Multi-dimensional effects on ion acceleration by a normally incident linearly polarized intense laser pulse interacting with a thin solid target have been investigated numerically, where the laser has the peak intensity of 1.37×1020 W/cm2, focused spot size of 6 μm, pulse duration of 33 fs, and total pulse energy about 3 J, which are commercially available now. We have checked the effects of simulation geometries by running one, two, and three dimensional (1D, 2D, 3D) particle-in-cell simulations. 3D simulation results show that, in the case of using a relatively thick target (in the opaque regime, i.e., 2 μm) with the so-called target normal sheath field acceleration mechanism, electrons spread almost uniformly along two transverse directions. While in the case of using an ultra-thin target (in the relativistic-induced transparent regime, i.e., 100 nm) with the so-called break-out afterburner mechanism, electrons spread more quickly along the direction orthogonal to the laser polarization direction especially at the early stage. The transverse spreading of electrons strongly decreases the electron density at the rear side of the target. Such an effect causes different estimation of electron temperatures in different simulation geometries. Usually, 1D and 2D simulations overestimate the temperature; and as a result, the maximum proton energy observed in 1D and 2D simulations is, respectively, about 3 and 2 times of that observed in 3D simulation.

Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.

A slice-cone target is proposed for the generation of quasi-monoenergetic proton bunches. In this new target structure, two symmetrical solid slices are adjoined obliquely to the tip of a hollow cone. Two-dimensional particle-in-cell simulations show that a large number of hot electrons are pulled out from the solid slices and accelerated forward by direct laser acceleration. Compared with the hollow cone target, a stronger electrostatic field at the rear surface of the slice-cone tip is set up by the hot electrons from the cone and the slices. As a result, the energy of the quasi-monoenergetic proton bunch produced through the target-normal sheath acceleration mechanism can be improved by 75%. It shows that the proton energy scales proportional to the square root of the laser intensity. For the incident laser with the focused intensity about 5 Â 10 20 W/cm 2 , one can obtain proton bunches with central energy 165 MeV and energy spread 13%.

A two-stage proton acceleration scheme using present-day intense lasers and a unique target design is proposed. The target system consists of a hollow cylinder with conical inner wall, which is followed by the main target with a flat front and a dishlike flared rear surface. At the center of the latter is a tapered proton layer, which is surrounded by side proton layers at an angle to it. In the first acceleration stage, protons in both layers are accelerated by target normal sheath acceleration. The center-layer protons are accelerated forward along the axis while the side protons are accelerated and focused towards them. As a result, the side-layer protons radially compress as well as axially further accelerate the front part of the center-layer protons in the second stage. Two-dimensional (2D) particle-in-cell (PIC) simulations show that a quasimonoenergetic proton bunch with the maximum energy over 250 MeV and energy spread $17% can be generated when such a target is irradiated with an 80 fs laser pulse with focused intensity 3:1 Â 10 20 W=cm 2 . Three-dimensional (3D) PIC simulation gives the reduced maximum energy $112 MeV but even smaller energy spread $3% under the same laser conditions due to anisotropic electron acceleration with linearly polarized lasers.

Within the framework of plane-wave angular spectrum analysis of electromagnetic fields, a solution for the field of a tightly focused radially polarized (RP) chirped laser pulse is presented. With this solution, direct laser acceleration of protons by this kind of RP laser pulses is investigated numerically. It is found that a RP laser pulse with proper negative frequency chirps can lead to efficient proton acceleration, reaching sub-GeV at the laser intensity of 10 22 W=cm 2 from its injection energy of 45 MeV.