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Register a new userDiffusion of cosmic rays in MHD turbulence with magnetic mirrors
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As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turbulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the magnetic field, leading to a new type of parallel diffusion. This diffusion is in general slower than the diffusion of non-bouncing CRs with small pitch angles that undergo gyroresonant scattering. The critical pitch angle at the balance between magnetic mirroring and pitch-angle scattering is important for determining the diffusion coefficients of both bouncing and non-bouncing CRs and their scalings with the CR energy. We find non-universal energy scalings of diffusion coefficients, depending on the properties of MHD turbulence.
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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.
Astrophysical plasmas are turbulent and magnetized. The interaction between cosmic rays (CRs) and magnetohydrodynamic (MHD) turbulence is a fundamental astrophysical process. Based on the current understanding of MHD turbulence, we revisit the trapping of CRs by magnetic mirrors in the context of MHD turbulence. In compressible MHD turbulence, isotropic fast modes dominate both trapping and gyroresonant scattering of CRs. The presence of trapping significantly suppresses the pitch-angle scattering and the spatial diffusion of CRs along the magnetic field. The resulting parallel diffusion coefficient has a weaker dependence on CR energy at higher energies. In incompressible MHD turbulence, the trapping by pseudo-Alfv{e}n modes dominates over the gyroresonant scattering by anisotropic Alfv{e}n and pseudo-Alfv{e}n modes at all pitch angles and prevents CRs from diffusion.
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.
The rate of magnetic field diffusion plays an essential role in several astrophysical plasma processes. It has been demonstrated that the omnipresent turbulence in astrophysical media induces fast magnetic reconnection, which consequently leads to large-scale magnetic flux diffusion at a rate independent of the plasma microphysics. This process is called ``reconnection diffusion (RD) and allows for the diffusion of fields which are dynamically important. The current theory describing RD is based on incompressible magnetohydrodynamic (MHD) turbulence. In this work, we have tested quantitatively the predictions of the RD theory when magnetic forces are dominant in the turbulence dynamics (Alfv{e}nic Mach number $M_A < 1$). We employed the textsc{Pencil Code} to perform numerical simulations of forced MHD turbulence, extracting the values of the diffusion coefficient $eta_{RD}$ using the Test-Field method. Our results are consistent with the RD theory ($eta_{RD} sim M_A^{3}$ for $M_A < 1$) when turbulence approaches the incompressible limit (sonic Mach number $M_S lesssim 0.02$), while for larger $M_S$ the diffusion is faster ($eta_{RD} sim M_A^{2}$). This work shows for the first time simulations of compressible MHD turbulence with the suppression of the cascade in the direction parallel to the mean magnetic field, which is consistent with incompressible weak turbulence theory. We also verified that in our simulations the energy cascading time does not follow the scaling with $M_A$ predicted for the weak regime, in contradiction with the RD theory assumption. Our results generally support and expand the RD theory predictions.
Non-thermal acceleration of particles in magnetohydrodynamic (MHD) turbulence plays a central role in a wide variety of astrophysical sites. This physics is addressed here in the context of a strong turbulence, composed of coherent structures rather than waves, beyond the realm of quasilinear theory. The present description tracks the momentum of the particle through a sequence of frames in which the electric field vanishes, in the spirit of the original Fermi scenario. It connects the sources of energy gain (or loss) to the gradients of the velocity of the magnetic field lines, in particular the acceleration and the shear of their velocity flow projected along the field line direction, as well as their compression in the transverse plane. Those velocity gradients are subject to strong intermittency: they are spatially localized and their strengths obey powerlaw distributions, as demonstrated through direct measurements in the incompressible MHD simulation of the Johns Hopkins University database. This intermittency impacts the acceleration process in a significant way, which opens up prospects for a rich phenomenology. In particular, the momentum distribution, which is here captured through an analytical random walk model, displays extended powerlaw tails with soft-to-hard evolution in time, in general agreement with recent kinetic numerical simulations. Extensions to this description and possible avenues of exploration are discussed.
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