Injection to the pick-up ion regime from high energies and induced ion power-laws

Abstract

Though pick-up ions (PUIs) are a well-known phenomenon in the inner heliosphere, their phase-space distribution nevertheless is a theoretically unsettled problem. Especially the question of how PUIs form their suprathermal tails, extending to far above their injection energies, still now is unsatisfactorily answered. Though Fermi-2 velocity diffusion theories have revealed that such tails are populated, they nevertheless show that resulting population densities are much less than seen in observations showing power-laws with a velocity index of "−5". We first investigate here, whether or not observationally suggested power-laws can be the result of a quasi-equilibrium state between suprathermal ions and magnetohydrodynamic turbulences in energy exchange with each other. We demonstrate that such an equilibrium cannot be established, since it would require too high PUI pressures enforcing a shock-free deceleration of the solar wind. We furthermore show that Fermi-2 type energy diffusion in the outer heliosphere is too inefficient to determine the shape of the distribution function there. As we can show, however, power-laws beyond the injection threshold can be established, if the injection takes place at higher energies of the order of 100 keV. As we demonstrate here, such an injection is connected with modulated anomalous cosmic ray (ACR) particles at the lower end of their spectrum when they again start being convected outwards with the solar wind. Therefore, we refer to these particles as ACR-PUIs. In our quantitative calculation of the PUI spectrum resulting under such conditions we in fact find again power-laws, however with a velocity-power index of "−4" and fairly distance-independent spectral intensities. As it seems these facts are observationally well supported by VOYAGER measurements in the lowest energy channels.

The inner heliospheric source for keV-energetic IBEX ENAs

“…In the paper by Fahr et al (2009), the authors considered how shock-generated anomalous cosmic ray particles (ACRs) behave when diffusing inwards from the shock and getting modulated in energy due to adiabatic cooling processes. These authors showed that with the loss of particle energy and the associated decrease of the spatial diffusion coefficient, these ions eventually lose their diffusive mobility while propagating inwards and then are again convected outward with the bulk of the solar wind to increasing solar distances.…”

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

“…As turns out from our studies here, the diffusion coefficient D ΔU vv induced by stochastic bulk velocity fluctuations is constant in its magnitude with solar distance and thus its relevance is very different from diffusion coefficients connected with nonlinear wave-particle interactions falling off with distance, since the wave amplitudes are rapidly decreasing (for estimates see Fahr et al 2009). Thus at larger distances when the relevance of cooling disappears compared to diffusion, then the ion spectra should clearly tend towards (−3)-power spectra, as can be seen from Eq.…”

“…(15) was thought (without giving details) to describe Fermi-2 acceleration due to quasilinear particle interactions with Alfven turbulence (see Schlickeiser 1989) which, at larger distances (r ≥ 5 AU), is however considered to be too ineffective compared to the other terms (see Fisk & Gloeckler 2008;Fahr et al 2009). Instead of this conventional, ineffective diffusion term, we now derive a new diffusion term, based on the bulk velocity formalism described above.…”

“…In this region power laws with power indices γ v −5 have been found (see Gloeckler 2003;Fisk & Gloeckler 2006;Dayeh et al 2009;Hill et al 2009). Velocity space diffusion in form of Fermi-2 acceleration by nonlinear ion interactions with counterstreaming Alfvenic or magnetosonic, convected turbulences has been shown as being too ineffective to energize freshly injected PUIs (see Fahr et al 2009). Even a consistent description of turbulence generation by freshly injected PUIs and energization of PUIs by nonlinear interaction with this turbulence cannot produce these tails as shown by Chalov et al (2004Chalov et al ( , 2006.…”

“…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). …”