Approximate Analytical Solutions of the gyrophase-averaged ion transport equation

Physics

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2114 Energetic Particles, Heliospheric (7514), 2118 Energetic Particles, Solar, 7807 Charged Particle Motion And Acceleration, 7867 Wave/Particle Interactions

Scientific paper

Solving the gyrophase-averaged transport equation for the spatial and velocity dependence of solar wind ion distribution functions generally requires a numerical treatment even when simplifications such as radial magnetic field and constant solar wind and wave phase speeds are assumed. We assume that sufficient wave power is available at all heliocentric radial distances to provide for rapid pitch-angle diffusion of resonant ions due to ion-cyclotron interactions. We present a solution method based on approximations that provide for a predominantly analytical solution to the transport equation which includes gravity, the ambipolar electric field and mirroring in a radially diverging magnetic field. This analytical treatment preserves the essential physics and yields important, interpretable results for ion distribution functions for constant solar wind and wave phase speeds. The one small region of the ion distribution function solution space inaccessible analytically is solvable numerically using standard integral equation solution techniques. In addition to the novel solution method, we present several important results including: isodensity contours of the ion distribution function, the condition for free escape of ions, and the effectiveness of our method on predicting non-thermal features such as preferential heating, differential streaming, and double beams.

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