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Viscoresistive magnetohydrodynamic turbulence, driven by a twodimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The downgradient momentum flux, as expected, originates from the largescale instability. However, continual upgradient momentum transport by largescale linearly stable but nonlinearly excited eigenmodes is identified, and found to nearly cancel the downgradient transport by unstable modes. The stable modes effectuate this by depleting the largescale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the longknown observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the upgradient transport by the stable modes is at least twothirds of the downgradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98% . These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.more » « less

Straining of magnetic fields by largescale shear flow, which is generally assumed to lead to intensification and generation of small scales, is reexamined in light of the persistent observation of largescale magnetic fields in astrophysics. It is shown that, in magnetohydrodynamic turbulence, unstable shear flows have the unexpected effect of sequestering magnetic energy at large scales due to counteracting straining motion of nonlinearly excited largescale stable eigenmodes. This effect is quantified via dissipation rates, energy transfer rates, and visualizations of magnetic field evolution by artificially removing the stable modes. These analyses show that predictions based upon physics of the linear instability alone miss substantial dynamics, including those of magnetic fluctuations.more » « less

Viscoresistive magnetohydrodynamic turbulence, driven by a twodimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The downgradient momentum flux, as expected, originates from the largescale instability. However, continual upgradient momentum transport by largescale linearly stable but nonlinearly excited eigenmodes is identified and found to nearly cancel the downgradient transport by unstable modes. The stable modes effectuate this by depleting the largescale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the longknown observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Even when imposing a strong magnetic field that almost completely suppresses the instability, the upgradient transport by the stable modes is at least twothirds of the downgradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98%. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

ABSTRACT Understanding the timescales for diffusive processes and their degree of anisotropy is essential for modelling cosmic ray transport in turbulent magnetic fields. We show that the diffusion timescales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to numerical simulations. Very good agreement for a large parameter space is found, transforming classical scattering relation predictions into a computational prescription for the perpendicular component. We discuss and compare these findings, in particular, the timescales to become diffusive with the timescales that particles reside in astronomical environments, the socalled escape timescales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the timescales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.

Abstract Cosmicray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is twofold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmicray signatures. One of the most important aspects in the modeling of cosmicray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By taking the wave spectrum boundaries into account, we quantify cosmicray diffusion parallel and perpendicular to the guide field direction at turbulence levels above 5% of the total magnetic field. We apply our results of the parallel and perpendicular diffusion coefficient to the Milky Way. We show that simple purely diffusive transport is in conflict with observations of the inner Galaxy, but that just by taking a Galactic wind into account, data can be matched in the central 5 kpc zone. Further comparison shows that the outer Galaxy at $$>5$$ > 5 kpc, on the other hand, should be dominated by perpendicular diffusion, likely changing to parallel diffusion at the outermost radii of the Milky Way.more » « less

null (Ed.)ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusivepropagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasilinear theory does not provide a universally accurate description in the resonantscattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reducedrigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulenceleveldependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.more » « less

Using hybrid simulations (kinetic ionsfluid electrons), we test the linear theory predictions of the cosmic ray (CR) streaming instability. We consider two types of CR distribution functions: a "hot" distribution where CRs are represented by a drifting power law in momentum and an anisotropic "beam" of monochromatic particles. Additionally, for each CR distribution we scan over different CR densities to transition from triggering the resonant to the nonresonant (Bell) streaming instability. We determine the growth rates of these instabilities in simulations by fitting an exponential curve during the linear stage, and we show that they agree well with the theoretical predictions as a function of wave number agree. We also examine the magnetic helicity as a function of time and wave number, finding a general good agreement with the predictions, as well as some unexpected nonlinear features to the instability development.more » « less