A new ion acceleration method, namely, phase-stable acceleration, using circularly-polarized laser pulses is proposed. When the initial target density $n_0$ and thickness $D$ satisfy $a_L\sim (n_0/n_c)D/{\lambda }_L$ and $D>l_s$ with $a_L$, ${\lambda }_L$, $l_s$, and $n_c$ the normalized laser amplitude, the laser wavelength in vacuum, the plasma skin depth, and the critical density of the incident laser pulse, respectively, a quasiequilibrium for the electrons is established by the light pressure and the space charge electrostatic field at the interacting front of the laser pulse. The ions within the skin depth of the laser pulse are synchronously accelerated and bunched by the electrostatic field, and thereby a high-intensity monoenergetic proton beam can be generated. The proton dynamics is investigated analytically and the results are verified by one- and two-dimensional particle-in-cell simulations.

We report the experimental generation of highly energetic carbon ions up to 48 MeV per nucleon by shooting double-layer targets composed of well-controlled slightly underdense plasma and ultrathin foils with ultraintense femtosecond laser pulses. Particle-in-cell simulations reveal that carbon ions are ejected from the ultrathin foils due to radiation pressure and then accelerated in an enhanced sheath field established by the superponderomotive electron flow. Such a cascaded acceleration is especially suited for heavy ion acceleration with femtosecond laser pulses. The breakthrough of heavy ion energy up to many tens of $\mathrm{MeV}/\mathrm{u}$ at a high repetition rate would be able to trigger significant advances in nuclear physics, high energy density physics, and medical physics.

By 3D particle-in-cell simulation and analysis, we propose a plasma lens to make high intensity, high contrast laser pulses with a steep front. When an intense, short Gaussian laser pulse of circular polarization propagates in near-critical plasma, it drives strong currents of relativistic electrons which magnetize the plasma. Three pulse shaping effects are synchronously observed when the laser passes through the plasma lens. The laser intensity is increased by more than 1 order of magnitude while the initial Gaussian profile undergoes self-modulation longitudinally and develops a steep front. Meanwhile, a nonrelativistic prepulse can be absorbed by the overcritical plasma lens, which can improve the laser contrast without affecting laser shaping of the main pulse. If the plasma skin length is properly chosen and kept fixed, the plasma lens can be used for varied laser intensity above ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2$.

The fundamental idea of Laser Wakefield Acceleration (LWFA) is reviewed. An ultrafast intense laser pulse drives coherent wakefields of relativistic amplitude with the high phase velocity robustly supported by the plasma. The structures of wakes and sheaths in plasma are contrasted. While the large amplitude of wakefields involves collective resonant oscillations of the eigenmode of the entire plasma electrons, the wake phase velocity ~ c and ultrafastness of the laser pulse introduce the wake stability and rigidity. When the phase velocity gets smaller, wakefields turn into sheaths. When we deploy laser ion acceleration or high density LWFA in which the phase velocity of plasma excitation is low, we encounter the sheath dynamics. A large number of world-wide experiments show a rapid progress of this concept realization toward both the high energy accelerator prospect and broad applications. The strong interest in this has driven novel laser technologies, including the Chirped Pulse Amplification, the Thin Film Compression (TFC), the Coherent Amplification Network, and the Relativistic Compression (RC). These in turn have created a conglomerate of novel science and technology with LWFA to form a new genre of high field science with many parameters of merit in this field increasing exponentially lately. Applications such as ion acceleration, X-ray free electron laser, electron and ion cancer therapy are discussed. A new avenue of LWFA using nanomaterials is also emerging, adopting X-ray laser using the above TFC and RC. Meanwhile, we find evidence that the Mother Nature spontaneously created wakefields that accelerate electrons and ions to very high energies.

We show a novel self-matching resonance acceleration regime for generating dense relativistic electron beams by using ultraintense circularly polarized laser pulses in near-critical density plasmas. When the self-generated quasistatic axial magnetic field is strong enough to pinch and trap thermal relativistic electrons, an overdense electron bunch is formed in the center of the laser channel. In the trapping process, the electron betatron frequencies and phases can be adjusted automatically to match the resonance condition. The matched electrons are accelerated continuously and a collimated electron beam with overcritical density, helical structure, and plateau profile energy spectrum is hence generated.

A novel approach is proposed to demonstrate the two-photon Breit-Wheeler process by using collimated and wide-bandwidth $\gamma$-ray pulses driven by 10-PW lasers. Theoretical calculations suggest that more than $3.2\times {10}^8$ electron-positron pairs with a divergence angle of 7° can be created per shot, and the signal-to-noise ratio is higher than $10^3$. The positron signal, which is roughly 100 times higher than the detection limit, can be measured by using the existing spectrometers. This approach, which could demonstrate the $e^{-}{e}^{+}$ pair creation process from two photons, would provide important tests for two-photon physics and other fundamental physical theories.