Abstract. By conserving momentum during the mixing of fast solar wind flow and slow planetary ion flow in an inelastic way, mass loading converts kinetic energy to other forms – e.g. first to electrical energy through charge separation and then to thermal energy (randomness) through gyromotion of the newly born cold ions for the comet and Mars cases. Here, we consider the Earth's exterior cusp and plasma mantle, where the ionospheric origin escaping ions with finite temperatures are loaded into the decelerated solar wind flow. Due to direct connectivity to the ionosphere through the geomagnetic field, a large part of this electrical energy is consumed to maintain field-aligned currents (FACs) toward the ionosphere, in a similar manner as the solar wind-driven ionospheric convection in the open geomagnetic field region. We show that the energy extraction rate by the mass loading of escaping ions (ΔK) is sufficient to explain the cusp FACs, and that ΔK depends only on the solar wind velocity accessing the mass-loading region (usw) and the total mass flux of the escaping ions into this region (mloadFload), as ΔK ∼ −mloadFloadu2sw∕4. The expected distribution of the separated charges by this process also predicts the observed flowing directions of the cusp FACs for different interplanetary magnetic field (IMF) orientations if we include the deflection of the solar wind flow directions in the exterior cusp. Using empirical relations of u0 ∝ Kp + 1.2 and Fload ∝ exp(0.45Kp) for Kp = 1–7, where u0 is the solar wind velocity upstream of the bow shock, ΔK becomes a simple function of Kp as log10(ΔK) = 0.2 ⋅ Kp + 2 ⋅ log10(Kp + 1.2) + constant. The major contribution of this nearly linear increase is the Fload term, i.e. positive feedback between the increase of ion escaping rate Fload through the increased energy consumption in the ionosphere for high Kp, and subsequent extraction of more kinetic energy ΔK from the solar wind to the current system by the increased Fload. Since Fload significantly increases for increased flux of extreme ultraviolet (EUV) radiation, high EUV flux may significantly enhance this positive feedback. Therefore, the ion escape rate and the energy extraction by mass loading during ancient Earth, when the Sun is believed to have emitted much higher EUV flux than at present, could have been even higher than the currently available highest values based on Kp = 9. This raises a possibility that the ion escape has substantially contributed to the evolution of the Earth's atmosphere.
Estimating Ion Escape from Unmagnetized Planets
