especially when extended to TNSA regimes [37] where submicron-thick target foils start to become transparent.