The nonresonant streaming instability (Bell instability) plays a pivotal role in the acceleration and confinement of cosmic rays (CRs), yet the exact mechanism responsible for its saturation and the magnitude of the final amplified magnetic field have not been assessed from first principles. Using a survey of hybrid simulations (with kinetic ions and fluid electrons), we study the evolution of the Bell instability as a function of the parameters of the CR population. We find that at saturation, the magnetic pressure in the amplified field is comparable with the initial CR anisotropic pressure, rather than with the CR energy flux, as previously argued. These results provide a predictive prescription for the total magnetic field amplification expected in the many astrophysical environments where the Bell instability is important.
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Abstract We compare the performance of energy-based and entropy-conserving schemes for modeling nonthermal energy components, such as unresolved turbulence and cosmic rays, using idealized fluid dynamics tests and isolated galaxy simulations. While both methods are aimed to model advection and adiabatic compression or expansion of different energy components, the energy-based scheme numerically solves the nonconservative equation for the energy density evolution, while the entropy-conserving scheme uses a conservative equation for modified entropy. Using the standard shock tube and Zel’dovich pancake tests, we show that the energy-based scheme results in a spurious generation of nonthermal energy on shocks, while the entropy-conserving method evolves the energy adiabatically to machine precision. We also show that, in simulations of an isolated
L ⋆galaxy, switching between the schemes results in ≈20%–30% changes of the total star formation rate and a significant difference in morphology, particularly near the galaxy center. We also outline and test a simple method that can be used in conjunction with the entropy-conserving scheme to model the injection of nonthermal energies on shocks. Finally, we discuss how the entropy-conserving scheme can be used to capture the kinetic energy dissipated by numerical viscosity into the subgrid turbulent energyimplicitly , without explicit source terms that require calibration and can be rather uncertain. Our results indicate that the entropy-conserving scheme is the preferred choice for modeling nonthermal energy components, a conclusion that is equally relevant for Eulerian and moving-mesh fluid dynamics codes. -
ABSTRACT Cosmic rays (CRs) are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated magnetic fluctuations induce particle diffusion in extended regions around the source, so that CRs build up a large pressure gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid particle-in-cell simulations, we show that such a pressure gradient excavates a cavity around the source and leads to the formation of a cosmic ray dominated bubble, inside which diffusivity is strongly suppressed. Based on the trends extracted from self-consistent simulations, we estimate that, in the absence of severe damping of the self-generated magnetic fields, the bubble should keep expanding until pressure balance with the surrounding medium is reached, corresponding to a radius of ∼10–50 pc. The implications of the formation of these regions of low diffusivity for sources of Galactic CRs are discussed. Special care is devoted to estimating the self-generated diffusion coefficient and the grammage that CRs might accumulate in the bubbles before moving into the interstellar medium. Based on the results of 3D simulations, general considerations on the morphology of the γ-ray and synchrotron emission from these extended regions also are outlined.
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Abstract A strong super-Alfvénic drift of energetic particles (or cosmic rays) in a magnetized plasma can amplify the magnetic field significantly through nonresonant streaming instability (NRSI). While the traditional analysis is done for an ion current, here we use kinetic particle-in-cell simulations to study how the NRSI behaves when it is driven by electrons or by a mixture of electrons and positrons. In particular, we characterize the growth rate, spectrum, and helicity of the unstable modes, as well the level of the magnetic field at saturation. Our results are potentially relevant for several space/astrophysical environments (e.g., electron strahl in the solar wind, at oblique nonrelativistic shocks, around pulsar wind nebulae), and also in laboratory experiments.more » « less