Observational evidence from Helios plasma data has been obtained for the occurrence of proton pitch-angle diffusion (Marsch and Tu, 2001b). A comparison of the cyclotron-wave diffusion plateau, as it is predicted by using the cold plasma dispersion relation in the plateau condition of Equation (56), with the Helios observations is shown in Figure 14. The VDFs in the left and right frames show the plateaus defined by vanishing pitch-angle gradients (also implying marginal plasma stability). Parts of the isodensity contours in velocity space shown in Figure 14 are outlined well by a sequence of segments of circles centered at the respective phase speeds (bold dots indicate its location), which are assumed to vary slightly, and due to dispersion are smaller than the local Alfvén speed. For the contours between 0.2 and 0.4 of the maximum density, the plateau can be as wide as 70 degrees in pitch angle as calculated in the wave frame. The horizontal axis refers to the parallel proton velocity component, whereby an outward velocity has a positive value. The dotted lines show the density contours observed by Helios at 0.3 AU in a high-speed wind. In the right frame, , , and . The diffusion plateaus of protons in resonance with left hand polarised cyclotron waves are shown by the solid lines. For , a proton is in resonance with outward waves, and for with inward propagating waves. The solid lines are the numerical solutions of Equation (56).
The observations shown in Figure 14 suggest that Alfvén-cyclotron fluctuations propagating parallel or antiparallel to the background magnetic field influence the shape of the ion VDFs. The waves may be generated at low, non-resonant frequencies and, by propagation through the inhomogeneous coronal plasma, approach the ion-cyclotron resonances and by proton scattering cause their anisotropy. In turn, ion thermal anisotropies of sufficient magnitude can lead to growth of ion-cyclotron instabilities. The resulting enhanced Alfvén-cyclotron fluctuations scatter the ions and thereby reduce their original anisotropy.
Gary and Saito (2003) have carried out particle-in-cell simulations of Alfvén-wave-scattering of protons in a magnetised, homogeneous, collisionless model plasma of electrons and one ion species to study the evolution of the VDFs in response to these scattering processes. A solar wind simulation with a spectrum of right-travelling Alfvén-cyclotron fluctuations initially imposed leads according to Gary and Saito (2003) to highly non-Maxwellian proton VDFs. Their computations are illustrated in Figure 15 and show that the pitch-angle scattering of left-travelling (with ) ions becomes weaker, as their parallel speed becomes less negative, but also that such scattering can even transport ions across the line at . This important numerical result confirms the basic observational features.
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