Perpendicular Transport of Energetic Charged Particles in Nonaxisymmetric Two‐Component Magnetic Turbulence

Abstract

Q1,Q2 We examine energetic charged particle diffusion perpendicular to a mean magnetic field B 0 due to turbulent fluctuations in a plasma, relaxing the common assumption of axisymmetry around B 0 and varying the ratio of two fluctuation components, a slab component with parallel wavenumbers and a two-dimensional (2D) component with perpendicular wavenumbers. We perform computer simulations mostly for 80% 2D and 20% slab energy and a fluctuation amplitude on the order of B 0. The nonlinear guiding center (NLGC) theory provides a reasonable description of asymptotic perpendicular diffusion as a function of the nonaxisymmetry and particle energy. These values are roughly proportional to the particle speed times the field line diffusion coefficient, with a prefactor that is much lower than in the classical field line random walk model of particle diffusion. NLGC predicts a prefactor in closer agreement with simulations. Next we consider extreme fluctuation anisotropy and the approach to reduced dimensionality. For 99% slab fluctuation energy, field line trajectories are diffusive, but the particle motion is subdiffusive. For 99% 2D fluctuation energy, both field lines and particle motions are initially subdiffusive and then diffusive, but NLGC gives unreliable results. The time dependence of the running particle diffusion coefficient shows that in all cases asymptotic diffusion is preceded by free streaming and subdiffusion, but the latter differs from standard compound subdiffusion. We can model the time profiles in terms of a decaying negative correlation of the perpendicular velocity due to the possibility of backtracking along magnetic field lines.

Magnetic Field Line Random Walk for Disturbed Flux Surfaces: Trapping Effects and Multiple Routes to Bohm Diffusion

“…Previous computer simulations have shown that in some cases, corresponding to Regime 3 above, temporary topological trapping and suppressed diffusive escape apply to subsets of field lines (with "conditional statistics" that depend on the initial conditions) but have little effect on the ensemble average statistics. In the context of the 2D+slab model, to see a substantial reduction in the ensemble average diffusion coefficient requires a very weak slab contribution and hence was noticed only recently (Ruffolo et al 2008). Subdiffusion has also been found in computer simulations ( Figure 3(b); see also Ruffolo et al 2008).…”

“…Thus, the random walk of magnetic field lines in space is directly relevant to the transport of such particles perpendicular to the large-scale magnetic field (e.g., Jokipii 1966;Urch 1977;Matthaeus et al 2003;Ruffolo et al 2008). Early descriptions of the field line random walk (FLRW) in magnetic turbulence used a quasilinear theory (Jokipii 1966;Jokipii & Parker 1968), which is now known to apply to fluctuations that vary mainly along a large-scale field, such as parallel-propagating Alfvén waves, or for which the Kubo number (see Kubo 1963) is much less than 1 (if it exists).…”

“…That work predicted that the FLRW would exhibit quasilinear diffusion when the slab component dominates and Bohm diffusion when the 2D component dominates, which was confirmed by Gray et al (1996) for a wide range of parameters. However, as part of a survey of particle transport properties, Ruffolo et al (2008) performed a simulation run for a very low slab energy fraction, f s = 0.01, and an unusual FLRW was found: free streaming was followed by transient subdiffusion and lower asymptotic diffusion than expected. (Note that Ottaviani (1992) previously found transient subdiffusion followed by asymptotic diffusion at high Kubo number for a different fluctuation model in a transport problem analogous to the FLRW.)…”

Pitch-Angle Dependent Perpendicular Diffusion of Energetic Particles Interacting With Magnetic Turbulence

“…From these particle orbits one can obtain the diffusion parameters κ ∥ and κ ⊥ . This procedure can be seen as standard approach and it was performed by numerous authors (see, e.g., Michałek & Ostrowski, 1996;Mace et al, 2000;Qin et al, 2002aQin et al, , 2002bPommois et al, 2005;Zimbardo et al, 2006;Pommois et al, 2007;Ruffolo et al, 2008;Tautz, 2010;Qin & Shalchi, 2012;Tautz & Shalchi, 2013). However, one can also be interested in the pitch-angle dependence of the different transport parameters.…”

The role of magnetic helicity for field line diffusion and drift

“…Ruffolo et al 2006Ruffolo et al , 2008: (i) early measurements in the solar system revealed a 4:3 ratio of solar wind fluctuation energy in the azimuthal direction relative to the radial and the z directions (Belcher & Davids 1971); (ii) the solar wind near Earth has a two-dimensional (2D) turbulence component that is symmetric with respect to the mean field, while another component has wave vectors along the radial direction. But the mean magnetic field follows a spiral structure, thus breaking the axisymmetry (Saur & Bieber 1999); (iii) nonaxisymmetric fluctuations may be important in enhanced latitudinal transport of cosmic rays at high heliographic latitudes (Jokipii et al 1995;Burger & Hattingh 1998).…”