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Register a new userInfluence of Ion-Neutral Damping on the Cosmic-Ray Streaming Instability: Magnetohydrodynamic Particle-in-cell Simulations
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We explore the physics of the gyro-resonant cosmic ray streaming instability (CRSI) including the effects of ion-neutral (IN) damping. This is the main damping mechanism in (partially-ionized) atomic and molecular gas, which are the primary components of the interstellar medium (ISM) by mass. Limitation of CRSI by IN damping is important in setting the amplitude of Alfven waves that scatter cosmic rays and control galactic-scale transport. Our study employs the MHD-PIC hybrid fluid-kinetic numerical technique to follow linear growth as well as post-linear and saturation phases. During the linear phase of the instability -- where simulations and analytical theory are in good agreement -- IN damping prevents wave growth at small and large wavelengths, with the unstable bandwidth lower for higher ion-neutral collision rate $ u_{rm in}$. Purely MHD effects during the post-linear phase extend the wave spectrum towards larger $k$. In the saturated state, the cosmic ray distribution evolves toward greater isotropy (lower streaming velocity) by scattering off of Alven waves excited by the instability. In the absence of low-$k$ waves, CRs with sufficiently high momentum are not isotropized. The maximum wave amplitude and rate of isotropization of the distribution function decreases at higher $ u_{rm in}$. When the IN damping rate approaches the maximum growth rate of CSRI, wave growth and isotropization is suppressed. Implications of our results for CR transport in partially ionized ISM phases are discussed.
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The gyro-resonant cosmic-ray (CR) streaming instability is believed to play a crucial role in CR transport, leading to growth of Alfven waves at small scales that scatter CRs, and impacts the interaction of CRs with the ISM on large scales. However, extreme scale separation ($lambda ll rm pc$), low cosmic ray number density ($n_{rm CR}/n_{rm ISM} sim 10^{-9}$), and weak CR anisotropy ($sim v_A/c$) pose strong challenges for proper numerical studies of this instability on a microphysical level. Employing the recently developed magnetohydrodynamic-particle-in-cell (MHD-PIC) method, which has unique advantages to alleviate these issues, we conduct one-dimensional simulations that quantitatively demonstrate the growth and saturation of the instability in the parameter regime consistent with realistic CR streaming in the large-scale ISM. Our implementation of the $delta f$ method dramatically reduces Poisson noise and enables us to accurately capture wave growth over a broad spectrum, equally shared between left and right handed Alfven modes. We are also able to accurately follow the quasi-linear diffusion of CRs subsequent to wave growth, which is achieved by employing phase randomization across periodic boundaries. Full isotropization of the CRs in the wave frame requires pitch angles of most CRs to efficiently cross $90^circ$, and can be captured in simulations with relatively high wave amplitude and/or high spatial resolution. We attribute this crossing to non-linear wave-particle interaction (rather than mirror reflection) by investigating individual CR trajectories. We anticipate our methodology will open up opportunities for future investigations that incorporate additional physics.
Cosmic ray propagation is determined by the properties of interstellar turbulence. The multiphase nature of interstellar medium (ISM) and diversity of driving mechanisms give rise to spatial variation of turbulence properties. Meanwhile, precision astroparticle experiments pose challenges to the conventional picture of homogeneous and isotropic transport of cosmic rays (CRs). We are beginning a new chapter of CR propagation research when studies of particle transport and interstellar turbulence confront each other. Here we review our recent developement on understandings of magnetohydrodynamic (MHD) turbulence and its connection to the fundamental processes governing cosmic ray propagation, different regimes of particle transport, that are augmented with observational discovery and analysis from multi-wavelength observations.
Modelling of cosmic ray transport and interpretation of cosmic ray data ultimately rely on a solid understanding of the interactions of charged particles with turbulent magnetic fields. The paradigm over the last 50 years has been the so-called quasi-linear theory, despite some well-known issues. In the absence of a widely accepted extension of quasi-linear theory, wave-particle interactions must also be studied in numerical simulations where the equations of motion are directly solved in a realisation of the turbulent magnetic field. The applications of such test particle simulations of cosmic rays are manifold: testing transport theories, computing parameters like diffusion coefficients or making predictions for phenomena beyond standard diffusion theories, e.g. for cosmic ray small-scale anisotropies. In this review, we seek to give a low-level introduction to test particle simulations of cosmic rays, enabling readers to perform their own test particle simulations. We start with a review of quasi-linear theory, highlighting some of its issues and suggested extensions. Next, we summarise the state-of-the-art in test particle simulations and give concrete recipes for generating synthetic turbulence. We present a couple of examples for applications of such simulations and comment on an important conceptual detail in the backtracking of particles.
We use particle-in-magnetohydrodynamics-cells to model particle acceleration and magnetic field amplification in a high Mach, parallel shock in three dimensions and compare the result to 2-D models. This allows us to determine whether 2-D simulations can be relied upon to yield accurate results in terms of particle acceleration, magnetic field amplification and the growth rate of instabilities. Our simulations show that the behaviour of the gas and the evolution of the instabilities are qualitatively similar for both the 2-D and 3-D models, with only minor quantitative differences that relate primarily to the growth speed of the instabilities. The main difference between 2-D and 3-D models can be found in the spectral energy distributions (SEDs) of the non-thermal particles. The 2-D simulations prove to be more efficient, accelerating a larger fraction of the particles and achieving higher velocities. We conclude that, while 2-D models are sufficient to investigate the instabilities in the gas, their results have to be treated with some caution when predicting the expected SED of a given shock.
We formulate a magnetohydrodynamic-particle-in-cell (MHD-PIC) method for describing the interaction between collisionless cosmic ray (CR) particles and a thermal plasma. The thermal plasma is treated as a fluid, obeying equations of ideal MHD, while CRs are treated as relativistic Lagrangian particles subject to the Lorentz force. Backreaction from CRs to the gas is included in the form of momentum and energy feedback. In addition, we include the electromagnetic feedback due to CR-induced Hall effect that becomes important when the electron-ion drift velocity of the background plasma induced by CRs approaches the Alfven velocity. Our method is applicable on scales much larger than the ion inertial length, bypassing the microscopic scales that must be resolved in conventional PIC methods, while retaining the full kinetic nature of the CRs. We have implemented and tested this method in the Athena MHD code, where the overall scheme is second-order accurate and fully conservative. As a first application, we describe a numerical experiment to study particle acceleration in non-relativistic shocks. Using a simplified prescription for ion injection, we reproduce the shock structure and the CR energy spectra obtained with more self-consistent hybrid-PIC simulations, but at substantially reduced computational cost. We also show that the CR-induced Hall effect reduces the growth rate of the Bell instability and affects the gas dynamics in the vicinity of the shock front. As a step forward, we are able to capture the transition of particle acceleration from non relativistic to relativistic regimes, with momentum spectrum $f(p)sim p^{-4}$ connecting smoothly through the transition, as expected from the theory of Fermi acceleration.
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