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The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Jüttner model distributions. The main properties of the competing modes ͑developing parallel, transverse, and oblique to the beam͒ are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.

The generation of ultra-relativistic positron beams with short duration (τ e + ≤ 30 fs), small divergence (θ e + 3 mrad), and high density (n e + 10 14 − 10 15 cm −3 ) from a fully optical setup is reported. The detected positron beam propagates with a high-density electron beam and γ-rays of similar spectral shape and peak energy, thus closely resembling the structure of an astrophysical leptonic jet. It is envisaged that this experimental evidence, besides the intrinsic relevance to laserdriven particle acceleration, may open the pathway for the small-scale study of astrophysical leptonic jets in the laboratory.Creating and characterizing high-density beams of relativistic positrons in the laboratory is of paramount importance in experimental physics, due to their direct application to a wide range of physical subjects, including nuclear physics, particle physics, and laboratory astrophysics. Arguably, the most practical way to generate them is to exploit the electromagnetic cascade initiated by the propagation of an ultra-relativistic electron beam through a high-Z solid. This process is exploited to generate low-energy positrons in injector systems for conventional accelerators such as the Electron-Positron Collider (LEP) [1]. In this case, an ultra-relativistic electron beam (E e − ≈ 200 MeV) was pre-accelerated by a LINAC and then directed onto a tungsten target. The resulting positron population, after due accumulation in a storage ring, was further accelerated by a conventional, large-scale (R ≈ 27 km), synchrotron accelerator up to a peak energy of 209 GeV. The large cost and size of these machines have motivated the study of alternative particle accelerator schemes. A particularly compact and promising system is represented by plasma devices which can support much higher accelerating fields (of the order of 100s of GV/m, compared to MV/m in solid-state accelerators) and thus significantly shorten the overall size of the accelerator. Laser-driven generation of electron beams with energies per particle reaching [2][3][4][5], and exceeding [6], 1 GeV have been experimentally demonstrated and the production of electron beams with energies approaching 100 GeV is envisaged for the next generation of highpower lasers (1 -10 PW) [7]. Hybrid schemes have also been proposed and successfully tested in first proof-ofprinciple experiments [8,9]. On the other hand, laserdriven low energy positrons (E e + ≈ 1−5 MeV) have been first experimentally obtained by C. Gahn and coworkers [10] and recently generated during the interaction of a picosecond, kiloJoule class laser with thick gold targets [11][12][13][14]. Despite the intrinsic interest of these results, the low energy and broad divergence reported (E e + ≤ 20 MeV and θ e + ≥ 350 mrad , respectively) still represent clear limitations for future use in hybrid machines.The possibility of generating high density and high energy electron-positron beams is of central importance also for astrophysics, due to their similarity to jets of long gamma-ray bursts (GRBs), whic...

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The surfatron offers the possibility of particle acceleration to arbitrarily high energies, given a sufficiently large system. Surfatron acceleration of electrons by waves excited by ions reflected from supernova remnant (SNR) shocks is investigated using particle simulations. It is shown that surfatron and stochastic acceleration could provide a seed population for the acceleration of cosmic ray electrons at SNR shocks.