Simulations of Ion Acceleration at Non-relativistic Shocks. I. Acceleration Efficiency

We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfv\'enic Mach numbers, produces universal power-law spectra proportional to p^(-4), where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shock drift acceleration, but they only gain a factor of a few in momentum, and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region), and we identify two dynamical signatures peculiar of efficient particle acceleration, namely the formation of an upstream precursor and the alteration of standard shock jump conditions.Comment: 21 pages, 14 figures, Minor changes reflecting the version accepted to Ap

Ab-initio pulsar magnetosphere: three-dimensional particle-in-cell simulations of axisymmetric pulsars

We perform first-principles relativistic particle-in-cell simulations of aligned pulsar magnetosphere. We allow free escape of particles from the surface of a neutron star and continuously populate the magnetosphere with neutral pair plasma to imitate pair production. As pair plasma supply increases, we observe the transition from a charge-separated electrosphere solution with trapped plasma and no spin-down to a solution close to the ideal force-free magnetosphere with electromagnetically-dominated pulsar wind. We calculate the magnetospheric structure, current distribution and spin-down power of the neutron star. We also discuss particle acceleration in the equatorial current sheet.Comment: 6 pages, 5 figures, published in ApJ Letter

Laser Shaping and Optimization of the Laser-Plasma Interaction

The physics of energy transfer between the laser and the plasma in laser wakefield accelerators is studied. We find that wake excitation by arbitrary laser shapes can be parameterized using the total pulse energy and pulse depletion length. A technique for determining laser profiles that produce the required plasma excitation is developed. We show that by properly shaping the longitudinal profile of the driving laser pulse, it is possible to maximize both the transformer ratio and the wake amplitude, achieving optimal laser-plasma coupling. The corresponding family of laser pulse shapes is derived in the nonlinear regime of laser-plasma interaction. Such shapes provide theoretical upper limit on the magnitude of the wakefield and efficiency of the accelerating stage by allowing for uniform photon deceleration inside the laser pulse. We also construct realistic optimal pulse shapes that can be produced in finite-bandwidth laser systems and propose a two-pulse wake amplification scheme using the optimal solution.Comment: 12 pages, 5 figures, contributed to the Advanced Accelerator Concepts 2000 worksho

Simulations of Ion Acceleration at Non-relativistic Shocks. III. Particle Diffusion

We use large hybrid (kinetic protons-fluid electrons) simulations to investigate the transport of energetic particles in self-consistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to $10-20\%$ in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitch-angle scattering of energetic ions is comparable with their gyroradii calculated in the self-generated turbulence. For moderately-strong shocks, magnetic field amplification proceeds in the quasi-linear regime, and particles diffuse according to the self-generated diffusion coefficient, i.e., the scattering rate depends only on the amount of energy in modes with wavelengths comparable with the particle gyroradius. For very strong shocks, instead, the magnetic field is amplified up to non-linear levels, with most of the energy in modes with wavelengths comparable to the gyroradii of highest-energy ions, and energetic particles experience Bohm-like diffusion in the amplified field. We also show how enhanced diffusion facilitates the return of energetic particles to the shock, thereby determining the maximum energy that can be achieved in a given time via diffusive shock acceleration. The parametrization of the diffusion coefficient that we derive can be used to introduce self-consistent microphysics into large-scale models of cosmic ray acceleration in astrophysical sources, such as supernova remnants and clusters of galaxies.Comment: 8 pages, 7 figures, Minor changes reflecting the version accepted to Ap

Simulations of relativistic collisionless shocks: shock structure and particle acceleration

We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization ("sigma" parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. At low magnetizations the shock is mediated mainly by the Weibel instability which generates transient magnetic fields that can exceed the initial field. At larger magnetizations the shock is dominated by magnetic reflections. We demonstrate where the transition occurs and argue that it is impossible to have very low magnetization collisionless shocks in nature (in more than one spatial dimension). We further discuss the acceleration properties of these shocks, and show that higher magnetization perpendicular shocks do not efficiently accelerate nonthermal particles in 3D. Among other astrophysical applications, this may pose a restriction on the structure and composition of gamma-ray bursts and pulsar wind outflows.Comment: 6 pages, invited talk at "Astrophysical Sources of High Energy Particles and Radiation," Torun, June 20 - 24, 200