Recent modelling of solar energetic particles (SEPs) propagation through the
heliospheric turbulence, also discussed in this workshop, has investigated
the role of the pitch-angle scattering and the perpendicular transport in
spreading particles in heliolongitude, as shown by multi-spacecraft
measurements (STEREO A/B, ACE, SOHO, etc.) at 1 AU in various energy
ranges. In some events the first-order pitch-angle anisotropy of the particles distribution is not-negligible. We calculate the average
perpendicular displacement due to the gradient/curvature drift in an
inhomogeneous turbulence accounting for pitch-angle dependence for two MHD turbulence models: (a) 3-D isotropic,
(b) anisotropic as conjectured by Goldreich-Sridhar. We find in both cases that the drift scales as
In recent years, the multi-spacecraft monitoring by STEREO A/B, ACE, SOHO or
Test-particle simulations
Recent phenomenological models of charged particle transport in the
heliosphere include a dependence of the perpendicular diffusion coefficient
on the pitch-angle of the particle velocity with respect to the global
average magnetic field (
In this short note we outline the calculation of the perpendicular transport
coefficient due to gradient/curvature drift originating from the
inhomogeneity of the magnetic turbulence for an anisotropic pitch-angle
distribution of the particles. The results for the 3-D isotropic turbulence
and the MHD anisotropic turbulence conjectured by
We consider a spatially homogeneous
time-independent magnetic field with superimposed fluctuations. The amplitude
of the fluctuation (
In the Eq. (
With these assumptions, the cross-field diffusion coefficient (limit for large times of the average square displacement) associated to gradient/curvature
drift of the guiding center due to the turbulence inhomogeneity (in other
words the diffusive motion of the guiding center away from the field lines)
reads
We note that
Also in this case we consider a
spatially homogeneous, fluctuating, time-independent global magnetic field
According to the GS95 conjecture, the pseudo-Alfvén modes are carried
passively by the shear-Alfvén modes with no contribution to the turbulence
cascade to small scales which is seeded by collisions of shear modes only.
Following the calculation in the Appendix of
Due to the lack of space, we omit here the corresponding result for the
shear- modes. For a 25 MeV proton at 1 AU, by taking
We have calculated the time-dependent average square displacement DD(t) due
to gradient/curvature drift for two distinct MHD turbulence models: (a)
3-D-isotropic and (b) anisotropic as conjectured by Goldreich and
Sridhar (1995); the assumption of the pitch-angle isotropy of the particle
distribution function has been relaxed to account for recently measured first
order anisotropy. In both cases, we find
The author acknowledges useful discussions with W. Dröge and R. D. Strauss and constructive feedback of the referees. This work was supported, in part, by NASA under grant NNX13AG10G. This work benefited from discussions at the team meetings “First principles physics for charged particle transport in strong space and astrophysical magnetic turbulence” at ISSI in Bern, Switzerland. Edited by: P. Desiati Reviewed by: two anonymous referees