The perturbations caused to the proton angular distribution by the self-generated B -fields at high laser intensities are illustrated in Fig. It is characterized by a hollow ring structure with the proton flux peaking at a finite angle with respect to the target-rear normal. We stress that this ring pattern is observed only for high protons energies compare Fig. The observed ring pattern could be potentially attributed to a different effect, such as hole boring Since thin 1.
At that moment, however, according to the PICLS simulation, proton acceleration is already completed and exhibits a clear signature of magnetic deflections in the sheath field.
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We will now discuss several strategies to limit the magnetization effects on proton acceleration. First, an important factor is the relative timescale of the B -field growth compared to the proton acceleration timescale which is of the order of the laser pulse duration. This would be consistent with the fact that, experimentally, proton acceleration with ultrashort laser pulses seems to display a better scaling vs. To confirm this, precise in situ measurements of the B -field temporal dynamics e. Nonetheless, we expect that at very high intensities, even for the shortest pulse durations, the magnetic field strength will unavoidably become large enough that the magnetization effect highlighted here will start to be effective, and hence pose a fundamental limit to laser-based ion acceleration.
We tested in the simulations yet another possible strategy for minimizing the B -fields by using small-width targets so-called reduced mass targets or RMTs , in which the lateral recirculation of electrons homogenizes the sheath and relaxes its transverse gradient of the longitudinal E -field This agrees with the trend seen in Fig.
Note that in particular circumstances e. The magnetic inhibition effect highlighted in this study will likely impact not only sheath-accelerated ions, but also alternative ion acceleration schemes, such as relativistic transparency 47 and radiation pressure 12 , 14 , 48 , that are envisioned to be efficient at even higher laser intensities than discussed here.
In principle, radiation pressure acceleration does not require, and even desires to minimize, hot electrons which are at the source of the B -fields investigated here; hence it could be seen to be immune to magnetic inhibition, as supported by simulations of thin targets irradiated by high-contrast, ultraintense laser pulses Supplementary Fig. However, as recently shown 14 , at high laser intensities, tight laser focusing tends anyway to produce hot electrons, which could reintroduce magnetic inhibition of ion acceleration.
Both employed either direct irradiation of the targets positioned at the laser focus, or refocusing of the laser by an ellipsoidal plasma mirror EPM 31 , 40 , Note that since the laser pulse durations employed here are not extremely short, all of the above intensity calculations do not depend on spatiotemporal couplings within the laser pulse, which can, however, affect the intensity distribution of broadband, ultrashort laser pulses The EPM is made of glass treated with an anti-reflection coating at the laser wavelength.
It refocuses the laser with a change in the beam numerical aperture. The final FWHM spot size is then reduced to 0. The laser spot at the EPM focus was measured and optimized before each shot. The electron temperature T e t depends on the cumulated fluence The expansion length of the EPM surface is expected to be slightly larger in the SNL experiment due to longer pulse duration: about 0. To evaluate the impact of this expansion on the beam focus after the EPM, we performed ray-trace simulations, assuming that the plasma expands normally to the local EPM surface.
With a 0. Also, note that the paraxial approximation starts to fail in the high-NA operating conditions of the EPM. Similarly to a plasma mirror 50 , the EPM also acts as an ultrafast light reflector that is activated only in the rising edge of the laser pulse, hence leading to high-contrast interaction conditions. To obtain similar high-contrast conditions for the direct shots and thus allow meaningful comparison of their performance , we made use of frequency-doubled pulses at LULI i.
The targets consisted of 0. The plasma expands into the vacuum due to electrons pulling out protons through the space-charge electrostatic field. This scaling, suggested by Kluge et al. Furthermore, we found that this scaling gives the closest match to our numerical simulation results. Here the factor 0. At that moment, according to the PICLS simulation, proton acceleration is already completed for the case of laser pulse durations we explored here. It leads to steady growth of the magnetic field up to the stage when the magnetic pressure becomes comparable with the plasma pressure.
We note that other sources e. We consider here the electric field in the plateau region of the sheath where most of the particles are confined.
After the laser pulse, as the electrons progressively give their energy to the ions and cool down in the expansion, T e decreases with time Fig. To analyze the plasma dynamics at play during and following the intense laser irradiation, we resort to PIC numerical codes, which provide a first-principles simulation framework more adequate than magneto-hydrodynamics MHD codes.
Indeed, MHD is based on the assumptions of quasi-neutrality, small particle Larmor radii, and thermal particle distributions. PICLS features binary collisions among charged particles and dynamic ionization Absorbing boundary conditions are used for particles in the transverse direction i. The resulting two-layer target can lead to modulations in the low-energy side of the proton spectrum 56 , especially if the protons in the contaminant layer are depleted 57 , 58 , but this cannot affect the proton maximum energy 56 , the observable on which we concentrate here.
The electron density increases dynamically during the laser irradiation via ionization processes. The spatial resp. The laser focal spot and temporal shape obey Gaussian distributions.
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The data that support the findings of this study are available from the corresponding authors upon reasonable request. Macchi, A. Ion acceleration by superintense laser-plasma interaction. Snavely, R. Intense high-energy proton beams from Petawatt-laser irradiation of solids. Schreiber, J. Analytical model for ion acceleration by high-intensity laser pulses. Fuchs, J. Laser-driven proton scaling laws and new paths towards energy increase.
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Robson, L. Scaling of proton acceleration driven by petawatt-laser—plasma interactions. Ceccotti, T et al. Proton acceleration with high-intensity ultrahigh-contrast laser pulses. Passoni, M. Energetic ions from next generation ultraintense ultrashort lasers: Scaling laws for Target Normal Sheath Acceleration. Methods Phys. A , 46 Green, J. Enhanced proton flux in the MeV range by defocused laser irradiation. Wagner, F. Maximum proton energy above 85 MeV from the relativistic interaction of laser pulses with micrometer thick CH2 targets.
Kaluza, M. Influence of the laser prepulse on proton acceleration in thin-foil experiments. Antici, P. Energetic protons generated by ultrahigh contrast laser pulses interacting with ultrathin targets. Plasmas 14 , Henig, A. Enhanced laser-driven ion acceleration in the relativistic transparency regime. Buffechoux, S. Hot electrons transverse refluxing in ultraintense laser-solid interactions. Dollar, F.
Finite spot effects on radiation pressure acceleration from intense high-contrast laser interactions with thin targets. Kim, I. Transition of proton energy scaling using an ultrathin target irradiated by linearly polarized femtosecond laser pulses. Zigler, A.
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Enhanced proton acceleration by an ultrashort laser interaction with structured dynamic plasma targets. High efficiency proton beam generation through target thickness control in femtosecond laser-plasma interactions. Bin, J. Ion acceleration using relativistic pulse shaping in near-critical-density plasmas. Mora, P. Plasma expansion into a vacuum. Thin-foil expansion into a vacuum. E 72 , Murakami, M. Self-similar expansion of finite-size non-quasi-neutral plasmas into vacuum: Relation to the problem of ion acceleration.
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