Intense particle beams generated from the interaction of ultrahigh intensity lasers with sample foils provide options in radiography, high-yield neutron sources, high-energy-density-matter generation, and ion fast ignition. An accurate understanding of beam transportation behavior in dense matter is crucial for all these applications. Here we report the experimental evidence on one order of magnitude enhancement of intense laser-accelerated proton beam stopping in dense ionized matter, in comparison with the current-widely used models describing individual ion stopping in matter. Supported by particle-in-cell (PIC) simulations, we attribute the enhancement to the strong decelerating electric field approaching 1 GV/m that can be created by the beam-driven return current. This collective effect plays the dominant role in the stopping of laser-accelerated intense proton beams in dense ionized matter. This finding is essential for the optimum design of ion driven fast ignition and inertial confinement fusion.

A Monte Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. This approach is based on multiple electron-electron, electron-ion, and ion-ion binary collision and accounts for both the free and the bound electrons in the plasmas. This approach enables one to calculate the stopping of particles in a more natural manner than existing theoretical treatment. In the low-temperature limit, when “all” electrons are bound to the nucleus, the stopping power coincides with the predictions from the Bethe-Bloch formula and is consistent with the data from the National Institute of Standard and Technology database. At higher temperatures, some of the bound electrons are ionized, and this increases the stopping power in the plasmas, as demonstrated by A. B. Zylstra et al. [ Phys. Rev. Lett. 114, 215002 (2015)]. At even higher temperatures, the degree of ionization reaches a maximum and thus decreases the stopping power due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.

A high-order implicit multidimensional particle-in-cell (PIC) method is developed for simulating plasmas at solid densities. The space-time arrangement is based on Yee and a leapfrog algorithm for electromagnetic fields and particle advancement. The field solver algorithm completely eliminates numerical instabilities found in explicit PIC methods with relaxed time step and grid resolution. Moreover, this algorithm eliminates the numerical cooling found in the standard implicit PIC methods by using a pseudo-electric-field method. The particle pusher algorithm combines the standard Boris particle pusher with the Newton-Krylov iteration method. This algorithm increases the precision accuracy by several orders of magnitude when compared with the standard Boris particle pusher and also significantly decreases the iteration time when compared with the pure Newton-Krylov method. The code is tested with several benchmarks, including Weibel instability, and relativistic laser plasma interactions at both low and solid densities.

Direct numerical simulation of intense laser–solid interactions is still of great challenges, because of the many coupled atomic and plasma processes, such as ionization dynamics, collision among charged particles and collective electromagnetic fields, to name just a few. Here, we develop a new particle-in-cell (PIC) simulation code, which enables us to calculate laser–solid interactions in a more realistic way. This code is able to cover almost ‘all’ the coupled physical processes. As an application of the new code, the generation and transport of energetic electrons in front of and within the solid target when irradiated by intense laser beams are studied. For the considered case, in which laser intensity is $10^{20}~\text{W}\cdot \text{cm}^{-2}$ and pre-plasma scale length in front of the solid is $10~\unicode[STIX]{x03BC}\text{m}$ , several quantitative conclusions are drawn: (i) the collisional damping (although it is very weak) can significantly affect the energetic electrons generation in front of the target, (ii) the Bremsstrahlung radiation will be enhanced by 2–3 times when the solid is dramatically heated and ionized, (iii) the ‘cut-off’ electron energy is lowered by an amount of 25% when both collision damping and Bremsstrahlung radiations are included, and (iv) the resistive electromagnetic fields due to Ohmic heating play nonignorable roles and must be taken into account in such interactions.

We show that a high current quasi-monoenergetic electron beam and a peaked brilliant gamma-ray beam can be generated by irradiating an ultra-intense laser pulse on uniform near critical density plasma, with a laser spot radius $R_L\sim (\lambda /\pi )\sqrt{2a/n}$ , here λ is the laser wave length, a denotes the normalized laser intensity, and n denotes the normalized plasma density. Due to a relativistic resonant phase locking mechanism, high energy oscillating electrons are trapped to ride on the laser electric field, and an unprecedented ultra-fast ultra-brilliant gamma-ray pulse is emitted from the electrons. Both the high energy electrons and gamma-ray photons are emitted in a small polar angle range. It is similar to a conventional wiggler synchrotron, except that the curvature radius of electron orbits in the laboratory coordinate frame measures in microns rather than in meters.

It is shown that the transverse Rayleigh-Taylor-like (RT) instability in the hole-boring radiation pressure acceleration can be suppressed by using an elliptically polarized (EP) laser. A moderate $\mathit{J}\times \mathit{B}$ heating of the EP laser will thermalize the local electrons, which leads to the transverse diffusion of ions, suppressing the short wavelength perturbations of RT instability. A proper condition of polarization ratio is obtained analytically for the given laser intensity and plasma density. The idea is confirmed by two-dimensional particle-in-cell simulations, showing that the ion beam driven by the EP laser is more concentrated and intense compared with that of the circularly polarized laser.