Toward an effective use of laser-driven very high energy electrons for radiotherapy: Feasibility assessment of multi-field and intensity modulation irradiation schemes

Radiotherapy with very high energy electrons has been investigated for a couple of decades as an effective approach to improve dose distribution compared to conventional photon-based radiotherapy, with the recent intriguing potential of high dose-rate irradiation. Its practical application to treatment has been hindered by the lack of hospital-scale accelerators. High-gradient laser-plasma accelerators (LPA) have been proposed as a possible platform, but no experiments so far have explored the feasibility of a clinical use of this concept. We show the results of an experimental study aimed at assessing dose deposition for deep seated tumours using advanced irradiation schemes with an existing LPA source. Measurements show control of localized dose deposition and modulation, suitable to target a volume at depths in the range from 5 to 10 cm with mm resolution. The dose delivered to the target was up to 1.6 Gy, delivered with few hundreds of shots, limited by secondary components of the LPA accelerator. Measurements suggest that therapeutic doses within localized volumes can already be obtained with existing LPA technology, calling for dedicated pre-clinical studies.

As said in the main text, the divergence and spectrum of the electron bunch were measured using the setup described in the Methods. The FWHM divergence (measured by removing from the e-beam path the collimator and the magnetic dipole) was measured to be of ∼ 14 mrad. A spectrum, obtained upon averaging over 10 laser shots, is shown in Figure 1. Our spectrometer range had a lower bound of ∼ 50 MeV. The experimental spectrum featured a high energy component peaking at ∼ 200 MeV. A strong component was also present in the range ∼ 50 − 125 MeV, whose origin was clarified by means of Particle-In-Cell (PIC) simulations, discussed in the following Subsection.
The PIC code PIC simulations have been carried out to get a better undertsanding of the acceleration mechanism in our regime and check the main experimental bunch parameters against the simulated ones. Simulations were carried out using the FBPIC code [1] on a single 32GB NVIDIA Tesla V100 SXM2 GPU. FBPIC is a spectral, quasi-cylindrical PIC code based on an azimuthal Fourier decomposition; it does not suffer from numerical dispersive errors in the electromagnetic field propagation. In order to take into account a linearly polarized laser pulse, the code was run using two azimuthal modes (see below).

Simulations
We approximated the laser driver as a bi-gaussian pulse, both in the longitudinal and transverse directions, with an energy E = 3J, a waist w 0 = 30µm and a longitudinal duration τ f whm = 30fs, corresponding to a laser strength parameter of a 0 1.75. Based on previous interferometric measurements, the density profile was modelled using an initial and final linear ramps, each with length 250 µm, and a 900 µm long plateau, where the (peak) density of the neutral gas was n 0 = 4×10 18 cm −3 . We modeled the laser-plasma interaction using the standard moving window technique, using a simulation box with ∼ 3w 0 transverse size; in the longitudinal direction, the size was adjusted so as to fit both the laser pulse and the first trailing plasma oscillation. The single cells composing the electromagnetic lattice had longitudinal size ∆z = λ 0 /32 and radial size ∆r = λ 0 /12. The background plasma was described employing 16 computational particles per cell. As said in the text, the gas was a mixture of He and N 2 , with 2.5% at. N 2 concentration.
At laser intensities of the order of the one at play in our experiment, we expect two concurrent processes to contribute to the electron bunch formation, namely the electron self (or bubble) injection and the ionization injection. Some parametric scans have been carried out to investigate whether one of the two was dominant in the bunch generation to ensure an optimized choice of the numerical parameters in use. In particular, from previous experiences, we know that to provide a decent modelling of the self injection mechanism, FBPIC requires at least 3 azimuthal modes. The ionization process is instead strongly dependent on the longitudinal cell size, since Figure 2: Density log map of the background plasma after a laser propagation of ct = 1200µm.
An injected particle bunch is visible in the center of the plasma bubble. The oscillating laser field is shown and the self-focusing effect is clear on the rear of the pulse. the laser oscillation must be well resolved. We thus initially performed a numerical scan at a reduced longitudinal resolution using 3 modes. This scan showed a negligible contribution of the self injection mechanism, so that we could run further simulations with an increased longitudinal resolution with 2 azimuthal modes. FBPIC is equipped with an ionization module based on the well-established ADK model, that randomly extract an electron from every nitrogen background atom.

Results
In Figure 2, we show the density map of the background plasma when the pulse is located around the center of the gas jet. We can see the laser pulse focusing effect giving rise to the characteristic plasma bubble accelerating a very long injected bunch, that extends from z ∼ 1163µm to z ∼ 1173µm. Figure 3 shows the electron Lorentz gamma factor overlapped to the longitudinal accelerating electric field.
We show in Figure 4 the electron spectrum as provided by the PIC simulation at the end of the plasma; for the sake of a comparison with the epxerimental spectrum, a selection on the transverse momentum was performed, by retaining only particles entering our collimator (see main text). Beside a very low energy component (E 30 MeV), two broad peaks can be Figure 3: Particles gamma as a function of the longitudinal position. Red lines represents a centerline of the accelerating field normalized to be visible in the plot. The front of the particle bunch is dephased and does not accelerate anymore. The center of the bunch is the most energetic part, while the rear, carrying the greatest part of the charge, produces a strong beam loading effect.
identified, located at relatively low energy ( 50 MeV) and at 200 MeV. By following the phase space distribution in time we found out that the peculiar double-peaked energy spectrum is due to the underlying injection mechanism. Indeed, at the first stages of the acceleration dynamics, the laser pulse extracts some (newborn) electrons, following the ionization from N 5+ to N 6+ that get trapped in the wakefield and start to accelerate. While the laser pulse selffocuses, the wakefield amplitude and wavelength increase, and the first extracted particles find themselves in a region near the zero of the accelerating field. On the other hand, particles extracted at a later time start to experience the highest accelerating field and therefore reach higher energies.
However, since the ionization mechanism does not stop until late in the process, electrons are continuously injected in the wakefield, increasing the beam loading effect and therefore slowing down their acceleration. The tail of the injected bunch contains a remarkable part of its charge, highlighted in Figure 5, which forms the low energy peak in the spectrum.

Monte Carlo simulation of the dose contamination by photons
Bremsstrahlung (as well as fluorescence) photons are expected to be emitted in our experimental setup as a result of the interaction of the electrons with the structures of the collimator as well as of the flange/vacuum window. The contribution to the dose due to the photons was estimated using the Monte Carlo (GEANT4 based) simulations (see Methods in the main text). Figure 6 shows a 2D map of the dose in the water phantom due to the photon only (bottom plot); for the sake of comparison, the total dose in also shown in the top plot (this is the same plot as the one reported in the main text). As it emerges, the "dose contamination" from photons is negligible.