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

Abstract

Context. The phase space transport of pick-up ions (PUIs) in the heliosphere has been studied for the cases that these particles are experiencing a second-order Fermi process, i.e. velocity diffusion, a convection with the solar wind, and adiabatic or "magnetic" cooling, i.e. cooling connected with the conservation of the magnetic moment. Aims. The study aims at a quantification of the process of "magnetic cooling" that has recently been introduced as a modification of adiabatic cooling in the presence of frozen-in magnetic fields. Methods. The isotropic PUI velocity distributions are obtained as numerical solutions of a Fokker-Planck phase space transport equation. Results. It is demonstrated that this newly discussed process is, like adiabatic energy changes, not limited to cooling but can also, depending on the shape of the distribution function, result in heating. For pure cooling with negligible velocity diffusion a v −5 velocity power law is found for magnetic cooling, thus confirming earlier analytical results. For non-negligible second-order Fermi acceleration, the tails of the distribution functions exhibit different shapes, which in special cases are also close to the prominent v −5 behaviour, which is often found in observations. Conclusions. The existence of an exact v −5 power law of PUI distribution functions can be confirmed for insignificant velocity diffusion and its approximate validity for specific choices of the velocity dependence of the diffusion coefficient.

Transit-time aspects of ENA production models for the inner heliosheath

“…Including these corrections into our modeling requires integrating the transittime along the radial solar wind outflow using an apropriate transport equation (see e.g. Fahr & Fichtner 2011) in the framework of the formalism we introduce for the inner heliosheath plasma flow in the next paragraph. However, fully quantitative calculations of these aspects in a realistic heliospheric model are not the main point of this study.…”

“…Fahr & Fichtner 2011), which, however, for our purposes may not be needed in full generality due to the following arguments: first, we expect the heliosheath plasma to be characterized by fairly low effective Mach numbers (M 0.1), allowing the assumption that the heliosheath plasma flow is practically incompressible, and therefore, no adiabatic cooling occurs. Even though the Voyager observations of the TS suggest that the downstream plasma is still supersonic, this may be misleading because the Voyagers are unable to observe all plasma components of the solar wind.…”

On the radial evolution of κ distributions of pickup protons in the supersonic solar wind

“…Assuming the so-called magnetic cooling, the equation describing the time evolution of the isotropic part of the proton phase space distribution f (r, v, t) (in a mixed frame: solar rest frame in configuration and comoving frame in velocity space) reads as follows [Isenberg, 1987;Chalov et al, 1995;Fichtner et al, 1996;Fahr and Fichtner, 2011]:…”

“…Motivated by this and by the finding that distributions have been found to be reasonable approximations not only in the supersonic solar wind [e.g., Scudder, 1996;Leubner, 2004;Pierrard and Lazar, 2010] but also in the heliosheath [Heerikhuisen et al, 2008;Opher et al, 2013;Zirnstein et al, 2014], we investigate-starting from a phase space transport equation like the one used by Fahr and Fichtner [2011] and specifying the velocity distribution as a function-whether one can derive a differential equation describing the evolution of the parameter with heliocentric distance.…”

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

“…Here the first term on the right hand side (RHS) replaces the unspecified velocity-diffusion term used by Fahr & Fichtner (2011), the second term describes the standard convective change of f , the third term the magnetic ion cooling of ions comoving with the bulk, and the fourth term, S (r, v, t), is the pickup ion injection function. The velocityŪ = (U 1 + U 2 )/2, in case of equally extended fast and slow bulk flow trains, is the average bulk speed by which ions are transported radially outwards to larger solar distances.…”