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Astron. Astrophys. 358, 347-352 (2000)

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2. Turbulence models and the coefficient of spatial diffusion

Energetic charged particles like ACRs and GCRs can interact resonantly with plasma waves embedded in the solar wind. These waves are of low-frequency and mainly determined by their magnetic field component. Within the framework of quasilinear theory the coefficient of spatial diffusion along an external magnetic field is defined as the integral

[EQUATION]

where [FORMULA] and v are the pitch-angle and the particle speed, respectively. [FORMULA] denotes a Fokker-Planck coefficient which is determined by the composition and geometry of the plasma wave turbulence.

Here we consider three different turbulence models from the plasma wave viewpoint: slab Alfvén waves (A), isotropic fast magnetosonic waves and a mixture of both (M). Schlickeiser (1989) and Schlickeiser & Miller (1998) have calculated the coefficients of spatial diffusion for these three cases. In their calculations they assumed for the plasma wave spectrum [FORMULA] a Kolmogorov-like power-law dependence above some minimum wavenumber [FORMULA], i.e. [FORMULA] with [FORMULA]. Using their results with, for simplicity, (1) considering forward and backward propagating modes with equal intensities, (2) assuming identical spectral shapes, scales and intensities of Alfvén and fast mode waves, i.e. [FORMULA], [FORMULA] and [FORMULA], and, furthermore, (3) using the empirical relationship [FORMULA] ([FORMULA]) as well as (4) the approximation [FORMULA], one finds the following unified representation of the coefficients of spatial diffusion for the three turbulence models:

[EQUATION]

where the superscript [FORMULA] refers to the different models labeled (A), (F) and (M) above. The reference value [FORMULA], which might be different for the three turbulence models, is taken at [FORMULA] and [FORMULA] which denotes an arbitrary reference momentum. The dimensionless exponents [FORMULA] are determined by the composition and geometry of the heliospheric plasma wave turbulence. These exponents follow from the considerations described in Appendix A and are given by [FORMULA] for slab Alfvén waves, [FORMULA] in the case of isotropic fast mode waves, and [FORMULA] for the mixed turbulence.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000
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