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An electrostatic instability driven by counter-propagating tenuous proton beams that traverse a bulk plasma consisting of electrons and protons is considered. The system is spatially homogeneous and is evolved in time with a one-dimensional particle-in-cell simulation, which allows for a good statistical plasma representation. Mildly and highly relativistic beam speeds are modeled. The proton beams with a speed of 0.9c result in waves that saturate by the trapping of electrons. The collapse of the phase space holes in the electron distribution scatters these to a flat-top momentum distribution. The final electric fields are weak and the proton beams are weakly modulated. No secondary instabilities are likely to form that could thermalize the proton beams. The proton beams moving with 0.99c initially heat the bulk plasma through a three-wave interaction. Coalescing phase space holes in the bulk proton distribution arising from the saturation of ion acoustic waves transport wave energy to low wavenumbers. Highly relativistic phase space holes form in the electron distribution, which are not spatially homogeneous. The spatial envelope of these electron phase space holes interacts with the fluctuations driven by the phase space holes in the bulk protons, triggering a modulational instability. A Langmuir wave condensate forms that gives rise to strong and long electrostatic wave packets, as well as to a substantial modulation of the proton beams. The final state of the system with the highly relativistic proton beams is thus more unstable to further secondary instabilities that may transfer a larger beam energy fraction to the electrons and thermalize the proton beams more rapidly.

A thorough analysis of the electromagnetic instabilities encountered in the beam plasma interaction physics shows that the most unstable modes are not the ones usually studied. We characterize these most unstable modes and determine the patterns they create. A fluid model able to reproduce the kinetic results in the small temperature regime is presented, as well as exact kinetic calculations in the high temperature limit.

Contemporary lasers allow us to create shocks in the laboratory that propagate at a speed that matches that of energetic astrophysical shocks like those that ensheath supernova blast shells. The rapid growth time of the shocks and the spatio-temporal resolution, with which they can be sampled, allow us to identify the processes that are involved in their formation and evolution. Some laser-generated unmagnetized shocks are mediated by collective electrostatic forces and effects caused by binary collisions between particles can be neglected. Hydrodynamic models, which are valid for many large-scale astrophysical shocks, assume that collisions enforce a local thermodynamic equilibrium in the medium; laser-generated shocks are thus not always representative for astrophysical shocks. Laboratory studies of shocks can improve the understanding of their astrophysical counterparts if we can identify processes that affect electrostatic shocks and hydrodynamic shocks alike. An example is the nonlinear thin-shell instability (NTSI). We show that the NTSI destabilises collisionless and collisional shocks by the same physical mechanism. Funding Agencies|visiting fellowship of CRAL; EPSRC [EP/P010059/1, EP/K022415/1, EP/N027175/1]; Spanish Ministerio de Educacion [ENE2016-75703-R]; Grand Equipement National de Calcul Intensif (GENCI) [x2014046960]

Quantum and collisional effects on the unstable spectrum of a relativistic electron beam-plasma system are investigated through a two-fluids model. Application is made to the near target center interaction of the relativistic electron beam in the Fast Ignition Scenario. Partial degeneracy effects are found negligible while the most influential factors are the beam temperature and the electron-ion collision frequency of the plasma. The introduction of the latter triggers some oblique unstable modes of much larger wave length than the collisionless ones. Transition from the collisionless regime to the resistive one is thus documented and found discontinuous., Comment: To appear in PPCF