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Register a new userTest particle simulations of cosmic rays
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Philipp Mertsch
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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.
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The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particles Larmor radius $R_L$ and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least $10^{6}$ times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to $10^{-2}lesssim R_L/l_c lesssim 10^{3}$, where $l_c$ is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for $R_L/l_c ll 1$, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.
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