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

Abstract

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 ≤ γ v ≤ 6.6, perhaps favourably seem to have velocity power indices of γ v (−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 γ v = (−3), instead of 4.4 ≤ γ v ≤ 6.6. These latter states, which generally show up in observations, thus may characterize an off-equilibrium state as we discuss in this paper.

Pick-up ion transport under conservation of particle invariants: how important are velocity diffusion and cooling processes?

“…Depending then on the effectiveness of cooling he obtains asymptotic power law spectra with spectral indices s ≤ −3. Fahr & Siewert (2011) show that a chain of bulk velocity jumps passing over a co-moving ion population under favourite quasi-equilibrium conditions leads to power laws. In order to validate this, two particle invariants should be conserved at bulk velocity jumps and during the interim periods between the passage of consecutive bulk velocity jumps the jump-induced anisotropic distribution should isotropize by pitch-angle scattering.…”

“…Another form of ion acceleration, for instance, is due to ion interactions with compressive MHD fluctuations like recently treated by Zhang (2010) or Fahr & Siewert (2011). Zhang (2010 describes the acceleration of suprathermal particles by compressional plasma wave trains represented by an infinite chain of identical, consecutive bulk velocity jumps characterizing traveling rarefaction and compression regions.…”

“…Conservation of particle invariants as used by Fahr & Siewert (2011) in addition can only be valid for ions with subcritical velocities v ≤ v c = 3L 2 U ΔU/ΛΔL. If, to the contrast, passage times of jump structures and diffusion times are becoming comparable, i.e.…”

Solar wind bulk velocity fluctuations acting as velocity space diffusion on comoving ions

“…In the recent paper by (Fahr & Siewert 2011), kinetic relations of ions at repeated passages over solar wind bulk velocity jumps had been derived. Under the conservation of two characteristic ion invariants specific relations between the ion velocity components upstream and downstream of this bulk velocity structure were obtained, which not only permit to determine the unique positions in velocity space to which upstream ions are translocated when passing from upstream to downstream, but in addition fulfilling the continuity of differential phasespace flux according to Liouville's theorem.…”

“…Therefore some alternative ideas have more recently come up that perhaps could bring a solution here. One is connected with the injection of low-energy anomalous cosmic rays into the PUI regime at higher energies of about 100 keV (Fahr et al 2009), another with the hope for a stationary equilibrium of an ion plasma interacting with compressive turbulence in a thermally isolated system (Fisk & Gloeckler 2007, and a third one with the study of ion energization due to travelling shocks passing over a background ion population (Zhang 2010;Fahr & Siewert 2011). …”