It is usually assumed that ions are accelerated most efficiently in the case of non-expanded targets irradiated by femtosecond ultra-intense laser pulse, alternatively with only short scale preplasma on their front side. Here, we demonstrate that the ions in an expanded foil with near-critical density plasma before its interaction with the main petawatt pulse may be accelerated to higher energies than that from ultra-thin foils. In order to investigate the mechanisms responsible for the acceleration of the most energetic ions, we used particle tracking in particle-in-cell simulations. It is demonstrated that high-energy ions originate from a small region of the depth below 1 μm and the width about the laser focal spot size (3 - 4 μm) in the case of semi-expanded target (with gradually increasing density up to the maximum density from the front side) and of a thin foil. On the other hand, the length of this region exceeds 5 μm for the expanded target. When the laser pulse propagates through near-critical density targets, a high density electron bunch is formed and travels with the laser pulse behind the target. Behind this electron bunch, a relatively long longitudinal electric field is generated and this field accelerates ions. Longitudinal electric field can be also generated due to expanding transverse magnetic field, which is observed for the expanded target.
Laser plasma physics is a field of big interest because of its implications in basic science, fast ignition, medicine (i.e. hadrontherapy), astrophysics, material science, particle acceleration etc. 100-MeV class protons accelerated from the interaction of a short laser pulse with a thin target have been demonstrated. With continuing development of laser technology, greater and greater energies are expected, therefore projects focusing on various applications are being formed, e.g. ELIMAIA (ELI Multidisciplinary Applications of laser-Ion Acceleration). One of the main characteristic and crucial disadvantage of ion beams accelerated by ultra-short intense laser pulses is their large divergence, not suitable for the most of applications. In this paper two ways how to decrease beam divergence are proposed. Firstly, impact of different design of targets on beam divergence is studied by using 2D Particlein-cell simulations (PIC). Namely, various types of targets include at foils, curved foil and foils with diverse microstructures. Obtained results show that well-designed microstructures, i.e. a hole in the center of the target, can produce proton beam with the lowest divergence. Moreover, the particle beam accelerated from a curved foil has lower divergence compared to the beam from a flat foil. Secondly, another proposed method for the divergence reduction is using of a magnetic solenoid. The trajectories of the laser accelerated particles passing through the solenoid are modeled in a simple Matlab program. Results from PIC simulations are used as input in the program. The divergence is controlled by optimizing the magnetic field inside the solenoid and installing an aperture in front of the device.