Analytic Solution to Charge-Exchange between Kappa-Distributed Pickup Ions and Maxwellian Neutral Atoms when an Energy-Dependent Cross-Section is Included

An analytic solution to the problem of charge-exchange between kappa distributed pickup ions (PUIs) and Maxwellian neutral atoms will be discussed. PUIs are prevalent throughout the heliosphere and their dynamics modifies many characteristics, such as the termination shock distance as well as the heliosheath thickness. When modeling the heliosphere computationally, care must be taken when simulating PUIs in addition to the background plasma. One simplifying assumption is to use a kappa distribution for the total proton population that represents the PUIs and background plasma. One difficulty is that the energy-dependent cross-section must be included when suprathermal protons are present. Our results show that for smaller values of kappa (1.5 < k < 20), the momentum and energy charge-exchange source terms are smaller than for a Maxwellian proton distribution since the cross-section reduces the energy transfer by highly energetic protons. We also discuss the fact that the analytic solutions are tractable for computer codes, thus providing a viable method to include PUIs in heliospheric models.