Spectral shaping of laser generated proton beams

S M Pfotenhauer¹, O Jäckel¹, A Sachtleben¹, J Polz¹, W Ziegler¹, H-P Schlenvoigt¹, K-U Amthor¹, M C Kaluza¹, K W D Ledingham², R Sauerbrey³, P Gibbon⁴, A P L Robinson⁵ and H Schwoerer⁶

¹ Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
² Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK
³ Forschungszentrum Dresden-Rossendorf, POB 510119, 01314 Dresden, Germany
⁴ John von Neumann Institute for Computing, ZAM, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
⁵ Central Laser Facility, Rutherford-Appleton Laboratory, Chilton, Oxon, OX11 0QX, UK
⁶ Laser Research Institute, University of Stellenbosch, Private Bag X1 7602 Matieland, South Africa

E-mail: pfotenhauer@ioq.uni-jena.de

Received 3 January 2008
Published 27 March 2008

Contents

• 1. Introduction
• 2. Generation of monoenergetic proton beams from laser plasmas
• 3. Target considerations and experimental set-up
• 4. Results
  • 4.1. Narrow-band proton spectra
  • 4.2. Rear side ablation
  • 4.3. Energy scaling and future prospects
• Acknowledgments
• References

1. Introduction

Throughout the past decade, high intensity lasers have ventured widely into the domain of particle acceleration [1, 2]. Current table-top laser systems of the 10 terawatt (TW) class readily generate ion beams of mega-electron-volt (MeV) energy [3]–[5] and bunches of relativistic electrons [6]–[8] by the interaction of ultraintense, ultrashort light pulses with matter. These particle beams possess a number of unique properties. They are initially very short pulsed, presumably comparable to the laser pulse duration [3]. Within this short time, they carry charges of pico- to nanocoulomb, which corresponds to currents exceeding 10³ A. Moreover, laser accelerated protons show an excellent laminarity [9].

The proton acceleration process typically takes place on a micrometre scale, which has excited many speculations about the potential applications of such compact laser driven particle sources. However, most applications depend crucially on the availability of monoenergetic beams. Proposed schemes for the fast ignition of inertial confinement fusion with high energy particle pulses would benefit greatly from the availability of an intense, monoenergetic proton beam for the penetration of a pellet target [10]. The use of laser plasma sources as injectors [11] for conventional accelerators requires proton beams with small bandwidth and emittance in order to match the injected bunch to the subsequent conventional accelerator. And especially for cancer radiation therapy—as one of the most attractive applications—spectral control is an inevitable key criterion [1, 12]. However, hitherto laser produced proton beams commonly displayed a broad, quasi-thermal energy spectrum (see for example [3, 5, 13]), until in two recent proof-of-principle experiments laser accelerated ion beams with narrow-band spectra were achieved for the first time [14, 15].

Here, we present major advances in the laser production of monoenergetic proton beams. By improving substantially the microstructured targets first used in [15], it was possible to increase the quality of the resulting spectra both in terms of central peak energy and peak width. Importantly, an unprecedented reproducibility of  >  80% for the appearance of monoenergetic spectra was achieved after having investigated in detail the systematic removal of parasitic contamination layers on the target back side via laser ablation. This degree of reliability represents a vital improvement in comparison with the previous proof-of-principle experiments [14, 15]. Distinctly peaked spectra with approximately 10% bandwidth at 2 MeV were recorded for hundreds of laser shots. From this large number of spectra, a dependency of the average peak position on the laser pulse energy was deduced. The energy dependency is 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.

2. 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 = (ε₀ k_B T_e/e² 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 10¹² 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 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 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].

3. 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 μm² 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 m². With the help of a fast-switching Pockels cell a pulse contrast of I_main/I_ASE > 10⁸ 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 = 1–5×10¹⁹ 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. ΔE_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 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 at the TCC-CV28 cyclotron of the Physikalisch-Technische Bundesanstalt (German National Metrology Institute) in Braunschweig, Germany.

4. Results

4.1. Narrow-band proton spectra

Figure 3 shows a comparison between spectra obtained from shots on micro-dots of 20×20×0.2 μm³ (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 ΔE_FWHM = 0.25 MeV≈15% energy width for shot #1 (dark grey line), and at E_center = 2.5 MeV with ΔE_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 2ΔE_FWHM (i.e. ≈4000/400 for shot #1 and ≈1000/100 for shot #2). Shot #1 contains about 3×10⁴ 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  > 10⁹ protons per shot in case of shot #1.

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 0.2×10 μm mixed slab of protons at 40 n_crit (m_p/m_e = 1830) and heavy ions at 40 n_crit(m_i/m_e = 3660), sitting on a 1.2 μm substrate slab containing only heavy ions (m_i/m_e = 3660) at a density of 80 n_crit. The laser pulse is normally incident at the centre of the foil. The temporal profile of the pulse is triangular, and it has a full width at half maximum (FWHM) duration of 80 fs. The simulation box is 20×20 μm, and the cell sizes are Δx = Δy = 2.5 nm. Initially, 64 particles were placed per species in each cell. The foil is initially centred in y, and the front surface of the foil is at x = 5 μm. The simulations were run up to 350 fs.

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 = 2.7×10¹⁹ 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 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.

4.2. 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 Φ = 0.01 to 10 J cm^–2. Above a well-defined threshold fluence of Φ_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 10¹² 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 Δt = 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_BT)^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 = 6×10¹⁵ 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 (Φ = 1.7 J cm^–2 > Φ_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.

4.3. 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 Φ_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 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 (ΔE≈–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_peak^scale/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 10⁹ 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.

Acknowledgments

This work was funded by the Deutsche Forschungsgemeinschaft (DFG) within the transregional collaborative research center `Relativistic Laser Plasma Dynamics' under contract TR18. We thank Burgard Beleites and Falk Ronneberger for their extensive support at JETI, as well as Waltraud Gräf and Dr Hans-Jörg Fuchs from the Institute of Applied Physics (IAP), Jena, for their help with the target fabrication. We also thank Volker Dangendorf, Roland Lauck, Kai Tittelmeier and the PTB Braunschweig for their support with the MCP calibration at the PTB cyclotron facility. SMP thanks Dr Nikita Arnold from the Johannes-Kepler-Universität Linz for his helpful comments on laser ablation, and the `Evangelisches Studienwerk Villigst' for a long-term scholarship. APLR is grateful for the use of computing resources provided by Science and Technolgy Facilities Council's e-Science facility.

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