Asymmetric diffusion of magnetic field lines in turbulence

Stochasticity of magnetic field lines is paramount to understanding particle transport and mixing (Rechester and Rosenbluth 1978 Phys. Rev. Lett. 40 38-41). In this paper we study magnetic field separation in turbulent plasmas, which feature so-called superdiffusion, where field lines separate faster than diffusively. We discovered that turbulent superdiffusion can be pronouncedly asymmetric, so that the separation of field lines will be different if one follows magnetic field lines along the direction of the field or follows them in the opposite direction. Particle transport perpendicular to the magnetic field is primarily due to the field line separation in collisionless, well-magnetized plasmas. The asymmetry in diffusion, however, was certainly unexpected, as it will create free energy in particles that follow field lines, e. g. it will create large-scale streaming out of particle gradients perpendicular to the mean magnetic field. While the symmetry of the flow is broken by the so-called imbalance or cross-helicity, the difference between forward and backward diffusion is not directly due to imbalance, but a non-trivial consequence of both imbalance and non-reversibility of turbulence. It therefore follows that this peculiar property of field lines is directly related to turbulence being a dissipative phenomenon, and that turbulence can directly channel part of its free energy to particles.