Abstract:
The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: A 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space.

Abstract:
An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.

Abstract:
We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we generalize the magneto-hydrodynamical jump conditions for a multi-component plasma, including information about the specific adiabatic constants for the different species. The impact of deviations from the standard model of an ideal gas is compared in theory and particle-in-cell simulations, showing that the standard-MHD model is a good approximation. The simulations of shocks in electron-positron-ion plasmas are for the first time multi-dimensional, transverse effects are small in this configuration and 1D simulations are a good representation if the initial magnetization is chosen high. 1D runs with a mass ratio of 1836 are performed, which identify the Larmor frequency \omega_{ci} as the dominant frequency that determines the shock physics in mixed component plasmas. The maximum energy in the non-thermal tail of the particle spectra evolves in time according to a power-law proportional to t^\alpha with \alpha in the range 1/3 < \alpha < 1, depending on the initial parameters. A connection is made with transport theoretical models by Drury (1983) and Gargate & Spitkovsky (2011), which predict an acceleration time proportional to \gamma and the theory for small wavelength scattering by Kirk & Reville (2010), which predicts a behavior rather as proportional to \gamma^2. Furthermore, we compare different magnetic field orientations with B_0 inside and out of the plane, observing qualitatively different particle spectra than in pure electron-ion shocks.

Abstract:
A new magnetic field generation mechanism in electrostatic shocks is found, which can produce fields with magnetic energy density as high as 0.01 of the kinetic energy density of the flows on time scales $ \tilde \, 10^4 \, {\omega}_{pe}^{-1}$. Electron trapping during the shock formation process creates a strong temperature anisotropy in the distribution function, giving rise to the pure Weibel instability. The generated magnetic field is well-confined to the downstream region of the electrostatic shock. The shock formation process is not modified and the features of the shock front responsible for ion acceleration, which are currently probed in laser-plasma laboratory experiments, are maintained. However, such a strong magnetic field determines the particle trajectories downstream and has the potential to modify the signatures of the collisionless shock.

Abstract:
We assess the impact of non-thermally shock-accelerated particles on the magnetohydrodynamic (MHD) jump conditions of relativistic shocks. The adiabatic constant is calculated directly from first principle particle-in-cell simulation data, enabling a semi-kinetic approach to improve the standard fluid model and allowing for an identification of the key parameters that define the shock structure. We find that the evolving upstream parameters have a stronger impact than the corrections due to non-thermal particles. We find that the decrease of the upstream bulk speed yields deviations from the standard MHD model up to 10%. Furthermore, we obtain a quantitative definition of the shock transition region from our analysis. For Weibel-mediated shocks the inclusion of a magnetic field in the MHD conservation equations is addressed for the first time.

Abstract:
The theoretical model by Sorasio et al. (2006) for the steady state Mach number of electrostatic shocks formed in the interaction of two plasma slabs of arbitrary density and temperature is generalized for relativistic electron and non-relativistic ion temperatures. We find that the relativistic correction leads to lower Mach numbers, and as a consequence, ions are reflected with lower energies. The steady state bulk velocity of the downstream population is introduced as an additional parameter to describe the transition between the minimum and maximum Mach numbers in dependence of the initial density and temperature ratios. In order to transform the soliton-like solution in the upstream region into a shock, a population of reflected ions is considered and differences to a zero-ion temperature model are discussed.

Abstract:
In plasmas where the thermal energy density exceeds the magnetic energy density ($\beta_\parallel > 1$), the aperiodic ordinary mode (O-mode) instability is driven by an excess of parallel temperature $A = T_\perp /T_\parallel < 1$ (where $\parallel$ and $\perp$ denote directions relative to the uniform magnetic field). When stimulated by parallel plasma streams the instability conditions extend to low beta states, i.e., $\beta_\parallel <1$, and recent studies have proven the existence of a new regime, where the anisotropy threshold decreases steeply with lowering $\beta_\parallel \to 0$ if the streaming velocity is sufficiently high. However, the occurrence of this instability is questionable especially in the low-beta plasmas, where the electrostatic two-stream instabilities are expected to develop much faster in the process of relaxation of the counterstreams. It is therefore proposed here to identify the instability conditions for the O-mode below those required for the onset of the electrostatic instability. An hierarchy of these two instabilities is established for both the low $\beta_\parallel <1$ and large $\beta_\parallel > 1$ plasmas. The conditions where the O-mode instability can operate efficiently are markedly constrained by the electrostatic instabilities especially in the low-beta plasmas.

Abstract:
Collisionless shocks are pervasive in astrophysics and they are critical to understand cosmic ray acceleration. Laboratory experiments with intense lasers are now opening the way to explore and characterise the underlying microphysics, which determine the acceleration process of collisionless shocks. We determine the shock character - electrostatic or electromagnetic - based on the stability of electrostatic shocks to transverse electromagnetic fluctuations as a function of the electron temperature and flow velocity of the plasma components, and we compare the analytical model with particle-in-cell simulations. By making the connection with the laser parameters driving the plasma flows, we demonstrate that shocks with different and distinct underlying microphysics can be explored in the laboratory with state-of-the-art laser systems.

Abstract:
Collisionless shocks occur in various fields of physics. In the context of space and astrophysics they have been investigated for many decades. However, a thorough understanding of shock formation and particle acceleration is still missing. Collisionless shocks can be distinguished into electromagnetic and electrostatic shocks. Electromagnetic shocks are of importance mainly in astrophysical environments and they are mediated by the Weibel or filamentation instability. In such shocks, charged particles gain energy by diffusive shock acceleration. Electrostatic shocks are characterized by a strong electrostatic field, which leads to electron trapping. Ions are accelerated by reflection from the electrostatic potential. Shock formation and particle acceleration will be discussed in theory and simulations.

Abstract:
The spatial-temporal evolution of the purely transverse current filamentation instability is analyzed by deriving a single partial differential equation for the instability and obtaining the analytical solutions for the spatially and temporally growing current filament mode. When the beam front always encounters fresh plasma, our analysis shows that the instability grows spatially from the beam front to the back up to a certain critical beam length; then the instability acquires a purely temporal growth. This critical beam length increases linearly with time and in the non-relativistic regime it is proportional to the beam velocity. In the relativistic regime the critical length is inversely proportional to the cube of the beam Lorentz factor $\gamma_{0b}$. Thus, in the ultra-relativistic regime the instability immediately acquires a purely temporal growth all over the beam. The analytical results are in good agreement with multidimensional particle-in-cell simulations performed with OSIRIS. Relevance of current study to recent and future experiments on fireball beams is also addressed.