A comparison between .LAMBDA.|| obtained by simulations and deduced from quasi-linear theory.

Abstract

Spatial diffusion coefficients of parallel (K||) to the direction (z) of averaged magnetic field ‹B› are obtained in the simulated interplanetary magnetic field fluctuations (slab model) by directly calculating the displacement (Δz) of particles along ‹B› and also by using the simple relation ofK||=limΔt→∞[‹Δz2›/(2Δt)], where ‹Δz2› is the mean square of the displacement of particles during the time interval Δt. The calculations are performed under the parameters of η=‹ΔB2›1/2/‹B›, where ‹ΔB2›1/2 is the root mean square of one component of fluctuations perpendicular to z, γ, the power exponent of the magnetic field power spectrum for large wave numbers, and L, correlation length, respectively.The deduced parallel mean free path λ|| (in AU) from λ||=3K||/v for η=0.42, L=6×1011cm and ‹B›=5nT, is well expressed asλ||=0.204(R/R0)0.5+0.109(R/R0)2 for γ=1.5, andλ||=0.217(R/R0)0.15+0.0658(R/R0)2 for γ=2.0, in the rigidity regions of 0.09-9GV, where v and R are velocity and rigidity in units of GV, respectively. Here R0 is 9GV corresponding to the resonant wave numbers of 1/L. λ|| for γ=1.5 and 2.0 are shorter than the values expected in the quasi-linear theory (QLT) by 30-40% and 40-60% respectively in 0.09-3GV (0.01<ρ/L<0.33), where ρ is the cyclotron radius of particles around ‹B›. The scaling law concerning L is also confirmed by the simulations. η2 dependence of λ|| at fixed rigidity predicts that QLT is applicable only below η=0.14-0.1. The comparisons of our λ|| with the values from the observations of solar flare particles show that λ|| for γ=2.0 corresponds better with the observed λ|| in the rigidity of -0.1—a few GV than one for γ=1.5.