Ultrafast Laser-Driven Microlens to Focus and Energy-Select Mega-Electron Volt Protons

^* To whom correspondence should be addressed. E-mail: oswald.willi{at}laserphy.uni-duesseldorf.de

The recent development of ultra-intense laser pulses (1) has opened up opportunities for applications in many areas, including particle acceleration (2–5), inertial fusion energy (6), generation of intense x-ray pulses (7), laser-driven nuclear physics (8), and laboratory astrophysics (9). In particular, the acceleration of mega–electron volt ions from the interaction of high-intensity laser-pulses with thin solids has major applicative prospects because of the high beam quality of these ion bursts (10, 11). Such proton beams are already applied to produce high-energy density matter (12) or to radiograph transient processes (13), and they offer promising prospects for tumor therapy (14), isotope generation for positron emission tomography (15), fast ignition of fusion cores (16), and brightness increase of conventional accelerators. However, because these proton beams are polyenergetic and divergent at the source, reduction and control of their divergence and energy spread are essential requirements for most of these applications.

Focusing of energetic proton beams is usually achieved with electrostatic or magnetic lenses (17), which have several drawbacks, including slow switching times, large sizes, asymmetry in the transverse plane for the focused beam, aberrations, inability to focus large currents, and large heat dissipation. It has been proposed that particle selection and beam collimation of laser-produced protons applicable for tumor therapy could be achieved by means of superconducting magnet systems (18). Relativistic laser-plasma devices appear in principle more suitable for achieving the required angular and spectral control of laser-accelerated ion beams because they can withstand large ion beam currents, can be switched over picosecond time scales, and can support large deflecting fields on microscales.

Advances in ion beam tailoring have been achieved so far mainly with the use of target engineering techniques. Geometrical focusing of laser-driven protons has been attained with the use of curved targets (12). Demonstration of this technique has been limited so far to focal distances of a few millimeters and to the low-energy component of the proton spectrum. Very recently, quasi-monochromatic acceleration from laser irradiated microstructured targets has been reported (19, 20). In these approaches, the focusing or energy-selection effect is achieved by directly acting on the source. As a consequence, these techniques rely on relatively complex target fabrication or preparation procedures.

We describe here an alternative approach, which provides tunable, simultaneous focusing and energy selection of mega–electron volt proton beams. Furthermore, our approach decouples the beam tailoring stage from the acceleration stage, allowing for their independent optimization. This leads to a system with higher flexibility than the methods above, considerably relaxing the target fabrication constraints. The method uses a compact laser-driven microlens arrangement (Fig. 1A). The underlying physical process begins with relativistic electrons injected through the cylinder's wall produced by the laser operating in chirped pulse amplification (CPA) mode, which spread evenly on the cylinder's inner walls and initiate hot plasma expansion (Fig. 1, B and C). The transient electric fields associated with the expansion are used in a radial geometry to focus protons accelerated by a separate CPA laser pulse from a thin planar foil. The microlens operation was demonstrated in experiments carried out at the Laboratoire pour l'Utilisation des Lasers Intenses (LULI), which used the 100-TW laser (21) operating at a wavelength of 1 µm. After amplification, the laser pulse was split into two separate pulses (CPA₁ and CPA₂), which were recompressed in separate grating compressors to a 350-fs duration. The delay between the two pulses was controlled optically with picosecond precision. The CPA₁ pulse (irradiance I = 5 x 10¹⁹ W/cm²) was used to accelerate a high-current, diverging beam of up to 15-MeV protons from a 25-µm-thick Al foil target [the protons are produced from hydrocarbon impurities (22) on the target rear surface (23, 24)]. The CPA₂ pulse (I = 3 x 10¹⁸ W/cm²) was focused onto the outer wall of a hollow cylinder. The proton beam from the first foil was directed through the cylinder and detected with a stack of radiochromic films (RCF), a dosimetric detector (25), positioned at a variable distance (from 2 to 70 cm) from the proton source. The RCF stack was used to measure the proton beam divergence. It also provided a coarse energy resolution due to the energy deposition properties of the ions (3)(most of the energy of a proton is released in the so-called Bragg peak, located at a distance in the detector which depends on the incident proton energy). It was shielded with an 11-µm Al foil allowing protons with energies greater than 1.5 MeV to be recorded. In some cases, a central millimetersized hole was bored through the RCF to allow downstream high spectral resolution measurements with the use of a magnetic spectrometer with a 0.6-T permanent magnet. The spectral resolution determined by the slit width and the dispersion of the spectrometer is 0.2 MeV at 6 MeV and 0.7 MeV at 15 MeV. The distance between the proton production foil and cylinder and the distance between the cylinder and detector were varied throughout the experiment. At a source-cylinder distance of 1 mm, the proton flux increase due to focusing by the microlens was so strong that saturation of the film occurred. Quantitative data could only be obtained when the cylinder was moved to 4 mm from the proton foil, in order to collect a smaller part of the diverging proton beam.

Fig. 1. (A) Schematic of the microlens device. A proton beam is accelerated from a planar foil by the CPA1 laser pulse. The proton beam propagates through a hollow cylinder side irradiated by the CPA2 laser pulse. (B and C) Schematic of the operation's principle of the microlens. The CPA2 laser pulse injects hot electrons within the cylinder. These spread evenly onto the cylinder's inner wall. In the early stage (B), these electrons, confined over a Debye length on the cylinder's surface, generate a space-charge field (indicated by the radially pointing arrows), which then induces plasma expansion (C) from the cylinder's inner walls. The resulting radial electric field, still indicated by the arrows and decreasing in time as the plasma expands, focuses the protons. The field is peaked at the front but extends toward the cylinder's wall. [View Larger Version of this Image (35K GIF file)]

An RCF pack placed 9.5 cm away from the proton target recorded the proton beam after its propagation through a laser-irradiated dural cylinder 3 mm in length, 700 µm in diameter, and 50 µm in wall thickness. The fifth and sixth in the stack, corresponding to protons of 9 and 7.5 MeV, respectively, are shown in Fig. 2A. The entrance plane of the cylinder was placed 4 mm from the proton-producing foil. The distance from the proton-producing foil to the CPA₂ irradiation point on the cylinder was 5 mm. As expected, no focusing effect is observed for the 9 MeV protons. Indeed, the electric field is triggered by the CPA₂ laser pulse 20 ps after these protons exit the cylinder. For the 7.5-MeV protons, the electric field develops while these protons are close to exit the cylinder, and a small spot about 600 µm [full width at half maximum (FWHM)] in diameter is seen on the RCF at the center of the cylinder's shadow (spots as small as 200 µm have been observed, depending on the detector position). In this case, the proton flux within the spot at the film plane is increased as many as 12 times compared with the unfocused part not captured by the cylinder (Fig. 2B). Based on the known properties of the proton source and on the decay time of the focusing fields [inferred to be 10 ps from particle-in-cell (PIC) simulations and experimental results (26)], a focused current of about 5 A can be estimated for the conditions of Fig. 3. We also studied the evolution of the beam size, as a function of the propagation distance from the cylinder. This was done under the same conditions of Fig. 2. The behavior of the 7.5-MeV proton component is shown in Fig. 3. For this energy, the beam size is only 8 mm after 70 cm of propagation, whereas when freely propagating, thesizeofthebeamwouldhavebeen 260 mm. An energy spectrum was obtained, in the same experimental configuration, with the use of the magnetic spectrometer, having an entrance slit of 250 µm positioned 70 cm away from the proton source (Fig. 4). As a reference, we also show a typical exponential spectrum collected in the same conditions but without the microlens. The data clearly shows the energy-selection capability of the microlens: Because of selective collimation of the 6.25-MeV protons, these could be transmitted efficiently through the spectrometer slit (acting as an angular filter), and their density after the slit in the spectrally dispersed plane is enhanced as compared with the free-space expansion case. For this shot, the 6.25-MeV protons experience the focusing fields for 5 ps before exiting the cylinder. We obtained an energy spread of 0.2 MeV—limited by the spectrometer energy resolution—for the peak located at 6.25 MeV. The numerical simulations performed in the same conditions as in the experiment suggest that the spectral width of the peak is about 0.1 MeV and hence narrower than demonstrated by the experimental spectrum shown (Fig. 4). By varying the optical delay between the laser beams, the location of this peak on the energy axis can be tuned selectively (as demonstrated experimentally), thereby allowing us to tailor the energy distribution of the transmitted beam, a necessary step for many applications. Notably, with this approach, focusing and energy selection are provided simultaneously.

Fig. 2. (A) RCF layers showing the proton beam focusing effect due to a 3-mm-long, 700-µm-diameter dural (95% Al, 4% Cu, and 1% Mg) laser–irradiated cylinder with 50-µm wall thickness. For the energies reaching the Bragg peak in the two layers shown, the protons with an energy of 9 MeV pass through the cylinder before the electric field is present, showing no focusing, whereas the divergence of the protons with an energy of 7.5 MeV is strongly reduced by the electric field that has developed inside the cylinder. The shadow of the cylinder and of the 50-µm tungsten holding wire can be seen clearly. The cylinder was positioned far from the proton source intentionally to reduce the number of protons entering the cylinder and avoid RCF saturation. The distance between the entrance plane of the cylinder and the proton production foil was 4 mm. (B) Flux increase with respect to the unfocused flux for 7.5-MeV protons as deduced from the layer shown in (A). [View Larger Version of this Image (62K GIF file)]

Fig. 3. Evolution of the FWHM of the proton beam along its propagation, for protons with energy of 7.5 MeV (the propagation distance is calculated from the proton source). The black circles correspond to the case without the microlens (free-space divergence), the blue diamonds to the particle-tracer simulation in the fields given by the PIC simulation, and the red squares to the experimental results with the use of the microlens. The RCF shown on the right of Fig. 2A corresponds to the red point at 9.5 cm. [View Larger Version of this Image (36K GIF file)]

Fig. 4. Experimental proton spectra measured with a magnetic spectrometer without the microlens (black line) and with the microlens (green line), and proton spectra obtained from simulations (red and blue lines) performed with the use of the experimental proton beam parameters and the magnetic spectrometer parameters (i.e., distance from the source and slit characteristics). The red and blue curves were obtained with the use of energy bins of 0.2 and 0.1 MeV, respectively. The simulated spectrum was obtained by tracing, for each energy bin, 5000 protons through the fields predicted by the PIC simulation. [View Larger Version of this Image (32K GIF file)]

We performed one-dimensional (1D) and 2D PIC simulations of field generation at the microlens's walls and 3D test-particle simulations of proton propagation through the microlens. The simulations were performed in three steps with the use of the CALDER code (27). First, we verified with 2D simulations that the laser pulse triggering the microlens by irradiating the cylinder's outer wall generated a population of hot electrons that spread evenly on the cylinder's walls. We then used a 1D code to simulate the plasma expansion within the cylinder (i.e., we simulated the expansion of two slabs of plasma separated by the cylinder's diameter of 700 µm). The expansion is driven by a hot-electron population that has a Boltzmann distribution with a temperature of 400 keV, as given by the ponderomotive potential at the irradiance of CPA₂ (28). The initial electron density at the cylinder's wall was estimated by considering that a 40% fraction of the laser energy [inferred from experimental measurements (29)] is converted into hot electrons and that these are then spread evenly on the cylinder's walls. This results in a hot-electron density of 6 10¹⁶ cm^–3. We assumed that when the plasma expansion starts, the field obtained in the PIC simulation is the same along the whole cylinder. Finally, we simulated the propagation of a proton beam in the cylinder through the space- and time-dependent fields obtained from the PIC simulation. The proton source used in the simulations has a divergence and energy spectrum as measured in the experiment.

The successful comparison between the simulations and the data (Figs. 3 and 4) supports the scenario in which laser-triggered transient fields drive the selective deflection of the protons. The transient field (30) is associated with a hot-electron sheath that extends over a Debye length ahead of the plasma, expanding toward the cylinder's axis (26, 31). The different energy components present in the proton beam spectrum transit through the cylinder at different times depending on their different velocities, with higher energy protons crossing the cylinder at earlier times. Protons passing through the microlens before it is triggered (as in Fig. 2A for the 9-MeV layer) do not experience any fields and are therefore not deflected. Protons which are crossing the cylinder and are close to its end when it is triggered and that therefore experience the fields for only a short time will exit the cylinder with a very low divergence (as in Fig. 2A for the 7.5-MeV layer). Lower energy protons will experience a larger cumulated field along their propagation through the cylinder. The particle-tracing simulations suggest that they are therefore focused at a short distance from the exit plane of the microlens and diverge strongly after focus. This is consistent with the diluted beam observed on the RCF stack positioned a few centimeters away and with the strong dip observed in the spectrum of Fig. 4 below 6 MeV. Finally, protons that have very low energy (i.e., below 4 MeV in the case of Fig. 4) pass through the microlens after the fields have vanished and do not experience any deflection. Additional simulations were performed to test the scalability of the microlens to higher proton energies, as needed for applications such as proton therapy. We computed that, using the same cylinder as in our experiment and a slightly more intense CPA₂ triggering laser pulse (10¹⁹ W/cm²), one could reduce the divergence of 270-MeV protons. Protons of such high energy transit through the microlens in a short time (13 ps); therefore, even higher laser intensities, on the order of 10²⁰ W/cm², would be required to focus them. The focusing device described in this paper has potential use in all applications of energetic protons in which reduced divergence, large flux, or narrow energy range are required. These include most of the proposed applications in scientific, medical, and technological areas. For example, focusing ion beams provides a different perspective, which may lead to further developments in areas such as hadron therapy for cancer treatment, accelerator physics, and inertial fusion physics. In addition to applications that use laser-driven ion beams, such a device might find application in conventional accelerator beams as a focusing or fast-switching tool.

References and Notes

The editors suggest the following Related Resources on Science sites:

In Science Magazine

PERSPECTIVES
APPLIED PHYSICS: Laser-Driven Particle Accelerators

Mike Dunne (21 April 2006)
Science 312 (5772), 374. [DOI: 10.1126/science.1126051]
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