The Common Spectrum for Accelerated Ions in the Quiet-Time Solar Wind

Suprathermal tails, formed in part from accelerated interstellar pickup ions, are observed ubiquitously in the solar wind. In quiet-time conditions, the tails are found to have a common spectral shape, a distribution function in velocity space that is a power law with a spectral index of -5. It is shown that such a spectral index is to be expected if the tails are formed by stochastic acceleration due to compressional turbulence in the solar wind, in which the particles are accelerated by, and do an equal amount of work on, the turbulence. The spectrum is formed by a cascade in energy, analogous to turbulent cascades.