We explore the physics of shock evolution and particle acceleration in non-relativistic collisionless shocks using multidimensional hybrid (kinetic ions/fluid electrons) simulations. We analyze a wide range of physical parameters relevant to the acceleration of cosmic rays (CRs) in astrophysical nonrelativistic shock scenarios, such as in supernova remnant (SNR) shocks. We explore the evolution of the shock structure and particle acceleration efficiency as a function of Alfvénic Mach number and magnetic field inclination angle θ. We show that there are fundamental differences between high and low Mach number shocks in terms of the electromagnetic turbulence generated in the pre-shock zone and downstream; dominant modes are resonant with the streaming CRs in the low Mach number regime, while both resonant and non-resonant modes are present for high Mach numbers. Energetic power law tails for ions in the downstream plasma can account for up to 15% of the incoming upstream flow energy, distributed over ∼ 5% of the particles in a power law with slope −2±0.2 in energy. Quasiparallel shocks with θ ≤ 45 • are good ion accelerators, while power-laws are greatly suppressed for quasi-perpendicular shocks, θ > 45 • . The efficiency of conversion of flow energy into the energy of accelerated particles peaks at θ = 15 • to 30 • and M A = 6, and decreases for higher Mach numbers, down to ∼ 2% for M A = 31. Accelerated particles are produced by Diffusive Shock Acceleration (DSA) and by Shock Drift Acceleration (SDA) mechanisms, with the SDA contribution to the overall energy gain increasing with magnetic inclination. We also present a direct comparison between hybrid and fully kinetic particle-in-cell results at early times; the agreement between the two models justifies the use of hybrid simulations for longer-term shock evolution. In SNR shocks, particle acceleration will be significant for low Mach number quasi-parallel flows (M A < 30, θ < 45). This finding underscores the need for effective magnetic amplification mechanism in SNR shocks.

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A massively parallel simulation code, called dHybrid, has been developed to perform global scale studies of space plasma interactions. This code is based on an explicit hybrid model; the numerical stability and parallel scalability of the code are studied. A stabilization method for the explicit algorithm, for regions of near zero density, is proposed. Three-dimensional hybrid simulations of the interaction of the solar wind with unmagnetized artificial objects are presented, with a focus on the expansion of a plasma cloud into the solar wind, which creates a diamagnetic cavity and drives the Interplanetary Magnetic Field out of the expansion region. The dynamics of this system can provide insights into other similar scenarios, such as the interaction of the solar wind with unmagnetized planets.

In this paper we present in-situ satellite data, theory and laboratory validation that show how small scale collisionless shocks and mini-magnetospheres can form on the electron inertial scale length. The resulting retardation and deflection of the solar wind ions could be responsible for the unusual "lunar swirl" patterns seen on the surface of the Moon.Miniature magnetospheres have been found to exist above the lunar surface [1] and are closely related to features known as "lunar swirls" [2]. Mini-magnetospheres exhibit features that are characteristic of normal planetary magnetospheres namely a collisionless shock. Here we show that it is the electric field associated with the small scale collisionless shock that is responsible for deflecting the incoming solar wind around the minimagnetosphere. These ions impacting the lunar surface resulting in changes to the appearance of the albedo of the lunar "soil" [2]. The form of these swirl patterns therefore, must be dictated by the shapes of the collisionless shock.Collisionless shocks are a classic phenomena in plasma physics, ubiquitous in many space and astrophysical scenarios [3]. Well known examples of collisionless shocks exist in the heliosphere, where the shock is formed by the solar wind interacting with a magnetised planet. What is a surprise is the size of the mini-magnetospheres, of the order of several 100 km; orders of magnitude smaller than the planetary versions. Results from various lunar survey missions have built up a good picture of these collisionless shocks.These collisionless shocks have a characteristic structure in which the ions are reflected from a rather narrow layer, of the order of the electron skin depth c/ω pe (where c is the speed of light and ω pe is the electron plasma frequency), by an electrostatic field that is a consequence of the magnetised electrons and unmagnetised ions. The narrow discontinuity in the shock structure produces a specular reflected ion component with a velocity equal to or greater than the incoming solar wind velocity. The reflected ions from a counter-propagating component to the solar wind flow that form the magnetic foot region, which extends about an ion Larmor orbit upstream from the shock. This occurs when the Mach number (the ratio of flow velocity to Alfvén velocity) is of the order 3 or less.We have carried out laboratory experiments using a plasma wind tunnel, to investigate mini-magnetospheres

A non-resonant instability for the amplification of the interstellar magnetic field in young supernova remnant (SNR) shocks was predicted by Bell, and is thought to be relevant for the acceleration of cosmic-ray (CR) particles. For this instability, the CRs streaming ahead of SNR shock fronts drive electromagnetic waves with wavelengths much shorter than the typical CR Larmor radius, by inducing a current parallel to the background magnetic field. We explore the nonlinear regime of the non-resonant mode using Particle-in-Cell hybrid simulations, with kinetic ions and fluid electrons, and analyze the saturation mechanism for realistic CR and background plasma parameters. In the linear regime, the observed growth rates and wavelengths match the theoretical predictions; the nonlinear stage of the instability shows a strong reaction of both the background plasma and the CR particles, with the saturation level of the magnetic field varying with the CR parameters. The simulations with CR-tobackground density ratios of n CR /n b = 10 −5 reveal the highest magnetic field saturation levels, with energy also being transferred to the background plasma and to the perpendicular velocity components of the CR particles. The results show that amplification factors > 10 for the magnetic field can be achieved, and suggest that this instability is important for the generation of magnetic field turbulence, and for the acceleration of CR particles.