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The intensity of present x-ray lasers is still far from relativistic due to equipment damage by the powerful radiation involved in the generation process. We propose to use a microscopic concave plasma lens to tightly focus terawatt x-ray pulses to relativistic intensity by avoiding the destructive instabilities arising from the laser-plasma interaction in the focusing process. Three-dimensional particle-in-cell simulations show that an intense x-ray laser pulse can be focused to a tiny spot of the wavelength scale at ultrahigh intensity while well preserving its original spatiotemporal profile. The resulting pulse can exceed the relativistic intensity threshold [(1.37×10^{24}/λ_{nm}^{2})W/cm^{2}, with λ_{nm} being the wavelength normalized by nanometers] by two orders of magnitude. Such intense nano-sized x-ray pulses can be useful for exploring nonlinear phenomena in the strong-field quantum electrodynamics regime, as well as in high-energy-density science and astrophysics.

Target-normal sheath acceleration (TNSA) of monoenergetic proton bunches using a triple-layer target consisting of a long slightly-above-critical-density carbon preplasma, a thin solid-density carbon main target layer, and a thin hydrogen layer attached to its back, is considered. The target-back space-charge field the consists of mainly the preplasma electrons that have been accelerated and heated by the relativistic laser pulse. The backside electron cloud is thus denser and more favorably profiled for TNSA of the protons from the hydrogen layer. It is found that a proton beam with a ∼460 MeV monoenergetic peak energy can be generated. The corresponding energy and angular spread are ∼33 MeV and ∼3°, respectively.

It is shown by particle-in-cell simulations that a narrow electron beam with high energy and charge density can be generated in a subcritical-density plasma by two consecutive laser pulses. Although the first laser pulse dissipates rapidly, the second pulse can propagate for a long distance in the thin wake channel created by the first pulse and can further accelerate the preaccelerated electrons therein. Given that the second pulse also self-focuses, the resulting electron beam has a narrow waist and high charge and energy densities. Such beams are useful for enhancing the target-back space-charge field in target normal sheath acceleration of ions and bremsstrahlung sources, among others.

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 3.1×10^{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.

Two-dimensional particle-in cell simulation shows that protons in a small target located in an underdense high-mass plasma can be accelerated by the radiation pressure of a short circularly polarized laser pulse as well as by the wake bubble field of the laser in the background plasma. The radiation-pressure preaccelerated protons are easily trapped and accelerated stably in front of the bubble for a relatively long distance. It is found that a quasimonoenergetic proton beam of 38 GeV peak energy and 12.6% energy spread as well as small divergence angle can be obtained with a 10^{23} W/cm^{2} 18.26 kJ laser pulse in a tritium plasma of density 5.2×10^{20} cm^{-3}.