Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.