THE DEVELOPMENT OF PROTON BEAM IN THE SOLAR WIND

In this paper a new mechanism to form the proton density distribution to explain the radial evolution of the relative beam density （n_b/n_p） is suggested. It is found that it is the resonance between protons and cyclotron waves that drives the protons to form such a unique distribution. First, several possible cyclotron waves are calculated to give the cold plasma dispersion relation. Among those possible waves, the waves propagating outside will play an essential role in the beam distribution formation and the waves propagation both inside and outside will help the core distribution formation. With the axial symmetry assumption, the quasi-linear two-dimensional diffusion equation are solved numerically by using Lax-Wendroff and FTCS scheme combining cold plasma dispersion relation and wave-particle resonant condition. The boundary conditions are not the common ones. A specific explanation about the conditions is given. In the simulating process, an original isotropic proton velocity distribution and the plasma dispersion relations remain constant are assumed. Thus, with diffusion equation we simulated the transformation of solar wind proton density as it flowed from 0.35 AU to 0.9 AU. The contours of proton density distribution show explicitly that the core and beam parts of proton density distribution. In the solar wind plasma, with increasing heliocentric radial distance, the Alfven velocity decreases and more and more protons can be resonant with the second-branch left hand polarized waves, so a part of core protons can enter into beam distributions and become beam protons. From the numerical distribution the radial variation of proton density from 0.35 AU to 0.9 AU and is obtained the calculated results are compared with observed results. Although the cold plasma dispersion relation is assumed, which is not a self-consistent assumption, the simulating results are accordant with the observations. The result shows clearly that the ratio of proton beam number density to proton core number density increases with increasing heliocentric radial distance.