Isotropic ion distribution functions triggered by consecutive solar wind bulk velocity jumps: a new equilibrium state

Context. Throughout the heliosphere, ion power spectra have been found in observations to exhibit suprathermal tails that follow power laws. Ion power-law spectra, though having a broad range of spectral indices 4.4 <= gamma(nu) <= 6.6, perhaps favourably seem to have velocity power indices of gamma nu approximate to (-5), a phenomenon that can more or less ubiquitously be found in heliospheric space plasmas. This is probably indicative of an as yet unidentified quasi-equilibrium state of collisionless space plasmas. Aims. We develop the idea that these forms of ion spectra could be produced by a continuous back-and forth-shuffling of wind convected ions in consecutive jumps from fast to slow, and vice-versa, bulk velocity regimes. Methods. The appearance of a quasi-equilibrium state due to this shuffling and re-shuffling, as we show, naturally results in ion distribution functions that are superpositions of a series of weighted Maxwellians resulting into power laws beyond a critical velocity border. Spectral intensities thereby anticorrelate with bulk velocities, but power indices depend only slightly on bulk velocity. Results. The fully developed equilibrium state is shown here, however, to be characterized by a power law with power index gamma(nu) = (-3), instead of 4.4 <= gamma(nu) <= 6.6. These latter states, which generally show up in observations, thus may characterize an off-equilibrium state as we discuss in this paper.