Understanding the time-scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic ray transport in turbulent magnetic fields. We show that the diffusion time-scales 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 time-scales to become diffusive with the time-scales that particles reside in astronomical environments, the so-called escape time-scales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the time-scales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.
Transport coefficients in turbulence are comprised of correlation functions between turbulent fluctuations and efficient methods to calculate them are desirable. For example, in mean-field dynamo theories used to model the growth of large-scale magnetic fields of stars and galaxies, the turbulent electromotive force is commonly approximated by a series of tensor products of turbulent transport coefficients with successively higher order spatial derivatives of the mean magnetic field. One ingredient of standard models is the kinematic coefficient of the zeroth-order term, namely the averaged kinetic pseudo-tensor $\boldsymbol \alpha$, that converts toroidal to poloidal fields. Here we demonstrate an efficient way to calculate this quantity for rotating stratified turbulence, whereby the pre-averaged quantity is calculated for the motion of a single plume, and the average is then taken over an ensemble of plumes of different orientations. We calculate the plume dynamics in the most convenient frame, before transforming back to the lab frame and averaging. Our concise configuration space calculation gives essentially identical results to previous lengthier approaches. The present application exemplifies what is a broadly applicable method.
more » « less- PAR ID:
- 10485819
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society: Letters
- Volume:
- 483
- Issue:
- 1
- ISSN:
- 1745-3925
- Format(s):
- Medium: X Size: p. L104-L108
- Size(s):
- p. L104-L108
- Sponsoring Org:
- National Science Foundation
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