Spectral shaping of laser generated proton beams

The rapid progress in the field of laser particle acceleration has stimulated a debate about the promising perspectives of laser based ion beam sources. For a long time, the beams produced exhibited quasi-thermal spectra. Recent proof-of-principle experiments demonstrated that ion beams with narrow energy distribution can be generated from special target geometries. However, the achieved spectra were strongly limited in terms of monochromacity and reproducibility. We show that microstructured targets can be used to reliably produce protons with monoenergetic spectra above 2 MeV with less than 10% energy spread. Detailed investigations of the effects of laser ablation on the target resulted in a significant improvement of the reproducibility. Based on statistical analysis, we derive a scaling law between proton peak position and laser energy, underlining the suitability of this method for future applications. Both the quality of the spectra and the scaling law are well reproduced by numerical simulations.

3 summarized in an empirical scaling law, which is the first scaling law for monoenergetic spectra and deviates significantly from previous scalings obtained for the maximum proton energy of thermal spectra [3], [16]- [18]. The observed spectra and the scaling can be explained in terms of recent theoretical models and are strongly supported by two dimensional (2D) particle-in-cell (PIC) simulations.

Generation of monoenergetic proton beams from laser plasmas
When a high intensity laser pulse hits a thin metal foil, a hot plasma is formed at the target front side. In this plasma, electrons are accelerated by the laser field to relativistic energies and pushed into the target [19]. If the target is sufficiently thin, hot electrons are expelled at the back, where the restoring Coulomb force counteracts the charge separation. The main part of the hot electron population is trapped and constitutes an electron sheath behind the target [20,21]. The sheath density scale length is that of a screened Coulomb potential in a free electron plasma, i.e. the Debye length λ D = (ε 0 k B T e /e 2 n e ) 1/2 , where T e is the hot electron temperature and n e the hot electron density behind the target. The resulting electric field between the sheath and the positively charged target is of the order of 10 12 V m −1 and suffices to field-ionize the foil material as well as contaminants present on the target surface (mainly hydrocarbons and water). The generated ions are accelerated immediately in the field, where the ions with the highest charge to mass (q/m) ratio, i.e. typically protons, are favoured for acceleration. This process is known as target normal sheath acceleration (TNSA) [21].
The proton beams produced show an exponential, quasi-thermal energy spectrum with a distinct cutoff energy E cut-off of typically a few MeV, which depends strongly on the laser and target parameters [13]. This broad distribution can be explained mainly by three contributions: first, the accelerating TNSA field is inhomogeneous in the transverse direction, which means that the maximum energy a proton can reach is determined by its radial position. Protons located in the centre of the field are accelerated the most, up to the maximum energy E cut-off , whereas protons outside the centre experience a lower electric field strength and consequently are accelerated to lower energies. The inhomogeneous TNSA field distribution was measured with transverse probing of the electron density behind the foil, using proton deflectometry [22] or all optical probing set-ups [23], and exhibited a bell-shaped symmetry. This observation is in agreement with measurements of the beam divergence, which demonstrate that the proton emission takes place within symmetrical energy cones [9,24]. A second contribution to the broad spectrum can be found in screening effects: as the electric field decays when reaching into regions of higher particle density, deeper sited protons in the source layer will be (partially) screened from the electric field by their faster predecessors. Both because of such screening effects as well as the transverse inhomogeneity, the resulting spectrum has a strong correlation to the initial distribution of the protons to be accelerated on the target. Thirdly, the acceleration process follows some intrinsic dynamics, which are correlated to the temporal profile of the incident laser pulse. While analytical models for proton acceleration sometimes refer to static parameters like an 'effective acceleration time' [3], numerical simulations show that the TNSA field actually takes some time to build up to its maximum field strength [25] so that the proton source is affected by different field strengths throughout the whole interaction.
Following this understanding, Esirkepov et al [26] proposed an acceleration scheme for the generation of monoenergetic proton beams, where all protons are radially confined to a 'dot' source within the central field region (figure 1). If the proton source is furthermore sufficiently Figure 1. Confined TNSA from a micro-dot source. A TW-laser pulse hits a thin titanium foil at the front side exactly opposite to a polymer dot microstructure and creates a hot electron plasma. The electrons are accelerated in the laser field through the target and form a radially symmetric electron sheath at the back side, which gives rise to an electric of the order of a few TV m −1 . In this sheath field, surface atoms are ionized immediately and accelerated according to their charge to mass ratio up to MeV energies, whereas the light protons from the polymer dot outrun the heavier carbon ions and the titanium ions from the foil bulk. If a dot-like proton source is placed in the central part of the electron sheath field, protons from the dot will experience a uniform fraction of the transversely inhomogeneous field only [15,26]. Numerical simulations show that the dot does not need to be as thin as possible (so as to avoid spectral broadening due to screening effects), but that the formation of monoenergetic spectra is caused by the low relative proton density in the polymer dot with respect to heavier ions. The additional charge separation between the protons and the different carbon charge states then creates a discontinuity in the charge density, which accelerates those protons close to the heavy ion front in a monoenergetic manner [27,28]. In addition, one has to take care of parasitic proton contributions from surrounding contamination layers (e.g. oil or water vapour), which can be removed by controlled laser ablation of the target back side (cf below). thin so that screening effects are negligible, all protons experience the same potential and are accelerated to a monoenergetic distribution. However, in a more recent theoretical study, Robinson and Gibbon [27] found that limiting the thickness of the proton layer is not a critical criterion: for thicker dots, the formation of monoenergetic spectra is supported by the charge separation between the light protons and more inert ions (e.g. carbon) at an early acceleration stage, where the slower ion front causes a discontinuity in the charge density and hence an electrostatic shock which accelerates protons like 'test particles' in front of a quasi-static 5 positive background. Similar charge separation arguments were involved in the explanation of the observed monoenergetic deuterons from droplet targets [29,30], and spectral 'dips' as seen in [31]. Numerical simulations concerning micro-dot targets prove that this mechanism holds for robust dots of up to µm-thicknesses and may in fact vanish if the source layer is chosen too thin. The resulting proton spectrum thus has a strong dependency on the initial relative proton density in the source layer, and smaller relative proton densities may even lead to more pronounced monoenergetic spectra [27,32]. The described radial confinement of the proton source was first realized by Schwoerer et al, where a proton rich dot was deposited on the target back side and located exactly opposite to the impact position of a TW laser pulse. Other approaches to monoenergetic ion beams include active spectral selection with laser driven micro-lenses [33,34].

Target considerations and experimental set-up
The manufacturing of the microstructured targets for the proposed source confinement was realized in two steps. First, a layer of polymethyl methacrylate (PMMA) was applied on the back side of a 5 µm titanium foil using a spin coating technique ('double layer target') [35,36].
In previous experiments, a typical increase in total proton number by a factor of 6 was observed for an extended PMMA layer of 500 nm thickness on a 5 µm titanium foil in comparison to an uncoated titanium foil [37]. In a second step, the coated target surface was microstructured with a femtosecond laser and a micrometre positioning system, where square dots of 20 × 20 µm 2 were carved out of the PMMA surface. Alternatively, the microstructuring could be performed with an excimer laser through a lithographic mask, which yielded round dots of 10 µm diameter (figures 2b and (c)). From both types of targets, narrow band spectra were obtained consistently.
The experiments were carried out with the Jena 10 TW titanium : sapphire laser system (JETI), which delivered pulses of 800 mJ within 80 fs at a repetition rate of 10 Hz, focussed to a spot size of A FWHM = 5.5 m 2 . With the help of a fast-switching Pockels cell a pulse contrast of I main /I ASE > 10 8 between the main laser pulse and the prior pedestal of amplified spontaneous emission (ASE) was attained 300 ps before the main pulse. The JETI laser pulse hit the thin foil target exactly opposite to the dot position (figure 2). For this purpose, the target back side was observed with a long distance microscope with micrometre resolution, and the JETI incidence position was marked on the observation screen such that the dots only needed to be translated to this reference position in order to achieve proper alignment. The overall accuracy of the alignment procedure could be estimated to about 5 µm.
In order to ensure the dots were the only proton source, a second laser was used to remove the parasitic hydrocarbon adsorption layers around the dots (cf figure 2). A frequency-doubled Nd : YAG ablation laser (532 nm, 5 ns pulse duration) hit the target back side under an angle of 22.5 • co-centred with the JETI incidence position (figure 2). The laser was weakly focused on the target (d foc (1/e) ≈ 600 µm) to cover the whole proton source area around the dot [38], and was attenuated with a variable set of density filters to apply well-defined ablation fluences.
In the experiment, the microstructured targets were irradiated with intensities of I = 1-5 × 10 19 W cm −2 , where the intensity was varied by changing the laser pulse energy. The generated proton and ion beams were limited by an aperture (0.3, 1 or 3 mm) and subsequently dispersed with a Thomson spectrometer (figure 2), whereas the aperture diameter defined the energy resolution of the detection set-up, e.g. E res = 50 keV for 1 MeV protons with the 1 mm aperture. The particles were detected either with CR39 track detection plates or with an online The laser pulse hits the thin foil target at the front side exactly opposite to a micro-dot. Protons from the dot are accelerated within the central, homogeneous field region of the TNSA field and analysed with a Thomson spectrometer. The ions can be detected either with CR39 track detection plastics or an online imaging system (micro channel plate (MCP)). A second laser, which hits the target on the back side concentrically with respect to the first, is used for the cleaning of the target from residual contamination layer protons. (b) and (c) Microstructured target foils. (b) A 5 µm titanium foil carries polymer (PMMA) dots of 0.2 µm thickness, 20 × 20 µm 2 extent and 80 µm separation. The dots were 'carved out' from a polymer layer with the help of a femtosecond laser system. (c) Lithography targets. Round dots of 0.2 µm thickness and 10 µm diameter with 80 µm separation were generated on the back side of a 5 µm titanium foil via lithography with a pulsed excimer laser. The second technique allows for a more flexible fabrication of micro-dots, which are, however, considerably more sensitive to laser ablation than those produced with the femtosecond system.
imaging system based on micro channel plates (MCPs). The use of an MCP allowed for a very flexible experimentation and facilitated the collection of large amounts of data. Since the MCP delivers only relative spectra, it was calibrated against both the absolute CR39 spectra and 7 at the TCC-CV28 cyclotron of the Physikalisch-Technische Bundesanstalt (German National Metrology Institute) in Braunschweig, Germany. Figure 3 shows a comparison between spectra obtained from shots on micro-dots of 20 × 20 × 0.2 µm 3 (dark grey and black line), and shots on a plain unstructured 5 µm titanium foil (black line). The black curve represents an average over six spectra and yields the typical smooth thermal distribution. In contrast, the dot spectra display distinct peak features, which are located at E center = 1.7 MeV with E FWHM = 0.25 MeV ≈ 15% energy width for shot #1 (dark grey line), and at E center = 2.5 MeV with E FWHM = 0.2 MeV ≈ 8% for shot #2 (black line). The relative peak contrast between the peak maximum and the low energy background is typically 10 within 2 E FWHM (i.e. ≈ 4000/400 for shot #1 and ≈ 1000/100 for shot #2). Shot #1 contains about 3 × 10 4 protons within 1 µSr solid angle of observation, whereas the maximum exceeds the exponential distribution by a factor of 4. Conservative estimations based on beam divergence measurements at JETI and PIC simulations suggest that the full angle of emission of the narrow band protons is at least 24 mSr [15], which would yield a total number of >10 9 protons per shot in case of shot #1.

Narrow-band proton spectra
Drawing on the results from earlier numerical investigations [26,27,32], a 2D-PIC simulation was carried out for the micro-dot geometry, using the OSIRIS code [39]. The target consists of a dot, represented by a 0. Monoenergetic peaks appear consistently for a wide range of simulation parameters (e.g. varying focal spot size, pulse energy, simulation run time), if a micro-dot is irradiated. Figure 3(b) shows an exemplary spectrum obtained for I = 2.7 × 10 19 W cm −2 . A distinct peak is visible at 1.0 MeV, with 10% FWHM energy width and a contrast ratio of about 2 : 1, which is in good agreement with the experimental results. Since the formation of monoenergetic peaks strongly depends on the charge separation between different ion species, the slightly lower peak position can be attributed to the simplified resemblance of the dot composition, which contained only two ion species instead of multiple elements and ionization degrees, and the foil material, which was given by the dot heavy ion species instead of the heavier titanium, thus providing a smaller number of electrons.
Furthermore, it can be seen that the peak is not located at the cutoff energy of the proton spectrum, which continues with an exponential high energy tail. This behaviour can be explained as follows: besides the radial source confinement, the peak formation is affected by the electrostatic shock due to the charge separation between protons and carbons [28], whereas the protons that constitute the peak are those close to the ion front. As the heavy ion front is always slower than the fastest protons (lower q/m, screening effects), the central peak energy MeV with E FWHM = 0.2 MeV = 8% for shot #2. The ablation has suppressed the parasitic low-energy component of the spectrum and enables the acceleration of monoenergetic protons from the confined dot source. Narrow band features appear consistently once an ablation threshold fluence of thr = 1.2 J cm −2 at 532 nm is surpassed. In contrast, the irradiation of a plain titanium foil (black line) yields the typical thermal distribution (average over 6 spectra). (b) Results of the 2D-PIC simulation carried out with the OSIRIS code. The interaction of a laser pulse with a 1 µm heavy ion foil carrying a microdot (0.2 µm thickness, 10 µm radius) was simulated for an intensity of I = 2.7 × 10 19 W cm −2 (corresponding to E laser = 0.5 J on target), whereas the dot consisted of 50% protons and 50% heavy ions. In good agreement with the experimental results, the calculated spectrum yields a distinct peak at 1.0 MeV with 10% bandwidth. The spectrum further possesses an exponential high energy tail, which indicates that the peak formation occurs at lower energy than the cutoff energy of corresponding thermal spectra. The inset of figure 3(b) shows the results of a simulation carried out for a laser pulse energy of 15 J. The obtained peak at 9.3 MeV underlines the suitability of the presented technique for future applications (cf also figure 5).
is necessarily below the maximum cutoff. This theoretical reasoning is in good agreement with experimental observations: monoenergetic peaks sometimes appear on top of an exponential background, and the detected peak positions are typically 30-50% lower in energy than the maximum achievable cutoff energy for thermal proton spectra obtained with the JETI laser. The separation between peak position and cutoff energy underlines that the reduced bandwidth is not merely a simple geometrical effect, but involves fundamentally different physics, which will be of importance when discussing the scalability of the effect to higher laser energies below.

Rear side ablation
Laser ablation can be used to clean the target surface from adsorbates and hence suppress the homogeneously distributed and hence unwanted regular TNSA proton source [40]. We first studied the impact of frequency-doubled Nd:YAG laser pulses (λ = 532 nm, τ pulse ≈ 5 ns) on plain titanium foils by varying the ablation fluence from = 0.01 to 10 J cm −2 . Above a welldefined threshold fluence of thr = (1.2 ± 0.3) J cm −2 , the proton signal reduces to almost zero. The observed threshold corresponds to typical values for the ablation of organic layers from surfaces [41]. Below the threshold fluence, no ablation of contamination layers is expected, and indeed no effect on the proton acceleration could be identified.
In the next step, the effect of laser ablation was studied on microstructured targets. Below the threshold fluence, the observed proton beams correspond largely to those obtained from unstructured targets, i.e. they exhibit quasi-thermal spectra. However, once the threshold is surpassed, the continuous spectra are suppressed and distinct peak features appear (figure 3). We conclude that all contaminants have been eliminated; only the PMMA dot has resisted the ablation and remained as a confined proton source on the surface. Note that the ablation threshold of PMMA is about 3 J cm −2 at 308 nm [42], and should be even higher at 532 nm. In accordance with other results [40], the acceleration of titanium ions (Ti 1+ -Ti 4+ ) from the foil bulk is observed when removing the contamination layer on the target back side, which agrees well with the estimated TNSA field strength of a few 10 12 V m −1 .
Due to the vacuum conditions of the experiment, the ablated layers will start to recover immediately after the ablation has stopped. The timescale of such a recovery was studied by setting a delay between the last ablation shot and the JETI pulse. It turned out that after a delay of t = 5 s the spectrum had regained its exponential form completely, which is, however, well above the 100 ms between two consecutive ablation shots. The recovery time of adsorption layers can be estimated by the particle impact rate on the surface R = p/(3m k B T ) 1/2 [43], which follows directly from kinetic gas theory. Here, m is the mass of the adsorbed molecule and T the temperature in the target chamber. Assuming conservatively that the chamber pressure p = 10 −5 mbar is determined by hydrocarbons only (m CH4 ≈ 2.7 × 10 −25 kg), the impact rate at T = 293 K attains R = 6 × 10 15 cm −2 s −1 . A 12 Å contamination layer (as put forth in [44]) hence needs about 6 s to recover, in good agreement with our observations.
The ablation impact was also studied under single shot conditions. After one shot at the threshold fluence, almost all of the recorded spectra still display an exponential shape (figure 4). After two to four consecutive shots of ablation, the ratio between peaked and non-peaked spectra is evenly distributed, whereas for six or more shots the large majority of the spectra show a strongly reduced bandwidth. An irradiation with a higher fluence ( = 1.7 J cm −2 > thr ) reveals an even stronger dependence on the number of ablation shots. After two shots, 70% of the spectra are peaked, whereas after four shots almost all spectra show narrow-band features. This behaviour could be ascribed to initial incubation effects: the radiation induces defects in the contamination layer, which modifies the interatomic bonds and their coupling to the metal. The actual disposal of layers may thus not start immediately, but only after a critical number of defects have been accumulated [41]. However, with the help of controlled laser ablation, the generation of monoenergetic proton spectra from microstructured targets proves to be a highly reliable mechanism: an unprecedented reproducibility >80% was achieved over hundreds of shots, which represents a significant advance in laser proton acceleration. Relative frequency of peaked spectra as a function of the number of ablation shots. The back surface of the microstructured 5 µm titanium foil was ablated with a pulsed Nd:YAG laser (λ = 532 nm, τ pulse = 5 ns) in single shot mode, whereas the desorption of the surface contaminants is subject to initial incubation effects. After six consecutive ablation shots at the threshold fluence thr = 1.2 J cm −2 , 60% of the produced proton beams showed narrow-band spectra (whitened circles), which impressively demonstrates the reliability of the aiming and ablation procedure. For an increased fluence of = 1.7 J cm −2 > thr , an equally high reproducibility was reached after two shots already (black squares). In both cases, the relative frequency for the occurrence of peaked spectra approaches one when increasing the number of ablation shots. This means that narrow-band spectra are observed consistently, if a micro-dot is irradiated.

Energy scaling and future prospects
A subject of central interest for the generation of monoenergetic proton beams is the scalability of the technique to higher laser powers. We evaluated the peak position for many hundred spectra as a function of the JETI pulse energy while keeping all other parameters fixed. The use of an online detection system like an MCP facilitates the collection of such large amounts of data. It turned out that the average peak position increases from 1.42 to 1.63 MeV when the JETI pulse energy is increased from 0.5 to 0.8 J on target (figure 5, black squares). The four data points comprise a total of 140 spectra, all taken with 5 µm titanium foils carrying 200 nm thick dots, after ten consecutive shots of rear side ablation at the threshold fluence thr = (1.2 ± 0.3) J cm −2 . The energy range covered by the four data points was limited by the available laser energy and the range of the spectrometer. The error bars give the standard deviation of the sample sets and indicate the shot-to-shot fluctuation between the individual shots.
Various scaling laws have been proposed to connect the proton energy to the laser energy or intensity [16], [3]- [18]. All of these scalings refer to the cut-off energy of thermal spectra from plain foils, and it is known from previous measurements that the model by Fuchs et al [3] indeed The laser pulse energy on target was varied from 0.5 to 0.8 J, which corresponds to intensities of 2.9 − 4.7 × 10 19 W cm −2 . Consequently, the average peak position rose from 1.42 to 1.63 MeV (black squares). All other parameters were kept fixed (identical micro-dots on a 5 µm titanium foil; constant ablation conditions of ten consecutive shots at the threshold fluence). The four data points include a total of 140 monoenergetic spectra, which lends sufficient statistical significance to the results. The error bars represent the standard deviation of the statistical sample and thus delineate the shot-to-shot fluctuation. The observed proportionality is excellently reproduced by 2D-PIC simulations carried out for our experimental parameters (grey circles). The calculated peak positions lie slightly outside the standard deviation, but are well within statistical range of the sample sets. Together with an additional simulation for 15 J pulse energy (cf figure 3(b)), the calculated peak positions follow a linear function, E scale peak /MeV = 0.56 × E laser /J + 0.87 (grey line), which represents the first scaling law particularly for monoenergetic spectra. All previous scaling laws refer to the cutoff energy of thermal spectra from plain foils and fail to account for our data. For example, the model by Fuchs et al [3] predicts much higher energies and a steeper slope (grey crosses) for the current parameters.
successfully predicts the observed cut-off energies at JETI. However, it has been shown above that the peak position does not coincide with the cutoff energy of the corresponding thermal spectrum, but is bound to the slower heavy ion front. Thus, the scaling laws cannot account for our peak positions. In fact, a comparison of our data with the scaling law from [3] shows a strong discrepancy for our narrow parameter interval already: the model by Fuchs et al predicts much higher energy values and an eight times steeper slope (grey crosses). We therefore conclude that cutoff energy scalings are inapplicable for the generation of monoenergetic spectra from microstructured targets.
In order to substantiate this conclusion, we extended our PIC simulation to the different laser energies applied in the analysis. The results are shown in figure 5 as grey circles: when the laser energy is increased from 0.5 to 0.8 J, the calculated peak position shifts from 1.17 to 1.35 MeV. In agreement with the discussion of figure 3(b), the numerical results are systematically lower ( E ≈ −300 keV) than the experimental values. The calculated peak positions lie slightly outside the standard deviation, which still places them well into the statistical range of the sample sets.
The good accordance encouraged us to investigate the potential of micro-dot assisted proton acceleration for higher laser energies. An additional simulation was carried out for a pulse energy of 15 J, which is clearly in the range of the upcoming PW laser generation. The simulation yielded a monoenergetic peak at 9.3 MeV (inset figure 3(b)). In combination with the four calculated spectra between 0.5 and 0.8 J, the peak position was thus found to approximately follow a linear function E scale peak /MeV = 0.56 × E laser /J + 0.87 (grey line in figure 5). It is striking how closely the slope of the simulation data matches that of the experimental data, as illustrated by the black line in figure 5 depicting the same linear fit function upshifted only by 320 keV. This accordance lends authority to the observed proportionality, which represents the first scaling law specifically for monoenergetic spectra.
Clearly, monoenergetic proton beams at 9.3 MeV central energy will not yet be a competitor for conventional accelerators. They will, however, be of great value when starting to investigate the suitability of laser accelerators as pre-acceleration stages for e.g. storage rings, which would be a first step to combine the unique acceleration fields of laser plasma sources with the mature conventional accelerator technology. Also, they will open up the possibility of the first biophysical experiments, such as pulsed proton irradiation of biological tissue. 10 MeV protons are capable of penetrating up to 1.2 mm into biological tissue, which-in conjunction with the narrow bandwidth-would allow for a concise dose application. For more conclusive estimations, the dependency of the peak properties on other laser parameters such as pulse duration and intensity has to be investigated, which will be the subject of future experiments. The continuation of the present work will also include the study of micro-dot targets both with reduced hydrogen concentration (as proposed in [27,32]) as well as heavier dot materials (e.g. carbon dots). In the prospect of these promising experiments, however, today's capability of reliably generating 10 9 quasi-monoenergetic protons with less than 10% bandwidth by means of a scalable technique marks an important step towards application and will contribute significantly to the future of laser particle acceleration.